Performance Analysis in Basketball: Reliability and Applications of the Game-Related Statistics

DOCTORAL DISSERTATION

Performance analysis in basketball: Reliability and applications of the game-related statistics

Alexandra Pérez Ferreirós

International mention 2019

International Doctoral School

Alexandra Pérez Ferreirós

DOCTORAL DISSERTATION

Performance analysis in basketball: Reliability and applications of the game-related statistics

Análisis del rendimiento en baloncesto: Fiabilidad y aplicaciones de las estadísticas de juego

Supervised by: Dr. Ezequiel Rey Eiras

2019 International mention

Tesis por compendio de publicaciones

La presente tesis doctoral cumple el requisito establecido en la normativa de doctorado de la Universidad de Vigo, para ser presentada como compendio de artículos. Está formada por tres artículos publicados en revistas incluidas en el Journal Citation Report® (JCR) de los cuales, por lo menos en uno, la doctoranda es la primera autora.

Publicaciones:

I. Pérez-Ferreirós, A., Kalén, A., Gómez, M.-Á., & Rey, E. (2019). Reliability of teams’ game-related statistics in basketball: Number of games required and minimal detectable change. Research Quarterly for Exercise and Sport. Advanced online publication. doi:10.1080/02701367.2019.1597243

II. Pérez-Ferreirós, A., Kalén, A., & Rey, E. (2018). Short- and mid-term effects of the 2010 rule changes on game-related statistics in European basketball championships: An interrupted time series analysis. International Journal of Sports Science & Coaching, 13(6), 1081–1089. doi:10.1177/1747954118765738

III. Kalén, A., Pérez-Ferreirós, A., Rey, E., & Padrón-Cabo, A. (2017). Senior and youth national team competitive experience: influence on player and team performance in European basketball championships. International Journal of Performance Analysis in Sport, 17(6), 832–847. doi:10.1080/24748668.2017.1405610

Revistas:

I. Research Quarterly for Exercise and Sport. ISSN: 0270-1367. JCR® 2017 índice de impacto = 2.268; posición 32/81 (Q2); área de Sports Sciences y posición 38/78 (Q2); área de Psychology.

II. International Journal of Sport Science & Coaching. ISSN: 1747-9541. JCR® 2017 índice de impacto = 0.856; posición 43/50 (Q4); área de Hospitality, Leisure, Sport and Tourism.

III. International Journal of Performance Analysis in Sports. ISSN: 1474-8185. JCR® 2017 índice de impacto = 1.144; posición 66/81 (Q4); área de Sports Sciences.

Además de las publicaciones mencionadas que forman la tesis, la doctoranda también tiene otras publicaciones:

I. Fernández-Villarino, M. A., Hernáiz-Sánchez, A., Alvariñas Villaverde, M., & Pérez-Ferreirós, A. (in press). Estereotipos de género en el deporte. El papel socializador de la familia. Egitania e Sciencia.

II. Kalén, A., Pérez-Ferreirós, A., Barcala-Furelos, R., Fernández-Méndez, M., Padrón-Cabo, A., Prieto, J. A., Ríos-Ave, A., & Abelairas-Gómez, C. (2017). How can lifeguards recover better? A cross-over study comparing resting, running, and foam rolling. The American Journal of Emergency Medicine, 35(12), 1887–1891. doi:10.1016/j.ajem.2017.06.028

III. Fernandez-Mendez, F., Saez-Gallego, N. M., Barcala-Furelos, R., Abelairas Gómez, C., Padron-Cabo, A., Perez-Ferreiros, A., Garcia-Magan, C., Moure- Gonzalez, J., Contreras-Jordán, O., & Rodríguez Núñez, A. (2017). Learning and treatment of anaphylaxis by laypeople. A simulation study using pupilar technology. BioMed Research International. doi:10.1155/2017/9837508

Agradecimientos

Quiero agradecer a todas las personas que me ayudaron en este largo proceso, con sus consejos y sus inquietudes para llegar hasta aquí, y que hicieron que esta tesis doctoral fuera posible.

En primer lugar, quiero agradecer a mi director Ezequiel Rey, que tras años de admiración como profesor fue un lujo tenerte como director. Gracias por tu dedicación, tus consejos y por tu ayuda en estos tres años. También a mi tutor, Roberto Barcala por su orientación, atención y ayuda durante estos años.

Además, quiero dar las gracias a Marián Fernández y Cristina Varela, compañeras del grupo de investigación REMOSS. Por estar siempre disponibles para cualquier duda, por toda la ayuda y consejos durante este proceso. Gracias a vosotras también.

A mis compañeros de doctorado y compañeros de batalla, por las mil horas de debate, de resolver dudas, de feedback, de ayuda. Alexis Padrón y Carlos Lago Fuentes, siempre fuisteis un ejemplo a seguir y fue un placer compartir esta etapa con vosotros, gracias por todo.

También quiero agradecer al coordinador del programa de doctorado Carlos Lago Peñas por sus consejos y sus críticas que han contribuido a mi desarrollo profesional y al desarrollo de la tesis. Así como agradecer al programa de doctorado en ciencias del deporte, educación física y actividad física saludable; a la Escuela Internacional de Doctorado (EIDO) y a la Universidad de Vigo.

Por su ayuda a la hora de hacer posibles las publicaciones, quiero dar las gracias a los coautores y a los revisores de los artículos; en especial a Miguel Ángel Gómez por sus aportaciones.

I also want to thank all the people at The Swedish School of Sport and Health Sciences (Stockholm, Sweden) where I made a 3-month research stay. Thank you to Victoria Blom my supervisor for accepting me to stay, to the people in the KK project for allowing me to collaborate and help, and to the psychology department for letting me be a part of it and help me in the last steps of my doctorate studies.

Igualmente agradecer a mis profesores de la Universidad de Vigo que han contribuido en mi formación académica durante la carrera, el máster, y ahora, el doctorado. Y, a mis compañeros de facultad durante la carrera y el doctorado. A todos, mi más sincero agradecimiento.

A mis amigas, que seguramente sin ellas hubiera acabado antes la tesis, pero que siempre están ahí para sacarme de casa, sacar una sonrisa y hacer mil planes. Gracias Erea, Elsa, Keka por ser como sois y por aguantarme todos estos años. Vosotras también formáis parte de este proyecto.

Gracias a mi familia, a mis padres Hortensia y Fernando que siempre me han prestado un gran apoyo incondicional. Por todos los sacrificios que han hecho para que pudiera llegar hasta aquí. Me habéis educado en los valores de respeto, humildad y constancia en la vida. Gracias por darme todo lo que tengo y enseñarme que en esta vida el saber no ocupa lugar.

Y, sobre todo, gracias a Anton, por ser mi compañero de vida y de trabajo. Thank you for celebrating everything with me in this journey, for your support and your help, you make me a better person. Thank you for your patience, and for being there for me always, in the best and worst moments. You bring out the best in me.

Table of content

TABLE OF CONTENT ...... I LIST OF FIGURES ...... III LIST OF TABLES ...... V ABBREVIATIONS ...... VII RESUMEN ...... IX

CHAPTER 1: GENERAL INTRODUCTION ...... 1 1.1. PERFORMANCE ANALYSIS ...... 3 1.2. GAME-RELATED STATISTICS ...... 5 1.1.1. Previous studies ...... 5 1.1.2. Methodological considerations ...... 9 1.3. SCOPE AND RATIONALE ...... 14 1.1.3. Reliability ...... 14 1.1.4. Rule change ...... 17 1.1.5. Competitive experience ...... 20 1.4. AIM OF THE THESIS ...... 22

CHAPTER 2: STUDY 1. RELIABILITY OF TEAMS’ GAME-RELATED STATISTICS IN BASKETBALL: NUMBER OF GAMES REQUIRED AND MINIMAL DETECTABLE CHANGE ...... 23 2.1. RESUMEN ...... 25 2.2. ABSTRACT ...... 26 2.3. INTRODUCTION ...... 27 2.4. METHOD ...... 30 2.4.1. Sample ...... 30 2.4.2. Variables and procedure ...... 30 2.4.3. Statistical analyses ...... 31 2.5. RESULTS ...... 34 2.6. DISCUSSION ...... 40 2.7. CONCLUSIONS ...... 44 2.8. WHAT DOES THIS ARTICLE ADD? ...... 45 2.9. SUPPLEMENTARY MATERIAL ...... 46

CHAPTER 3: STUDY 2. SHORT- AND MID-TERM EFFECTS OF THE 2010 RULE CHANGES ON GAME-RELATED STATISTICS IN EUROPEAN BASKETBALL CHAMPIONSHIPS: AN INTERRUPTED TIME SERIES ANALYSIS ...... 53 3.1. RESUMEN ...... 55 3.2. ABSTRACT ...... 56 3.3. INTRODUCTION ...... 57 3.4. METHOD ...... 60 3.4.1. Sample ...... 60 3.4.2. Variables and procedure ...... 60 3.4.3. Statistical analysis ...... 61 3.5. RESULTS ...... 63 3.6. DISCUSSION ...... 69 3.7. CONCLUSIONS ...... 73 3.8. SUPPLEMENTARY MATERIAL ...... 74

CHAPTER 4: STUDY 3. SENIOR AND YOUTH NATIONAL TEAM COMPETITIVE EXPERIENCE: INFLUENCE ON PLAYER AND TEAM PERFORMANCE IN EUROPEAN BASKETBALL CHAMPIONSHIPS ...... 75 4.1. RESUMEN ...... 77 4.2. ABSTRACT ...... 78 4.3. INTRODUCTION ...... 79 4.4. METHOD ...... 81 4.4.1. Sample ...... 81 4.4.2. Procedure ...... 81 4.4.3. Statistical analysis ...... 82 4.5. RESULTS ...... 84 4.5.1. Players ...... 84 4.5.2. Teams ...... 87 4.6. DISCUSSION ...... 90 4.6.1. Senior championships ...... 90 4.6.2. Youth championships ...... 91 4.6.3. Age ...... 92 4.6.4. Player classification ...... 93 4.7. CONCLUSIONS ...... 95

CHAPTER 5: GENERAL CONCLUSIONS ...... 97 5.1. CONCLUSIONS ...... 99 5.2. PRACTICAL APPLICATIONS ...... 101 5.3. LIMITATIONS ...... 102 5.4. FUTURE LINES OF INVESTIGATION ...... 103

CHAPTER 6: REFERENCES ...... 105

APPENDICES ...... 123 APPENDIX A – ACEPTACIÓN DE LOS COAUTORES DE LA UTILIZACIÓN DE LAS PUBLICACIONES COMO PARTE DE UNA TESIS ...... 125 APPENDIX B – RENUNCIA DE LOS COAUTORES NO DOCTORES A LA UTILIZACIÓN DE LAS PUBLICACIONES COMO PARTE DE OTRA TESIS ...... 127 APPENDIX C – PUBLICATION STUDY 1 ...... 129 APPENDIX D – PUBLICATION STUDY 2 ...... 145 APPENDIX E – PUBLICATION STUDY 3 ...... 157

List of figures

Figure 1.1. Visual representation of (a) perfect absolute and relative reliability; (b) perfect relative reliability and poor absolute reliability; (c) poor absolute and relative reliability...... 15 Figure 1.2. Court modifications implemented by FIBA in 2010...... 18 Figure 2.1. Number of games required to be able to detect a medium change (d > .5)...... 35 Figure 2.2. Number of games required to be able to detect a small change (d > .2)...... 35 Figure 2.3. Number of games required to achieve good ICC (≥ .75)...... 37

Figure 3.1. Trend before rule change (Before), impact of rule change (After) and predicted trend without rule change (Predicted), for ball possessions (POS) and turnovers (TO) in all categories...... 67

Figure 3.2. General trend before rule change (Before), impact of rule change (After) and predicted trend without rule change (Predicted) for 2-point field goals attempted (2PTa), and 3-point field goals attempted (3PTa)...... 68

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List of tables

Table 1.1. Number of playing positions and terminology used...... 8 Table 1.2. Categorisations by final score difference in points and terminology used...... 13 Table 2.1. Descriptive statistics and absolute reliability...... 34 Table 2.2. Relative reliability...... 36 Table 2.3. Descriptive statistics and absolute reliability for the clusters...... 38 Table 2.4. Relative reliability for the clusters...... 39 Table 2.5. Reliability of non-standardised game-related statistics...... 46 Table 2.6. Reliability of opponents’ game-related statistics normalised to 100 ball possessions...... 47 Table 2.7. Reliability of opponents’ non-standardised game-related statistics...... 48 Table 2.8. Reliability of standardised game-related statistics per season...... 49 Table 3.1. Results of segmented regression analyses for general effects of the rule modifications. 64

Table 3.2. Results of the pairwise comparison between categories for differences in effects of the rule change...... 65 Table 3.3. Distribution of analysed games by category and season...... 74 Table 4.1. Analysis of variance for men’s players between levels of performance...... 85 Table 4.2. Analysis of variance for women’s players between levels of performance...... 86

Table 4.3. Analysis of variance for women’s players between levels of performance when controlled for age...... 86 Table 4.4. Analysis of variance for men’s teams between different stages reached...... 88 Table 4.5. Analysis of variance for women’s teams between different stages reached...... 89

Table 4.6. Analysis of variance for women’s teams between different stages reached when controlled for age...... 89

Abbreviations

2PT% 2-point field goal percentage 2PTa/2PTA 2-point field goal attempted 2PTm/2PTM 2-point field goal made 3PT% 3-point field goal percentage 3PTa/3PTA 3-point field goal attempted 3PTm/3PTM 3-point field goal made ACB Spanish men’s first league ANCOVA Analysis of Covariance ANOVA Analysis of Variance AST Assist BLK Block CI Confidence Interval DREB Defensive rebound DRtg Defensive rating EFF Efficiency eFG% Effective field goal percentage ES Effect Size FG% Field goal percentage FGa/FGA Field goal attempted FGm/FGM Field goal made FIBA International Basketball Federation FT% Free-throw percentage FTa/FTA Free-throw attempted FTm/FTM Free-throw made FTr Free-throw rate ICC Intra-class Correlation Coefficient MDC Minimal Detectable Change

MDCES Standardised Minimal Detectable Change MIN Minutes played MS Men Senior

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MY Men Youth NBA National Basketball Association OREB% Offensive rebound percentage OREB Offensive rebound ORtg Offensive rating PF Personal foul POS Possessions PTS Points scored RAE Relative age effect REB Rebound SD Standard Deviation SEM Standard Error of Means STL Steal TO Turnover TOr Turnover rate U16 Under 16 U17 Under 17 U18 Under 18 U19 Under 19 U20 Under 20 U21 Under 21 WS Women Senior WY Women Youth

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Resumen

La presente tesis doctoral se realiza en formato por compendio de publicaciones y la estructura y resumen de cada capítulo se describe a continuación. El Capítulo 1 está formado por una introducción general sobre el análisis del rendimiento en baloncesto y las estadísticas de juego que da coherencia a la temática para la inclusión de los 3 artículos.

En ciencias del deporte, existe una línea de investigación orientada a analizar qué indicadores pueden ayudar tanto a entrenadores para mejorar el rendimiento del equipo como a jugadores para mejorar su propio rendimiento, esto se conoce como análisis del rendimiento. Para ello, la forma más común de analizar el rendimiento es a través de la definición y medida de un número de factores que se relacionan con el rendimiento individual o del equipo, normalmente conocidos como indicadores del rendimiento. En baloncesto, normalmente, se utilizan las estadísticas de juego como indicadores de rendimiento común que captan las acciones técnico-tácticas en la competición (Oliver, 2004). Estas estadísticas de juego han sido utilizadas extensamente en estudios científicos sobre el rendimiento en baloncesto. A nivel de equipo, se ha encontrado que pueden discriminar entre, por ejemplo, ganadores y perdedores (Csataljay, James, Hughes, & Dancs, 2012), jugar en casa o fuera (García, Ibáñez, Gómez, & Sampaio, 2014), o posiciones finales en una competición (García, Ibáñez, Martinez De Santos, Leite, & Sampaio, 2013). A nivel individual, se han utilizado por ejemplo para estudiar la influencia del efecto de la edad relativa (Arrieta, Torres-Unda, Gil, & Irazusta, 2016), la variabilidad de partido a partido (Zhang et al., 2017), o para diferenciar entre posiciones de juego (Sindik & Jukić, 2011). La presente tesis se centra en las siguientes líneas de investigación: la fiabilidad de las estadísticas de juego, los efectos de los cambios de normas, y la relación entre la experiencia competitiva previa y el rendimiento.

Es necesario asegurarse de que una medida es tanto válida como fiable para poder sacar conclusiones correctas de los estudios científicos. Normalmente, la fiabilidad se define como la ausencia de error en la medida (Atkinson & Nevill, 1998), aunque también se puede considerar como la consistencia de la entidad que

se está midiendo (Lames & McGarry, 2007). En ambas consideraciones se pueden distinguir dos tipos de fiabilidad, la relativa que se refiere al grado en que el orden de los individuos en una muestra permanece medidas, y la absoluta que se refiere a la cantidad de variación de un individuo entre medidas repetidas (Baumgartner, 1989). Cuando se considera la fiabilidad como la ausencia de error en la medida o el acuerdo entre medidas, en el análisis observacional se suele evaluar utilizando las medidas de correlación intra e inter observador. Existen varios estudios en baloncesto que evaluaron la fiabilidad inter e intra observador en diferentes ligas y competiciones profesionales, encontrando valores excelentes en estas medidas (Gómez, Jiménez, Navarro, Lago-Penas, & Sampaio, 2011; Gómez, Lorenzo, Jiménez, Navarro, & Sampaio, 2015; Sampaio, Lago, & Drinkwater, 2010; Sampaio et al., 2015). Cuando se habla de fiabilidad refiriéndose a la consistencia de la entidad que se está midiendo, en estudios sobre el análisis del rendimiento se conoce como estabilidad de rendimiento o perfiles normativos. Existen algunos estudios en deportes de raqueta donde se investigó la cantidad de variabilidad en el rendimiento calculando el número de partidos necesarios para obtener una estimación del rendimiento fiable (Hughes, Evans, & Wells, 2001; O’Donoghue & Ponting, 2005). Como se ha descrito anteriormente, las estadísticas de juego son muy utilizadas tanto en las investigaciones como en la práctica, por ello, es necesario determinar cuántos partidos son necesarios para que las estadísticas de juego se estabilicen y se puedan utilizar como indicadores fiables del rendimiento.

Las reglas de un deporte son lo que determinan la lógica interna del mismo y, por ello, se ha planteado en la literatura científica la importancia de estudiar los posibles cambios de reglas. Uno de los cambios más grandes de los últimos años se produjo en 2010. Siendo el más importante el incremento de la distancia de la línea de 3 puntos (pasando de 6.25m a 6.75m) y la reducción del tiempo de posesión en algunas situaciones (International Basketball Federation, 2010). Algunos estudios han utilizado las estadísticas de juego para analizar el efecto directo de este cambio de reglas, encontrando, sobre todo, una disminución de los lanzamientos de 3 puntos y un efecto opuesto en los lanzamientos de 2 puntos (Gryko, Słupczyński, & Kopiczko, 2016; Montero, Vila, & Longarela, 2013; Štrumbelj, Vračar, Robnik-Šikonja, Dežman, & Erčulj, 2013). En cambio, en un estudio a medio plazo (5 años),

encontraron un ligero aumento de los lanzamientos de 3 puntos (Ibañez, García- Rubio, Gómez, & Gonzalez-Espinosa, 2018). Esta diferencia de resultados implica la presencia de una evolución del rendimiento a lo largo del tiempo. Por ello, es necesario analizar tanto los efectos inmediatos como a medio plazo del cambio de reglas en las estadísticas de juego. Dentro de esto, todos los estudios se realizaron en categoría masculina senior, por lo que es importante también analizar estos efectos en categoría femenina y también en junior.

Una línea de investigación común en las ciencias del deporte es sobre qué factores facilitan la adquisición de pericia. Por ejemplo, se ha investigado la importancia de diferentes actividades de desarrollo, encontrando que los deportistas de élite tienen una mayor cantidad de práctica deliberada, juego libre y otras actividades deportivas (Baker, Cote, & Abernethy, 2003b; Ericsson, Krampe, & Tesch-Römer, 1993; Hornig, Aust, & Güllich, 2016). Una posible explicación de esta relación encontrada en deportes individuales entre el rendimiento en categoría junior y senior es que la competición es una actividad beneficiosa para el desarrollo de la pericia deportiva. Lo cual está en línea con los hallazgos encontrados en baloncesto y otros deportes colectivos, donde los expertos tenían casi tres veces más horas en competición que los no expertos. Por ello, es necesario investigar la influencia que tiene la participación en campeonatos internacionales junior y senior en el rendimiento de jugadores y equipos en campeonatos senior.

Al final de este capítulo se encuentra el objetivo general, que consiste en investigar las estadísticas de juego en baloncesto, centrándose en las potenciales aplicaciones en estudios sobre el desarrollo del talento y regulación deportiva. A partir de este, surgen los tres objetivos específicos que se corresponden con cada investigación. El primero consiste en determinar el número de partidos necesarios para obtener buenos valores de fiabilidad absoluta y relativa de las estadísticas de juego de los equipos. Tanto para los partidos en general, como para los partidos agrupados en igualados y no igualados. El segundo consiste en analizar si las modificaciones de las reglas en 2010 tuvieron influencia en las estadísticas de juego, utilizando un análisis de series de tiempo interrumpidas. Además, comparar si los cambios de reglas tuvieron la misma influencia en baloncesto masculino y femenino, y en categoría senior y junior. Y, el tercero consiste en explorar si el

número de campeonatos previos senior y junior de selecciones nacionales se relaciona con el rendimiento en campeonatos, tanto a nivel de equipo como a nivel de jugador, en baloncesto femenino y masculino.

Los Capítulos 2, 3 y 4 se corresponden con los 3 artículos originales de investigación, publicados en revistas internacionales indexadas en el Journal Citation Report (JCR). A continuación, se realizará un resumen de las partes más importantes de la tesis, que son los 3 artículos mencionados anteriormente. En el Capítulo 2 se encuentra la primera investigación, titulada “Reliability of team’s game-related statistics in basketball: Number of games required and minimal detectable change”. Este estudio tiene como objetivo analizar la cantidad de partidos necesarios para obtener una buena fiabilidad relativa y absoluta de las estadísticas de juego de los equipos profesionales de la liga española ACB. Tanto para todos los partidos en general como de forma específica para los partidos igualados y no igualados. Se analizaron un total de 884 partidos correspondientes a las temporadas 2015-16 a la 2017-18, contando con un total de 53 equipos en total. Se utilizaron las estadísticas de juego estándar recogidas de la página oficial de la competición, y a continuación se normalizaron a 100 posesiones para controlar la variabilidad en el ritmo de juego (Kubatko, Oliver, Pelton, & Rosenbaum, 2007; Sampaio & Janeira, 2003). Seguidamente, los partidos se clasificaron según la diferencia de puntos finales en el marcador (partidos igualados y no igualados) usando un análisis de conglomerados bietápico. Para el análisis de la fiabilidad relativa se calculó el coeficiente de correlación intraclase (ICC) para un partido y para la media de todos los partidos. A partir del ICC, se calculó el número de partidos necesarios para obtener una buena fiabilidad a través de la fórmula de la profecía Spearman-Brown (Eisinga, te Grotenhuis, & Pelzer, 2013; Sasaki et al., 2018). Para el análisis de la fiabilidad absoluta, se calculó el mínimo cambio detectable (MDC) entre dos partidos para un equipo. A partir del MDC, se calculó el número de partidos necesarios para detectar un cambios pequeños y medianos, convirtiendo el MDC en tamaño del efecto estándar.

Usando todos los partidos, los resultados mostraron que el número mínimo de partidos necesarios en cada grupo fue de 30 para detectar un cambio medio (d > .5), 187 para un cambio pequeño (d > .2), y 100 para una buena fiabilidad relativa (ICC

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≥ .75). Usando partidos igualados y no igualados, el número mínimo de partidos necesarios en cada grupo fue respectivamente 31 y 30 para detectar un cambio medio (d > .5), 190 y 188 para un cambio pequeño (d > .2), y 191 y 121 para una buena fiabilidad relativa (ICC ≥ .75). La muestra debe constar de al menos 30 partidos en cada grupo para detectar un cambio mediano, y al menos 190 partidos para detectar un cambio pequeño. Para poder clasificar a los equipos con buena fiabilidad, se necesitan al menos 100 partidos cuando se incluyen tanto los partidos igualados como los no igualados. Este estudio proporciona nueva información sobre el mínimo tamaño de muestra necesario para obtener medidas fiables cuando se utilizan las estadísticas de juego a nivel de equipo en baloncesto.

El Capítulo 3 está formado por la segunda investigación que se titula “Short- and mid-term effects of the 2010 rule changes on game-related statistics in European basketball championships: An interrupted time series analysis”. El objetivo de este estudio fue analizar si las modificaciones de las reglas de la FIBA en 2010 influyeron en las estadísticas de juego, tanto a corto como a medio plazo mediante el análisis de series de tiempo interrumpido en campeonatos europeos. Además, también se analizó si los cambios de reglas tuvieron la misma influencia en diferentes grupos de edad y en categoría masculina y femenina. La muestra estuvo compuesta por 5296 partidos de los campeonatos europeos desde 2005 a 2016 para hombres y mujeres, tanto en competiciones senior como junior (formada por U20, U18 y U16). Se recogieron las estadísticas estándar de juego de la página oficial de la competición, y se normalizaron a 100 posesiones para controlar la variabilidad en el ritmo de juego (Kubatko et al., 2007; Sampaio & Janeira, 2003). Se utilizó un análisis de series interrumpidas para analizar el impacto de los cambios de reglas, tanto directamente como con el paso del tiempo. Para ello, se utilizó una regresión segmentada multinivel que consistió en una variable continua de tiempo, una variable dicotómica indicando si el campeonato fue antes o después del cambio de reglas, y una variable continua de tiempo después del cambio. También se incluyó la categoría de competición como un factor fijo y el campeonato como un factor aleatorio.

Los resultados del estudio muestran que el número de posesiones parece que incrementa directamente en categoría senior, y la tendencia previa hacia

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menos posesiones parece que se ha parado o revertido. Directamente después del cambio de reglas, el número de lanzamientos de 2 puntos aumentan mientras que el número de lanzamientos de 3 puntos disminuyen, pero se mantiene la tendencia hacia más lanzamientos de 3 puntos y menos lanzamientos de 2 puntos. El porcentaje de lanzamientos de 2 puntos disminuyó directamente, mientras que se encontraron efectos mixtos sobre el porcentaje de lanzamientos de 3 puntos. Después de la modificación de las reglas, en la categoría senior femenina cambió la tendencia hacia menos pérdidas de balón. Como conclusiones del estudio, se ha encontrado que las modificaciones de 2010 afectaron a las estadísticas de juego, tanto directamente como a lo largo del tiempo. El ritmo de juego ha aumentado o ha dejado de disminuir después de las modificaciones de las reglas. Además, el desarrollo hacia una mayor proporción de lanzamientos de campo que han sido de 3 puntos ha continuado, aunque la proporción se redujo directamente después de las modificaciones reglamentarias. También se encontró que las mujeres senior parecen ser la categoría en la que las modificaciones de las reglas tuvieron el mayor efecto en el desarrollo continuo. Por último, no se encontró un patrón general de diferencias en los efectos entre las categorías.

