Universidade Estadual De Campinas Faculdade De Educação Física

UNIVERSIDADE ESTADUAL DE CAMPINAS FACULDADE DE EDUCAÇÃO FÍSICA

Tiago Guedes Russomanno

DESENVOLVIMENTO DE FERRAMENTAS DE ANÁLISE

DE DESEMPENHO DE ATLETAS EM 3 DIFERENTES

MODALIDADES: HANDEBOL, PROVAS COMBINADAS E

SALTO COM VARA

Campinas, 2011 1

UNIVERSIDADE ESTADUAL DE CAMPINAS

FACULDADE DE EDUCAÇÃO FÍSICA

TIAGO GUEDES RUSSOMANNO

DESENVOLVIMENTO DE FERRAMENTAS DE ANÁLISE

DE DESEMPENHO DE ATLETAS EM 3 DIFERENTES

MODALIDADES: HANDEBOL, PROVAS COMBINADAS E

SALTO COM VARA

Tese de Doutorado apresentada a Faculdade de Educação Física da Universidade Estadual de Campinas para obtenção do título de Doutor em Educação Física na Área de Concentração de Biodinâmica do Movimento Humano

PROF. DR. RENÉ BRENZIKOFER

ESTE EXEMPLAR CORRESPONDE À VERSÃO FINAL DA TESE DEFENDIDA PELO ALUNO, E ORIENTADA PELO PROF. DR.

CAMPINAS 2011 2

FICHA CATALOGRÁFICA ELABORADA POR DULCE INES LEOCÁDIO DOS SANTOS AUGUSTO – CRB8/4991 BIBLIOTECA “PROF. ASDRUBAL FERREIRA BATISTA” FEF - UNICAMP

Russomanno, Tiago Guedes, 1979- R921d Desenvolvimento de ferramentas de análise de desempenho de atletas em 3 diferentes modalidades: Handebol, Provas Combinadas e Salto com Vara / Tiago Guedes Russomanno. --Campinas, SP: [s.n], 2011.

Orientador: René Brenzikofer. Tese (doutorado) – Universidade Estadual de Campinas, Faculdade de Educação Física.

1. Biomecânica. 2. Atletismo - biomecânica. 3. Handebol. 4. Programas de rastreamento. I. Brenzikofer, René. II. Universidade Estadual de Campinas. Faculdade de Educação Física. III. Título.

Informações para Biblioteca Digital

Título em inglês: Development of tools for performance analysis of athletes in three different modalities: handball, combined events and pole vault. Palavras-chave em inglês : Biomechanics Athletics - Biomechanics Handball Screnning programs Área de Concentração: Biodinâmica do Movimento Humano Titulação: Doutor em Educação Física Banca Examinadora: René Brenzikofer [Orientador] Luiz Eduardo Barreto Martins Nelson Prudêncio Ricardo da Silva Torres Data da defesa: 29-07-2011 Programa de Pós-Graduação: Educação Física

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Dedicatória

"A imaginação é mais importante que o conhecimento." Albert Einstein

Aos meus pais pelo incentivo e apoio. Aos amigos, que sempre estiveram do meu lado. 6 7