La tercera investigación se encuentra en el Capítulo 4, y se titula “Senior and youth national team competitive experience: Influence on player and team performance in European basketball championships”. El objetivo de este estudio fue descubrir si el número de campeonatos previos de las selecciones nacionales senior y junior se relaciona con el rendimiento del equipo y el jugador en los campeonatos de baloncesto europeos masculinos y femeninos. La muestra estuvo compuesta por todos los equipos nacionales y sus jugadores que participaron en el Campeonato de Europa 2011, 2013 y 2015 para hombres (equipos n = 72; jugadores n = 697) y mujeres (equipos n = 52, jugadores = 520). Las estadísticas de juego se recogieron de la página oficial de cada campeonato. Para el rendimiento del equipo se recogió la etapa más alta alcanzada (semifinal, cuartos de final, segunda ronda o primera ronda). Para el rendimiento de los jugadores, se calculó el índice de eficiencia (Arrieta et al., 2016) y se utilizó un agrupamiento de k-medias para agruparlos según su rendimiento (alto, medio, o bajo). Se incluyó la edad en el análisis de los jugadores y equipos para tener en cuenta algún efecto de la

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experiencia general. Para comparar las diferencias entre los grupos de jugadores se utilizó un análisis de varianza (ANOVA) de un factor de Kruskal-Wallis. En la categoría femenina, para corregir el efecto de la edad, se utilizó para el análisis de los equipos un análisis de covarianza (ANCOVA).

Los equipos y jugadores con mejor rendimiento tuvieron un mayor número de campeonatos senior previos disputados. Esto indica que la experiencia competitiva previa es un factor importante en el rendimiento de jugadores y equipos. La experiencia competitiva diferencia a los jugadores de bajo rendimiento en ambos sexos, pero solo distingue a los jugadores de alto rendimiento con los de rendimiento medio para mujeres. No se encontraron diferencias en el número de campeonatos junior. Los cual sugiere que la participación previa en campeonatos junior no tiene una influencia directa en el rendimiento del equipo senior. Parece ser necesario tener una cantidad suficiente de experiencia competitiva de alto nivel acumulada dentro del equipo para alcanzar la fase semifinal, tanto para los equipos nacionales masculinos como para los femeninos.

En el Capítulo 5 se encuentran las conclusiones generales de la tesis, así como las limitaciones, aplicaciones prácticas y futuras líneas de investigación. Basándonos en los estudios explicados anteriormente, las conclusiones de la presente tesis son:

I. Las estadísticas de juego pueden proporcionar una estimación fiable del rendimiento de los equipos si se incluye una muestra lo suficientemente grande para el análisis. Si el objetivo del análisis es evaluar los cambios o las diferencias en el rendimiento, se necesitan al menos 30 partidos en cada grupo para compararlos. Si el objetivo es clasificar el rendimiento de los equipos, se necesitan entre 14 y 100 partidos, según qué estadísticas de juego se incluyan en el análisis.

II. La evaluación de los cambios tanto directos como longitudinales en las estadísticas de juego después de las modificaciones de las reglas utilizando un análisis de series de tiempo interrumpidas permite extraer conclusiones más completas que solo simples comparaciones pre-post. En concreto, el cambio de normas del 2010 en baloncesto mostró un cambio de tendencia

en el número de posesiones hacia un aumento en el ritmo de juego. Además, la proporción de lanzamientos de 3 puntos disminuyó directamente después del cambio, mientras que la tendencia hacia una mayor proporción de lanzamientos de 3 puntos no fue afectada. La modificación de las reglas parece que afectó de manera diferente a las categorías masculina y femenina, teniendo un mayor impacto en la femenina.

III. La experiencia competitiva previa puede ser un predictor del rendimiento de jugadores y equipos, tanto en baloncesto femenino como masculino. En particular, hubo una relación entre el número de campeonatos senior disputados y el rendimiento tanto de jugadores como de equipos. Sin embargo, esta relación no se encontró para el número de campeonatos junior jugados. Lo cual indica la importancia de que la experiencia competitiva sea específica al contexto del rendimiento.

En general, las estadísticas de juego son una medida valiosa del rendimiento en investigaciones en baloncesto, como por ejemplo en el desarrollo del talento y regulaciones deportivas.

La mayor limitación de los estudios es que en todos se utilizan datos de una competición en específico. Por lo tanto, es possible que no se puedan generalizar los hallazgos a todas las competiciones de baloncesto. Otra limitación es el hecho de que tanto el estudio 2 como el estudio 3 utilizan metodología observacional. Por lo que es posible que las relaciones encontradas en esos estudios sean total o parcialmente debidas a otros efectos externos o al azar.

Como aplicaciones prácticas de esta tesis, podemos encontrar que la estimación del número de partidos necesarios para obtener medidas fiables de las estadísticas de juego puede ser utilizada por investigadores a la hora de plantear diseños para futuros estudios. También muestra a los entrenadores y clubes que deben tener cuidado a la hora de sacar conclusiones basándose en las estadísticas de juego de un número reducido de partidos. Por otro lado, los resultados de los efectos del cambio de reglas del 2010 pueden ayudar a las organizaciones deportivas a entender cómo estas modificaciones afectaron al juego en las diferentes categorías. Esto puede proporcionar información valiosa a la hora de

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considerar futuros cambios de reglas. Además, la relación encontrada entre la experiencia competitiva previa y el rendimiento muestra a los entrenadores de selecciones nacionales y a las federaciones la importancia de tener jugadores que disputen varios campeonatos senior para poder rendir mejor en los próximos campeonatos.

A partir de los estudios, se sugieren varias líneas de investigación para futuros estudios. Hay una necesidad de evaluar adicionalmente la fiabilidad de las estadísticas de juego en diferentes ligas, competiciones, categorías de edad, y en baloncesto femenino. En baloncesto, las reglas cambian frecuentemente y, por ello, existe una necesidad continua de investigaciones que evalúen el impacto de estas modificaciones en competición. También, ampliar el estudio sobre la experiencia competitiva previa, teniendo en cuenta otros aspectos, como la inclusión de otros tipos de actividades de desarrollo y una medida general de rendimiento en la liga.

Las referencias generales de la tesis se encuentran en el Capítulo 6. Y, por último, se encuentra el Apartado de anexos. Los anexos A y B recogen el documento de aceptación de los coautores para la utilización de los artículos como parte de la tesis y el documento de renuncia de los coautores no doctores a la utilización de las publicaciones como parte de otra tesis. Por ultimo, los anexos C, D y E están formados por las publicaciones finales de las investigaciones de los capítulos 2, 3 y 4.

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CHAPTER 1: General introduction

1.1. Performance analysis

Within sports science, one line of research is to find indicators that will help both coaches to improve the performance of the team and practitioners to improve their performance. This area is called performance analysis. Despite that the name already explains what it consists on, in the literature authors define it from different perspectives. Hughes and Bartlett (2008) consider that performance analysis is composed by biomechanical analysis, that analyses individual sports’ techniques, and notational analysis, which studies tactics and strategy in team sports (e.g., movement patterns). However, O’Donoghue (2010, 2015) consider performance analysis to be the study of the actual performance of games and practices, and that usually excludes self-reports and laboratory experiments. The main characteristics that distinguish performance analysis from other areas are that it is done mostly observational, is applied and therefore analyses the actual sport either in match or practice situations, and it can analyse the physical, technical, or tactical performance.

In performance analysis, the standard method to assess performance is through defining and measuring a number of factors that are thought to relate to the individual or team performance, generally referred to as performance indicators (Hughes, 2004). They define either a part or all aspects of performance through a selection or combination of action variables that analysts and coaches use to assess or compare individual, team, or elements of a team’s performance (Hughes & Bartlett, 2004).

Sport biomechanics has focused the analysis of performance in sports where the movement technique is crucial, using kinematic variables or parameters (e.g., body segments speed or angles) as performance indicators (Hughes & Bartlett, 2004). On the other hand, notational analysis has focused on the analysis of performance mostly in team sports, analysing the interactions, movements, and behaviours between players (Hughes & Bartlett, 2004). The performance indicators in team sports can be categorised as scoring indicators (e.g., goals, baskets) or as indicators of quality of the performance (e.g., turnovers, passes, shots per

possession), and both measure positive and negative performance (Hughes & Bartlett, 2004).

However, the type of performance indicators used in research varies between sports (O’Donoghue, 2010). The type of sport to analyse and its characteristics will affect the key aspects that the performance indicators should measure. Another factor that affects which performance indicators to use is that it will depend on which data is available in each competition.

In any case, there are some aspects of the collection and analysis of the data that are common to all types of performance analysis, as summarised by Hughes (2004) in the following steps:

1. Define the performance indicators.

2. Determine the relative importance of the performance indicators.

3. Provide reliability of the data gathered.

4. Establish stability of the performance profiles.

5. Compare sets of data.

6. Model performances.

In performance analysis in basketball, most studies used a predefined set of performance indicators, which are normally provided by the official competition, referred to as the game-related statistics. Therefore, in the subsequent sections of the introduction, key concepts of performance analysis in basketball and game- related statistics will be defined. As well as some concepts that are not deeply studied, and that will be the foundation for the main body of the thesis.

1.2. Game-related statistics

Game-related statistics have traditionally been used in basketball research as common performance indicators that capture technical-tactical actions in competition (Oliver, 2004). They are recorded in a standardised fashion regulated by the International Basketball Federation (FIBA) and are included in the official box-scores in most leagues and championships. They are actions performed by players and teams in real competition settings and are composed of variables related to shooting, rebounding, fouling, blocking, or passing (International Basketball Federation, 2016).

The standard game-related statistics are: time played, points scored, two- point field goals made, two-point field goals attempted, three-point field goals made, three-point field goals attempted, free-throws made, free-throws attempted, offensive rebounds, defensive rebounds, total rebounds, assists, turnovers, steals, blocks, and personal fouls.

1.1.1. Previous studies

Finding differences between final game outcomes is one of the most common uses of the game-related statistics in the scientific literature. Studies have investigated which game-related statistics better discriminate winners and losers in a wide variety of settings. For example, in women’s league (Gómez Ruano & Lorenzo Calvo, 2005), men’s European youth championship (Lorenzo, Gómez, Ortega, Ibáñez, & Sampaio, 2010), men’s European senior championship (Csataljay, O’Donoghue, Hughes, & Dancs, 2009), men’s top national leagues (Csataljay, James, Hughes, & Dancs, 2012; Gómez, Lorenzo, Sampaio, & Ibáñez, 2006; Gómez, Lorenzo, Sampaio, Ibáñez, & Ortega, 2008), and men’s lower national leagues (Gómez, Ibáñez, Parejo, & Furley, 2017). In general, the studies have revealed that defensive rebounds and 2-point field goals made, and to lesser extent assists, free-throws made, and personal fouls, are the performance indicators that more consistently discriminate between winning and losing teams. Offensive rebounds have not been shown to discriminate in any of the studies; and free-throw attempts, steals, and blocks seldom do.

The game-related statistics have also been used to study the influence of game location, commonly known as the effect of home advantage. It has been done in the Spanish league, both for men and women (García, Ibáñez, Gómez, & Sampaio, 2014; Gómez, Lorenzo, Barakat, Ortega, & Palao, 2008; Gómez Ruano, Lorenzo Calvo, Ortega Toro, & Olmedilla Zafra, 2007). Gómez, Lorenzo, Barakat, et al. (2008) and Gómez Ruano et al. (2007) compared game-related statistics between teams winning and losing at home and away. They found that 2-point field goals made and defensive rebounds, and to lesser extent assists and 3-point field goals missed, are the game-related statistics that best discriminate between teams winning and losing both at home and away (Gómez Ruano et al., 2007). García et al. (2014) analysed the home advantage comparing the game-related statistics of teams when winning at home and losing away, as well as when losing at home and winning away, both for balanced and unbalanced games. They found that assist was the performance indicator that best discriminated both in balanced and unbalanced games between winning and losing home or away (García et al., 2014).

Further, there is a wide variety of studies using the game-related statistics to analyse different perspectives of team performance. For example, Ibáñez et al. (2008) identified the game-related statistics that discriminate between teams that finish in the first and last positions in the second Spanish basketball league. Also, Ibáñez, García, Feu, Lorenzo, and Sampaio (2009) identified the game-related- statistics that differenciate winners and losers in a condensed format of 3 consecutive games. The game-related statistics that distinguish between teams in the regular season and play-offs have been studied in Spanish men’s first league (ACB; García, Ibáñez, Martinez De Santos, Leite, & Sampaio, 2013) and men’s Euroleague (Marmarinos, Apostolidis, Bolatoglou, Kostopoulos, & Apostolidis, 2016). Several studies have analysed the relationship between game-related statistics and game outcome based on team quality (Doğan, Işik, & Ersöz, 2016; Marmarinos et al., 2016; Sampaio, Drinkwater, & Leite, 2010; Zhang et al., 2019). Also, Sampaio, Ibáñez Godoy, and Feu (2004) identified the basketball game-related statistics that best discriminate the performance of teams between men and women and level of competition (senior and youth). Lastly, Madarame (2018b) identified the game-related statistics that discriminate between women’s U18

championships in different continents. In these studies, the game-related statistics that consistently differentiate between groups are defensive rebounds and assists. Meanwhile, offensive rebounds, 3-point field goals, and free-throws missed very rarely do.

On a player level, the game-related statistics have been used to add performance measures as an additional dimension to research on relative age effect (RAE) in basketball (Arrieta, Torres-Unda, Gil, & Irazusta, 2016; Ibáñez, Mazo, Nascimento, & García-Rubio, 2018). RAE refers to the difference in age of players within the same age category, i.e., players born earlier and later in the year (Barnsley, Thompson, & Barnsley, 1985). Arrieta et al. (2016) found that players born earlier in the year get more playing time by the coaches in both men and women, as well as in all age categories. In general, the players born earlier seem to perform only slightly better than later born players (Arrieta et al., 2016). This is especially evident in women, where the relationship between RAE and performance completely disappear in the U20 category (Arrieta et al., 2016). The relationship between RAE and performance seems to be weak also in elite U18 men competition (Ibáñez, Mazo, et al., 2018). Further, there seem to be some position-specific differences in this relationship (Ibáñez, Mazo, et al., 2018). In conclusion, the game- related statistics have helped to reveal that it exists only a weak relationship between RAE and performance in basketball with some differences between gender, age groups, and positions.

When analysing players performance in basketball, it is common to do it dividing them by their playing position. There is not a consensus on how to classify playing positions, and it differs both between different scientific studies and between leagues. The most common classification is in three playing positions, but two, four, and five have also been used (Table 1.1). Some studies have also compared the performance between the different playing positions (Gómez Ruano et al., 2007; Sampaio, Janeira, Ibáñez, & Lorenzo, 2006; Sindik & Jukić, 2011). The main findings have shown that 3-point field goals made and missed, defensive rebounds, and assists are the game-related statistics that discriminate better between the playing positions. Meanwhile, free-throws missed, steals, turnovers, and personal fouls hardly ever differ between positions.

Table 1.1. Number of playing positions and terminology used. Article No Terminology Arrieta et al., 2016 5 Point guard, Shooting guard, Small forward, Power forward, Center Gómez Ruano et al., 2007 3 Guards, Forwards, Centres Ibáñez et al., 2018a 3 Guards, Forwards, Centers Mateus et al., 2015 3 Guards, Forwards, Centers Sampaio et al., 2006b 3 Guards, Forwards, Centres Sindik et al., 2011 2 Guards, Forwards/Centers 4 Point guard, Shooting guard, Small forward, Power forward/Center Zhang et al., 2017 3 Guards, Forwards, Centres Note. No = Number of playing positions. aIbáñez, Mazo, Nascimento, & García-Rubio, 2018. bSampaio, Janeira, Ibáñez, & Lorenzo, 2006.

The differences in performance between starters and non-starters have also been studied using the game-related statistics in two articles (Gómez, Lorenzo, Ortega, Sampaio, & Ibáñez, 2009; Sampaio, Ibáñez, Lorenzo, & Gómez, 2006). Both studies performed the analysis separately for players in best and worst teams and winning and losing. The results showed differences in most performance indicators except for 3-point field goals made and free-throws missed which do not seem to discriminate between the groups (Gómez et al., 2009; Sampaio, Ibáñez, et al., 2006).

Other studies are using game-related statistics on a player level to study a wide variety of topics. One example is to analyse game-to-game variability of players’ performance in the National Basketball Association (NBA; Mateus et al., 2015; Zhang et al., 2017). The results from these studies are inconclusive on the effect of situational variables on the players’ game-to-game variability in performance. However, Mateus et al. (2015) showed an inverse relationship between playing time and performance variability. Another example is Sampaio, Drinkwater, et al. (2010), who study the effect of season period, team quality, and playing time on players’ performance in the ACB. Their main finding was that the performance remains stable throughout the season. Lorenzo, Lorenzo, Conte, and Giménez (2019) studied the evolution of ACB players’ performance throughout their careers. They found that the number of assists and free-throw percentage increased throughout the career of the majority of the players. Lastly, game-related statistics have been used to compare the performance of NBA and Euroleague players when competing in the European Championship (Paulauskas, Masiulis,

Vaquera, Figueira, & Sampaio, 2018). The results indicate that NBA players outperformed Euroleague player in two-point field goals made and missed, free- throws made, defensive rebounds, blocks, and received fouls.

1.1.2. Methodological considerations

As previously stated, game-related statistics can be used to analyse performance. However, some methodological considerations should be taken into account when using game-related statistics. The following issues have been raised in the literature: (a) to calculate new variables combining existing game-related statistics; (b) to normalise the data according to game rhythm or playing time; (c) to analyse the data in function of game type, final outcome, game location, team quality, and scoring difference (Kubatko, Oliver, Pelton, & Rosenbaum, 2007; Oliver, 2004; Sampaio & Janeira, 2003).

Calculated variables

Other commonly used game-related statistics do not appear in the box- score of the game and that are calculated from them.

For shooting, field goals made (FGm) and attempted (FGa) are not often included in the box-score and can be calculated. They are the sum of 2-point field goals and 3-point field goals.

The shooting percentages sometimes appear in the box-scores and sometimes they do not. They are usually free-throw percentage (FT%), 2-point field goals percentage (2PT%), 3-point field goals percentage (3PT%), and field goals percentage (FG%). They are calculated by dividing the number of made shots by the number of attempted shots.

In a game, both teams have approximately the same number of possessions. In order to win a game, teams try to score more points per possession than the opponent. Therefore, this variable provides useful insight about the efficiency of a team. It exists several ways to calculate it, but the most common is (Kubatko et al., 2007; Oliver, 2004):

POS = 2PTa + 3PTa + TO + 0.4 × FTa − OREB

After defining possessions, the efficiency per possession of a team can be calculated. The offensive rating (ORtg) is calculated dividing the points scored by the possessions, and multiplying it by 100 (Kubatko et al., 2007; Oliver, 2004):

789 3456 = × 100 739

The defensive rating (DRtg) is calculated dividing the points scored of the opponent by the possessions, and multiplying it by 100 (Kubatko et al., 2007; Oliver, 2004):

3<< 789 ;456 = × 100 739

The above formulas provide a general estimate of the team performance, but they do not explain which factors contribute to the overall performance of the team. To capture specific aspects of the team performance, some calculated variables regarding shooting, rebounding, free-throws, and turnovers have been proposed (Kubatko et al., 2007; Oliver, 2004). These so-called four factors overcome some of the issues of using the standard game-related statistics to capture performance.

For shooting, effective field goal percentage (eFG%) is used because it adjusts for the fact that 3-point field goals are worth 50% more than 2-point field goals, and is calculated as (Kubatko et al., 2007; Oliver, 2004):

(278C + 1.5 × 378C) >?@% = 278F + 378F

Offensive rebound percentage (OREB%), as it is expressed as a % of the total possible offensive rebounds, it takes away the correlation between offensive rebounds and missed shots. It is calculated as (Kubatko et al., 2007; Oliver, 2004):

34GH 34GH% = × 100 34GH + 3<<;4GH

The free-throw rate (FTr) represents how well the shoot from the free-throw line in relation to the total amount of shots they take, and is calculated as (Kubatko et al., 2007; Oliver, 2004):

?8C ?8I = 278F + 378F

It can also be calculated using the free-throw attempts to express how often a team gets to the free-throw line.

Turnover percentage (TOr) is the adjusted number of turnovers in relation to the possessions of a team. Calculated as (Kubatko et al., 2007; Oliver, 2004):

83 83I = 739

These four factors all capture different aspects of the team’s offensive performance. By calculating them for the opponent team, they provide a measure of the team’s defensive performance.

The efficiency (EFF) is an individual offensive efficiency calculation that, the same as offensive rating for the team, explains the player’s performance. There are plenty of ways to calculate the efficiency, most of which are similar (Martínez, 2010a, 2010b). One of the most common way in the scientific literature is (Oliver, 2004):

G?? = 789 + 4GH + J98 + 98K + HKL − (?@F − ?@C) − (?8F − ?8C) − 83

Normalising variables

In order to compare performance more accurately between teams or players, the game-related statistics should be normalised. For teams, normalisation to 100 ball possessions is made to take into account differences in game rhythm (Sampaio & Janeira, 2003). This means that the game-related statistics are first divided by the team’s number of ball possessions and after multiplied by 100. For players, the game-related statistics are generally normalised to per minute played (Kubatko et al., 2007), which allows the comparison between the performance of players with different number of minutes played. It is done dividing the game-related statistics by minutes played for each player.

Situational variables

As previous literature has shown, situational variables can affect the performance of teams and players (Csataljay et al., 2012; García et al., 2013, 2014).

Therefore, as suggested by Sampaio and Janeira (2003), they should be accounted for when using game-related statistics. The most common situational variables to include are the final outcome of the game (i.e., winning or losing), game location (i.e., playing home or away), and game type (i.e., regular season or play-off game).

Another situational variable often included in the literature is the team quality, which takes into account the effect that the level of the teams has on the performance. There are several methods used to classify the teams’ quality in the literature. The most common is to divide the teams into two groups (best and worst; strong and weak), either by top and bottom half (Doğan et al., 2016) or by qualified and not qualified to play-offs (Ibáñez et al., 2008; Marmarinos et al., 2016; Sampaio, Drinkwater, et al., 2010; Sampaio, Ibáñez, et al., 2006; Zhang et al., 2017, 2019). Another way used to split the teams is by cluster analysis by the teams’ win percentage (Gómez, Ibáñez, et al., 2017) or by points scored, points allowed, and win percentage (Sampaio, Drinkwater, et al., 2010). This has an additional advantage in enabling the number of groups to be determined empirically, in the case of Sampaio, Drinkwater, et al. (2010) the teams were clustered into three groups (strong, intermediate, and weak).

Game final score differences

Studies have shown differences in team performance between games won or lost with a small compared to big margin (Gómez et al., 2006; Sampaio & Janeira, 2003). It has therefore been suggested to take into consideration the final score in a game when performing analyses involving the game-related statistics. Generally, this is done by categorising the games into groups based on the score difference. This classification is most often made empirically using some cluster procedure, and the exact cut-off values will, therefore, vary depending on the sample. The number of groups to classify the teams into have sometimes been predetermined by the investigator, and sometimes by the cluster analysis. In both cases, 2 or 3 groups are typically used with different terminologies, i.e., balance and unbalanced (Gómez et al., 2006); close, balanced, and unbalanced (Sampaio & Janeira, 2003); or balanced, unbalanced, and blowout (García et al., 2014). Examples of different categorisations used in the literature can be found in Table 1.2.

Table 1.2. Categorisations by final score difference in points and terminology used. Article G1 G2 G3 Terminology Csataljay et al., 2009 1–9 10–22 22–34 Close, Balanced, Unbalanced Çene, 2018 <10 10–21 >21 Close, Balanced, Unbalanced García et al., 2013 ≤12 13–28 >28 Balanced, Unbalanced, Very unbalanced García et al., 2014 1–12 13–28 >28 Balanced, Unbalanced, Blowout Gómez et al., 2015b 0–9 >10 Balanced, Unbalanced Gómez et al., 2015c 1–6 7–12 13–21 Close, Balanced, Unbalanced Gómez et al., 2006 ≤12 ≥12 Balanced, Unbalanced Gómez et al., 2008a ≤12 ≥12 Balanced, Unbalanced Lorenzo et al., 2010 ≤9 10–29 ≥30 Close, Balanced, Unbalanced Madarame, 2017 ≤15 16–39 ≥40 Balanced, Unbalanced, Very unbalanced Madarame, 2018a ≤16 17–39 ≥40 Balanced, Unbalanced, Very unbalanced Sampaio et al., 2003 1–8 9–17 ≥18 Close, Balanced, Unbalanced Note. G1 = Group 1; G2 = Group 2; G3 = Group 3. aGómez, Lorenzo, Sampaio, Ibáñez, and Ortega (2008). bGómez, Alarcón, and Ortega (2015). cGómez, Battaglia et al. (2015).

1.3. Scope and rationale

The game-related statistics have been used in numerous studies on a variety of topics, both on a team and player level revealing important information on what can affect the performance in basketball. However, even though several methodological considerations have been addressed, the reliability of the game- related statistics have not been addressed, apart from evaluations of observer reliability. Further, there seems to be a potential for the game-related statistics to be used in other areas, such as talent development and sport regulation studies. Therefore, in the present thesis, the focus will be on the following topics: the reliability of the game-related statistics, effects of rule changes, and relationship between previous competitive experience and performance.

1.1.3. Reliability

To be able to draw correct conclusions from studies, it is necessary to ensure that the measurement is both valid and reliable. Validity is the ability of the tool to measure what is supposed to measure, while reliability is its ability to do so with a small error or consistently between measurements (Atkinson & Nevill, 1998). If a tool cannot give consistent and accurate results, it cannot measure what it is supposed to measure. Therefore, reliability is a requisite for validity and needs to be established first (Atkinson & Nevill, 1998).

As the scientific literature shows, the term reliability can be defined from different perspectives. Typically, reliability is considered as the agreement between measures, i.e., as the absence of measurement error (Atkinson & Nevill, 1998; Koo & Li, 2016). However, since some error is always present, it can be defined as the amount of error that is allowed for the practical use of a measurement tool (Atkinson & Nevill, 1998). It is usually assessed using measures of intra and inter- rater agreement in observational analysis. Another sense of the term reliability is when it refers to the performance variability, i.e., the consistency of the entity that is being measured (Lames & McGarry, 2007). In performance analysis research, this is sometimes referred to as the stability of the performance or as the normative profile (Hughes, Evans, & Wells, 2001).

Baumgartner (1989) defined two types of reliability: absolute and relative. The degree to which the order of individuals in a sample remains between multiple measures is known as relative reliability (Baumgartner, 1989). In Figure 1.1, there is perfect relative reliability in (a) and (b), as all individuals are in the same order in measure 1 and 2. The amount of variation for an individual between repeated measures is known as absolute reliability (Baumgartner, 1989). In Figure 1.1, there is perfect absolute reliability in (a), as the values are the same in measure 1 and 2 for all individuals.

(a) (b) (c)

Figure 1.1. Visual representation of (a) perfect absolute and relative reliability; (b) perfect relative reliability and poor absolute reliability; (c) poor absolute and relative reliability.

As mentioned before, when referring to the reliability as the agreement between measures, there are two ways of assessing it: inter-rater and intra-rater. The degree to which an observer can be reliable from one time to another is referred to as intra-rater reliability (Koo & Li, 2016). To test it, the same observer analyses a part of the sample sometime later after the first analysis. The degree to which two observers can be reliable is referred to as inter-rater reliability (Koo & Li, 2016). It is tested selecting part of the sample and both observers analyse it separately. Both of these ways of assessing reliability can be measured in the two types of reliability, that are sometimes called absolute agreement (for absolute reliability) and consistency (for relative reliability).

The game-related statistics in basketball are recorded by official technicians assigned by the leagues. These are recorded in a standardised way according to the FIBA statisticians’ manual (International Basketball Federation, 2016). To ensure

that this data is in fact reliable, several studies have assessed the inter-rater reliability in different competitions, such as ACB (García et al., 2014; Gómez, Lorenzo, Jiménez, Navarro, & Sampaio, 2015; Sampaio, Drinkwater, et al., 2010), men’s European championship (Gómez, Jiménez, Navarro, Lago-Penas, & Sampaio, 2011), Spanish U20 league (Ibáñez et al., 2009), NBA (Sampaio et al., 2015), and the Olympic Games (Sampaio, Lago, & Drinkwater, 2010). Most of them showed an excellent inter-rater reliability with Cohen’s Kappa (κ) or percentage of agreement above 0.95, except for the study on NBA (κ > 0.91; Sampaio et al., 2015), as well as the assists in two of the studies (κ = 0.88 and 0.92; García et al., 2014; Sampaio, Lago, et al., 2010). Further, two of these articles also tested the intra-rater reliability in ACB (Sampaio, Drinkwater, et al., 2010) and Spanish U20 league (Ibáñez et al., 2009), showing excellent intra-rater reliability (κ > 0.97). In conclusion, it seems that the process of recording the game-related statistics has excellent reliability across competitions.

As for the amount of variability in the performance itself, some research has been done mostly in racquet sports on the number of matches required to obtain a reliable performance estimate (Hughes et al., 2001; O’Donoghue & Ponting, 2005). This was done by comparing the cumulative mean up until and including each match with the mean of all matches. The number of games required was determined by when the cumulative mean (Hughes et al., 2001) or its confidence intervals (O’Donoghue & Ponting, 2005) fell within a certain limit of agreement (generally 5 or 10%).

However, there has not been any attempt to determine the number of games necessary to obtain a stable estimate of the performance in basketball. The game-related statistics are heavily used in both research and practice (e.g., by coaches to evaluate the performance of their own and opponent team, by clubs in the recruitment of players, or by the media). Therefore, there is a need to determine how many games are required for the game-related statistics in basketball to stabilise and consequently be used as reliable performance indicators.

1.1.4. Rule change

The internal logic of a sport is determined by its rules. Therefore, a way to change the game conditions is by modifying the rules (Arias, Argudo, & Alonso, 2011). It has been stated in the scientific literature that is important to analyse these rule changes and how they can affect the game before being introduced (Arias et al., 2011). In their review, Arias et al. (2011) explained the common aims of changing the rules: (a) improve the performance of the players; (b) adapt to the interests of the media and attract spectators; (c) adapt the sport to children’s possibilities and interests; (d) prevent injuries; and (e) attract athletes. In basketball, there have been numerous rule changes throughout its 128 years of existence (Ferreira, Ibáñez, & Sampaio, 2009; Pluta, Andrzejewski, & Lira, 2014). The interest of unifying the rules, the increasing level of competition, as well as the necessity to make the game more appealing to the spectators, has made it necessary to modify the rules several times in the last two decades in basketball.

Several studies have analysed different rule changes in basketball. Pluta et al. (2014) studied how the scoring structure in men professional basketball evolved over 78 years and which rule changes had a bigger effect on the final score. They concluded that several of the modifications did not have a direct impact on the final score. The largest effect was seen after the introduction of 3-seconds rule and 30-seconds shot-clock rule, in 1956. Also, to a lesser extent, the introduction of the 3-point line, increased court size, modification of the 5 and 30-second rules, and that seven team fouls per team and half result in a free-throw, in 1984 (Pluta et al., 2014). Cormery, Marcil, and Bouvard (2008) studied if the physiological characteristics changed after the rule change in 2000 (when the shot-clock changed from 30 to 24 seconds and the game was divided into four quarters) of 68 French basketball players that participated in European championships. They found an increase in the number of actions per player and the specificity in each playing position increased as well (Cormery et al., 2008). Podmenik, Leskošek, and Erčulj (2012) observed a decrease in shooting percentage when a smaller and lighter basketball (size 6) was introduced in female basketball.

One of the major revisions of the basketball rules in modern times was decided in 2008 by FIBA, with the aim to “further unify all existing game rules and to have, in the future, only one set of rules for the game of basketball worldwide” (International Basketball Federation, 2008, para. 4). The majority of these changes were modifications to the court (Figure 1.2) and shot-clock, which came into effect for the 2010-11 season (International Basketball Federation, 2010). First and foremost, the 3-point line was moved to 6.75m from 6.25m, which was the original distance since its introduction in 1984. The 3-second area was reshaped into a rectangle moving away from the trapezoid shape that was used since the 1950s. Further, a no-charge semicircle was added underneath the basket, restricting the possibility for the defensive player to draw an offensive foul close to the basket. Lastly, the rules for the shot-clock changed, so it resets to 14 seconds or stays in the remaining time for inbounds in the frontcourt, and no longer to 24, as was the case since the reduction from 30 to 24 seconds in 2000. It has been argued that these rule changes “were aimed not only at making the rules uniform, but also at making the game more appealing and more popular, thanks to adjusting it to the requirements of the media” (Gryko, Słupczyński, & Kopiczko, 2016). As similar goals, such as improving the players performance and increasing the spectacularity of the game, have been argued as common reasons for changing the rules (Arias et al., 2011), it is reasonable to believe that the 2010 rule change was in fact also meant to influence how the game was played to achieve these type of goals.

Figure 1.2. Court modifications implemented by FIBA in 2010.

Several studies have analysed the impact of the 2010 rule changes on the game (Gryko et al., 2016; Ibañez, García-Rubio, Gómez, & Gonzalez-Espinosa, 2018; Montero, Vila, & Longarela, 2013; Štrumbelj, Vračar, Robnik-Šikonja, Dežman, & Erčulj, 2013). Most of them have focused on the changes in 2 and 3-point field goals after the rule modification. For example, Montero et al. (2013) compared the number of 3-point field goals attempted, made, and percentage in ACB between the seasons 2009-10 (line at 6.25m) and 2010-11 (line at 6.75m). The increased distance of the 3-point line decreased the number of attempted and made 3-point shots both during regular season and play-off, and the percentage decreased during the regular season (Montero et al., 2013). Similarly, Štrumbelj et al. (2013) compared all the standard game-related statistics the season before and after the rule change in Euroleague. In line with Montero et al. (2013), they found a decrease in 3-point field goals attempted and percentage (Štrumbelj et al., 2013). Further, a decrease in free-throws attempted and 2-point field goal percentage, together with an increase in 2-point field goals attempted, total rebounds, and number of possessions was found (Štrumbelj et al., 2013).

Another study analysing the effects of the rule change in the top 3 teams of the Polish league, used an observational method to also analyse a wider set of variables (Gryko et al., 2016). They also found a decrease in the number of possessions and 3-point field goals attempted, as well as an increase in the amount of 2-point field goals attempted, however only inside the 3-second area (Gryko et al., 2016). Ibañez, García-Rubio, et al. (2018) analysed the mid-term effects of the rule change in the Spanish league cup (Copa del Rey) by comparing 10 tournaments before and five after. Opposite to the earlier studies, they found a slight increase in 3-point field goals attempted and made (Ibañez, García-Rubio, et al., 2018). This indicates that there might be a difference in the direct and longer-term effects of the rule change.

The difference seen between the direct and longer-term effects of the rule change implies the presence of an evolution over time of the performance. This is supported by the positive autocorrelations found for several variables by Ibañez, García-Rubio, et al. (2018). There is, therefore, a need to analyse both the immediate and longer-term effects together, taking into account both the direct effect and the

effect on the trend of the rule change. Further, all studies were performed on men’s professional competition and, consequently, the differences in effects between men and women, as well as in different age groups need to be studied.

1.1.5. Competitive experience

One popular area of research, especially in sport sciences, is expertise, and what structures and developmental activities facilitate expert performance. These studies often compare traits or activities between groups of experts or elite and non-experts or non-elite (Baker, Cote, & Abernethy, 2003b; Cleary & Zimmerman, 2001; Ericsson, Krampe, & Tesch-Römer, 1993). Early research on the area focused heavily on how the amount of deliberate practice (effortful, not inherently fun, with the aim of improving performance) within the specific sport or activity affects the attainment of sport-specific expertise (Ericsson & Charness, 1994; Ericsson et al., 1993). The results from the musical and sports domains suggested a close relationship between the amount of deliberate practice and level of expertise acquired (Ericsson et al., 1993). However, later research in sports has focused on how a wider range of developmental activities influences the attainment of expertise (Baker et al., 2003b; Hornig, Aust, & Gullich,̈ 2016). For example, when comparing elite and non-elite athletes in basketball, field hockey, football and netball, the elite athletes had accumulated a higher amount of both sport specific practice and play, as well as higher number of sport activities outside their main sport during adolescence (Baker et al., 2003b; Hornig et al., 2016).

Another line of research on expertise in sports has investigated the relationship between performance at youth level and subsequent performance on senior level. In individual sports, athletes that perform at higher level in youth are more likely to perform at high level as seniors in cycling (Schumacher, Mroz, Mueller, Schmid, & Ruecker, 2006), gymnastics (Pereira, Faro, Stotlar, & Fonseca, 2014), and tennis (Brouwers, De Bosscher, & Sotiriadou, 2012). Schumacher et al. (2006), found that cyclists who had previously competed in junior World championships performed better times at senior World championships. In tennis, Brouwers et al. (2012) showed that it is not necessary to perform at an international level in youth categories to reach an international top ranking in senior level.

However, they found a slight correlation between top rankings as youth and senior, indicating that competing at a high youth level might be advantageous to achieve senior success (Brouwers et al., 2012). Finally, gymnasts that finished top 6 in youth Portuguese championships have been shown to be more likely to achieve top placement in senior Portuguese championships (Pereira et al., 2014). In basketball, one of the factors that have been shown to influence the performance in the NBA is the quality of the college attended before entering the league (Moxley & Towne, 2015).

One possible explanation for the relationship seen between youth level and senior performance is that competition (and particularly high-level competition) is an advantageous activity to develop sport expertise. This is supported by the findings that experts in basketball, field hockey, and netball had competed nearly three times as much as non-experts with similar career length (Baker, Côté, & Abernethy, 2003a). Further, the experts found competition to be the most important activity to develop perception and decision-making, and one of the most important to develop execution and physical fitness (Baker et al., 2003a). There is some support for the notion that competition, and specifically, high-level competition, is an important activity to develop expertise. In basketball, the national team championships provide one of the best competitive experiences available both for senior and youth players. For example, the European championships are arranged in U16, U18, U20, and senior categories for both men and women. Many national federations invest a substantial amount of resources to give this competitive experience to their most talented players with the hope of increasing the performance of the players and team. However, the importance of competitive experience on expertise in basketball has not been clearly established. Moreover, it is not clear whether competitive experience during the youth or senior years have a larger effect on the performance. Therefore, there is a need to study the relationship between participation in youth and senior championships on performance, and whether the relationship is similar in both men’s and women’s basketball.

1.4. Aim of the thesis

The game-related statistics in basketball have traditionally been used in research on player or team performance and have generally not been used in other research areas. Therefore, the general aim of the thesis is to investigate the game- related statistics in basketball, with focus on their potential applications in talent development and sport regulation studies.

To accomplish this, three specific aims are presented, which correspond to the three scientific articles that form the present compilation thesis:

I. To determine the number of games required to obtain a good relative and absolute reliability of the teams’ game-related statistics both in general and specifically for balanced and unbalanced games (Chapter 2 and Appendix C).

II. To analyse if the 2010 rule modifications influenced the game-related statistics, both short- and mid-term using an interrupted time series analysis. Further, to compare if the rule changes had the same influence on men and women senior and youth categories (Chapter 3 and Appendix D).

III. To explore if the number of previous senior and youth national team championships played relates to the team and player championship performance for men and women (Chapter 4 and Appendix E).

CHAPTER 2: Study 1. Reliability of teams’ game-related statistics in basketball: Number of games required and minimal detectable change

2.1. Resumen

En baloncesto, las estadísticas de juego son la medida más común del rendimiento. Sin embargo, la literatura que evalúa su fiabilidad es escasa. Objetivo: Analizar la cantidad de partidos necesarios para obtener una buena fiabilidad relativa y absoluta de las estadísticas de juego de los equipos. Método: Se analizaron un total de 884 partidos de la liga profesional masculina española de la temporada 2015-16 a la 2017-18 utilizando todos los partidos y se agruparon por diferencia de puntuación. Se calculó el coeficiente de correlación intraclase (ICC) para cada variable. El número de partidos necesarios para detectar un cambio y lograr una buena fiabilidad relativa se calculó utilizando el cambio mínimo detectable y la fórmula de profecía Spearman-Brown, respectivamente. Resultados: Usando todos los partidos, los resultados mostraron que el número mínimo de partidos necesarios en cada grupo fue de 30 para detectar un cambio medio (d > .5), 187 para un cambio pequeño (d > .2), y 100 para una buena fiabilidad relativa (ICC ≥ .75). Usando partidos igualados y no igualados, el número mínimo de partidos necesarios en cada grupo fue respectivamente 31 y 30 para detectar un cambio medio (d > .5), 190 y 188 para un cambio pequeño (d > .2), y 191 y 121 para una buena fiabilidad relativa (ICC ≥ .75). Conclusiones: La muestra debe constar de al menos 30 partidos en cada grupo para detectar un cambio mediano, y al menos 190 partidos para detectar un cambio pequeño. Para poder clasificar a los equipos con buena fiabilidad, se necesitan al menos 100 partidos cuando se incluyen tanto los partidos igualados como los no igualados.

Palabras clave: profecía Spearman-Brown; fiabilidad absoluta; fiabilidad relativa; análisis de conglomerados bietápico.

2.2. Abstract

In basketball, game-related statistics are the most common measure of performance. However, the literature assessing their reliability is scarce. Purpose: Analyse the number of games required to obtain a good relative and absolute reliability of teams’ game-related statistics. Method: A total of 884 games from the 2015-16 to 2017-18 seasons of the Spanish men’s professional league were analysed using all games and clustered by scoring difference. Intra-class correlation coefficient (ICC) was calculated for each variable. The number of games required to detect a change and to achieve good relative reliability was calculated using minimal detectable change and Spearman-Brown prophecy formula respectively. Results: Using all games, the results showed that the minimal number of games required in each group was 30 to detect a medium change (d > .5), 187 for a small change (d > .2), and 100 for good relative reliability (ICC ≥ .75). Using balanced and unbalanced games, the minimal number of games required in each group was respectively 31 and 30 to detect a medium change (d > .5), 190 and 188 for a small change (d > .2), and 191 and 121 for good relative reliability (ICC ≥ .75). Conclusions: The sample needs to consist of at least 30 games in each group to detect a medium size change, and at least 190 games to detect a small size change. To be able to rank teams with good reliability, at least 100 games are required when including both balanced and unbalanced games.

Keywords: Spearman-Brown prophecy; absolute reliability; relative reliability; two-step cluster.

2.3. Introduction

One of the research areas that has reached strong relevance within basketball analytics is modelling players’ and teams’ performance (Sampaio, Gonçalves, Mateus, Shaoliang, & Leite, 2018). This topic is in constant development and requires some data analytics and mathematical skills when collecting, processing and analysing performance during competition (Hughes, 2004). Specifically, performance analysts and sport scientists should follow some steps within this process (Hughes, 2004): (i) define performance indicators; (ii) determine the most important performance indicators; (iii) assess data reliability; (iv) ensure stable performance profiles from enough data; (v) compare sets of data; and (vi) model performance.

According to this scientific approach, basketball research has traditionally used game-related statistics as common performance indicators that best capture technical-tactical actions in competition (Oliver, 2004). These indicators are included in the official box-scores in most leagues and championships, and gather variables related to shooting, rebounding, fouling, blocking, or passing. Basketball research has used game-related statistics to try to explain players’ and teams’ performance; identifying the most important indicators discriminating winning teams (Sampaio & Janeira, 2003), the effects of game location (García et al., 2014), team season-long success (Ibáñez et al., 2008), rule changes (Pérez-Ferreirós, Kalén, & Rey, 2018), and between sexes and age groups (Sampaio et al., 2004).

In order to use game-related statistics for performance analysis and scouting, the reliability of the data must be ensured (Hughes, 2004). Reliability can refer to the ability to measure performance in a consistent way and with a high degree of agreement between measures, both from different observers (inter-rater reliability) and from the same observer (intra-rater reliability) (Atkinson & Nevill, 1998; Koo & Li, 2016). The inter and intra-rater reliability of performance indicators in basketball have been assessed in several different leagues and competitions with very good values (Cohen’s κ ≥ 0.91) of reliability (Gómez et al., 2011; Gómez, Lorenzo, et al., 2015; Sampaio et al., 2015).

Alternatively, in a wider perspective, reliability can also refer to the stability of the performance itself (Lames & McGarry, 2007). A sufficient amount of games should therefore be used for the performance indicators to provide a stable measure of the players’ and teams’ fixed performance patterns, or “normative profile” (Hughes et al., 2001; O’Donoghue & Ponting, 2005). Previous research has considered the full championship or season as enough data to analyse performance profiles or model performance (Csataljay et al., 2009; García et al., 2013). However, the available research focused on the ways to assess how much data is needed to obtain stabilised performance measures are scarce (Hughes et al., 2001; O’Donoghue & Ponting, 2005). Therefore, further performance analyses in basketball must include both measures of reliability, the consistency of the observational process, and the stability (performance) of the conditions under analysis according to the variables studied (Atkinson & Nevill, 1998; Hughes et al., 2001; Lames & McGarry, 2007).

Recent research showed the game-to-game variability of individual player’s game-related statistics in the NBA according to playing positions and minutes of play (Mateus et al., 2015; Zhang et al., 2017). The main findings showed that players playing fewer minutes have less stable performance, and that three-point shooting performance indicators showed the greatest variability (Mateus et al., 2015; Zhang et al., 2017). However, it is not clear how this variability may affect the reliability of game-related statistics for teams. Particularly, one problem with the stability of performance indicators in basketball is the source of variability from contextual factors within games and competitions (Lames & McGarry, 2007). Some factors previously studied are game types, such as balanced or unbalanced (Csataljay et al., 2009; García et al., 2013); competition structure, such as the Olympic Games (Sampaio, Lago, et al., 2010); or game pace, i.e., fast and slow games (Gómez, Ibáñez, et al., 2017).

Based on this rationale, there is a need for studies assessing the reliability of game-related statistics in basketball and identifying the minimum number of games required. Therefore, the absolute reliability (to compare the game-related statistics between teams and groups of teams) and relative reliability (to assess changes over time), must be controlled for in future basketball studies (Atkinson &

Nevill, 1998; Hopkins, 2000). Thus, this study aims to analyse the number of games required to obtain a good relative and absolute reliability of the teams’ game- related statistics in the ACB.

2.4. Method

2.4.1. Sample

The study analysed a total of 884 games from the 2015-16 to 2017-18 ACB seasons. The seasons 2015-16 and 2017-18 consisted of 18 teams while the 2016-17 season consisted of 17 teams. Therefore, a total of 53 teams were included. Each season comprised 34 rounds and a total sum of 1768 observations (games and teams) were used for the analyses.

2.4.2. Variables and procedure

The following game-related statistics were gathered for each game from ACB’s official website (http://www.acb.com): 2-point field goals made, attempted and percentage; 3-point field goals made, attempted and percentage; free-throws made, attempted and percentage; offensive and defensive rebounds; assists; steals; turnovers; blocks; personal fouls; and points scored. The collected data were gathered by ACB professional technicians. In order to do the analyses, game-related statistics of both teams were analysed.

According to Hughes and Bartlett (2004) performance indicators should be standardised in order to reduce variability within a game and allow stable performance comparisons. Therefore, game-related statistics were normalised to 100 ball possessions to control for game pace variability (Kubatko et al., 2007; Sampaio & Janeira, 2003). We also performed all analyses with the raw non- normalized game-related statistics; the results are presented in Supplementary material Table 2.5–2.7.

The number of ball possessions were calculated as follows (Kubatko et al., 2007): Possessions = 2-point attempts + 3-point attempts + Turnovers + 0.4 x Free- throw attempts – Offensive rebounds. From the raw statistics, effective field-goal percentage, offensive rebound percentage, defensive rebound percentage, free- throw rate, and turnover percentage, were calculated (Kubatko et al., 2007).

The games were also classified based on the difference in the final score between the winner and loser using a two-step cluster analysis (Csataljay et al.,

2009; García et al., 2013). Two categories of games were identified; balanced, with a final difference between 1-14 points, and unbalanced, with a final difference in points higher than 15.

2.4.3. Statistical analyses

Earlier studies have elaborated methods to estimate the sample size needed to produce a stable measure of performance indicators within an acceptable error range based on limits of agreement and central limit theorem (Hughes et al., 2001; O’Donoghue & Ponting, 2005). As the current study is focused on determining the reliability of game-related statistics for comparisons between teams and group of teams, intra-class correlation (ICC), and standard error of means (SEM) were used to calculate the number of games required (de Boer et al., 2005; de Vet, Bouter, Bezemer, & Beurskens, 2001; Eisinga, te Grotenhuis, & Pelzer, 2013).

The mean and standard deviation (SD) for each variable were calculated. A linear mixed model with game week as a fixed effect and team as a random effect was used to examine the presence of systematic bias for each variable. The coefficient for the game week indicated if there were any systematic change throughout the season. The normality and homogeneity of variance were verified graphically and using Anderson-Darling’s and Levene’s tests respectively.

For the measurement of relative reliability, the ICC with 95% Confidence Intervals (CI) of a two-way random model was used (Shrout & Fleiss, 1979). The ICC(2,1) for a single game and the ICC(2,k) for the average of all games was calculated (Shrout & Fleiss, 1979). An ICC lower than .5 was considered as poor reliability, ICC between .5 and .75 as moderate reliability, ICC between .75 and .9 as good reliability, and ICC higher than .9 as excellent reliability (Koo & Li, 2016). To calculate the minimum number of games required for good reliability (ICC ≥ .75), the Spearman-Brown prophecy formula was used (Eisinga et al., 2013; Sasaki et al., 2018):

NOO( ) ⁄S1 − NOO( )T M = P,R P,R (1 − .75)⁄. 75

For the measurement of absolute reliability we first calculated the SEM from the SD and the ICC(2,1) as (Atkinson & Nevill, 1998):

9GW = 9;X1 − NOO(P,R)

Then, the minimal detectable change (MDC) between two games for an individual team was defined as the upper 95% CI of the SEM and was calculated as (Beckerman et al., 2001):

W;O = 1.962 × √2 × 9GW

To calculate the number of games needed to detect medium and small changes respectively, the MDC was first converted to standardised effect size (ES) (d) by dividing it by the SD (Cohen, 1992).

W;O W;O = \] 9;

ES was considered as trivial when ≤ .19, small between .20-.49, medium between .50-.79 and large when ≥ .80 (Cohen, 1992). The formula for group MDC (de Boer et al., 2005; de Vet et al., 2001) was used to calculate the minimum number of games required in each group (n) to detect a medium or small effect:

W;O P M = ^ \]` _

Earlier studies have indicated that game location influences game-related statistics (García et al., 2014). A preliminary analysis showed practically no difference in reliability when accounting for game location and it was therefore not used in the final analysis. An additional analysis by season was also performed, with results available in the Supplementary material Table 2.8.

In addition, a two-step cluster analysis with log-likelihood as the distance measured and Schwartz’s Bayesian criterion was used to classify games by the final score difference and ball possessions (Garson, 2014). As the model performed poorly (silhouette measure of .5), the model was run only with the final score difference (silhouette measure of .7). Then, the model identified two clusters that

were categorised as balanced (scoring difference ≤ 14, n = 1,226) and unbalanced (scoring difference ≥ 15, n = 542).

A significance level of p < .05 was used for all inference. The cluster analysis was performed using SPSS 25 for Mac (IBM Corp., Armonk, NY, USA). All other statistical analyses were performed in R 3.4.1.

2.5. Results

The test for systematic bias revealed a significant decrease in the number of steals over the season (coefficient = -.029, p = .001). No other variables showed any systematic bias.

The descriptive statistics together with the SEM, MDC, and the number of games required to detect a medium and small change are presented in Table 2.1.

The MDCES for all variables corresponds to a large ES. The minimum number of games required to detect a medium and small change are presented in Figure 2.1 and Figure 2.2, respectively. The number of games required in each group to detect a medium change (d > .5) ranged from 25.4 to 29.9 and to detect a small change (d > .2) from 158.5 to 186.8.

Table 2.1. Descriptive statistics and absolute reliability.