Agradecimentos

Agradeço ao Professor René Brenzikofer pela oportunidade e dedicação, paciência e pelas inúmeras correções feitas e pela realização deste trabalho e por ter aceitado me orientar nessa empreitada final. Aos professores Nelson Prudêncio, Ricardo da Silva Torres, Mario Hebling Campos, Luiz Eduardo Barreto Martins e Sergio Augusto Cunha pelas sugestões e contribuições nesse trabalho. Aos amigos do laboratório (LIB) que de uma forma ou de outra contribuíram para realização deste trabalho e para a minha formação. Ao professor Ricardo Torres e professora Denise Vaz de Macedo pelas conversas e ensinamentos nos momentos mais difíceis. Ao Cezar Augusto de Freitas Anselmo pelas inúmeras contribuições neste trabalho tanto na parte estatística quanto no desenvolvimento do método de pontuação e na realização do Multiathlon e pela amizade em todos esses anos de Unicamp. Ao Antonio Soeiro Junior pelo companheirismo, amizade e pelas inúmeras correções e revisões de português no texto ao longo do Doutorado, por sempre estar me apoiando em todos os momentos nessa jornada, inclusive nos estudos durante as intermináveis listas de exercícios do Prof. Siome. Ao José Vitor Viera Salgado pela amizade, pelo apoio e por ter me ajudado a realizar um sonho que foi a corrida da Unicamp e por hoje estarmos juntos trabalhando com a equipe de atletismo da Unicamp. À Carolina Tanoue pelas inúmeras correções e revisões de inglês em artigos e congressos, pela amizade, companheirismo e por tudo que vivemos. À Juliana Andreotti pela amizade nesses mais de 12 anos de convívio, pela paciência e por todas as broncas e apoio durante o doutorado. À Luciana Higa pelo apoio, pela amizade, pela paciência, pelo companheirismo e por tudo que você fez e vem fazendo e por ter sempre acreditado em mim. Aos amigos de todas as horas (na alegria ou na tristeza), que sempre estiveram ao meu lado em especial: Cleber Akira Nakandakare, Alexander (Yoda) Aguina, Vitor Garcia, Rodrigo Palma, José Ribamar, Henri Zurmely, Leandro Hirata, Gisele Chan, Márcia Morita e Thais Ito. Aos colegas da república que me aturaram todos estes anos de convívio (Antonio Soeiro, Felipe Magaldi, José Vitor Viera Salgado, Cesar Beselga, Paul Hecker, Caio Sakalauskas, Bruno Miguel, Fabiano Farah, Baba Aye, Roberto) Aos amigos, que me ajudaram e foram amigos em todos os momentos, desde as conversas no bandejão, os almoços e jantares, as baladas e a noites acordados jogando... e de vez em quando estudando, aos inúmeros churrascos e cinemas e a todas as viagens que fizemos juntos.. Aos amigos estrangeiros Luca Oggiano, Hiroaki Hobara, Mahendran Kaliyamoorthy, Peter Chenfu Huang que mesmo longe e nos encontrando raramente em congressos, sempre estiveram dispostos a ajudar. 8 9

Ao Milton Misuta, Pascual Figueroa e Bruno Cedraz por tudo que vocês me ajudaram e ensinaram durante o Doutorado. Ao Élson Miranda e a Fabiana Murer pelas contribuições e esclarecimentos sobre o salto com vara. A todos os atletas da equipe de atletismo da Unicamp que ao longo desses 11 anos, acreditaram no meu trabalho e ajudaram no fortalecimento e no desenvolvimento da equipe, nas vitorias e nas derrotas. Às atléticas da Unicamp que ajudaram a fortalecer o movimento esportivo na Unicamp durante os anos que estive na presidência da LAU (Liga das Atléticas da Unicamp). Aos professores Ricardo Anido e Carlos Anjos pelo apoio ao esporte universitário. Aos funcionários na Faculdade de Educação Física da Unicamp. À CAPES e ao COB pelo apoio financeiro recebido.

À minha família especialmente que sempre me apoiou e esteve do meu lado durante todo o meu trabalho, acreditando no meu potencial e na realização de mais um sonho. E aos meus pais, que sem eles nada disso seria possível.

Obrigado a todos.

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Russomanno, Tiago G. Desenvolvimento de ferramentas de análise de desempenho de atletas em 3 diferentes modalidades: Handebol, Provas Combinadas e Salto com Vara . 2011. (Doutorado em Educação Física). Faculdade de Educação Física. Universidade Estadual de Campinas, Campinas, 2011.

Resumo

Palavras-chaves: biomecânica, handebol, provas combinadas, salto com vara 12 13

Russomanno, Tiago G. Development of tools for performance analysis of athletes in three different modalities: Handball, Combined Events and Pole Vault . 2011. (Doutorado em Educação Física). Faculdade de Educação Física. Universidade Estadual de Campinas, Campinas, 2011.