Variable Mean SD SEM MDC MDCES Points scored 110.6 13.9 13.1 36.5 2.6 Two-point attempts 51.3 7.8 7.5 20.8 2.7 Two-point made 27.1 5.5 5.2 14.4 2.6 Two-point % 53.1 8.3 8.0 22.2 2.7 Three-point attempts 33.9 6.7 6.1 17.0 2.6 Three-point made 12.0 4.1 3.9 10.9 2.6 Three-point % 35.3 9.8 9.6 26.6 2.7 Free-throw attempts 26.8 9.1 9.0 24.9 2.7 Free-throw made 20.4 7.6 7.4 20.6 2.7 Free-throw % 75.7 11.0 10.8 29.8 2.7 Defensive rebounds 32.7 5.8 5.5 15.2 2.6 Offensive rebounds 13.8 4.8 7.9 22.0 2.7 Assists 21.8 5.6 5.1 14.2 2.5 Steals 9.6 3.7 3.5 9.7 2.7 Turnovers 17.9 4.5 4.4 12.2 2.7 Blocks 3.1 2.2 2.1 5.8 2.7 Personal fouls 29.5 4.9 4.7 13.1 2.7 Possessions 72.9 4.6 4.2 11.7 2.6 Effective field-goal % 53.1 7.7 7.3 20.3 2.6 Defensive rebound % 70.6 8.4 8.2 22.6 2.7 Offensive rebound % 29.4 8.3 4.6 12.8 2.7 Free-throw rate 32.2 12.5 12.3 34.1 2.7 Turnover % 17.9 4.5 4.4 12.2 2.7 Note. SD = Standard Deviation; SEM = Standard Error of Measurement; MDC = Minimal Detectable Change; MDCES = Standardized Minimal Detectable Change.

Assists 25.4

Three−point attempts 26.1

Possessions 26.3

Points scored 27.5

Three−point made 27.7

Two−point made 27.8

Effective field−goal % 27.8

Defensive rebounds 27.8

Steals 28.2

Two−point attempt 28.3

Offensive rebound % 28.4

Two−point % 28.4

Personal Fouls 28.7

Offensive rebounds 28.9

Blocks 29.1

Turnover % 29.1

Deffensive rebound % 29.1

Three−point % 29.4

Free−throw % 29.7

Free−throw made 29.7

Free−throw attempts 29.8

Free−throw rate 29.9 0 10 20 30 40 50

Figure 2.1. Number of games required to be able to detect a medium change (d > .5).

Assists 158.5

Three−point attempts 163.1

Possessions 164.3

Points scored 171.8

Three−point made 173.1

Two−point made 173.6

Effective field−goal % 173.9

Defensive rebounds 174.0

Steals 176.5

Two−point attempt 176.6

Offensive rebound % 177.4

Two−point % 177.5

Personal Fouls 179.5

Offensive rebounds 180.6

Blocks 181.6

Turnover % 181.8

Deffensive rebound % 182.1

Three−point % 183.9

Free−throw % 185.6

Free−throw made 185.8

Free−throw attempts 186.1

Free−throw rate 186.8 0 50 100 150 200 250

Figure 2.2. Number of games required to be able to detect a small change (d > .2).

The ICC(2,1) and ICC(2,k) are presented with their respective 95% CI in Table 2.2. None of the game-related statistics reached an acceptable level of single-game relative reliability. Using the average of all games, points scored, two-point attempts, two-point made, three-point attempts, three-point made, defensive rebounds, assists, steals, possessions, and efficient field goal percentage reached a good level of reliability. The number of games required to achieve good relative reliability (ICC ≥ .75) is presented in Figure 2.3.

Table 2.2. Relative reliability.

ICC(2,1) ICC(2,k) Variable ICC 95% CI ICC 95% CI Points scored .107 .070–.167 .804 .719–.872 Two-point attempts .083 .051–.134 .754 .648–.840 Two-point made .098 .063–.155 .787 .696–.862 Two-point % .078 .048–.127 .742 .631–.832 Three-point attempts .152 .105–.226 .860 .799–.909 Three-point made .101 .065–.158 .792 .703–.865 Three-point % .044 .023–.080 .612 .446–.748 Free-throw attempts .033 .015–.064 .538 .341–.700 Free-throw made .034 .016–.066 .548 .355–.706 Free-throw % .036 .017–.068 .557 .367–.712 Defensive rebounds .096 .062–.152 .783 .690–.859 Offensive rebounds .078 .048–.128 .742 .632–.833 Assists .177 .124–.257 .879 .828–.922 Steals .083 .052–.134 .754 .650–.840 Turnovers .055 .031–.096 .666 .523–.783 Blocks .056 .032–.097 .670 .528–.785 Personal fouls .068 .040–.113 .711 .587–.812 Possessions .146 .100–.218 .853 .790–.905 Effective field-goal % .096 .062–.152 .784 .691–.859 Defensive rebound % .054 .030–.094 .660 .515–.779 Offensive rebound % .062 .036–.105 .691 .559–.799 Free-throw rate .029 .012–.058 .506 .295–.679 Turnover % .055 .031–.096 .666 .523–.783 Note. ICC = Intra-class Correlation Coefficient; CI = Confidence Interval.

Assists 14.0

Three−point attempts 16.7

Possessions 17.5

Points scored 24.9

Three−point made 26.8

Two−point made 27.6

Effective field−goal % 28.1

Defensive rebounds 28.2

Steals 33.2

Two−point attempt 33.4

Offensive rebound % 35.4

Two−point % 35.5

Personal Fouls 41.4

Offensive rebounds 45.5

Blocks 50.3

Turnover % 51.2

Deffensive rebound % 52.5

Three−point % 64.6

Free−throw % 81.1

Free−throw made 84.1

Free−throw attempts 87.5

Free−throw rate 99.5 0 25 50 75 100

Figure 2.3. Number of games required to achieve good ICC (≥ .75).

The analyses were also performed for the non-normalized and opponents’ game-related statistics (Supplementary material Table 2.5–2.7). Further, the analyses were performed separately for each season (Supplementary material Table 2.8).

The MDCES and the number of games required to detect a medium and small change for balanced and unbalanced games are presented in Table 2.3. The MDCES for all variables in both groups corresponds to a large effect size. The number of games required in each group to detect a medium change (d > .5) ranged from 26.2 to 30.3 for balanced games and 20.8 to 30.0 for unbalanced games. Compared to the full sample, between 0.2 fewer and 2.6 more games (average 0.6 more) were needed for balanced games, between 6.7 fewer and 0.6 more games (average 2.0 less) were needed for unbalanced games. To detect a small change (d > .2) between 163.7 to 189.5 games were required for balanced games and 130.1 to 187.8 for unbalanced games. Compared to the full sample, between 1.0 fewer and 16.3 more games (average 3.8 more) were needed for balanced games, between 41.7 fewer and 4.0 more games (average 12.6 less) were needed for unbalanced games.

Table 2.3. Descriptive statistics and absolute reliability for the clusters. Balanced (n = 1226) Unbalanced (n = 542) Number of games Number of games

required required Medium Small Medium Small Variable MDCES MDCES change change change change Points scored 2.7 30.1 188.2 2.3 20.8 130.1 Two-point attempts 2.7 28.3 177.1 2.7 28.6 178.6 Two-point made 2.6 27.9 174.6 2.6 26.8 167.5 Two-point % 2.7 29.4 184.0 2.5 25.4 159.0 Three-point attempts 2.6 26.2 163.7 2.6 26.0 162.6 Three-point made 2.7 28.4 177.5 2.5 24.6 153.6 Three-point % 2.8 30.3 189.5 2.5 25.0 156.3 Free-throw attempts 2.7 29.9 186.7 2.7 29.4 184.1 Free-throw made 2.7 30.2 188.6 2.7 28.1 175.9 Free-throw % 2.7 30.0 187.7 2.6 27.2 170.1 Defensive rebounds 2.7 29.9 186.7 2.3 21.8 136.0 Offensive rebounds 2.7 28.8 180.0 2.7 29.5 184.6 Assists 2.6 26.7 167.0 2.3 21.8 136.2 Steals 2.7 28.3 176.9 2.7 28.2 176.1 Turnovers 2.7 29.3 183.2 2.7 28.3 176.7 Blocks 2.7 29.1 181.8 2.6 28.0 175.3 Personal fouls 2.7 29.2 182.6 2.6 27.6 172.7 Possessions 2.6 26.8 167.5 2.5 24.8 154.9 Effective field-goal % 2.7 29.5 184.2 2.4 22.2 138.9 Defensive rebound % 2.7 30.0 187.7 2.5 25.8 161.0 Offensive rebound % 2.7 28.6 178.8 2.6 27.3 170.8 Free-throw rate 2.7 29.7 185.9 2.7 30.0 187.8 Turnover % 2.7 29.3 183.2 2.7 28.3 176.7

Note. MDCES = Standardized Minimal Detectable Change.

The ICC(2,1) and ICC(2,k) with 95% CI and the number of games required to achieve good relative reliability (ICC ≥ .75) for both groups are presented in Table 2.4. To achieve good relative reliability, the number of games required ranged from 17.0 to 190.2 for balanced games and 6.3 to 120.2 for unbalanced games. Compared to the full sample, between 15 fewer and 121.0 more games (average 24.9 more) were needed for balanced games, between 58.3 fewer and 25.0 more games (average 16.0 less) were needed for unbalanced games.

Table 2.4. Relative reliability for the clusters. Balanced (n = 1226) Unbalanced (n = 542) ICC(2,1) ICC(2,k) Number of ICC(2,1) ICC(2,k) Number of Variable ICC 95% CI ICC 95% CI games required ICC(2,1) 95% CI ICC(2,k) 95% CI games required Points scored .022 .007–.438 .443 .205–.637 131.1 .324 .246–.942 .942 .917–.962 6.3 Two-point attempts .080 .049–.747 .747 .638–.835 34.6 .072 .043–.725 .725 .607–.821 38.7 Two-point made .093 .059–.777 .777 .681–.855 29.3 .130 .087–.835 .835 .765–.893 20.1 Two-point % .044 .023–.609 .610 .443–.746 65.5 .174 .122–.877 .877 .825–.920 14.3 Three-point attempts .150 .103–.857 .857 .795–.907 17.0 .155 .107–.862 .862 .803–.910 16.3 Three-point made .078 .048–.742 .743 .633–.832 35.5 .202 .144–.896 .896 .851–.932 11.9 Three-point % .016 .002–.349 .355 .083–.579 190.2 .188 .133–.887 .887 .839–.927 13.0 Free-throw attempts .030 .013–.512 .519 .313–.687 97.2 .044 .023–.609 .609 .442–.745 65.6 Free-throw made .020 .006–.414 .418 .169–.621 144.3 .086 .054–.762 .762 .660–.845 31.9 Free-throw % .025 .009–.464 .450 .214–.642 117.9 .116 .077–.817 .817 .739–.881 22.8 Defensive rebounds .030 .013–.514 .508 .297–.680 96.5 .294 .220–.934 .934 .906–.957 7.2 Offensive rebounds .065 .038–.703 .702 .574–.806 43.2 .041 .021–.591 .591 .417–.734 70.5 Assists .132 .089–.838 .838 .769–.895 19.7 .292 .219–.934 .934 .905–.957 7.3 Steals .081 .050–.750 .748 .642–.836 34.1 .085 .053–.760 .760 .657–.844 32.3 Turnovers .048 .026–.634 .637 .481–.763 59.0 .082 .051–.752 .752 .646–.839 33.6 Blocks .055 .031–.666 .665 .522–.782 51.3 .089 .056–.769 .769 .670–.850 30.6 Personal fouls .052 .028–.649 .657 .510–.777 55.2 .103 .067–.796 .796 .709–.867 26.2 Possessions .130 .087–.835 .834 .763–.892 20.1 .195 .139–.892 .892 .846–.930 12.4 Effective field-goal % .043 .022–.603 .607 .440–.744 67.1 .278 .207–.929 .929 .899–.954 7.8 Defensive rebound % .025 .009–.463 .464 .234–.652 118.2 .164 .114–.869 .869 .813–.915 15.3 Offensive rebound % .071 .043–.722 .721 .602–.819 39.3 .113 .074–.812 .812 .731–.878 23.6 Free-throw rate .034 .016–.066 .547 .353–.705 84.5 .024 .009–.051 .459 .230–.647 120.2 Turnover % .048 .026–.634 .637 .481–.763 59.0 .082 .051–.752 .752 .646–.839 33.6 Note. ICC = Intra-class Correlation Coefficient; CI = Confidence Interval.

2.6. Discussion

This study aimed to analyse the number of games required to obtain a good relative and absolute reliability of the teams’ game-related statistics in the ACB. As was previously argued (Atkinson & Nevill, 1998; Hopkins, 2000; Sampaio et al., 2018), there is a need to assess absolute and relative reliability of game-related statistics in basketball to ensure that analyses modelling performance are robust and powerful. According to this rationale, the current findings support the importance of reliability studies in basketball. In particular, the results showed that standardised MDC between two games was large (d > 2.6) for all game-related statistics. To be able to detect a medium change (d > .5), the number of games needed in each group to be compared was between 25.4-29.9, for balanced games 26.2-30.3, and unbalanced games 20.8-30.8. To be able to detect a small change (d > .2), the number of games needed was between 158.5-186.8, for balanced games 163.7-189.5, and unbalanced games 130.1-187.8. The single-game relative reliability was poor, with ICC(2,1) < .177 for all game-related statistics. The relative reliability for the full season was good, with ICC(2,k) between .754 and .879 for ten of the 23 variables. The number of games required for good reliability was between 14.0-99.5, for balanced games 17.0-190.2, and unbalanced games 6.3-120.2.

Specifically, earlier studies have shown great game-to-game variability in the number of three-point shots attempted and made by individual players (Mateus et al., 2015; Zhang et al., 2017). In the current study, both these variables showed good relative reliability over a full season, with an ICC(2,k) of .860 and .792 respectively. One possible explanation for this discrepancy is that the previous studies analysed the NBA, which includes almost twice as many teams and, therefore, probably a bigger difference in quality between the teams. Hence, performance is not stable from a match to match perspective due to the considerable variability of the opposing team’s strength. However, ACB is characterised by a more collective tactical play that is based on organised and disciplined attacks that end with three-point shots irrespective of the shooter (George, Evangelos, Alexandros, & Athanasios, 2009). However, the three-point percentage showed moderate reliability, ICC(2,k) = .612. This could perhaps also be

explained by the redistribution of shots between players. For example, in a game where a high percentage shooter is not able to take as many three-point shots, a poorer shooter might take them instead, resulting in a varying three-point percentage. This discrepancy in results is an indication that there are important differences in the reliability of game-related statistics for teams and players.

In addition, the free-throw related variables showed the lowest season-long relative reliability, with ICC(2,k) between .506 and .557. This finding suggests that the free-throw related variables are not the most adequate to classify or distinguish different teams or groups of teams. In accordance with this finding, earlier studies have found free-throw related variables to seldom discriminate between, for example, winning and losing teams, final league classification, age groups, or genders (Ibáñez et al., 2008; García et al., 2013; Sampaio et al., 2004). However, most studies using free-throw related variables do so together with all the standard game-related statistics. Therefore, their low reliability should generally not affect the final results of studies substantially.

Finally, assists showed both the highest absolute and relative reliability of all variables included, with MDCES = 2.5 and ICC(2,k) = .879. This finding is in line with the low game-to-game variability of individual players’ assists in earlier studies (Mateus et al., 2015; Zhang et al., 2017). In fact, the game-to-game variability seems to be largely unaffected by contextual factors such as game location, game outcome and team strength (Mateus et al., 2015; Zhang et al., 2017). Further, assists have shown to be one of the game-related statistics that best discriminate the season-long success (Ibáñez et al., 2008). This indicates that the number of assists remains fairly stable throughout the season for the individual teams.

The results of the current study indicated that between 26 and 30 games were required to be able to detect a medium size change. It is important to note that this is the number of games per team (or group of teams) required before as well as after the change of interest. As each team has played 33 or 34 games per season in the seasons used, it is essentially necessary to compare a team’s full season to another to detect a medium change within a team. However, changes between seasons will probably be influenced by the changes teams make. For

example, Morse, Shapiro, McEvoy, and Rascher (2008) reported an average roster turnover of 36% in the NBA. This makes the analysis of changes in individual teams practically infeasible. To be able to detect a small change, between 159 and 187 games were required. This means, for example, that to assess changes between seasons, a minimum of six teams are needed in the sample. These findings point out the importance to correctly establish the sample of a study in order to model team performance (Sampaio et al., 2018).

As for the number of games required to reach good relative reliability, it varies widely between variables, ranging from 14 to 100 games. This finding refers to the number of games required for each team, or a group of teams, that is to be compared. For example, after half a season (17 games) only the three-point attempts, assists and possessions provide good reliability when comparing individual teams. When using a full 34-game season, points scored, two-point attempts, two-point made, three-point attempts, three-point made, defensive rebounds, assists, steals, possessions, and efficient field goal percentage also provide good reliability. To reach good relative reliability for all game-related statistics, the sample would need to include three seasons for each team. However, such results need to be treated cautiously as the teams may change between seasons due to playing styles, coaches’ management, or player recruitment (Morse et al., 2008). For single-season comparisons between groups of teams, the groups need to be composed by at least three teams each when using all game-related statistics.

Performance analysis in basketball usually classify the games based on the final scoring difference (cluster analyses), thereby enabling a more fine-grained analysis of performance (Csataljay et al., 2009; García et al., 2013). In general, using only balanced games required a higher number of games compared to using all games, both for relative and absolute reliability. The opposite was true when using unbalanced games: Fewer games were generally needed compared to using all games. This finding indicates that teams have a more stable performance in unbalanced than in balanced games. It is possible that the majority of unbalanced games for each team consists of either mostly big wins or big losses, while the balanced games might be a mix of wins and losses.

Dividing the games into balanced and unbalanced games has shown a minimal effect on the number of games needed to detect both a medium and small change. Considering balanced and unbalanced games, one additional game is needed (31 compared to 30) to detect a medium change. Similarly, to detect a small change, three additional games are needed (190 compared to 187). However, researchers need to consider that by dividing the games, the number of games in each group decrease. For example, in earlier studies, 65-77% of the total games were classified as balanced (Csataljay et al., 2009; García et al., 2013). Therefore, it is unlikely that the teams have a minimum of 31 balanced games in one season, which means that a single team’s season will probably not comprise a big enough sample to detect a medium change. For the relative reliability, there were bigger differences in the number of games needed between the full sample and when dividing by scoring difference. The highest number of games needed (three-point percentage for balanced games) was 191 games, requiring six seasons or teams to be used. However, studies dividing the sample by scoring difference have focused on comparing groups and not assessing change over time (Csataljay et al., 2009; García et al., 2013). Therefore, in these cases, the focus should be on obtaining a sufficient sample for good absolute reliability.

The current study has some limitations that need to be acknowledged. The first limitation is the representativeness of the sample. Since three seasons of the ACB league were used, these results may not be applied to other leagues. Especially if there is a great difference in the number of teams, the number of games or the competition structure. Further, the study did not analyse any potential difference in reliability over time. The evolution over time of the game might affect the reliability; therefore it is necessary to account for this effect. Finally, the present study analysed game-related statistics from a team level. Thus, this analysis does not provide information on the reliability of game-related statistics at a player level. Therefore, further research should analyse the reliability of game-related statistics on a player level and from a long-term analysis in different competitions (e.g., tournaments, play-offs and national leagues).

2.7. Conclusions

The study shows that using all games: (a) To detect a medium size change (d > .5) for all game-related statistics, a minimum of 30 games are required in each group to be compared; (b) to detect a small size change (d > .2) for all game-related statistics, a minimum of 187 games are required in each group to be compared; (c) to reach a good relative reliability (ICC ≥ .75) for all game-related statistics, a minimum of 100 games are required for each team or group of teams to be ranked. These recommendations are also applicable to both normalised and non- normalized game-related statistics.

The study also shows that when clustering the sample into balanced and unbalanced games: (a) To detect a medium size change (d > .5) for all game-related statistics, a minimum of 31 and 30 games are required for balanced and unbalanced games, respectively; (b) to detect a small size change (d > .2) for all game-related statistics, a minimum of 190 and 188 games are required, respectively; (c) to reach good relative reliability (ICC ≥ .75) for all game-related statistics, a minimum of 191 games for balanced and 121 for unbalanced are required for each team or group of teams to be ranked.

2.8. What does this article add?

This study provides new information about the minimal sample size needed to obtain reliable measures when using game-related statistics on a team level in basketball. To assess changes or differences in team performance, at least 30 games are needed for each team or time point, which means that it is only possible to find differences between full seasons on an individual team level. To reliably be able to rank the team performance, at least 100 games are needed, which means that a reliable ranking of individual teams’ season-long performance is not possible. However, the number of games needed varies greatly between the different game- related statistics. Therefore, if only a subset of the game-related statistics is used, the number of games needed can differ and should be addressed for the specific analysis. These results can help researchers when designing future studies, particularly, where the sample is divided into several subgroups, where the group sizes risk to get too small. From a practitioner’s perspective, the results provide useful information for coaches, clubs, and scouts on how to utilise the game- related statistics in their work.

2.9. Supplementary material

Table 2.5. Reliability of non-standardised game-related statistics. ICC(2,1) ICC(2,k) Number of games required

Variable Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change Small change ICC > .75 Points scored 80.6 10.9 10.2 28.3 2.6 .127 .085–.193 .832 .760–.891 26.9 168.0 20.6 Two-point attempts 37.3 6.1 5.8 16.1 2.6 .101 .065–.159 .793 .704–.865 27.7 173.0 26.6 Two-point made 19.8 4.2 3.9 10.9 2.6 .118 .078–.182 .820 .743–.883 27.2 169.7 22.4 Three-point attempts 24.7 4.8 4.4 12.2 2.5 .160 .110–.235 .866 .808–.913 25.9 161.8 15.8 Three-point made 8.7 3.0 2.8 7.9 2.6 .097 .062–.153 .785 .693–.860 27.8 173.8 28.0 Free-throw attempts 19.6 6.8 6.7 18.5 2.7 .041 .020–.075 .590 .415–.733 29.5 184.6 70.8 Free-throw made 14.8 5.6 5.5 15.2 2.7 .040 .020–.074 .587 .411–.731 29.6 184.7 71.7 Defensive rebounds 23.8 4.4 4.2 11.6 2.6 .100 .065–.158 .791 .702–.864 27.7 173.2 26.9 Offensive rebounds 10.0 3.4 3.3 9.1 2.7 .058 .033–.099 .675 .536–.789 29.0 181.4 49.1 Assists 15.9 4.1 3.7 10.4 2.5 .173 .121–.253 .877 .824–.920 25.5 159.1 14.3 Steals 7.0 2.7 2.6 7.1 2.6 .090 .057–.143 .770 .672–.850 28.0 175.2 30.5 Turnovers 13.1 3.5 3.4 9.4 2.7 .041 .020–.075 .590 .415–.733 29.5 184.7 70.9 Blocks 2.3 1.6 1.5 4.3 2.7 .057 .032–.097 .671 .529–.786 29.1 181.6 50.1 Personal fouls 21.5 3.6 3.5 9.7 2.7 .053 .029–.092 .655 .507–.776 29.2 182.3 53.7

Note. SD = Standard Deviation; SEM = Standard Error of Measurement; MDC = Minimal Detectable Change; MDCES = Standardized Minimal Detectable Change; ICC = Intra-class Correlation Coefficient; CI = Confidence Interval.

Table 2.6. Reliability of opponents’ game-related statistics normalised to 100 ball possessions. ICC(2,1) ICC(2,k) Number of games required

Variable Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change Small change ICC > .75 Points scored 110.6 14.0 13.4 37.1 2.7 .087 .055–.140 .765 .664–.847 28.1 175.7 31.4 Two-point attempts 51.3 7.8 7.3 20.2 2.6 .125 .083–.190 .829 .755–.889 27.0 168.5 21.1 Two-point made 27.1 5.6 5.4 14.9 2.7 .080 .049–.130 .747 .639–.836 28.3 177.1 34.5 Two-point % 53.1 8.4 8.1 22.4 2.7 .069 .041–.115 .717 .595–.816 28.7 179.1 40.3 Three-point attempts 33.9 6.7 6.1 16.8 2.5 .175 .122–.254 .878 .826–.921 25.4 158.9 14.2 Three-point made 12.0 4.1 3.8 10.7 2.6 .114 .075–.176 .814 .734–.879 27.3 170.6 23.4 Three-point % 35.3 9.9 9.8 27.1 2.7 .026 .010–.053 .472 .246–.656 30.0 187.5 114.1 Free-throw attempts 26.8 8.5 7.9 22.0 2.6 .129 .086–.195 .834 .763–.892 26.8 167.7 20.3 Free-throw made 20.3 7.1 6.6 18.3 2.6 .128 .086–.194 .833 .761–.891 26.9 167.9 20.5 Free-throw % 75.7 11.1 11.0 30.4 2.8 .017 .003–.041 .372 .104–.592 30.3 189.2 171.9 Defensive rebounds 32.7 5.7 5.4 15.1 2.7 .087 .055–.140 .764 .663–.847 28.1 175.7 31.5 Offensive rebounds 13.8 4.9 4.8 13.3 2.7 .028 .011–.057 .498 .283–.674 29.9 187.0 102.7 Assists 21.8 5.9 5.7 15.8 2.7 .079 .049–.129 .745 .637–.834 28.4 177.2 34.8 Steals 9.6 3.7 3.6 9.9 2.7 .064 .038–.108 .700 .572–.804 28.8 180.1 43.8 Turnovers 17.9 4.5 4.4 12.1 2.7 .062 .036–.104 .690 .558–.799 28.9 180.6 45.8 Blocks 3.1 2.1 2.1 5.7 2.7 .081 .050–.131 .749 .641–.836 28.3 177.0 34.3 Personal fouls 29.5 4.5 4.0 11.2 2.5 .187 .132–.270 .887 .838–.926 25.0 156.4 13.0 Effective field-goal % 53.1 7.9 7.6 21.1 2.7 .063 .037–.107 .696 .565–.802 28.9 180.3 44.6 Free-Throw rate 32.2 11.7 11.0 30.4 2.6 .130 .088–.197 .836 .766–.893 26.8 167.4 20.0 Turnover % 17.9 4.5 4.4 12.1 2.7 .062 .036–.104 .690 .558–.799 28.9 180.6 45.8

Table 2.7. Reliability of opponents’ non-standardised game-related statistics. ICC(2,1) ICC(2,k) Number of games required Small Variable Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change ICC > .75 change Points scored 80.6 11.1 10.5 29.1 2.6 .102 .066–.160 .795 .706–.866 27.7 172.8 26.4 Two-point attempts 37.3 5.9 5.4 15.1 2.6 .154 .106–.228 .861 .801–.909 26.1 162.9 16.5 Two-point made 19.8 4.2 4.0 11.1 2.6 .100 .065–.158 .791 .702–.864 27.7 173.2 26.9 Three-point 24.7 4.7 4.3 11.9 2.5 .184 .130–.266 .885 .835–.925 25.1 157.0 13.3 attempts Three-point made 8.7 3.0 2.8 7.7 2.6 .113 .074–.175 .812 .732–.878 27.3 170.7 23.5 Free-throw attempts 19.6 6.5 6.1 17.0 2.6 .117 .078–.180 .818 .741–.882 27.2 169.9 22.6 Free-throw made 14.8 5.4 5.0 14.0 2.6 .115 .076–.178 .816 .737–.880 27.2 170.3 23.0 Defensive rebounds 23.8 4.4 4.1 11.4 2.6 .110 .072–.171 .808 .726–.875 27.4 171.3 24.2 Offensive rebounds 10.0 3.4 3.3 9.2 2.7 .046 .024–.082 .621 .458–.753 29.4 183.6 62.3 Assists 15.9 4.3 4.2 11.6 2.7 .78 .048–.127 .741 .630–.832 28.4 177.5 35.6 Steals 7.0 2.7 2.7 7.4 2.7 .053 .029–.092 .655 .508–.775 29.2 182.3 53.8 Turnovers 13.1 3.4 3.3 9.1 2.7 .072 .044–.119 .725 .607–.821 28.6 178.6 38.7 Blocks 2.3 1.6 1.5 4.1 2.6 .088 .056–.142 .767 .667–.849 28.1 175.5 31.0 Personal fouls 21.5 3.4 3.1 8.6 2.5 .162 .113–.239 .868 .812–.914 25.8 161.2 15.5

Table 2.8. Reliability of standardised game-related statistics per season. ICC(2,1) ICC(2,k) Number of games required

Variable Year Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change Small change ICC > .75 Points scored 2015-16 110.3 13.8 12.7 35.2 2.6 0.155 0.081–0.311 0.862 0.751–0.939 26.0 162.7 16.4 2016-17 109.9 14.3 13.7 38.1 2.7 0.075 0.030–0.186 0.735 0.516–0.886 28.5 178.0 36.8 2017-18 111.6 13.7 13.1 36.2 2.6 0.094 0.043–0.214 0.780 0.604–0.903 27.9 174.3 28.8 Two-point attempt 2015-16 50.8 7.8 7.4 20.6 2.6 0.090 0.041–0.208 0.772 0.590–0.899 28.0 175.1 30.2 2016-17 51.0 7.8 7.5 20.8 2.7 0.082 0.035–0.198 0.752 0.549–0.894 28.3 176.7 33.6 2017-18 51.9 7.8 7.5 20.9 2.7 0.079 0.034–0.188 0.745 0.541–0.887 28.4 177.2 34.9 Two-point made 2015-16 26.8 5.4 5.1 14.2 2.6 0.108 0.052–0.237 0.805 0.649–0.914 27.5 171.7 24.8 2016-17 27.1 5.5 5.3 14.6 2.7 0.072 0.028–0.180 0.725 0.499–0.882 28.6 178.6 38.6 2017-18 27.5 5.6 5.2 14.5 2.6 0.116 0.056–0.250 0.817 0.671–0.919 27.2 170.1 22.9 Two-point % 2015-16 52.8 8.4 8.0 22.1 2.6 0.095 0.043–0.216 0.781 0.607–0.903 27.9 174.2 28.5 2016-17 53.4 8.3 8.0 22.2 2.7 0.061 0.022–0.160 0.689 0.432–0.867 28.9 180.7 46.0 2017-18 53.1 8.3 8.0 22.1 2.7 0.084 0.037–0.197 0.758 0.565–0.893 28.2 176.2 32.5 Three-point attempts 2015-16 33.2 6.6 6.1 16.8 2.5 0.168 0.090–0.331 0.873 0.771–0.944 25.6 160.1 14.9 2016-17 34.1 6.3 5.7 15.9 2.5 0.184 0.099–0.361 0.885 0.789–0.950 25.1 157.1 13.3 2017-18 34.5 6.9 6.5 18.1 2.6 0.112 0.054–0.243 0.810 0.659–0.916 27.4 171.0 23.9 Three-point made 2015-16 11.9 4.2 4.0 11.1 2.6 0.112 0.054–0.244 0.811 0.660–0.916 27.3 170.9 23.8 2016-17 11.9 4.1 3.9 10.7 2.6 0.113 0.053–0.251 0.812 0.657–0.919 27.3 170.7 23.6 2017-18 12.2 4.0 3.9 10.7 2.7 0.087 0.038–0.201 0.763 0.574–0.895 28.1 175.8 31.7 Three-point % 2015-16 35.7 10.1 9.8 27.2 2.7 0.065 0.025–0.163 0.704 0.467–0.869 28.8 179.9 42.9 2016-17 34.7 10.0 9.9 27.6 2.7 0.022 -0.001–0.084 0.432 -0.039–0.756 30.1 188.3 134.3 2017-18 35.3 9.2 9.0 25.1 2.7 0.046 0.013–0.127 0.621 0.317–0.832 29.4 183.6 62.4 Free-throw attempts 2015-16 27.4 9.5 9.3 25.8 2.7 0.036 0.008–0.109 0.561 0.211–0.806 29.7 185.5 79.7 2016-17 26.2 9.2 9.0 25.0 2.7 0.037 0.008–0.113 0.563 0.205–0.812 29.7 185.4 79.1 2017-18 26.8 8.7 8.6 23.9 2.7 0.025 0.002–0.087 0.470 0.056–0.764 30.0 187.6 115.0

ICC(2,1) ICC(2,k) Number of games required

Variable Year Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change Small change ICC > .75 Free-throw made 2015-16 21.0 7.9 7.8 21.5 2.7 0.033 0.006–0.103 0.538 0.169–0.796 29.8 186.1 87.6 2016-17 19.9 7.5 7.4 20.5 2.7 0.043 0.011–0.124 0.602 0.277–0.828 29.5 184.3 67.5 2017-18 20.0 7.2 7.2 19.9 2.7 0.023 0.000–0.082 0.443 0.005–0.752 30.1 188.1 128.3 Free-throw % 2015-16 76.5 10.2 9.9 27.5 2.7 0.052 0.017–0.138 0.650 0.373–0.845 29.2 182.5 54.8 2016-17 76.2 11.2 11.2 31.0 2.8 0.005 -0.010–0.047 0.140 -0.540–0.626 30.6 191.6 626.0 2017-18 74.5 11.5 11.3 31.3 2.7 0.039 0.009–0.114 0.578 0.240–0.813 29.6 185.0 74.6 Defensive rebounds 2015-16 32.4 5.8 5.4 15.0 2.6 0.131 0.066–0.275 0.837 0.707–0.928 26.8 167.2 19.9 2016-17 32.3 5.7 5.5 15.3 2.7 0.068 0.026–0.174 0.714 0.478–0.877 28.7 179.3 40.9 2017-18 33.3 5.8 5.5 15.4 2.7 0.080 0.034–0.190 0.748 0.547–0.889 28.3 177.0 34.3 Offensive rebounds 2015-16 13.5 4.8 4.7 12.9 2.7 0.046 0.014–0.128 0.623 0.323–0.833 29.4 183.6 61.8 2016-17 14.0 4.7 4.6 12.8 2.7 0.045 0.013–0.130 0.618 0.304–0.836 29.4 183.7 63.0 2017-18 14.0 4.8 4.5 12.6 2.6 0.093 0.042–0.212 0.777 0.599–0.901 27.9 174.6 29.3 Assists 2015-16 21.4 5.6 5.1 14.1 2.5 0.175 0.095–0.341 0.879 0.781–0.946 25.4 158.7 14.1 2016-17 21.7 5.7 5.2 14.3 2.5 0.176 0.094–0.349 0.879 0.779–0.948 25.4 158.7 14.1 2017-18 22.4 5.7 5.1 14.1 2.5 0.186 0.103–0.357 0.886 0.796–0.950 25.1 156.6 13.1 Steals 2015-16 10.5 3.6 3.5 9.7 2.7 0.064 0.025–0.161 0.701 0.464–0.867 28.8 180.1 43.6 2016-17 9.4 4.2 4.1 11.5 2.7 0.026 0.003–0.088 0.479 0.105–0.766 30.0 187.4 110.8 2017-18 8.7 3.3 3.1 8.7 2.7 0.069 0.027–0.170 0.716 0.488–0.874 28.7 179.2 40.5 Turnovers 2015-16 18.5 4.5 4.5 12.4 2.7 0.020 -0.002–0.076 0.406 -0.066–0.737 30.2 188.7 148.9 2016-17 18.4 4.4 4.3 12.1 2.7 0.045 0.013–0.130 0.617 0.301–0.836 29.4 183.8 63.3 2017-18 16.9 4.6 4.5 12.4 2.7 0.036 0.008–0.108 0.559 0.207–0.805 29.7 185.5 80.4 Blocks 2015-16 3.1 2.1 2.1 5.8 2.7 0.043 0.012–0.122 0.605 0.289–0.825 29.5 184.2 66.6 2016-17 2.8 2.1 2.0 5.5 2.7 0.056 0.019–0.151 0.668 0.394–0.858 29.1 181.7 50.6 2017-18 3.3 2.3 2.2 6.2 2.7 0.054 0.019–0.143 0.662 0.392–0.851 29.1 182.0 52.1 Personal Fouls 2015-16 30.6 5.0 4.9 13.5 2.7 0.050 0.016–0.135 0.642 0.357–0.842 29.3 182.8 56.9 2016-17 29.1 4.8 4.7 13.1 2.7 0.032 0.005–0.105 0.533 0.146–0.800 29.8 186.2 89.5 2017-18 28.7 4.8 4.7 13.1 2.7 0.050 0.016–0.135 0.643 0.361–0.841 29.2 182.8 56.7

ICC(2,1) ICC(2,k) Number of games required

Variable Year Mean SD SEM MDC MDCES ICC 95% CI ICC 95% CI Medium change Small change ICC > .75 Possessions 2015-16 72.4 4.7 4.4 12.2 2.6 0.131 0.066–0.274 0.836 0.706–0.928 26.8 167.3 20.0 2016-17 72.9 4.3 4.0 11.0 2.6 0.145 0.074–0.303 0.853 0.731–0.937 26.3 164.5 17.6 2017-18 73.3 4.6 4.2 11.8 2.5 0.164 0.087–0.324 0.869 0.765–0.942 25.8 161.0 15.3 Effective field-goal % 2015-16 53.2 7.7 7.1 19.8 2.6 0.144 0.074–0.294 0.851 0.731–0.934 26.4 164.8 17.9 2016-17 53.0 7.9 7.7 21.2 2.7 0.059 0.021–0.156 0.680 0.416–0.863 29.0 181.1 48.0 2017-18 53.1 7.5 7.2 19.9 2.6 0.093 0.042–0.212 0.777 0.599–0.901 27.9 174.6 29.3 Defensive rebound % 2015-16 70.9 8.5 8.1 22.6 2.7 0.081 0.035–0.191 0.749 0.551–0.889 28.3 176.9 34.1 2016-17 70.0 8.2 8.0 22.1 2.7 0.056 0.019–0.151 0.670 0.396–0.858 29.1 181.6 50.3 2017-18 70.6 8.4 8.3 23.1 2.7 0.029 0.003–0.094 0.500 0.103–0.778 29.9 187.0 102.1 Offensive rebound % 2015-16 29.1 8.5 8.2 22.6 2.7 0.076 0.032–0.181 0.735 0.526–0.883 28.5 177.9 36.7 2016-17 30.0 8.1 7.9 21.8 2.7 0.066 0.025–0.169 0.706 0.462–0.874 28.8 179.8 42.6 2017-18 29.4 8.1 7.7 21.4 2.6 0.100 0.046–0.223 0.790 0.623–0.907 27.7 173.3 27.1 Free-throw rate 2015-16 33.3 13.2 13.0 36.2 2.7 0.029 0.004–0.095 0.505 0.110–0.781 29.9 186.9 100.0 2016-17 31.5 12.5 12.3 34.2 2.7 0.033 0.005–0.105 0.533 0.149–0.799 29.8 186.2 89.3 2017-18 31.6 11.7 11.6 32.2 2.7 0.019 -0.002–0.074 0.395 -0.073–0.730 30.2 188.8 156.0

CHAPTER 3: Study 2. Short- and mid-term effects of the 2010 rule changes on game-related statistics in European basketball championships: An interrupted time series analysis

3.1. Resumen

En 2010, entró en vigor uno de los principales cambios de reglas en baloncesto. Incluyendo una extensión de la línea de 3 puntos de 6.25m a 6.75m, el cambio de forma del área de 3 segundos, la adición de semicírculos de no-carga, y las modificaciones del reloj de posesión. El objetivo de este estudio fue analizar si las modificaciones de las reglas influyeron en las estadísticas de juego, tanto a corto como a medio plazo mediante el análisis de series de tiempo interrumpido, y si los cambios de las reglas tuvieron la misma influencia en diferentes grupos de edad y en categoría masculina y femenina. La muestra estuvo compuesta por 5296 partidos de los campeonatos europeos 2005-2016 para hombres y mujeres, tanto en competiciones senior como junior. Se analizaron las estadísticas estándar de juego. El ritmo de juego ha aumentado o ha dejado de disminuir después de las modificaciones de las reglas. El desarrollo hacia una mayor proporción de lanzamientos de campo que han sido de 3 puntos ha continuado, aunque la proporción se redujo directamente después de las modificaciones reglamentarias. Las mujeres senior parecen ser la categoría en la que las modificaciones de las reglas tuvieron el mayor efecto en el desarrollo continuo. No se encontró un patrón general de diferencias en los efectos entre las categorías.

Palabras clave: cambio de reglas; análisis del rendimiento; indicadores de rendimiento; regresión segmentada; deportes colectivos; comparaciones por pares.

3.2. Abstract

In 2010, one of the major rule changes in basketball came into effect. Including an extension of the 3-point line from 6.25m to 6.75m, changed shape of the 3-second area, the addition of no-charge semicircles, and modifications of the shot-clock. This study aimed to analyse if the rule modifications influenced the game-related statistics, both short- and mid-term using interrupted time series analysis, and if the rule changes had the same influence on different age groups and genders. The sample was composed by 5296 games from the European championships 2005-2016 for men and women in both senior and youth competitions. The standard game-related statistics were analysed. The game pace has increased or ceased to decrease after the rule modifications. The development towards a higher proportion of field goals being 3-pointers has continued, although the proportion was lowered directly after the rule modifications. The women senior seems to be the category where the rule modifications had the most effect on the continuous development. No general pattern of differences in effects between categories was found.

Keywords: rule modification; performance analysis; performance indicators; segmented regression; team sports; pairwise comparisons.

3.3. Introduction

In 2008, the International Basketball Federation (FIBA) decided to make significant changes to the rules of the game (International Basketball Federation, 2008). These modifications, which came into effect from the season 2010-11, included moving the 3-point line from 6.25m to 6.75m, changing the shape of the 3-second area into a rectangle, adding a no-charge semicircle under the basket, and changing how and when to reset the shot-clock (International Basketball Federation, 2010). These rule changes ‘were strived by the attempt to further unify all existing game rules and to have, in the future, only one set of rules for the game of basketball worldwide’ (International Basketball Federation, 2008). This refers to modifying the rules to approach those of the NBA. However, the NBA organises only men’s senior competition, while the rule changes made by FIBA applies to all ages and genders.

An understanding of how rule modifications influence the physiological and technical demands, as well as the tactical dynamics in different categories could be helpful for basketball coaches, strength and conditioning coaches, and basketball organisations. Rule modifications could potentially influence the construction of the team, the game strategies adopted, and the physical training. FIBA has continuously changed the rules to adjust to the evolution of how the game is played, adjusting to new situations that arise, helping the referees to officiate the game, trying to remove behaviours that are not in the spirit of the game, and making the game more amusing for the spectators (Pluta et al., 2014). Rule changes in basketball do not only counter emerging trends but can also play an active part in shaping the future development of how the game is played (Arias et al., 2011; Pluta et al., 2014). It has been suggested that it is of vital importance to study how the rule changes affect the way the game is played, to see if they fulfilled their purpose, to try to identify secondary effects from those changes, and to help in the process of making new rule changes in the future (Arias et al., 2011; Williams, 2008). Arias et al. (2011) suggested that rule changes should be analysed before they are introduced and should be based on scientific knowledge. It is difficult for the people in charge of sports competitions to propose suitable rule changes, as there

is a lack of studies that analyse appropriate modifications to change rules (Arias et al., 2011).

The complexity of the sport, the amount of people involved in different roles, and the influence of previous experiences on the player’s actions, make it difficult to analyse the specific effects of a rule change (Arias et al., 2011; Pluta et al., 2014). All these factors are probably the reason why, to our knowledge, there have been few attempts to study the effect of rule changes on determinant aspects of the sport. The studies that do exist analyse widely different characteristics, using a range of different methodologies. After the introduction of the shot-clock in 1956 (together with the introduction of the 3-second area), the scoring increased in the men’s European Championships (Pluta et al., 2014). After its reduction from 30 to 24 seconds in 2000 the players’ fitness and the number of actions increased (Cormery et al., 2008). After the introduction of the 3-point line in 1984 (together with other modifications), the scoring increased in the men’s European Championships (Pluta et al., 2014). The increased distance of the 3-point line in 2010 decreased the number of attempted and made 3-point shots during the season following the change in the ACB and Euroleague (Montero et al., 2013; Štrumbelj et al., 2013).

In basketball, game-related statistics are the standard set of performance indicators and are almost uniformly presented in all major competitions (Sampaio, Ibáñez, & Lorenzo, 2013). They capture the major technical-tactical actions such as shooting, passing, rebounding, fouling, stealing, and losing possession of the ball, and blocking shots. These variables are also used to calculate other metrics, for example, the number of possessions to define the game pace, and player efficiency rating to capture the global performance of the players (Csataljay, Hughes, James, & Dancs, 2011; Kubatko et al., 2007; Oliver, 2004; Sampaio, Lago, et al., 2010). The game-related statistics have been used in studies that discriminate between winning and losing teams (Csataljay et al., 2012; Gómez, Lorenzo, Sampaio, et al., 2008; Sampaio & Janeira, 2003), analyse home advantage (García et al., 2014; Gómez, Lorenzo, Barakat, et al., 2008; Gómez Ruano et al., 2007; Sampaio, Ibáñez, Gómez, Lorenzo, & Ortega, 2008), discriminate between player’s positions (Sampaio,

Janeira, et al., 2006; Sindik & Jukić, 2011), and between starters and non-starters (Gómez et al., 2009; Sampaio, Ibáñez, et al., 2006) amongst others.

Štrumbelj et al. (2013) compared the game-related statistics the last season before and the first season after the 2010 rule modifications in men’s Euroleague. They found an increase in the number of 2-point field goals attempted, total rebounds, and possessions; and a decrease in the 2-point and 3-point field goal percentages, 3-point field goals attempted, and free-throws attempted (Štrumbelj et al., 2013). Over a period of five seasons after the 2010 rule modifications, the number of 2-point field goals attempted increased, while the number of 3-point field goals attempted decreased in the Spanish league cup (Copa del Rey) (Ibañez, García-Rubio, et al., 2018).

Articles analysing which variables better discriminated between winners and losers in men senior, women senior and men youth competitions have reported different results (Gómez et al., 2006; Gómez, Lorenzo, Sampaio, et al., 2008; Lorenzo et al., 2010). This difference was confirmed when comparing the game-related statistics between genders and competition levels (Sampaio et al., 2004). The difference also existed in possessional effectiveness and situational variables influencing the success (Gómez, Lorenzo, Ibañez, & Sampaio, 2013; Ortega, Palao, Gómez, Lorenzo, & Cárdenas, 2007).

However, to the best of our knowledge, no studies exist analysing the short- and mid-term effects of the 2010 rule changes on different levels and genders. Considering the potential influence of rule modifications in sports and the scarce literature on the area, this study aimed to analyse if the 2010 rule modifications influenced the game-related statistics, both short- and mid-term in the European championships between 2005 and 2016 using an interrupted time series analysis. Further, we aimed to compare if the rule changes had the same influence on men and women senior and youth categories.

3.4. Method

3.4.1. Sample

The study analysed a total of 5296 (available from 5563) games from the European championship for men and women, respectively in senior (n = 379 and n = 321) and youth (n = 2344 and n = 2252) between 2005 and 2016 (Supplementary material Table 3.3). The youth category was composed by the under 20, under 18, and under 16 groups. Games that were missing game-related statistics (n = 48) or that went into overtime (n = 197) were excluded. Also, the last year of women under 16 was removed because more than 60% of the games were missing. A total of 267 games were excluded.

3.4.2. Variables and procedure

This study analysed the following rule changes implemented by FIBA in 2010 (International Basketball Federation, 2008, 2010):

– Modifications to the court: (a) extending the distance of the 3-point line from 6.25m to 6.75m, (b) changing the shape of the 3-second area into a rectangle, and (c) introducing a no-charge semicircle under each basket.

– Modification of the shot-clock when fouls and other violations are committed in the frontcourt; change from resetting it to 24 seconds, to maintain the remaining time if more than 14 seconds and reset it to 14 seconds when less remains.

The following game-related statistics were gathered from FIBA’s official website (archive.fiba.com): 2-point field goals made and attempted (2PTm and 2PTa), 3-point field goals made and attempted (3PTm and 3PTa), free-throws made and attempted (FTm and FTa), offensive and defensive rebounds (OREB and DREB), assists (AST), steals (STL), turnovers (TO), blocks (BLK), personal fouls (PF), and points scored (PTS). The collected data were gathered by FIBA professional technicians. A data reliability test was not carried out since FIBA technicians have their proper reliability procedures. Furthermore, Sampaio, Lago, et al. (2010)

showed a perfect coefficient of agreement (κ = 1.0) for all variables except for assists that had a very high coefficient (κ = 0.92) in their reliability test.

For this paper, we collected game totals (sum of both teams), divided them by two to get the values on a per team scale, and normalised them to 100 ball possessions to control for game pace (Csataljay et al., 2011; Kubatko et al., 2007; Oliver, 2004; Sampaio & Janeira, 2003; Sampaio, Lago, et al., 2010). The percentage of free-throws (FT%), 2-point (2PT%) and 3-point field goals (3PT%) were calculated by dividing the number of made shots by the number of attempted. Ball possessions (POS) were calculated as: POS = 2PTa + 3PTa + TO + 0.4 × FTa − OREB (García et al., 2013; Kubatko et al., 2007; Oliver, 2004). Using game totals from all games in European championships minimise the effects of situational variables, such as team quality and competition stage.

3.4.3. Statistical analysis

We used an interrupted time series approach to analyse the impact of the rule modifications, both directly and over time on the variables grand means, controlling for their level and trend before the rule change (Wagner, Soumerai, Zhang, & Ross-Degnan, 2002). To account for the variability between championships, we used a multi-level segmented regression analysis to create the model for each of the variables (Erculǰ & Štrumbelj, 2015; Wagner et al., 2002). We included the competition categories and their interactions with the other factors using an effect coding to get the grand mean for each parameter, as well as being able to test for differences in the effect of the rule modifications between categories. The model was defined as:

Y4 = β6 + β78(:;<=>?@A8) + βC(=4) + βL(M?N<

+ βO8(?@A8) + βP8(@GH= :ℎ;K>= × :;<=>?@A8)

+ βQ8(M?N< ?@A8) + G7(

Where Yt is the mean value of the variable of interest at season t; category is the different genders and ages (Men senior, Women senior, Men youth, Women youth); time is the number of seasons that passed from where the sample starts (i.e., 2005 = 0, 2006 = 1 …); rule change is a dichotomous indicator of whether season t was played with the old or new rules (i.e., old = 0, new = 1); and post time is the

number of seasons that passed since the rule change (i.e., 2005-2010 = 0, 2011 = 1,

2012 = 2 …). b0 estimates the grand mean of the value at the first season in the model

(i.e., 2005); b1a the difference in 2005 value between the grand mean and each of the categories; b2 the trend before the change; b3 the changed value directly after the modifications; b4 the change in trend after the rule modifications. b5a, b6a, and b7a estimate the difference between the grand mean and value for categorya in time, rule change and post time respectively. No models showed problems of autocorrelation or non-convergence. P-values were adjusted for false discovery rates.

Further, for variables where interactions were present, we performed pairwise comparisons for the estimated values of the direct change and change in trend between the categories. The graphical representations include the fixed factors of the original model, as well as an estimate without rule change and post time to model the predicted evolution without the rule change. All confidence intervals were computed using a 500-iteration bootstrap method. The statistical analyses were made with the lme4 (Bates, Mächler, Bolker, & Walker, 2015) and multcomp (Hothorn, Bretz, & Westfall, 2008) packages in R 3.4.1. The significance level was set at p < .05.

3.5. Results

Results of the segmented regression analyses are presented in Table 3.1. The regression coefficients represent, in order: (i) the value at the 2005 season; (ii) the trend, i.e., the change from season to season; (iii) the immediate change after the rule modifications, i.e., the change between 2010 and 2011 seasons not accounted for by the trend; and (iv) the change of the trend after the rule modifications, i.e., the difference in season to season change before and after the rule modifications. Significant interactions indicate differences in effect between categories. For variables that had significant interactions, coefficients for each category and pairwise comparisons are presented in Table 3.2.

Table 3.1. Results of segmented regression analyses for general effects of the rule modifications. Constant Time Rule change Post time Time ´ Rule change ´ Post time ´ b 95% CI b 95% CI p-value b 95% CI p-value b 95% CI p-value competition competition competition POS 75.1 [74.1, 75.9] -0.9 [-1.2, -0.6] <.001 0.7 [-0.6, 2.1] .686 0.9 [0.5, 1.3] <.001 .283 .031 .675 PTS 46.5 [45.8, 47.2] 0.2 [-0.1, 0.4] .821 -1.4 [-2.5, -0.3] .115 0.0 [-0.3, 0.3] .946 .056 .041 .028 2PTa 29.0 [28.6, 29.4] -0.2 [-0.3, 0.0] .006 2.1 [1.3, 2.8] <.001 0.0 [-0.2, 0.2] .898 .021 .301 .144 2PT% 45.4 [48.8, 46.1] 0.1 [-0.2, 0.3] .860 -1.7 [-2.8, -0.6] .004 0.0 [-0.3, 0.4] .898 .759 .279 .136 3PTa 12.2 [11.9, 12.5] 0.4 [0.2, 0.5] <.001 -1.7 [-2.3, 1.2] <.001 -0.1 [-0.3, 0.1] .613 .561 .338 .917 3PT% 30.6 [29.8, 31.5] 0.0 [-0.3, 0.3] .681 -1.0 [-2.4, 0.3] .141 0.1 [-0.3, 0.5] .826 .046 .115 .077 FTa 13.4 [13.0, 13.8] -0.1 [-0.3, 0.0] .005 -0.2 [-0.9, 0.5] .951 0.0 [-0.2, 0.2] .898 .288 .336 .985 FT% 67.1 [65.8, 68.4] 0.3 [-0.2, 0.8] .265 -0.1 [-2.3, 2.1] .736 0.0 [-0.6, 0.7] .966 .993 .323 .774 OREB 7.6 [7.3, 7.8] 0.2 [0.1, 0.3] <.001 0.2 [-0.2, 0.6] .063 -0.3 [-0.4, -0.1] <.001 .003 .332 <.001 DREB 16.9 [16.6, 17.2] 0.2 [-0.1, 0.3] <.001 0.2 [-0.3, 0.6] .349 -0.2 [-0.3, -0.1] .033 .033 .455 .002 AST 7.5 [7.1, 7.8] 0.2 [0.1, 0.4] .011 -0.6 [-1.2, 0.1] .394 0.2 [0.0, 0.4] .731 .116 .391 .479 STL 6.6 [6.3, 6.8] -0.2 [-0.3, -0.1] <.001 -0.1 [-0.4, 0.3] .736 0.0 [-0.1, 0.2] .300 .605 .827 .521 TO 11.0 [10.7, 11.3] 0.1 [0.0, 0.2] .263 -0.1 [-0.5, 0.4] .863 -0.2 [-0.3, 0.0] .136 .011 .575 .034 BLK 1.8 [1.7, 1.9] 0.0 [0.0, 0.1] .860 0.0 [-0.2, 0.1] .686 0.0 [-0.1, 0.0] .898 .395 .234 .210 PF 13.5 [13.2, 13.8] 0.0 [-0.1, 0.1] .283 0.1 [-0.4, 0.6] .394 0.0 [-0.1, 0.2] .898 .097 .111 .503 Note. β = Regression Coefficients; CI = Confidence Interval; POS = Ball Possessions; PTS = Points Scored; 2PTa = 2-Point Field Goals Attempted; 2PT% = 2-Point Field Goals Percentage; 3PTa = 3-Point Field Goals Attempted; 3PT% = 3-Point Field Goals Percentage; FTa = Free-throws Attempted; FT% = Free-throws Percentage; OREB = Offensive Rebounds; DREB = Defensive Rebounds; AST = Assists; STL = Steals; TO = Turnovers; BLK = Blocks; PF = Personal Fouls.