Abstract

The high performance sport is no longer limited to the relation between coach and athlete. Simple observation and subjective perception of the coach and his intervention is no longer sufficient as a reference to correct or improve the performance of an athlete. Therefore the use of technology can help to improve the quality of information about the performance of an athlete. The main objective of this work is the use of evaluation methods in biomechanics and computer engineering through the integration of different methodologies and the development of methods of performance analysis of athletes in competitive situations in three different sports: Handball, combined events and pole vault. In handball was approached the problem of automatic tracking of players, which was proposed and evaluated a detector Boosting cascade automatically trained, based on morphological segmentation for tracking handball players. The proposed method was able to correctly detect 84% of the players when tested in the second half of the same game where he was trained and 74% when tested in a different game. Proved to be a useful tool for tracking in a team sports with prospects and possibilities to be used in other types of court or field games. For combined events we developed a new scoring system that uniformly evaluates the performance of athletes in the decathlon and heptathlon. Our method uses a normalized mirrored-logarithmic function which facilitates the free choice of its gradient (growth speed) according to competition needs.The method is simple, interpretable and even in all events and can be used in different combined events. In the pole vault was made an individual analysis in order to describe the biomechanics of the best Brazilian pole vault athlete and to compare with the best athletes in the world focusing on the mechanical energy of the pole vault, evaluating kinematic variables and energy parameters using a three-dimensional kinematic analysis system. The maximum height reached by the athlete's center of mass showed significant correlation with the final total energy (r = 0.82, P <0.01). The Brazilian athlete's muscle power was 1.18 ± 0.87 J / kg, while for the athletes during the final of the women's pole vault in Sydney was 5.74 ± 1.63 J / kg. Despite the low values of the muscular energy, the athlete has high values of E_Initial and E_Final with mean values of respectively 45.96 ± 0.82 J / kg and 47.14 ± 0.71 J / kg. When compared with other pole vaulter appearing in the elite of the sport, the Brazilian athlete is one of the fastest, with high values of E_Final and E_Initial, which places it among the five best athletes in the sport today. In all modalities analyzed we took into account the specificity of each modality and the most important variables for evaluating the performance of athletes with the main focus the use of computing resources to improve the analysis of performance in these modalities. keywords: biomechanics, handball, combined events, pole vault

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LISTA DE FIGURAS

FIGURE 1 SYNCHRONISED CAMERAS VIEWS USED FOR TRACKING AND MEASUREMENT ...... 32 FIGURE 2 INTEGRAL IMAGE FEATURES (A) - (D)...... 35 FIGURE 3 INTEGRAL IMAGE FEATURE APPLIED OVER AN IMAGE . (A) A RECTANGULAR REGION OF THE IMAGE . (B) A TYPICAL FEATURE , WHERE THE SUM OF THE INTENSITIES OF THE PIXELS ON THE WHITE RECTANGLE IS SUBTRACTED FROM THE SUM OF THE DARK RECTANGLE . (C) THE REGION WITH THE FEATURE OVERLAID ...... 35 FIGURE 4 STEPS OF MORPHOLOGICAL SEGMENTATION . (A) LOAD THE VIDEO SEQUENCE ; (B) DEFINITION OF IMAGE BOUNDARIES ; (C) BACKGROUND EXTRACTION ; (D) DIFFERENCE BETWEEN THE CURRENT FRAME AND BACKGROUND ; (E) IMAGE BINARISATION AND (F) MORPHOLOGICAL FILTERING AND LABELING ...... 38 FIGURE 5 ON THE LEFT , AUTOMATIC SEGMENTATION ; ON THE RIGHT , AUTOMATICALLY GENERATED POSITIVE EXAMPLES FOR BOOSTING DETECTOR TRAINING ...... 39 FIGURE 6 FLOWCHART OF THE OVERALL PROCESSING ...... 40 FIGURE 7 REPRESENTATION OF UNCERTAINTIES TO MEASURE AND RECONSTRUCT POSITIONS (N=10) IN 22 POSITIONS OF THE HANDBALL COURT . MEAN ± STANDARD DEVIATION . VALUES ARE IN METRES ...... 41 FIGURE 8 MANUAL (M) AND AUTOMATIC (A) TRAINING TIMES OF THE BOOSTING DETECTOR FOR HANDBALL PLAYERS LOCALISATION . THE NUMBER BESIDE THE LETTER M OR A INDICATES HOW MANY FIGURES WERE USED FOR TRAINING ...... 42 FIGURE 9 ACCUMULATED ERROR OF THE BOOSTING DETECTOR IN FUNCTION OF THE NUMBER OF IMAGES ANALYSED FOR MANUAL (M) AND AUTOMATIC (A) TRAINING , WITH DIFFERENT SIZES OF TRAINING SET . ERRORS IN PIXELS ...... 44 FIGURE 10 PERCENTAGE OF SUCCESSFUL DETECTION FOR MANUAL AND AUTOMATIC TRAINNING ...... 45 FIGURE 11 MOTION OF ONE PLAYER (X-COORDINATE ) IN FUNCTION OF FRAMES ANALYSED OVER 3MIN BY MANUAL , BOOSTING AND DVIDEO TRACKING ...... 45 FIGURE 12 MOTION OF ONE PLAYER (Y-COORDINATE ) IN FUNCTION OF THE FRAMES ANALYSED OVER 3MIN BY MANUAL , BOOSTING AND DVIDEO TRACKING ...... 46 FIGURE 13 TRAJECTORIES OF HANDBALL PLAYERS IN THE FIRST HALF -TIME (30 MIN ). DEFENCE ON THE RIGHT SIDE ...... 48 FIGURE 15 A) IMAGE OF THE PLAYERS; B) IMAGE OF THE COURT WITHOUT THE PLAYERS ; C) IMAGE SEGMENTATION RESULTS ; D) AUTOMATIC TRACKING RESULTS ...... 54 FIGURE 16 THE ACCUMULATED COVERED DISTANCES BY THE PLAYERS OF THE TEAMS A AND B. THE PLAYERS ARE IDENTIFIED AS RIGHT BACKCOURT PLAYER (RB), LEFT BACKCOURT PLAYER (LB), CENTRE BACKCOURT PLAYER (CB), LEFT WING PLAYER (WP), RIGHT WING PLAYER (RW) AND PIVOT (P). THE RESPECTIVE PLAYERS CB, RB (TEAM A) AND CB (TEAM B) WERE SUBSTITUTED DURING THE GAME ..... 56 FIGURE 17 PERCENTAGE OF TIME SPENT IN EACH TYPE OF MOVEMENT DURING THE GAME . THE FOLLOWING PLAYERS CB, RB (TEAM A) AND CB (TEAM B) WERE SUBSTITUTED DURING THE GAME ...... 57 FIGURE 18 SCORE CURVES OF THE DECATHLON FOR THE 10 EVENTS USING THE IAAF RANKING METHOD ...... 70 FIGURE 19 SCORE CURVES OF THE HEPTATHLON FOR THE 7 EVENTS USING THE IAAF RANKING METHOD ...... 71 FIGURE 20 SCORE CURVES FOR THE PROPOSED METHOD TO EVALUATE PERFORMANCE IN COMBINED EVENTS . 72 FIGURE 21 ALTURA DO GRIP NO MOMENTO DE TAKEOFF (GHTO)...... 87 FIGURE 22 DISTÂNCIA DO TAKEOFF (DTO)...... 88 FIGURE 23 CORDA DE VARA (MPB)...... 88 FIGURE 24 RETIFICAÇÃO DA VARA (GHPE)...... 89 FIGURE 25 ESQUEMA ILUSTRANDO AS VARIÁVEIS CALCULADAS NOS 4 MOMENTOS DEFINIDOS PARA O SALTO COM VARA E O CÁLCULO DA ENERGIA TOTAL DA SALTADORA COM VARA (ADAPTADO DE DE ARAMPATZIZ ET AL . (1997)...... 90 FIGURE 26 CURVAS DE ENERGIA MECÂNICA DO CENTRO DE MASSA CARACTERÍSTICA DO SALTO COM VARA FEMININO ...... 91