Table 3.2. Results of the pairwise comparison between categories for differences in effects of the rule change. Men senior Women senior Men youth Women youth Comparisons β 95% CI β 95% CI β 95% CI β 95% CI POS Constant 72.9 [70.8, 74.9] 74.2 [72.3, 76.1] 75.9 [74.7, 77.1] 77.6 [76.5, -78.8] Time -1.2 [-1.9, -0.4] -1.2 [-2.0, -0.5] -0.4 [-0.8, -0.1] -0.7 [-1.0, -0.3] Rule change 3.2 [-0.1, 6.5] 3.3 [-0.2, 6.7] -1.9 [-3.8, 0.0] -1.7 [-3.5, 0.2] MY, WY < MS*, WS* Post time 1.1 [0.1, 2.1] 1.1 [0.1, 2.1] 0.9 [0.4, 1.5] 0.5 [-0.1, 1.0] PTS Constant 49.9 [48.2, 51.6] 45.7 [44.1, 47.3] 48.1 [47.3, 49.0] 42.3 [41.4, 43.1] Time 0.9 [0.3, 1.6] -0.2 [-0.8, 0.5] -0.1 [-0.4, 0.1] 0.1 [-0.2, 0.3] Rule change -2.2 [-4.9, 0.5] -1.5 [-4.4, 1.4] 0.8 [-0.6, 2.1] -2.6 [-4.0, -1.2] WY < MY† Post time -0.9 [-1.7, -0.1] 1.0 [0.1, 1.8] -0.2 [-0.6, 0.1] 0.2 [-0.2, 0.6] MS < WS†, WY*; MY < WS* 2PTa Constant 25.8 [24.7, 26.9] 31.3 [30.3, 32.4] 28.8 [28.2, 29.4] 30.1 [29.5, 30.7] Time 0.3 [-0.1, 0.7] -0.5 [-0.9, -0.1] -0.4 [-0.6, -0.2] -0.1 [-0.3, 0.1] Rule change 0.8 [-1.0, 2.6] 2.4 [0.5, 4.3] 3.1 [2.1, 4.0] 2.1 [1.1, 3.0] Post time -0.4 [-0.9, 0.2] 0.5 [0.0, 1.1] 0.0 [-0.2, 0.3] -0.2 [-0.5, 0.1] MS, WY < WS* 3PT% Constant 32.0 [29.7, 34.2] 32.8 [30.7, 34.9] 30.2 [29.3, 31.0] 27.7 [26.8, 28.5] Time 1.0 [0.1, 1.8] -0.8 [-1.6, 0.0] -0.1 [-0.4, 0.2] -0.1 [-0.4, 0.2] Rule change -3.7 [-7.1, -0.4] 1.8 [-1.8, 5.5] -0.2 [-1.6, 1.2] -2.0 [-3.4, -0.5] MS < WS* Post time -0.9 [-1.9, 0.1] 1.1 [0.1, 2.2] 0.0 [-0.4, 0.4] 0.3 [-0.1, 0.7] MS < WS* OREB Constant 6.9 [6.2, 7.6] 7.0 [6.4, 7.6] 8.2 [7.9, 8.5] 8.2 [7.9, 8.5] Time 0.2 [-0.1, 0.4] 0.3 [0.0, 0.5] 0.0 [-0.1, 0.1] 0.3 [0.2, 0.4] Rule change 0.1 [-0.9, 1.1] -0.4 [-1.5, 0.6] 0.7 [0.3, 1.2] 0.5 [0.0, 0.9] Post time -0.2 [-0.5, 0.1] -0.2 [-0.5, 0.1] 0.0 [-0.2, 0.1] -0.6 [-0.7, -0.4] WY < MY‡

Men senior Women senior Men youth Women youth Comparisons β 95% CI β 95% CI β 95% CI β 95% CI DREB Constant 17.1 [16.4, 17.9] 16.8 [16.1, 17.6] 16.8 [16.5, 17.2] 16.7 [16.3, 17.0] Time 0.0 [-0.3, 0.3] 0.4 [0.1, 0.7] 0.1 [0.0, 0.2] 0.4 [0.3, 0.5] Rule change -0.2 [-1.3, 1.0] -0.1 [-1.4, 1.2] 0.1 [-0.5, 0.7] 0.8 [0.2, 1.3] Post time 0.1 [-0.2, 0.5] -0.6 [-0.9, -0.2] 0.0 [-0.1, 0.2] -0.4 [-0.6, -0.2] WS, WY < MS*, MY† TO Constant 10.5 [9.7, 11.2] 10.2 [9.5, 10.9] 11.0 [10.6, 11.3] 12.2 [11.9, 12.6] Time -0.3 [-0.6, 0.0] 0.4 [0.2, 0.7] 0.0 [-0.1, 0.2] 0.1 [0.0, 0.2] Rule change 0.7 [-0.5, 1.8] -0.7 [-2, 0.5] -0.2 [-0.8, 0.4] 0.0 [-0.6, 0.7] Post time 0.2 [-0.2, 0.5] -0.6 [-1.0, -0.2] 0.0 [-0.2, 0.2] -0.2 [-0.4, -0.1] WS < MS*, MY* Note. β = Regression Coefficients; CI = Confidence Interval; POS = Ball Possessions; PTS = Points Scored; 2PTa = 2-Point Field Goals Attempted; 3PT% = 3-Point Field Goals Percentage; OREB = Offensive Rebounds; DREB; Defensive Rebounds; TO = Turnovers; MS = Men Senior; WS = Women Senior; MY = Men Youth; WY = Women Youth. * p < .05. † p < .01. ‡ p < .001

The direct change in the number of POS was different for the senior categories compared to the youth. It seems to have increased in the senior while decreased in the youth categories. The trend had a general positive change after the rule modifications. Visual representations of the effect for POS in each category are presented in Figure 3.1.

No general change was evident in PTS. There was a difference in direct change between the two youth categories as the PTS decreased in women youth. There was a difference in trend change between men and women. It seems to have had a negative effect in men and positive in women, although not as evident in the youth categories.

Men Senior Women Senior Men Youth Women Youth

70 POS

60 95% CI

55 After 17.5 Before

15.0 Change Predicted 12.5 TO 10.0

7.5

5.0 2006 2009 2012 2015 2006 2009 2012 2015 2006 2009 2012 2015 2006 2009 2012 2015 season Figure 3.1. Trend before rule change (Before), impact of rule change (After) and predicted trend without rule change (Predicted), for ball possessions (POS) and turnovers (TO) in all categories.

The number of 2PTa generally increased, and 3PTa decreased directly. There was a positive change of the 2PTa trend in women senior, different from men senior and women youth. The 2PT% generally decreased directly. The 3PT% was generally unaffected. There were however different effects in the senior categories. The 3PT% decreased directly in men and might have increased in women senior, while there was a positive trend change in women senior and seems to be a negative change in men senior. Visual representations of the general effects for 2PTa and 3PTa are presented in Figure 3.2.

No general direct effects in OREB or DREB were found. There was a negative trend change for OREB in women youth, different from men youth. The trend for

DREB was affected negatively in both women categories, different from the men categories.

The trend for TO was negatively affected in women senior, different from the men categories. The variables FTa, FT%, AST, STL, BLK, and PF were unaffected by the rule modifications. Visual representations of the effects for TO in each category are presented in Figure 3.1.

2PTa 3PTa 35

30 95% CI 25 After Before 20 Change Predicted 15

10 2006 2009 2012 2015 2006 2009 2012 2015 season Figure 3.2. General trend before rule change (Before), impact of rule change (After) and predicted trend without rule change (Predicted) for 2-point field goals attempted (2PTa), and 3-point field goals attempted (3PTa).

3.6. Discussion

The present study investigated the short- and mid-term impact of the rule modifications implemented in 2010 by FIBA on the game-related statistics in basketball. It further examined whether the rule modifications impacted the genders and age groups differently. The number of POS seems to have increased directly in the senior categories, and the previous trend towards fewer POS has been stopped or reversed. The number of 2PTa increased while the number of 3PTa decreased directly after the modifications, but the trend towards more 3PTa and less 2PTa remained. The 2PT% decreased directly while there were mixed effects on the 3PT%. After the rule modifications, the trend changed towards fewer TO in women senior.

The number of ball possessions is in basketball the measurement used to quantify the game pace (Csataljay et al., 2011; Kubatko et al., 2007; Oliver, 2004; Sampaio, Lago, et al., 2010). The direct increase in the number of possessions for the senior categories is in line with earlier studies on the effect of the 2010 modifications (Štrumbelj et al., 2013). This effect could be expected as the rule modifications included a reduced time on the shot-clock after certain situations, such as offensive rebounds and personal fouls. Teams in younger categories tend to play with a higher number of possessions (Ibáñez, Feu, & Dorado, 2003), indicating that they are not using as much of the available time on the shot-clock. This is a possible explanation as to why the number of possessions did not increase in the youth categories.

A possible explanation for the positive trend change on the number of possessions is that the teams had to find new strategies to score faster in situations with a shorter shot-clock, such as after an offensive rebound or after a defensive foul. As they got better at it, more teams might have adopted these strategies in other game situations, creating a more transitional style of playing with shorter offensive possessions. Previous rule modifications speeding up the game pace have increased the physiological demands (Cormery et al., 2008). As the game pace has increased as a result of the 2010 rule modifications, it can be expected that the physiological demands have become higher.

In general, the modifications decreased the number of 3-point field goals attempted, while they increased the number of 2-point field goals attempted. These results are in accordance with earlier studies in men senior leagues (Montero et al., 2013; Štrumbelj et al., 2013). The influence of the 3-point line distance on the amount of 2-point and 3-point field goals attempted has been established in the NBA (Romanowich, Bourret, & Vollmer, 2007). Where a shortened distance resulted in higher amounts of 3-point attempts in relation to 2-point attempts and reversed when the line was moved back to the original distance (Romanowich et al., 2007). The trend of an increasing number of 3-point and decreasing number of 2-point field goals attempted remained unaffected after the modifications. This is in line with results from studies analysing the effect over several seasons (Ibañez, García- Rubio, et al., 2018).

The lower 2-point percentage directly after the rule modifications could be due to a change in which shot types were attempted. Argiriou, Rousanoglou, Boudolos, and Bolatoglou (2014) and Oudejans, Karamat, and Stolk (2012) have found that the technical and tactical actions preceding shots affect the shooting percentage. It is possible that a considerable amount of the extra 2-point field goals attempted were shot types with a lower percentage, such as from dribble as opposed to from pass (Argiriou et al., 2014; Oudejans et al., 2012).

The difference in 3-point percentage between men and women senior, both directly and over time, is notable as the accuracy for different shot types has been shown to be similar between the genders and competition levels (Argiriou et al., 2014; Erculǰ & Štrumbelj, 2015). This implies that men and women senior teams have adapted their shot selection differently to the extended 3-point line. Men senior teams might have shifted more towards moving into the shot, shooting from dribbling, getting the pass from the same side of the court or shooting under higher defensive pressure, while women teams have done the opposite (Argiriou et al., 2014).

The decreasing number of defensive rebounds in both women categories might be a result of the changed distribution between 2-point and 3-point shots, as the shot distance has been shown to influence the possibility of taking an offensive

or defensive rebound (Csátaljay, James, Hughes, & Dancs, 2017). The women youth have a decreasing number of both offensive and defensive rebounds. As the variables have been normalised in regard to game pace, this trend indicates a corresponding decrease in the number of missed field goal attempts. However, this is only partially supported by the results.

In women senior, the trend towards more turnovers was reversed after the rule change. Fylaktakidou, Tsamourtzis, and Zaggelidis (2011) analysed the turnovers in the women’s Greek league; 81.4% of the turnovers were made inside or around the 3-point line, and the most occurring type of turnover was passing errors. The widening of the 3-point line can, therefore, have created opportunities to play with more spacing in offence, forcing the defence to cover more area. As the women senior teams gradually adapted to the new space constraints, they were perhaps finding better passing options, and therefore reducing the risk of a defensive player being able to deflect the pass.

In the women senior championships, the rule modifications seem to have stimulated the offence more than it has in the other categories. They are playing at a faster pace, scoring more, shooting 3-pointers with higher percentage and making fewer turnovers. Many of these changes are different from the other categories. Therefore, it seems as the rule modifications had the most significant impact on the women senior category. However, there was no evident pattern of differences between genders or age.

It has been shown that altering the spatial and temporal constraints influence the technical-tactical actions performed in other team sports (Correia et al., 2012; Vilar, Araújo, Davids, Correia, & Esteves, 2013; Vilar, Duarte, Silva, Chou, & Davids, 2014). The changes after the 2010 rule modifications on the game-related statistics implicate that the changed spatial and temporal constraints imposed on the game have affected the extent to which different technical-tactical actions are being used. It is apparent that the rule modifications influenced the game not only directly but also its continuous development over time.

This study presents certain limitations as it used a correlational methodology, analysing changes in game-related statistics after the

implementation of rule modifications. It cannot be concluded that the rule modifications are the underlying cause for the results. These changes might also be influenced by the physiological development of the players, the continuous development of offensive and defensive strategies to counter each other and mimicking of trendsetting teams and players. Rule modifications cannot be considered as an isolated factor affecting the team’s performance (Arias et al., 2011; Cormery et al., 2008; Williams, 2008). Therefore, a multifactorial model (technical, tactical, strategical, physical and psychological) should be accounted for to better identify the non-linear evolution of the basketball game. This study was made on European championships, which might not be fully representative for all kind of basketball leagues and levels. However, it has been found that shooting variables remain similar between different competitions and age groups (Erculǰ & Štrumbelj, 2015).

Further studies on rule modifications are needed to understand its implications fully. The physiological effects need to be studied, as they could have direct implications for the design of training tasks and management of players during competition. Studies using other methods are needed to fully understand the technical-tactical implications of the rule modifications, analysing, for example, the distribution of technical and tactical actions, time-out effects, player rotations, and other situational variables.

3.7. Conclusions

To our knowledge, this is the first attempt to use an interrupted time series analysis to study rule modifications in sports. It helps to provide a deeper understanding of the implications as it enables the direct and longitudinal effects to be interpreted distinctively from each other.

The conclusions of this article are: (a) The 2010 FIBA rule modifications affected the game-related statistics, both directly and their development over time. (b) The game pace has increased or ceased to decrease after the rule modifications. (c) The development towards a higher proportion of field goals being 3-pointers has continued, although the proportion was lowered directly after the rule modifications. (d) The women senior seems to be the category were the rule modifications had the most effect on the continuous development. (e) No general pattern of differences in effects between categories was found.

This work may help to understand the implications of 2010 FIBA rule changes on the technical-tactical aspects of the basketball game. These findings can assist basketball coaches in adjusting practices and tactical decisions to the new rules. It can also help sporting organisations understand the effects of this and, therefore, future rule modifications.

The coaches both at senior and youth levels should consider the growing importance of the transition game in their practice planning and tactical philosophy. Strength and conditioning coaches should also consider the increasing game pace. To prepare the players to repeatedly run up and down the court at an increasing frequency, they could, for example, reduce the rest time during repeated sprint work.

Coaches should consider the growing importance of the 3-point field goals and continuously adapt their offensive and defensive strategies accordingly. As the amount of 3-point shots is increasing without any drop of shot efficiency in the youth categories, the tactical implications need to be considered already at this level. This also shows the need for technical and physical preparation of young basketball players to be able to shoot 3-point shots efficiently.

3.8. Supplementary material

Table 3.3. Distribution of analysed games by category and season. Year Men senior Women senior Men youth Women youth 2005 36 44 184 183 2006 184 189 2007 51 54 177 173 2008 176 177 2009 50 49 185 188 2010 201 202 2011 87 52 207 206 2012 205 198 2013 83 54 227 214 2014 229 210 2015 72 68 219 210 2016 150 102 Total 379 321 2344 2252

CHAPTER 4: Study 3. Senior and youth national team competitive experience: Influence on player and team performance in European basketball championships

4.1. Resumen

El objetivo de este estudio fue descubrir si el número de campeonatos previos de las selecciones nacionales senior y junior se relaciona con el rendimiento del equipo y el jugador en los campeonatos de baloncesto europeos. La muestra estuvo compuesta por todos los equipos nacionales y sus jugadores que participaron en el Campeonato de Europa 2011, 2013 y 2015 para hombres (equipos n = 72; jugadores n = 697) y mujeres (equipos n = 52, jugadores = 520). Los equipos se clasificaron en cuatro grupos según la etapa más alta alcanzada en el torneo. Se utilizó un agrupamiento de k-medias para agrupar a los jugadores según su rendimiento (alto, medio, o bajo) en función de su índice de eficacia. Se comparó el número de campeonatos anteriores senior y junior entre los grupos. Los equipos y jugadores con mejor rendimiento tuvieron un mayor número de campeonatos senior previos disputados. La experiencia competitiva diferencia a los jugadores de bajo rendimiento en ambos sexos, pero solo distingue a los jugadores de alto rendimiento con los de rendimiento medio para mujeres. No se encontraron diferencias en el número de campeonatos junior. Parece ser necesario tener una cantidad suficiente de experiencia competitiva de alto nivel acumulada dentro del equipo para alcanzar la fase semifinal, tanto para los equipos nacionales masculinos como para los femeninos.

Palabras clave: análisis del rendimiento; estadísticas de juego; desarrollo del talento; selecciones nacionales; carrera deportiva; pericia.

4.2. Abstract

This study aimed to discover if the number of previous senior and youth national team championships played relates to the team and player performance at the European basketball championships. The sample consisted of all national teams and their players participating in the 2011, 2013, and 2015 European Championships for men (teams n = 72; players n = 697) and women (teams n = 52, players = 520). The teams were classified into four groups based on their highest stage reached in the tournament. A k-means cluster was used to group the players as high, medium, or low performers according to their efficiency rating. The number of previous senior and youth championships was compared between groups. Better performing teams and players had a higher number of previous senior championships. The competitive experience differentiates low performing players for both genders, but only distinguishes high from medium performing players for women. No differences in the number of youth championships were found. It appears to be critical to have a sufficient amount of accumulated senior competitive experience within the team to reach the semi-final phase both for men’s and women’s national teams.

Keywords: performance analysis; game-related statistics; talent development; national team; athletic career; expertise.

4.3. Introduction

As in other high-intensity team sports, the ability to perform at a high level in basketball is multifaceted, depending on physical, psychological, technical, and tactical aspects. Physiologically it requires the ability to repeatedly perform high- intensity actions, requiring both the aerobic and anaerobic systems to be highly conditioned (Ben Abdelkrim, Castagna, El Fazaa, & El Ati, 2010; Narazaki, Berg, Stergiou, & Chen, 2009). Psychological factors such as self-regulation (Cleary & Zimmerman, 2001; Cleary, Zimmerman, & Keating, 2006), mental toughness (Newland, Newton, Finch, Harbke, & Podlog, 2013), and anxiety (Kais & Raudsepp, 2005) has been shown to affect the performance of basketball players. Tactical factors like pattern recall and decision-making have also been linked to the performance of the players (Gorman, Abernethy, & Farrow, 2013, 2015). Several of these factors have been shown to depend on the experience of the players (Cleary & Zimmerman, 2001; Gorman et al., 2013). It is, therefore, reasonable to suspect that experience can be a moderating factor for performance.

Investigations of the relationship between performance at senior level and the competitive experience have primarily been undertaken in individual sports. For example, top performance at youth level has been shown to increase the likelihood of top performance at the senior level in gymnastics and tennis (Brouwers et al., 2012; Pereira et al., 2014). Further, cyclists who participated in junior World Championships are more successful as seniors than cyclists that did not (Schumacher et al., 2006). In basketball, Moxley and Towne (2015) found that the quality of a player’s college is one of the best predictors of later performance in the NBA. Baker et al. (2003a) found that Australian national team players in basketball, field hockey, and netball had accumulated nearly three times as many hours of competition as their non-expert counterparts.

The influence that previous experience has in basketball and other team sports been widely investigated from the perspective of developmental activities during childhood and adolescence. Elite players have been shown to have accumulated more hours of sport-specific practice and play during adolescence compared with non-elite players (Baker et al., 2003b; Hornig et al., 2016). The

number of other sporting activities and non-organised activities in the athlete’s main sport have also been shown to positively influence the chance of becoming an elite athlete (Hornig et al., 2016), reducing the amount of sport-specific practice required to become an elite athlete (Baker et al., 2003b).

Some of the most commonly used measures of players performance in basketball are the game related statistics (Sampaio, Drinkwater, et al., 2010; Sampaio, Janeira, et al., 2006). They are collected during the games by official technicians of each respective competition and are defined in the Official Basketball Rules and the FIBA Statisticians’ Manual (International Basketball Federation, 2014, 2016). The game-related statistics capture different types of technical-tactical actions performed by the players during the games and includes two-point and three-point shots attempted and made, free-throws made and attempted, offensive and defensive rebounds, assists, turnovers, steals, and fouls.

Competition has been ranked by elite team sport athletes as the most helpful activity to develop perception and decision-making, and one of the most important to develop execution and physical fitness (Baker et al., 2003a). To our knowledge, the relationship between competitive experience and performance has not been investigated in basketball. Therefore, this study aims to discover if the number of previous senior and youth national team championships played relates to the team and player performance at the European basketball championships. We hypothesised that players and teams with better performance would have a higher number of previous championships played.

4.4. Method

4.4.1. Sample

The sample consisted of all national teams and their players participating in the 2011, 2013, and 2015 European Championships for men (teams n = 72, players n = 697) and women (teams n = 52, players = 520). Each participation of a national team and a player was recorded as an individual case, i.e., a single team can represent multiple cases. A single player can also have represented a national team on several occasions, however only a single national team. Naturalised players and players who had an average playing time less than five minutes per game during the championship were excluded (Sampaio, Drinkwater, et al., 2010; Sampaio, Janeira, et al., 2006).

4.4.2. Procedure

All data were gathered from the International Basketball Federation’s (FIBA) official data archive (archive.fiba.com). Previous studies have shown the inter-rater agreement of the game-related statistics to be excellent (Gómez, Silva, Lorenzo, Kreivyte, & Sampaio, 2017; Sampaio, Lago, et al., 2010).

For the performance of the teams, the highest stage each team reached (semi-final, quarter-final, second round or first round) was recorded. For the performance of the players, the efficiency was calculated using the following equation for the individual player’s statistics, adapted from Arrieta et al. (2016):

$%& + (!) + *&% + &%+ + )+, − ["/* − "/0] − ["%* − "%0] − %2 !"" = 034

Where EFF = efficiency, PTS = points scored, REB = rebounds, AST = assists, STL = steals, BLK = blocks, FGA = field goals attempted, FGM = field goals made, FTA = free throws attempted, FTM = free throws made, TO = turnovers, and MIN = minutes played.

Players were classified into three groups according to their efficiency (high- performance, medium-performance, and low-performance) using a k-means cluster analysis. Points scored per minute (points) were used as a secondary

measure of performance to validate the classification. Both measures of player performance were normalised per minute to control for playing time (Arrieta et al., 2016; Sampaio, Janeira, et al., 2006).

The number of previous championships played by each player was divided into senior and youth championships. The sum of previous youth and senior championships for all 12 players in each team was used for the team analysis. The following was considered senior championships: Olympic Games and Olympic Qualifications, World Championships, European Championships and European Championship Qualifications. The following was considered youth championships: all divisions of the U20, U18, and U16 European Championships and their qualifications; and U21, U19, and U17 World Championships.

The age was included in the analysis of players and teams to test for any potential effect of the general experience, as this has previously been linked to performance in football and rowing (Barnabé, Volossovitch, Duarte, Ferreira, & Davids, 2016; Penichet-Tomas, Pueo, & Jimenez-Olmedo, 2016).

4.4.3. Statistical analysis

Means with standard deviations, as well as 95% confidence intervals are reported for all groups. All variables were tested for normality using Shapiro-Wilks test when n < 50 and Kolmogorov-Smirnov when n > 50; the variables were not normally distributed on the individual player level, but did meet normality on the team level. Equality of variance for variables in the team analyses was assessed using Levene’s test.

A Kruskal-Wallis one-way analysis of variance with post-hoc Dunn’s test was used to compare differences between the groups of players. For the team analysis, a one-way analysis of variance (one-way ANOVA) with Bonferroni corrections for post-hoc analysis was used. Analysis of covariance (ANCOVA) with Bonferroni corrections for post-hoc analysis was used for women’s teams and Quade’s test with post-hoc Dunn’s test for women’s players to correct for effect of age.

All statistical analyses were made using SPSS 20 for Mac (IBM Corp., Armonk, NY, USA). The effect size for differences between means is reported using r

(Rosenthal & DiMatteo, 2001), and is interpreted as small when r ≥ .10, medium when r ≥ .30, and large when r ≥ .50 (Cohen, 1992). The significance level was set at a = .05.