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LISTA DE TABELAS

TABLE 1 DISTANCES COVERED BY SIX PLAYERS DURING 5 MIN OF GAME CALCULATED FROM THE DATA OBTAINED BY MANUAL , BOOSTING AND DVIDEO TRACKING . THE PERCENTAGE DIFFERENCES FROM DVIDEO AND BOOSTING TRACKING COMPARED TO MANUAL TRACKING ARE INDICATED IN BRACKETS.... 47 TABLE 2 COMPARISON OF THE TWO MODELS FOR THE FIRST TEN PLACES OF THE TOP 100 OF ALL TIME IN THE DECATHLON ...... 73 TABLE 3 COMPARISON OF THE TWO MODELS FOR THE FIRST TEN PLACES OF THE TOP 100 OF ALL TIME IN THE FEMALE HEPTATHLON ...... 73 TABLE 4 COMPARISON OF THE PERFORMANCE BETWEEN THE RESULTS OF THE 4TH AND 5TH ATHLETES FOR THE DECATHLON OF ALL TIMES UPDATED IN 2010 IN THE IAAF WEBSITE . SCORE T* IS THE POINTS AWARDED BY THE ATHLETES WITHOUT TRUNCATION , SCORE IAAF IS THE POINTS AWARDED BASED ON THE DECATHLON TABLES AND SCORE EQ 1.5 IS THE POINTS AWARDED BASED ON THE MODEL PROPOSED IN THIS WORK ...... 74 TABLE 5 INVERSIONS IN POSITION DUE TO THE TRUNCATION OF SCORES AWARDED IN THE DECATHLON FOR THE TOP 100 OF ALL TIME UPDATED IN 2010 IAAF WEBSITE ...... 75 TABLE 6 COMPARISON OF THE PERFORMANCE BETWEEN THE RESULTS OF THE 9TH AND 10 TH ATHLETE FOR THE HEPTATHLON OF ALL TIME UPDATED IN 2010 IAAF WEBSITE ...... 75 TABLE 7 DADOS DESCRITIVOS DE E_I NITIAL , E_F INAL , E_D ECREASE , E_I NCREASE , E_G AIN , V, VTO E HCM DA ATLETA FABIANA MURER DURANTE O TROFÉU BRASIL DE ATLETISMO ...... 93 TABLE 8 VALORES DO GRIP (M) PARA COMPARAÇÃO ENTRE AS SALTADORAS COM VARA NO MUNDIAL DE 2005 E OS DADOS DA SALTADORA FABIANA MURER EM 2008...... 94 TABLE 9 COMPRIMENTO DA CORDA DA VARA NO MOMENTO DE MÁXIMA DEFORMAÇÃO DA VARA E COEFICIENTE DE DEFORMAÇÃO DA VARA PARA DIFERENTES ATLETAS ...... 95 TABLE 10 VALORES DE VELOCIDADE MÉDIA DE APROXIMAÇÃO ENTRE AS ATLETAS FABIANA MURES E YELENA ISINBAYEVA ...... 95

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LISTA DE SIGLAS E ABREVIATURAS

AVI Audio video Interleave – formato de arquivo de vídeo CAPES Coordenação de Aperfeiçoamento de Pessoal de Nível Superior CCD (charge-coupled device ) dispositivo de carga acoplada – sensor de captação de imagens CBAt Conferação Brasileira de Atletismo CBT Computer Based Tracking: sistema de rastreamento COB Comitê Olímpico Brasileiro CM Centro de Massa CV Coeficiente de Variação DVideo Digital Vídeo for Biomechanics: sistema de análise biomecânica DLT Direct linear transformation: é um algoritmo que resolve um conjunto de variáveis de um conjunto de relações de similaridade para procedimentos de calibração e reconstrução tridimensional DTO Distância do takeoff E_Decrease Diminuição da energia mecânica total E_Final Energia mecânica final E_Gain Energia muscular E_Initial Energia mecânica inicial E_Increase Aumento da energia mecânica total E_MPB Energia mecânica no momento de máxima deformação da vara FAPESP Fundação de Amparo à Pesquisa do Estado de São Paulo GHPE Altura do grip (empunhadura) no momento de retificação da vara GHTO Altura do grip (empunhadura) no momento de takeoff HCM Altura máxima do centro de massa IAAF International Association of Athletics Federations (Federação Internacional de Atletismo) ISBS International Society of Biomechanics in Sports (Sociedade Internacional de Biomecânica do Esporte) GPS Global Positioning System (Sistema de Posicionamento Global) MPB Máxima deformação da vara OpenCV Open Source Computer Vision: biblioteca de programas e funções para visão computacional PR Momento de soltura da vara TO Takeoff do atleta VTO Velocidade no momento de takeoff %MPB Coeficiente de deformação da vara

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SUMÁRIO

Resumo...... 11 Lista de figuras ...... 15 Lista de tabelas ...... 17 Lista de Siglas e Abreviaturas ...... 19 Capítulo 1: Introdução...... 23 Capítulo 2: Measuring Handball players trajectories using an automatically trained boosting algorithm...... 27 Measuring handball players trajectories using an automatically trained boosting algorithm ..28 1. Introduction ...... 28 2. Description of the proposed method...... 32 2.1 Data acquisition and camera calibration...... 32 2.2 Training of the boosting detector algorithm...... 32 2.2.1 Training boosting detector using manually selected figures ...... 36 2.2.2 Training boosting detector using automatically selected figures ...... 37 2.3 Boosting detector...... 39 2.4 Tracking using the DVideo system ...... 39 3. Results and discussion...... 41 3.1 Evaluation of measurement uncertainty ...... 41 3.2 Evaluation of boosting tracking...... 42 3.2.1 Evaluation of selection and training times ...... 42 3.2.2 Evaluation of detection using manual and morphological segmentation training ...... 43 3.3 Evaluation of tracking ...... 45 3.4 Results of distances covered by handball players ...... 47 4. Conclusions ...... 49 Capítulo 3: Covered distances of handball players obtained by an automatic tracking method ...... 51 Covered distances of handball player obtained by an automatic tracking method ...... 52 1. Introduction ...... 52 2. Methods ...... 54 3. Results ...... 56 4. Discussion...... 58 5. Conclusion...... 59 Capítulo 4: Measurement of performance in combined events...... 61 Measurement of performance in combined events...... 62 Abstract...... 62 1. Introduction ...... 63 2. Model to evaluate performance ...... 64 3. The current scoring method...... 70 4. Results ...... 73 5. Discussion...... 76 6. Conclusion...... 78 Capítulo 5: Análise descritiva da energia mecânica do salto com vara da melhor atleta brasileira...... 79 22

Análise descritiva da energia mecânica do salto com vara da melhor atleta brasileira...... 81 1. Introdução...... 82 2. Metodologia...... 85 2.1 Participante ...... 85 2.2 Coleta de dados...... 85 2.3 Calibração...... 85 2.4 Medição ...... 86 2.5 Análise dos dados ...... 86 2.6 Estatística...... 92 3. Resultados...... 93 3.1 Individual da atleta brasileira ...... 93 3.2 Dados descritivos...... 94 4. Discussão e implicações ...... 96 5. Conclusões...... 100 Agradecimentos...... 100 Capítulo 6: Conclusões e possibilidades futuras ...... 101 Referências Bibliográficas...... 105 Glossário...... 111 ANEXOS...... 113 23

Capítulo 1: INTRODUÇÃO

O esporte de alto rendimento não se limita mais à relação entre o técnico e o atleta. A simples observação e percepção subjetiva do técnico e sua intervenção não é mais suficiente como referência para corrigir ou melhorar o nível de desempenho de um atleta. Diversos estudos (Hughes e Franks, 2008) demonstram que esse tipo de observação subjetiva é muitas vezes impreciso e que a utilização da tecnologia pode ajudar a melhorar a qualidade das informações referentes ao desempenho de um atleta, fornecendo informações relevantes durante um jogo ou uma sessão de treinamento permitindo ajustes finos na técnica e na melhora das aptidões físicas de um atleta. Os recursos disponíveis nos dias atuais permitem a um treinador monitorar variáveis fisiológicas e bioquímicas durante uma sessão de treino ou ao longo de uma temporada: análises que definem os percentuais de aproveitamento de um determinado fundamento durante um jogo; posições táticas ofensivas e defensivas; avaliações psicológicas traçam o perfil de cada atleta; avaliações biomecânicas buscam entender a mecânica por trás de cada movimento fornecendo dados importantes sobre a mecânica do atleta. Além de todos esses recursos a engenharia também desempenha um papel muito importante providenciando materiais mais leves, mais aerodinâmicos que favorecem o desempenho de atletas, um exemplo são as roupas de natação que reduzem o turbilhonamento e o atrito do atleta com a água, as varas mais flexíveis no salto com vara, as sapatilhas de corrida ou até mesmo os sistemas computacionais desenvolvidos para auxiliar a arbitragem nas provas de corrida do atletismo ou até mesmo no futebol americano e no tênis de campo. Com toda a tecnologia disponível dando suporte a atletas e treinadores é possível obter informações mais precisas que subsidiam os profissionais da área de esportes no desenvolvimento de melhorias na preparação física de seus atletas. Sendo assim diversos autores (Bangsbo et al., 1991; Arampatzis et al., 1997,1999; Pers and Kovacic, 2000; Pers et al. , 2002; Okuma et al., 2004; Schade et al., 2005; Kristan et al., 2006, Figueroa et al., 2006) desenvolveram métodos de análise de desempenho de atletas baseados em sistemas de análise cinemática, sistemas esses que permitem monitorar através de câmeras de vídeo ou sistemas de cinemetria as ações executadas pelos atletas com o mínimo de interferência 24 no ambiente, permitindo assim obter variáveis e dados relativos ao desempenho dos atletas em situações de treino e competição. Nesse âmbito a avaliação do desempenho de atletas em esportes coletivos é de grande importância para preparação de equipes em campeonatos ou mesmo em fase de pré- temporada. Diferentes ferramentas são utilizadas para avaliar o desempenho desses atletas em situação de treino e competição para as diferentes capacidades físicas. Uma das ferramentas utilizadas pela biomecânica é a cinemetria, que consiste em registrar os atletas em diferentes ações durante jogos para avaliar variáveis de interesse com diferentes finalidades. Interesse especial tem sido dedicado ao rastreamento automático de jogadores com o foco na análise do movimento dos jogadores e do jogo. Uma das variáveis que pode ser analisada é a distância percorrida pelos atletas durante uma partida, essa informação pode ser utilizada posteriormente para um melhor planejamento dos treinos subsequentes e também para avaliar o desempenho individual de cada jogador durante a competição, bem como associar esse desempenho a variáveis fisiológicas. Análises individuais de atletas também foram conduzidas no âmbito do atletismo em especial no trabalho realizado por Bruggeman et al., 1997 com atletas de elite durante o campeonato mundial de atletismo em Atenas. O projeto em conjunto com a IAAF(International Association of Athletics Federations) realizou coleta de dados durante as provas de atletismo no mundial de 1997 com o objetivo de atualizar o banco de dados de parâmetros biomecânicos de atletas de elite, dar respaldo a técnicos e atletas com informações quantitativas relativa aos aspectos técnicos individuais, melhorar o conhecimento e os fatores limitantes para o desempenho atlético, gerar dados específicos referentes as técnicas conforme o gênero e dar suporte a mídia internacional para produção competente e atrativa na cobertura e apresentação dos dados científicos coletados. O objetivo principal deste trabalho concentra-se na utilização de métodos de avaliação em biomecânica e engenharia de computação, através da integração de diferentes metodologias e no desenvolvimento de métodos de análise de desempenho de atletas, principalmente em situações competitivas. Neste trabalho utilizamos três diferentes modalidades (handebol, provas combinadas e salto com vara) para aplicar as ferramentas desenvolvidas nesse trabalho. 25