4.5. Results

4.5.1. Players

The analysis of variance for the difference between performance groups of male players is presented in Table 4.1. The low-performance group had fewer previous senior championships played than both the high-performance and medium-performance groups. The number of youth championships did not vary between the groups. The performance measures (efficiency and points) differed significantly between all three groups, ranging from the high-performance group having the highest to the low-performance group having the lowest performance.

The analysis of variance for the difference between performance groups of female players is presented in Table 4.2. The number of senior championships significantly varied among all the groups, where the high-performance group had the highest amount, followed by the medium-performance group, while the low- performance group had the least amount. The number of youth championships did not vary significantly between the groups. The performance measures (efficiency and points) differed significantly between all three groups, ranging from the high- performance group having the highest to the low-performance group having the lowest performance. When controlling for age (Table 4.3), the difference in the number of senior championships between medium and low-performance groups was not significant. Other than that, the results remained equal.

Table 4.1. Analysis of variance for men’s players between levels of performance. 1 2 3 High-performance (n = 210) Medium-performance (n = 348) Low-performance (n = 139) ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI c2 p 1 vs 2 1 vs 3 2 vs 3 Efficiency 0.38 ± 0.07 [0.37, 0.39] 0.21 ± 0.05 [0.21, 0.22] 0.03 ± 0.08 [0.01, 0.04] 584.82 .000 .84‡ .85‡ .78‡ Points 0.42 ± 0.12 [0.40, 0.43] 0.33 ± 0.12 [0.32, 0.35] 0.26 ± 0.12 [0.24, 0.28] 116.59 .000 .32‡ .53‡ .26‡ Age 27 ± 4 [26, 27] 27 ± 4 [27, 28] 27 ± 4 [27, 28] 3.56 .168 .08 .07 .00 Senior 2.3 ± 2.6 [2.0, 2.7] 2.2 ± 2.6 [2.0, 2.5] 1.5 ± 2.3 [1.2, 1.9] 14.85 .001 .02 .19‡ .16† Youth 2.5 ± 1.8 [2.3, 2.8] 2.2 ± 1.6 [2.0, 2.4] 2.4 ± 1.9 [2.0, 2.7] 4.58 .101 .09 .06 .02 Total 4.9 ± 3.1 [4.4, 5.3] 4.4 ± 3.2 [4.1, 4.8] 3.9 ± 2.9 [3.4, 4.4] 8.81 .012 .08 .16* .07 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

Table 4.2. Analysis of variance for women’s players between levels of performance. 1 2 3 High-performance (n = 138) Medium-performance (n = 259) Low-performance (n = 123) ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI c2 p 1 vs 2 1 vs 3 2 vs 3 Efficiency 0.34 ± 0.07 [0.33, 0.36] 0.18 ± 0.05 [0.18, 0.19] 0.01 ± 0.08 [0.00, 0.02] 438.31 .000 .82‡ .86‡ .81‡ Points 0.39 ± 0.12 [0.37, 0.41] 0.29 ± 0.10 [0.27, 0.30] 0.25 ± 0.13 [0.22, 0.27] 94.73 .000 .41‡ .52‡ .17* Age 28 ± 4 [27, 28] 27 ± 4 [27, 28] 26 ± 4 [26, 27] 10.16 .006 .07 .19† .12 Senior 3.6 ± 3.6 [3.0, 4.2] 2.2 ± 2.5 [1.9, 2.5] 1.5 ± 2.0 [1.2, 1.9] 29.43 .000 .18‡ .33‡ .14* Youth 3.2 ± 2.3 [2.8, 3.6] 3.3 ± 2.4 [3.0, 3.6] 3.4 ± 2.3 [3.0, 3.8] 1.21 .548 .02 .07 .04 Total 6.7 ± 4.1 [6.0, 7.4] 5.5 ± 3.3 [5.1, 5.9] 4.9 ± 2.8 [4.4, 5.4] 13.11 .001 .14‡ .22* .07 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

Table 4.3. Analysis of variance for women’s players between levels of performance when controlled for age. High-performance1 (n = 138) Medium-performance2 (n = 259) Low-performance3 (n = 123) ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI F p 1 vs 2 1 vs 3 2 vs 3 Efficiency 0.35 ± 0.06 [0.34, 0.36] 0.18 ± 0.06 [0.17, 0.19] 0.01 ± 0.07 [0.00, 0.02] 1237.12 .000 .82‡ .86‡ .80‡ Points 0.40 ± 0.12 [0.37, 0.41] 0.29 ± 0.11 [0.27, 0.30] 0.24 ± 0.11 [0.22, 0.26] 56.53 .000 .41‡ .51‡ .17* Senior 3.4 ± 2.4 [3.0, 3.8] 2.2 ± 2.4 [1.9, 2.5] 1.8 ± 2.4 [1.4, 2.2] 10.58 .000 .18† .28‡ .10 Youth 3.4 ± 1.9 [3.0, 3.7] 3.3 ± 1.9 [3.1, 3.5] 3.1 ± 1.9 [2.8, 3.5] .636 .530 .02 .07 .05 Total 6.7 ± 3.4 [6.2, 7.3] 5.5 ± 3.4 [5.1, 5.9] 4.9 ± 3.4 [4.3, 5.1] 7.71 .001 .14* .23‡ .08 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

4.5.2. Teams

The analysis of variance for the difference between stages for men’s teams is presented in Table 4.4. Teams that reached the semi-final stage had significantly higher number of previous senior championships than teams eliminated in the first or second round. There were no significant differences in the number of youth championships or age.

The analysis of variance for the difference between stages for women’s teams is presented in Table 4.5. Teams that reached the semi-final stage had significantly higher number of previous senior championships than teams eliminated in any of the three earlier rounds. There were no significant differences in the number of youth championships. There was a significant difference in age. When controlling for the difference in age (Table 4.6), the pairwise comparison did not show a significant difference between the semi-final and second-round teams. The other results did not change.

Table 4.4. Analysis of variance for men’s teams between different stages reached. Semi-final1 Quarter-final2 Second-round3 First-round4

(n = 12) (n = 12) (n = 16) (n = 32) ES ES ES ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI F p 1 vs 2 1 vs 3 1 vs 4 2 vs 3 2 vs 4 3 vs 4 Age 27 ± 1 [26, 28] 27 ± 2 [26, 28] 27 ± 1 [27, 28] 27 ± 1 [26, 27] 0.53 .661 .01 .02 .00 .04 .00 .03 Senior 39.8 ± 15.9 [29.6, 49.9] 26.5 ± 18.3 [14.9, 38.1] 21.8 ± 15.9 [13.3, 30.3] 12.9 ± 12.9 [8.3, 17.5] 9.80 .000 .14 .25* .44‡ .02 .15 .09 Youth 30.3 ± 5.8 [26.6, 34.0] 28.2 ± 4.9 [25.1, 31.3] 28.2 ± 8.0 [23.9, 32.4] 23.8 ± 8.6 [20.7, 26.8] 2.87 .043 .04 .02 .12 .00 .08 .06 Total 70.0 ± 20.6 [56.9, 83.1] 54.7 ± 21.1 [41.2, 68.1] 50.0 ± 21.1 [38.8, 61.2] 36.7 ± 18.9 [29.9, 43.5] 8.75 .000 .13 .20 .38‡ .01 .15 .10 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

Table 4.5. Analysis of variance for women’s teams between different stages reached. Semi-final1 Quarter-final2 Second-round3 First-round4

(n = 12) (n = 12) (n = 12) (n = 16) ES ES ES ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI F p 1 vs 2 1 vs 3 1 vs 4 2 vs 3 2 vs 4 3 vs 4 Age 27 ± 1 [27, 28] 26 ± 1 [26, 27] 27 ± 1 [26, 27] 26 ± 1 [26, 27] 3.26 .019 .26 .12 .20* .06 .00 .05 Senior 45.3 ± 13.4 [36.8, 53.8] 22.2 ± 17.5 [11.1, 33.3] 27.3 ± 22.2 [13.1, 41.4] 15.4 ± 10.1 [10.0, 20.8] 8.38 .001 .38† .21* .64‡ .02 .08 .17 Youth 43.8 ± 11.2 [36.7, 51.0] 40.9 ± 6.7 [36.6, 45.2] 34.8 ± 12.2 [27.1, 42.6] 38.6 ± 10.4 [33.1, 44.1] 1.63 .218 .03 .14 .06 .09 .02 .03 Total 89.2 ± 21.5 [75.5, 102.9] 63.1 ± 22.5 [48.8, 77.4] 62.1 ± 29.9 [43.1, 81.1] 54.0 ± 12.4 [47.4, 60.6] 6.34 .002 .28* .23* .53‡ .00 .09 .05 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

Table 4.6. Analysis of variance for women’s teams between different stages reached when controlled for age. Semi-final1 Quarter-final2 Second-round3 First-round4

(n = 12) (n = 12) (n = 12) (n = 16) ES ES ES ES ES ES Variable M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI M ± SD 95% CI F p 1 vs 2 1 vs 3 1 vs 4 2 vs 3 2 vs 4 3 vs 4 Senior 43.0 ± 16.8 [33.2, 52.7] 23.3 ± 16.1 [14.0, 32.6] 26.9 ± 15.9 [17.7, 36.1] 16.6 ± 16.2 [8.5, 24.7] 5.53 .002 .27* .21 .39‡ .01 .05 .11 Youth 45.5 ± 10.8 [39.2, 51.8] 40.2 ± 10.4 [34.1, 46.2] 35.1 ± 10.2 [29.1, 41.0] 37.8 ± 10.4 [33.0, 43.0] 2.13 .109 .06 .21 .11 .06 .02 .02 Total 88.4 ± 23.4 [74.8, 102.0] 63.4 ± 22.3 [50.5, 76.4] 62.0 ± 22.0 [49.2, 74.8] 54.4 ± 22.5 [43.1, 65.7] 4.99 .004 .24 .27* .35† .00 .04 .03 Note. ES = Effect Size; Senior = Number of Previous Senior Championships Played; Youth = Number of Youth Championships Played; Total = Total Number of Previous Senior and Youth Championships Played. * p ≤ .05; † p ≤ .01; ‡ p ≤ .001

4.6. Discussion

The purpose of this study was to determine whether the number of previous championships relates to the performance of players and teams in European basketball championships. The results confirm our hypothesis that the players and teams with better performance have played a higher number of previous championships. The difference was however only evident for the number of previous senior championships, with no differences in the number of youth championships between different levels of performance neither for players nor teams.

4.6.1. Senior championships

The low performing men’s players have a lower number of senior championships, while there was no difference between the medium and high performers. For the women’s players, there are differences between all three levels of performance, with a medium-sized difference between high and low- performance. The low performers have played in average 1.5 and medium performers 2.2 senior championships, with almost identical numbers for both men and women. Whereas the male high performers have a similar average as the medium performers, the female high performers have played in average 3.6 senior championships.

These results could suggest that players need to gain competitive experience from a few tournaments before they become able to perform well with their respective national team. Another possible explanation is that it exists a hierarchy in which new players are not given opportunities to perform until they have established themselves within the team. The fact that there is a difference in competitive experience between medium and high performers for women but not for men might indicate that the national team competitions play a more significant role in the player development for women than for men. This is possibly a result of the different economic situations of men’s and women’s basketball in Europe.

While the lack of competitive experience differentiates low performing players, the accumulation of it distinguishes the high-performing teams. As the

European Championships are played with a highly congested schedule – with games every one to two days – players accumulate fatigue (Montgomery, Pyne, Cox, et al., 2008; Montgomery, Pyne, Hopkins, et al., 2008). It is possible that teams who have a higher number of medium and high-performance players, perform better as it enables the coaches to distribute the playing time more even, resulting in lower accumulated fatigue. Since medium and high-performance players have a higher number of previous championships, the teams with a higher number of these players will have a higher accumulated competitive experience.

Another possible explanation for the relationship between team performance and accumulated competitive experience is that they are both results of a low roster turnover. In football, stability, in terms of low personnel turnover and strength of ties between players has been shown to predict team performance (Montanari, Silvestri, & Gallo, 2008). As the national teams have a limited time to prepare for competition due to club seasons, the importance of roster stability to create cohesion, group roles and player cooperation over several seasons might be even more significant than in club competitions. This is a potential line for further studies on determining factors of national team performance.

4.6.2. Youth championships

There are no differences in the number of youth championships for any gender, neither on an individual player level nor a team level. These results contradict earlier findings in gymnastics, tennis, and cycling (Brouwers et al., 2012; Pereira et al., 2014; Schumacher et al., 2006), which have linked international participation or performance at youth level with success as seniors. It is reasonable to assume that this difference is a result of the different characteristics of the sports; gymnastics and tennis are generally considered early specialization sports (Jayanthi, Pinkham, Dugas, Patrick, & LaBella, 2013; Law, Côté, & Ericsson, 2007; Malina, 2010), and basketball is generally considered to require a broader but less in-depth expertise than gymnastics and cycling.

The development of athletes has been shown to be a complex and non- linear process (Gulbin, Weissensteiner, Oldenziel, & Gagné, 2013). Around 40% of Portuguese senior national team players in football and volleyball had not

participated in any youth national team competition (Barreiros & Fonseca, 2012), and less than 20% of German senior football national team players had played with youth national teams before the age of 20 (Güllich, 2014).

This vague relationship between adolescent and senior performance in complex team sports might be attributed to several factors, of which differences in physical and psychological maturation is one of the more frequently discussed (Rees et al., 2016). The overrepresentation of athletes born in the first part of the year (relative age effect) is one of the demonstrations of the influence of maturity on performance (Cobley, Baker, Wattie, & McKenna, 2009; Rees et al., 2016). In European youth basketball championships, a correlation between players performance and their birth month has been found (Arrieta et al., 2016). As athletes reach final maturity as seniors this effect seems to disappear or even reverse (Gibbs, Jarvis, & Dufur, 2012; McCarthy & Collins, 2014; McCarthy, Collins, & Court, 2016).

While perceptual-cognitive skills seem to be a vital factor for senior performance (Williams, 2000), it does not clearly differentiate elite and sub-elite youth players (Elferink-Gemser, Kannekens, Lyons, Tromp, & Visscher, 2010; Vaeyens, Lenoir, Williams, Mazyn, & Philippaerts, 2007). This seems to indicate that the importance of different qualities on performance is not stable, but changes from adolescence to adulthood. The inconsistent difference in perceptual- cognitive skills between elite and sub-elite youth players can be expected, as it appears to develop over time with experience. This is evident in the development of tactical performance that takes place over time during late adolescence (Barnabé et al., 2016).

4.6.3. Age

There are no differences in age between any men’s player or team levels. This indicates that the general experience players accumulate over the years playing does not influence the performance during the European Championships. This could be explained by the differences between club and national team competitions. The club competitions usually are played over a large part of the year, with players living at home, and playing 1-2 games a week; the national team programme is on the other hand compressed into a few months during the

92 summer, with the players living away from home, and playing a much denser game schedule.

For women, there is a small difference in age between high and low- performance players as well as between semi-finalist and first-round teams. One possible explanation is the number of players available to choose from. As fewer girls engage in organised sport activities (Vilhjalmarsson & Kristjansdottir, 2003), it is reasonable that each country will have fewer female than male elite basketball players to select their national teams from. This, in turn, can result in earlier debuts for talented female players (Barreiros & Fonseca, 2012), and a longer national team career. Another possible factor is the players’ yearly schedule; women’s leagues are often shorter, and the European Championships for women are played in the early part of the summer. This could result in more opportunities for female players to rest in comparison to their male counterparts, and in turn, facilitates their continuous engagement with the national teams.

When correcting for this difference in age, the results remained mostly the same both for the women’s teams and players; only small differences in a few of the pairwise comparisons were evident. We can, therefore, conclude that the positive relationships between the number of previous championships and performance are not results of age differences. Neither was the lack of difference in the number of youth championships between performance levels due to age.

4.6.4. Player classification

Quantification of the technical-tactical performance of basketball players is a widely-debated topic, evident by the fact that Martínez (2010a) identified 228 different measures of player performance used by different basketball leagues, publications, and statistical websites. The calculation of a global performance measure based on the different game-related statistics is used in several of the major basketball leagues as a basis for individual performance evaluation. The different types of efficiency calculations relate very well to each other and with other types of performance measures (Martínez, 2010b).

Analysis of a second performance measure (points per minutes) between the groups – created by the cluster analysis in function of the players’ efficiency

rating – showed expected differences between all groups for both genders. This strengthens the notion that efficiency is a suitable measure of performance for basketball players.

4.7. Conclusions

This study aimed to investigate the influence of competitive experience on the players’ and teams’ performance in the European basketball championships. We found that better performing teams and players have a larger number of previous senior championships, indicating that the specific competitive experience is an important factor in the player and team performance. While this competitive experience seems to only be important to become an established national team player for men, it does seem to be important to become a top performing player for women. No differences in the number of youth championships were found, which suggests that youth national team participation does not directly influence the performance either with and of the senior national team. It appears to be critical to have a sufficient amount of accumulated senior competitive experience within the team to reach the semi-final phase both for men’s and women’s national teams.

CHAPTER 5: General conclusions

5.1. Conclusions

The overall aim of this thesis is to investigate the potential applications of the game-related statistics in basketball. It was done, in one part, through assessing the reliability (stability) of the game-related statistics and the number of games needed to obtain a stable estimate of performance. In another part, it was done by using the game-related statistics to analyse the effects of rule modifications and the role of previous competitive experience on performance. Based on the studies that are included in this thesis, the following conclusions can be drawn:

I. The game-related statistics can provide a reliable estimate of team performance given that a large enough sample of games is included for the analysis. If the aim of the analysis is to assess changes or differences in performance, at least 30 games are needed in each group to be compared. If the aim is to rank the teams’ performance, somewhere between 14 and 100 games are needed depending on which game-related statistics are included in the analysis.

II. Evaluating both the direct and longitudinal changes in the game-related statistics after rule modifications using an interrupted time series analysis enables richer conclusions to be drawn than only simple pre-post comparisons. Specifically, for the 2010 rule change in basketball, it revealed a change in trend for the number of possessions, towards an increased game pace. Further, the proportion of 3-point field goals decreased directly after the change while the trend towards a higher proportion was not affected. The rule change seems to have had affected men and women categories differently, with larger impact in women’s basketball.

III. Previous competitive experience can be a predictor of player and team performance, both in men and women’s basketball. Particularly, there was a relationship between the number of previous senior championships played and performance, both for players and teams. This relationship was however not found for the number of youth championships. This points towards the importance of competitive experience being specific to the performance context.

99 The game-related statistics can provide reliable measures of team performance to be used in basketball research provided a large enough sample of games. Further, analysing the game-related statistics seem to be a good approach to evaluate rule changes in basketball and the importance of previous competitive experience in developing expertise. Overall, the game-related statistics are a valuable measure of performance in basketball research such as talent development and sport regulation.

100

5.2. Practical applications

The studies in this thesis analysed the reliability of the game-related statistics, the short- and mid-term effects of the 2010 FIBA rule modifications, and the relationship between previous competitive experience and performance. Some potential practical applications of these works are:

I. The estimation of the number of games required to obtain reliable measures of the game-related statistics can be used by researchers when planning future studies. It also shows coaches and clubs to be careful when drawing conclusions based on the game-related statistics from a lower number of games.

II. The results on the effects of the 2010 FIBA rule change, can help sport organisations to understand how these modifications have affected the game in the different categories. This might provide valuable information when considering future rule changes.

III. The relationship found between previous competitive experience and performance shows national team coaches and federations the importance of having players participating in several senior championships in order to perform better in subsequent championships.

101 5.3. Limitations

The main limitation in the three studies that form this thesis is that they are all using data from specific competitions. In the first study, only the ACB was analysed; in study 2 and 3, the sample was composed of games from the European Championships. There are differences in playing format, number of teams, playing style, and game schedule between different leagues and championships. It may therefore not be possible to generalise the findings to all basketball competitions.

Another limitation is the fact that both study 2 and 3 use correlational methods. Therefore, care must be taken when interpreting the cause-effect relationship between the concepts of interest. It is possible that the relationships found in the studies are entirely or partially a result of other extraneous effects or due to chance.

102 5.4. Future lines of investigation

Based on the studies in this thesis, the following suggestions can be made for future studies:

I. There is a need for further assessments about the reliability of the game- related statistics in different leagues, competitions, age categories, and in women.

II. In basketball, the rules are frequently changed, and therefore, there is an ongoing need for studies evaluating the impact of these rule changes in competition.

III. Expand the research on previous competitive experience, taking other things into account, such as including other types of developmental activities and a measure of general performance in the leagues.

The present thesis shows that game-related statistics could be applied to different lines of investigation. For example, in sports medicine, they could be used to study the effects of injuries and recovery time on players’ performance. Another example is to investigate how the performance evolved over players’ careers and the relationship between age and performance. Lastly, one more example is to use the game-related statistics to analyse the effects of different competition schedules.

103

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APPENDICES

123 APPENDIX C – Publication study 1

Reliability of Teams’ Game-Related Statistics in Basketball: Number of Games Required and Minimal Detectable Change. Alexandra Pérez-Ferreirós, Anton Kalén, Miguel-Ángel Gómez and Ezequiel Rey

To cite this article: Pérez-Ferreirós, A., Kalén, A., Gómez, M.-Á., & Rey, E. (2018). Reliability of Teams’ Game-Related Statistics in Basketball: Number of Games Required and Minimal Detectable Change. Research Quarterly for Exercise and Sport. Advanced online publication. doi:10.1080/02701367.2019.1597243

The final authenticated version is available online at: https://doi.org/10.1080/02701367.2019.1597243

Abstract

In basketball, game-related statistics are the most common measure of performance. However, the literature assessing their reliability is scarce. Purpose: Analyze the number of games required to obtain a good relative and absolute reliability of teams’ game- related statistics. Method: A total of 884 games from the 2015–2016 to 2017–2018 seasons of the Spanish men’s professional league were analyzed using all games and clustered by scoring difference. Intra-class correlation coeffi-cient (ICC) was calculated for each variable. The number of games required to detect a change and to achieve good relative reliability was calculated using minimal detectable change and Spearman- Brown prophecy formula respectively. Results: Using all games, the results showed that the minimal number of games required in each group was 30 to detect a medium change (d > .5), 187 for a small change (d > .2), and 100 for good relative reliability (ICC ≥ .75). Using balanced and unbalanced games, the minimal number of games required in each group was respectively 31 and 30 to detect a medium change (d > .5), 190 and 188 for a small change (d > .2), and 191 and 121 for good relative reliability (ICC ≥ .75). Conclusions: The sample needs to consist of at least 30 games in each group to detect a medium size change, and at least 190 games to detect a small size change. To be able to rank teams with good reliability, at least 100 games are required when including both balanced and unbalanced games.

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APPENDIX D – Publication study 2

Pérez-Ferreirós, A., Kalén, A., & Rey, E. (2018). Short- and mid-term effects of the 2010 rule changes on game-related statistics in European basketball championships: An interrupted time series analysis. International Journal of Sports Science & Coaching, 13(6), 1081–1089. doi:10.1177/1747954118765738

145 Original research International Journal of Sports Science & Coaching 2018, Vol. 13(6) 1081–1089 Short- and mid-term effects of the 2010 ! The Author(s) 2018 Article reuse guidelines: rule changes on game-related statistics sagepub.com/journals-permissions DOI: 10.1177/1747954118765738 in European basketball championships: journals.sagepub.com/home/spo An interrupted time series analysis

Alexandra Pe´rez-Ferreiro´s , Anton Kale´n and Ezequiel Rey

Abstract In 2010, one of the major rule changes in basketball came into effect. Including an extension of the 3-point line from 6.25 m to 6.75 m, changed shape of the 3-s area, the addition of no-charge semicircles, and modifications of the shot-clock. This study aimed to analyse if the rule modifications influenced the game-related statistics, both short- and mid-term using interrupted time series analysis, and if the rule changes had the same influence on different age groups and genders. The sample was composed by 5296 games from the European championships 2005–2016 for men and women in both senior and youth competitions. The standard game-related statistics were analysed. The game pace has increased or ceased to decrease after the rule modifications. The development towards a higher proportion of field goals being 3-pointers has continued, although the proportion was lowered directly after the rule modifications. The women senior seems to be the category where the rule modifications had the most effect on the continuous development. No general pattern of differences in effects between categories was found.