Para cada uma das modalidades esportivas, foram desenvolvidos métodos de análise levando em consideração a especificidade e as variáveis biomecânicas mais importantes para a avaliação do desempenho dos atletas tendo como foco principal a utilização de recursos computacionais para uma melhor análise do desempenho nesses esportes. Cada capítulo desta tese é apresentado na forma de artigo, nos quais são abordados problemas específicos relacionados ao desenvolvimento de métodos e ferramentas de análise de desempenho para cada modalidade e as soluções propostas para análise de desempenho desses atletas nessas modalidades específicas. No capítulo 2 é abordado o problema relativo ao rastreamento automático de jogadores, problema este que vem sendo estudado nos últimos anos por pesquisadores tanto da área acadêmica como da área industrial, com considerável ênfase para mensurar as trajetórias dos jogadores através do rastreamento por imagens de vídeo. Interesse especial tem sido dedicado à análise de movimento devido às informações cinemáticas que podem ser fornecidas sobre o comportamento dos jogadores. Por exemplo, a distância percorrida por um jogador durante uma partida pode levar a uma melhora no planejamento dos treinos e na avaliação do desempenho dos jogadores ao longo de uma partida ou mesmo durante um campeonato. Considere, por exemplo, um jogo de handebol, que tem a duração de 60 minutos, o que representa 108.000 frames por câmera, filmando a uma freqüência de 30 Hz. Não há uma única solução automatizada que pode rastrear automaticamente ou lidar com todas as oclusões que ocorrem em um jogo de handball e muitas dessas oclusões acontecem em momentos chaves do jogo como uma “finta” e são parte inerente da modalidade. Aqui apresentamos um artigo que propõe e avalia um novo método de rastreamento para jogadores de handball baseado em um algoritmo de “boosting” (Barros et al., 2010). No capítulo 3 apresentamos uma aplicação do método de rastreamento automático proposto no capítulo 2, utilizando-o para quantificar as distâncias percorridas e as faixas de velocidade dos jogadores durante uma partida de handball. No capítulo 4 apresentamos uma nova proposta de avaliação do sistema de pontuação para provas combinadas no atletismo (Decatlo e heptatlo), uma vez que o sistema de pontuação atual da modalidade apresenta um viés relacionado à pontuação em cada um das dez provas conforme apontado por Westera, 2006. Esse viés provoca uma distorção no sistema de pontuação que privilegia algumas provas em relação a outras e vai 26 contra a proposta do decatlo que é a de determinar o atleta mais completo. Além disso, temos o problema relacionado ao truncamento das marcas e das pontuações devido à utilização de tabelas de pontuação. Sendo assim apresentamos uma solução simples, interpretável, uniforme e que pode ser automatizada evitando os erros causados pela utilização de tabelas de pontuação em provas combinadas. A solução proposta nesse capítulo foi apresentada previamente durante o First Joint International Pré-Olympic Conference of Sport Science (Freitas & Russomanno, 2008). No capítulo 5 apresentamos uma análise individual, na prova do salto com vara feminino durante o XXVII Troféu Brasil de Atletismo em 2008, avaliando variáveis cinemáticas e parâmetros energéticos utilizando um sistema de análise cinemática tridimensional, tendo como objetivo principal descrever a biomecânica do salto com vara da melhor atleta brasileira. Uma vez obtidos os dados cinemáticos referentes a melhor saltadora brasileira, esses foram comparados com os dados disponíveis na literatura das melhores atletas da modalidade no mundo quanto a energia mecânica do salto, com o objetivo de avaliar as diferenças de desempenho das atletas e possíveis características da atleta brasileira. No capítulo 6 apresentamos as conclusões e possibilidades futuras para utilização dos métodos propostos neste trabalho.