Keywords International Basketball Federation, performance analysis, rule modification, sport analytics, team sport

Introduction Rule modifications could potentially influence the con- In 2008, the International Basketball Federation (FIBA) struction of the team, the game strategies adopted and decided to make significant changes to the rules of the the physical training. FIBA has continuously changed game.1 These modifications, which came into effect from the rules to adjust to the evolution of how the game is the season 2010/2011, included moving the 3-point line played, adjusting to new situations that arise, helping from 6.25 m to 6.75 m, changing the shape of the 3-s area the referees to officiate the game, trying to remove into a rectangle, adding a no-charge semicircle under the behaviours that are not in the spirit of the game and basket, and changing how and when to reset the shot- making the game more amusing for the spectators.3 clock.2 These rule changes ‘were strived by the attempt Rule changes in basketball do not only counter to further unify all existing game rules and to have, in the future, only one set of rules for the game of basketball worldwide’.1 This refers to modifying the rules to approach those of the National Basketball Association Reviewers: Miguel-Angel Gœmez (Polytechnic University of Madrid, Spain) (NBA). However, the NBA organises only men’s senior Erik Strumbelj (University of Ljubljani, Slovenia) competition, while the rule changes made by FIBA applies to all ages and genders. Faculty of Education and Sport Sciences, University of Vigo, Pontevedra, An understanding of how rule modifications Spain influence the physiological and technical demands, as Corresponding author: well as the tactical dynamics in different categories Anton Kaleń, Faculty of Education and Sport Sciences, University of Vigo, could be helpful for basketball coaches, strength and Campus Universitario A Xunqueira s/n, Pontevedra 36005, Spain. conditioning coaches and basketball organisations. Email: [email protected]

147 emerging trends but can also play an active part in 2010 rule modifications, the number of 2-point field shaping the future development of how the game is goals attempted increased, while the number of played.3,4 It has been suggested that it is of vital import- 3-point field goals attempted decreased in the Spanish ance to study how the rule changes affect the way the league cup (Copa del Rey).25 game is played, to see if they fulfilled their purpose, to Articles analysing which variables better discrimi- try to identify secondary effects from those changes and nated between winners and losers in men senior, to help in the process of making new rule changes in the women senior and men youth competitions have future.4,5 Arias et al.4 suggested that rule changes reported different results.16,26,27 This difference was should be analysed before they are introduced and confirmed when comparing the game-related statistics should be based on scientific knowledge. It is difficult between genders and competition levels.28 The differ- for the people in charge of sports competitions to pro- ence also existed in possessional effectiveness and situ- pose suitable rule changes, as there is a lack of studies ational variables influencing the success.29,30 that analyse appropriate modifications to change rules.4 However, to the best of our knowledge, no studies The complexity of the sport, the amount of people exist analysing the short- and mid-term effects of the involved in different roles and the influence of previous 2010 rule changes on different levels and genders. experiences on the player’s actions, make it difficult to Considering the potential influence of rule modifications analyse the specific effects of a rule change.3,4 All these in sports and the scarce literature on the area, this study factors are probably the reason why, to our knowledge, aimed to analyse if the 2010 rule modifications influenced there have been few attempts to study the effect of rule the game-related statistics, both short- and mid-term in changes on determinant aspects of the sport. The studies the European championships between 2005 and 2016 that do exist analyse widely different characteristics, using an interrupted time series analysis. Further, we using a range of different methodologies. After the intro- aimed to compare if the rule changes had the same influ- duction of the shot-clock in 1956 (together with the intro- ence on men and women senior and youth categories. duction of the 3-s area), the scoring increased in the men’s European Championships.3 After its reduction from 30 s to 24 s in 2000, the players’ fitness and the number of Method 6 actions increased. After the introduction of the 3-point Sample line in 1984 (together with other modifications), the scoring increased in the men’s European Championships.3 The study analysed a total of 5296 (available from 5563) The increased distance of the 3-point line in 2010 games from the European championship for men and decreased the number of attempted and made 3-point women, respectively in senior (n 379 and n 321) shots during the season following the change in the and youth (n 2344 and n 2252)¼ between 2005¼ and men’s Spanish first league (ACB) and Euroleague.7,8 2016 (see supplemental¼ material).¼ The youth category In basketball, game-related statistics are the standard was composed by the under 20, under 18 and under 16 set of performance indicators and are almost uniformly groups. Games that were missing game-related statistics presented in all major competitions.9 They capture the (n 48) or that went into overtime (n 197) were major technical–tactical actions such as shooting, pas- excluded.¼ Also, the last year of women under¼ 16 was sing, rebounding, fouling, stealing and losing possession removed because more than 60% of the games were of the ball, and blocking shots. These variables are also missing. A total of 267 games were excluded. used to calculate other metrics, for example, the number of possessions to define the game pace, and player effi- Variables and procedure ciency rating to capture the global performance of the players.10–13 The game-related statistics have been used This study analysed the following rule changes imple- in studies that discriminate between winning and losing mented by FIBA in 2010:1,2 teams,14–16 analyse home advantage,17–20 discriminate between player’s positions21,22 and between starters – Modifications to the court: (a) extending the dis- and non-starters23,24 amongst others. tance of the 3-point line from 6.25 m to 6.75 m, (b) Sˇ trumbelj et al.8 compared the game-related statis- changing the shape of the 3-s area into a rectangle tics the last season before and the first season after the and (c) introducing a no-charge semicircle under 2010 rule modifications in men’s Euroleague. They each basket. found an increase in the number of 2-point field goals – Modification of the shot-clock when fouls and attempted, total rebounds and possessions; and a other violations are committed in the frontcourt; decrease in the 2-point and 3-point field goal percent- change from resetting it to 24 s, to maintain the ages, 3-point field goals attempted and free throws remaining time if more than 14 s and reset it to 14 s attempted.8 Over a period of five seasons after the when less remains.

148 Pe´rez-Ferreiro´s et al.

The following game-related statistics were gathered a dichotomous indicator of whether season t was played from FIBA’s official website (archive.fiba.com): 2-point with the old or new rules (i.e. old 0, new 1) and field goals made and attempted (2PTm and 2PTa), post time is the number of seasons¼ that passed¼ since 3-point field goals made and attempted (3PTm and the rule change (i.e. 2005–2010 0, 2011 1, 2012 ¼ ¼ ¼ 3PTa), free throws made and attempted (FTm 2 ...). 0 estimates the grand mean of the value at the and FTa), offensive and defensive rebounds (OREB first season in the model (i.e. 2005); 1a the difference in and DREB), assists (AST), steals (STL), turnovers 2005 value between the grand mean and each of the (TO), blocks (BLK), personal fouls (PF) and points categories; 2 the trend before the change; 3 the chan- scored (PTS). The collected data were gathered by ged value directly after the modifications; 4 the change FIBA professional technicians. A data reliability test in trend after the rule modifications. 5a, 6a and 7a was not carried out since FIBA technicians have their estimate the difference between the grand mean and proper reliability procedures. Furthermore, Sampaio value for categorya in time, rule change and post time et al.10 showed a perfect coefficient of agreement respectively. No models showed problems of autocorrel- (k 1.0) for all variables except for assists that had a ation or non-convergence. P values were adjusted for ¼ very high coefficient (k 0.92) in their reliability test. false discovery rates. For this paper, we¼ collected game totals (sum of Further, for variables where interactions were pre- both teams), divided them by two to get the values on sent, we performed pairwise comparisons for the esti- a per team scale, and normalised them to 100 ball pos- mated values of the direct change and change in trend sessions to control for game pace.10–13,15 The percent- between the categories. The graphical representations age of free throws (FT%), 2-point (2PT%) and 3-point include the fixed factors of the original model, as well field goals (3PT%) were calculated by dividing the as an estimate without rule change and post time to number of made shots by the number of attempted. model the predicted evolution without the rule Ball possessions (POS) were calculated as: change. All confidence intervals were computed using POS 2PTa 3PTa To 0:4 FTa OREB.11,12,31 a 500-iteration bootstrap method. The statistical ana- Using¼ game totalsþ fromþ all gamesþ inÂ EuropeanÀ champion- lyses were made with the lme434 and multcomp35 pack- ships minimise the effects of situational variables, such as ages in R 3.4.1. The significance level was set at p < .05. team quality and competition stage. Results Statistical analysis Results of the segmented regression analyses are pre- We used an interrupted time series approach to analyse sented in Table 1. The regression coefficients represent, the impact of the rule modifications, both directly and in order: (i) the value at the 2005 season; (ii) the trend, over time on the variables grand means, controlling for i.e. the change from season to season; (iii) the immedi- their level and trend before the rule change.32 To ate change after the rule modifications, i.e., the account for the variability between championships, we change between 2010 and 2011 seasons not accounted used a multi-level segmented regression analysis to for by the trend and (iv) the change of the trend after create the model for each of the variables.32,33 We the rule modifications, i.e. the difference in season to included the competition categories and their inter- season change before and after the rule modifications. actions with the other factors using an effect coding Significant interactions indicate differences in effect to get the grand mean for each parameter, as well as between categories. For variables that had significant being able to test for differences in the effect of the rule interactions, coefficients for each category and pairwise modifications between categories. The model was comparisons are presented in Table 2. defined as: The direct change in the number of POS was different for the senior categories compared to the youth. Yt 0 1a categorya 2 timet 3 rule changet It seems to have increased in the senior while decreased ¼ þ ð Þþ ð Þþ ð Þ in the youth categories. The trend had a general posi- 4 post timet 5a time categorya þ ð Þ ð Â Þ tive change after the rule modifications. Visual repre- rule change category þ 6að Â aÞ sentations of the effect for POS in each category are post time category u tournament e þ 7að Â aÞþ 1ð Þþ t presented in Figure 1. No general change was evident in PTS. There was a where Yt is the mean value of the variable of interest at difference in direct change between the two youth cate- season t; categoryis the different genders and ages (Men gories as the PTS decreased in women youth. There was a senior, Women senior, Men youth, Women youth); time difference in trend change between men and women. It is the number of seasons that passed from where the seems to have had a negative effect in men and positive in sample starts (i.e. 2005 0, 2006 1 ...); rule change is women, although not as evident in the youth categories. ¼ ¼

149 Â 0.675 0.144 0.136 0.917 0.077 0.985 0.774 0.479 0.521 0.210 0.503 0.028 0.001 0.002 0.034 Post time competition < Â 0.301 0.115 0.332 0.455 0.575 Rule change competition 0.031 0.041 Â 0.283 Time competition 0.021 0.046 0.011 value 0.001 0.001 0.003 0.033 0.033 P < < 0.1] 0.1] À À 0.3, 0.3] 0.946 0.056 0.2, 0.2] 0.898 0.3, 0.4] 0.898 0.759 0.279 0.3, 0.1] 0.613 0.561 0.338 0.3, 0.5] 0.826 0.2, 0.2] 0.898 0.288 0.336 0.6, 0.7] 0.966 0.993 0.323 0.4, 0.3, 0.1, 0.2] 0.300 0.605 0.827 0.3, 0.0] 0.136 0.1, 0.0] 0.898 0.395 0.234 0.1, 0.2] 0.898 0.097 0.111 À À À À À À À À À À À À À 95% CI 0.0 [ 0.0 [ 0.1 [ 0.3 [ 0.2 [ 0.2 [ b Post time À À À À value 0.001 0.004 0.001 P < < 0.3] 0.115 0.0 [ 0.6] À À 0.6, 2.1] 0.686 0.9 [0.5, 1.3] 2.5, 2.8, 2.3, 1.2] 2.4, 0.3] 0.141 0.1 [ 0.9, 0.5] 0.951 0.0 [ 2.3, 2.1] 0.736 0.0 [ 0.2, 0.6] 0.063 0.3, 0.6] 0.349 1.2, 0.1] 0.394 0.2 [0.0, 0.4] 0.731 0.116 0.391 0.4, 0.3] 0.736 0.0 [ 0.5, 0.4] 0.863 0.2, 0.1] 0.686 0.0 [ 0.4, 0.6] 0.394 0.0 [ À À À À À À À À À À À À À À 95% CI 0.7 [ 1.4 [ 2.1 [1.3, 2.8] 1.7 [ 1.7 [ 1.0 [ 0.2 [ 0.1 [ 0.2 [ 0.2 [ 0.6 [ 0.1 [ 0.1 [ b Rule change À À À À À À À À À value 0.001 0.006 0.001 0.005 0.001 0.001 0.011 0.001 P < < < < < 0.6] 0.1] À À 1.2, 0.1, 0.4] 0.821 0.2, 0.3] 0.860 0.3, 0.0] 0.3, 0.3] 0.681 0.3, 0.0] 0.2, 0.8] 0.265 0.1, 0.3] 0.3, 0.1, 0.1] 0.283 0.1 [ À À À À À À À À À À 95% CI 0.05 0.9 [ 0.2 [ 0.1 [ 0.2 [ < b À Time À À À p 95% CI Results of segmented regression analyses for general effects of the rule modifications. b Constant : Regression coefficients; CI: confidence interval; POS: ball possessions; PTS: points scored; 2PTa: 2-point field goals attempted; 2PT%: 2-point field goals percentage; 3PTa: 3-point field goals attempted; POS 75.1 [74.1, 75.9] Table 1. b 3PT%: 3-point field goals percentage;PF: FTa: free-throws personal attempted; fouls. FT%: Bold free-throws percentage; indicates OREB: offensive rebounds; DREB: defensive rebounds; AST: assists; STL: steals; TO: turnovers; BLK: blocks; PTS 46.5 [45.8, 47.2] 0.2 [ 2PTa 29.0 [28.6, 29.4] 2PT% 45.4 [48.8, 46.1] 0.1 [ 3PTa 12.2 [11.9, 12.5] 0.4 [0.2, 0.5] 3PT% 30.6 [29.8, 31.5] 0.0 [ FTa 13.4 [13.0, 13.8] FT% 67.1 [65.8, 68.4] 0.3 [ OREB 7.6 [7.3, 7.8] 0.2 [0.1, 0.3] DREB 16.9 [16.6, 17.2] 0.2 [ ASTSTL 7.5 [7.1, 7.8] 6.6 [6.3, 6.8] 0.2 [0.1, 0.4] TO 11.0 [10.7, 11.3] 0.1 [0.0, 0.2] 0.263 BLK 1.8 [1.7, 1.9] 0.0 [0.0, 0.1] 0.860 0.0 [ PF 13.5 [13.2, 13.8] 0.0 [

150 Pe´rez-Ferreiro´s et al.

Table 2. Results of the pairwise comparison between categories for differences in effects of the rule change.

Men senior Women senior Men youth Women youth

b 95% CI b 95% CI b 95% CI b 95% CI Comparisons POS Constant 72.9 [70.8, 74.9] 74.2 [72.3, 76.1] 75.9 [74.7, 77.1] 77.6 [76.5, 78.8] À Time 1.2 [ 1.9, 0.4] 1.2 [ 2.0, 0.5] 0.4 [ 0.8, 0.1] 0.7 [ 1.0, 0.3] À À À À À À À À À À À À Rule change 3.2 [ 0.1, 6.5] 3.3 [ 0.2, 6.7] 1.9 [ 3.8, 0.0] 1.7 [ 3.5, 0.2] MY, WY < MS*, WS* À À À À À À Post time 1.1 [0.1, 2.1] 1.1 [0.1, 2.1] 0.9 [0.4, 1.5] 0.5 [ 0.1, 1.0] À PTS Constant 49.9 [48.2, 51.6] 45.7 [44.1, 47.3] 48.1 [47.3, 49.0] 42.3 [41.4, 43.1] Time 0.9 [0.3, 1.6] 0.2 [ 0.8, 0.5] 0.1 [ 0.4, 0.1] 0.1 [ 0.2, 0.3] À À À À À Rule change 2.2 [ 4.9, 0.5] 1.5 [ 4.4, 1.4] 0.8 [ 0.6, 2.1] 2.6 [ 4.0, 1.2] WY < MY À À À À À À À À y Post time 0.9 [ 1.7, 0.1] 1.0 [0.1, 1.8] 0.2 [ 0.6, 0.1] 0.2 [ 0.2, 0.6] MS < WS , WY*; MY < WS* À À À À À À y 2PTa Constant 25.8 [24.7, 26.9] 31.3 [30.3, 32.4] 28.8 [28.2, 29.4] 30.1 [29.5, 30.7] Time 0.3 [ 0.1, 0.7] 0.5 [ 0.9, 0.1] 0.4 [ 0.6, 0.2] 0.1 [ 0.3, 0.1] À À À À À À À À À Rule change 0.8 [ 1.0, 2.6] 2.4 [0.5, 4.3] 3.1 [2.1, 4.0] 2.1 [1.1, 3.0] À Post time 0.4 [ 0.9, 0.2] 0.5 [0.0, 1.1] 0.0 [ 0.2, 0.3] 0.2 [ 0.5, 0.1] MS, WY < WS* À À À À À 3PT% Constant 32.0 [29.7, 34.2] 32.8 [30.7, 34.9] 30.2 [29.3, 31.0] 27.7 [26.8, 28.5] Time 1.0 [0.1, 1.8] 0.8 [ 1.6, 0.0] 0.1 [ 0.4, 0.2] 0.1 [ 0.4, 0.2] À À À À À À Rule change 3.7 [ 7.1, 0.4] 1.8 [ 1.8, 5.5] 0.2 [ 1.6, 1.2] 2.0 [ 3.4, 0.5] MS < WS* À À À À À À À À À Post time 0.9 [ 1.9, 0.1] 1.1 [0.1, 2.2] 0.0 [ 0.4, 0.4] 0.3 [ 0.1, 0.7] MS < WS* À À À À OREB Constant 6.9 [6.2, 7.6] 7.0 [6.4, 7.6] 8.2 [7.9, 8.5] 8.2 [7.9, 8.5] Time 0.2 [ 0.1, 0.4] 0.3 [0.0, 0.5] 0.0 [ 0.1, 0.1] 0.3 [0.2, 0.4] À À Rule change 0.1 [ 0.9, 1.1] 0.4 [ 1.5, 0.6] 0.7 [0.3, 1.2] 0.5 [0.0, 0.9] À À À Post time 0.2 [ 0.5, 0.1] 0.2 [ 0.5, 0.1] 0.0 [ 0.2, 0.1] 0.6 [ 0.7, 0.4] WY < MY À À À À À À À À z DREB Constant 17.1 [16.4, 17.9] 16.8 [16.1, 17.6] 16.8 [16.5, 17.2] 16.7 [16.3, 17.0] Time 0.0 [ 0.3, 0.3] 0.4 [0.1, 0.7] 0.1 [0.0, 0.2] 0.4 [0.3, 0.5] À Rule change 0.2 [ 1.3, 1.0] 0.1 [ 1.4, 1.2] 0.1 [ 0.5, 0.7] 0.8 [0.2, 1.3] À À À À À Post time 0.1 [ 0.2, 0.5] 0.6 [ 0.9, 0.2] 0.0 [ 0.1, 0.2] 0.4 [ 0.6, 0.2] WS, WY < MS*, MY À À À À À À À À y TO Constant 10.5 [9.7, 11.2] 10.2 [9.5, 10.9] 11.0 [10.6, 11.3] 12.2 [11.9, 12.6] Time 0.3 [ 0.6, 0.0] 0.4 [0.2, 0.7] 0.0 [ 0.1, 0.2] 0.1 [0.0, 0.2] À À À Rule change 0.7 [ 0.5, 1.8] 0.7 [ 2, 0.5] 0.2 [ 0.8, 0.4] 0.0 [ 0.6, 0.7] À À À À À À Post time 0.2 [ 0.2, 0.5] 0.6 [ 1.0, 0.2] 0.0 [ 0.2, 0.2] 0.2 [ 0.4, 0.1] WS < MS*, MY* À À À À À À À À b: Regression coefficients; CI: confidence interval; POS: ball possessions; PTS: points scored; 2PTa: 2-point field goals attempted; 3PT%: 3-point field goals percentage; OREB: offensive rebounds; DREB: defensive rebounds; TO: turnovers; MS: men senior; WS: women senior; MY: men youth; WY: women youth. *p < .05. p < .01. p < .001. y z

The number of 2PTa generally increased, and 3PTa in women senior and seems to be a negative change in men decreased directly. There was a positive change of the senior. Visual representations of the general effects for 2PTa trend in women senior, different from men senior 2PTa and 3PTa are presented in Figure 2. and women youth. The 2PT% generally decreased dir- No general direct effects in OREB or DREB were ectly. The 3PT% was generally unaffected. There were found. There was a negative trend change for OREB in however different effects in the senior categories. The women youth, different from men youth. The trend for 3PT% decreased directly in men and might have increased DREB was affected negatively in both women cate- in women senior, while there was a positive trend change gories, different from the men categories.

151 Men Senior Women Senior Men Youth Women Youth

70 POS

60 95% CI

55 After 17.5 Before

15.0 Change Predicted 12.5 TO 10.0

7.5

5.0 2006 2009 2012 2015 2006 2009 2012 2015 2006 2009 2012 2015 2006 2009 2012 2015 season

Figure 1. Trend before rule change (before), impact of rule change (after) and predicted trend without rule change (predicted), for ball possessions (POS) and turnovers (TO) in all categories.

2PTa 3PTa 35

30 95% CI 25 After Before 20 Change Predicted 15

10 2006 2009 2012 2015 2006 2009 2012 2015 season

Figure 2. General trend before rule change (before), impact of rule change (after) and predicted trend without rule change (predicted) for 2-point field goals attempted (2PTa) and 3-point field goals attempted (3PTa).

The trend for TO was negatively affected in women decreased directly while there were mixed effects on senior, different from the men categories. The variables the 3PT%. After the rule modifications, the trend chan- FTa, FT%, AST, STL, BLK, and PF were unaffected by ged towards fewer TO in women senior. the rule modifications. Visual representations of the The number of ball possessions is in basketball effects for TO in each category are presented in Figure 1. the measurement used to quantify the game pace.10–13 The direct increase in the number of possessions for the Discussion senior categories is in line with earlier studies on the effect of the 2010 modifications.8 This effect could The present study investigated the short- and mid-term be expected as the rule modifications included a impact of the rule modifications implemented in 2010 reduced time on the shot-clock after certain situations, by FIBA on the game-related statistics in basketball. such as offensive rebounds and personal fouls. Teams It further examined whether the rule modifications in younger categories tend to play with a higher number impacted the genders and age groups differently. of possessions,36 indicating that they are not using as The number of POS seems to have increased directly much of the available time on the shot-clock. This is a in the senior categories, and the previous trend towards possible explanation as to why the number of posses- fewer POS has been stopped or reversed. The number sions did not increase in the youth categories. of 2PTa increased while the number of 3PTa decreased A possible explanation for the positive trend change directly after the modifications, but the trend towards on the number of possessions is that the teams had to find more 3PTa and less 2PTa remained. The 2PT% new strategies to score faster in situations with a shorter

152 Pe´rez-Ferreiro´s et al. shot-clock, such as after an offensive rebound or after a analysed the turnovers in the women’s Greek league; defensive foul. As they got better at it, more teams might 81.4% of the turnovers were made inside or around have adopted these strategies in other game situations, the 3-point line, and the most occurring type of turnover creating a more transitional style of playing with shorter was passing errors. The widening of the 3-point line can, offensive possessions. Previous rule modifications speed- therefore, have created opportunities to play with more ing up the game pace have increased the physiological spacing in offence, forcing the defence to cover more demands.6 As the game pace has increased as a result of area. As the women senior teams gradually adapted to the 2010 rule modifications, it can be expected that the the new space constraints, they were perhaps finding physiological demands have become higher. better passing options, and therefore reducing the risk In general, the modifications decreased the number of of a defensive player being able to deflect the pass. 3-point field goals attempted, while they increased the In the women senior championships, the rule modi- number of 2-point field goals attempted. These results fications seem to have stimulated the offence more than are in accordance with earlier studies in men senior lea- it has in the other categories. They are playing at a gues.7,8 The influence of the 3-point line distance on the faster pace, scoring more, shooting 3-pointers with amount of 2-point and 3-point field goals attempted has higher percentage and making fewer turnovers. Many been established in the NBA.37 Where a shortened dis- of these changes are different from the other categories. tance resulted in higher amounts of 3-point attempts in Therefore, it seems as the rule modifications had the relation to 2-point attempts and reversed when the line most significant impact on the women senior category. was moved back to the original distance.37 The trend of However, there was no evident pattern of differences an increasing number of 3-point and decreasing number between genders or age. of 2-point field goals attempted remained unaffected It has been shown that altering the spatial and tem- after the modifications. This is in line with results from poral constraints influence the technical–tactical studies analysing the effect over several seasons.25 actions performed in other team sports.42–44 The The lower 2-point percentage directly after the rule changes after the 2010 rule modifications on the modifications could be due to a change in which shot game-related statistics implicate that the changed spa- types were attempted. Previous studies have found that tial and temporal constraints imposed on the game the technical and tactical actions preceding shots affect have affected the extent to which different technical– the shooting percentage.38,39 It is possible that a con- tactical actions are being used. It is apparent that the siderable amount of the extra 2-point field goals rule modifications influenced the game not only directly attempted were shot types with a lower percentage, but also its continuous development over time. such as from dribble as opposed to from pass.38,39 This study presents certain limitations as it used a The difference in 3-point percentage between men and correlational methodology, analysing changes in women senior, both directly and over time, is notable as game-related statistics after the implementation of the accuracy for different shot types has been shown to rule modifications. It cannot be concluded that the be similar between the genders (and competition rule modifications are the underlying cause for levels).33,38 This implies that men and women senior the results. These changes might also be influenced teams have adapted their shot selection differently to by the physiological development of the players, the the extended 3-point line. Men senior teams might continuous development of offensive and defensive have shifted more towards moving into the shot, shoot- strategies to counter each other and mimicking of ing from dribbling, getting the pass from the same side of trendsetting teams and players. Rule modifications the court or shooting under higher defensive pressure, cannot be considered as an isolated factor affecting while women teams have done the opposite.38 the team’s performance.4–6 Therefore, a multifactorial The decreasing number of defensive rebounds in model (technical, tactical, strategical, physical and both women categories might be a result of the changed psychological) should be accounted for to better iden- distribution between 2-point and 3-point shots, as the tify the non-linear evolution of the basketball game. shot distance has been shown to influence the possibil- This study was made on European championships, ity of taking an offensive or defensive rebound.40 The which might not be fully representative for all kind of women youth have a decreasing number of both offen- basketball leagues and levels. However, it has been sive and defensive rebounds. As the variables have been found that shooting variables remain similar between normalised in regard to game pace, this trend indicates different competitions and age groups.33 a corresponding decrease in the number of missed field Further studies on rule modifications are needed to goal attempts. However, this is only partially supported understand its implications fully. The physiological by the results. effects need to be studied, as they could have direct In women senior, the trend towards more turnovers implications for the design of training tasks and man- was reversed after the rule change. Fylaktakidou et al.41 agement of players during competition. Studies using

153 other methods are needed to fully understand the tech- Funding nical–tactical implications of the rule modifications, The author(s) received no financial support for the research, analysing, for example, the distribution of technical authorship, and/or publication of this article. and tactical actions, time-out effects, player rotations and other situational variables. ORCID iDs Alexandra Pe´ rez-Ferreiro´ s http://orcid.org/0000-0002- Conclusions 7482-4374 Anton Kale´ n http://orcid.org/0000-0002-8519-6596 To our knowledge, this is the first attempt to use an interrupted time series analysis to study rule modifications in sports. It helps to provide a deeper understand- Supplementary material ing of the implications as it enables the direct and Supplementary material is available for this article online. longitudinal effects to be interpreted distinctively from each other. References The conclusions of this article are: (a) The 2010 1. 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155 Supplementary material

Distribution of analysed games by category and season. Year Men senior Women senior Men youth Women youth 2005 36 44 184 183 2006 184 189 2007 51 54 177 173 2008 176 177 2009 50 49 185 188 2010 201 202 2011 87 52 207 206 2012 205 198 2013 83 54 227 214 2014 229 210 2015 72 68 219 210 2016 150 102 Total 379 321 2344 2252

156 APPENDIX E – Publication study 3

Senior and youth national team competitive experience: influence on player and team performance in European basketball championships

Anton Kalén, Alexandra Pérez-Ferreirós, Ezequiel Rey & Alexis Padrón-Cabo

To cite this article: Kalén, A., Pérez-Ferreirós, A., Rey, E., & Padrón-Cabo, A. (2017). Senior and youth national team competitive experience: influence on player and team performance in European basketball championships. International Journal of Performance Analysis in Sport, 17(6), 832–847. doi:10.1080/24748668.2017.1405610

The final authenticated version is available online at: https://doi.org/10.1080/24748668.2017.1405610

Abstract:

This study aimed to discover if the number of previous senior and youth national team championships played relates to the team and player performance at the European basketball championships. The sample consisted of all national teams and their players participating in the 2011, 2013 and 2015 European Championships for men (teams n = 72; players n = 697) and women (teams n = 52, players = 520). The teams were classified into four groups based on their highest stage reached in the tournament. A k- means cluster was used to group the players as high, medium or low performers according to their efficiency rating. The number of previous senior and youth championships was compared between groups. Better performing teams and players had a higher number of previous senior championships. The competitive experience differentiates low performing players for both genders, but only distinguishes high from medium performing players for women. No differences in the number of youth championships were found. It appears to be critical to have a sufficient amount of accumulated senior competitive experience within the team to reach the semi-final phase both for men’s and women’s national teams.

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