Capítulo 2: MEASURING HANDBALL PLAYERS TRAJECTORIES USING AN AUTOMATICALLY TRAINED BOOSTING ALGORITHM

Neste capítulo apresentamos o artigo “Measuring Handball players trajectories using an automatically trained boosting algorithm” publicado na revista Computer Methods in Biomechanics and Biomedical Engineering em 14 de dezembro de 2010 (Barros et al., 2010). O objetivo principal desse trabalho foi propor e avaliar um detector “boosting” em cascata treinado automaticamente, baseado em segmentação morfológica para rastreamento de jogadores de handball. O método proposto foi capaz de detectar corretamente 84% dos jogadores quando testado no segundo tempo do mesmo jogo onde foi treinado e 74% quando testado em um jogo diferente. Além disso, a análise do treinamento automático para um detector “boosting” revelou resultados relacionados ao tempo de treinamento do detector, que inicialmente aumenta com o número de imagens utilizadas, mas quando mais imagens foram adicionadas o tempo de treinamento diminui. A segmentação morfológica automática se mostrou um método rápido e eficiente de selecionar regiões na imagem para o detector “boosting” e permitiu uma melhora no rastreamento automático de jogadores de handball. Mostrando-se uma ferramenta útil para o rastreamento em modalidades coletivas com perspectivas e possibilidades de ser utilizada em outras modalidades de quadra ou campo para análise de desempenho de atletas. 28

MEASURING HANDBALL PLAYERS TRAJECTORIES USING AN AUTOMATICALLY TRAINED BOOSTING ALGORITHM

Ricardo M.L. Barros 1, Rafael P. Menezes 1, Tiago G. Russomanno 1, Milton S. Misuta 1, Bruno C. Brandão 2, Pascual J. Figueroa 2, Neucimar J. Leite 2 and Siome K. Goldenstein 2

1-Department of Physical Education, University of Campinas – Campinas - Brazil 2- Institute of Computing – University of Campinas – Campinas - Brazil

(Received 26 November 2009; final version received 14 May 2010)

The aim of the present paper is to propose and evaluate an automatically trained cascaded boosting detector algorithm based on morphological segmentation for tracking handball players. The proposed method was able to detect correctly 84% of players when applied to the second period of that same game used for training and 74% when applied to a different game. Furthermore, the analysis of the automatic training using boosting detector revealed general results such as the training time initially increased with the number of figures used, but as more figures were added, the training time decreased. Automatic morphological segmentation has shown to be a fast and efficient method for selecting image regions for the boosting detector and allowed an improvement in the automatic tracking of handball players.

Keywords: tracking; sport; biomechanics

1. Introduction

In the past few years, both academic and industrial researchers have been investing considerable effort measuring the trajectories of players in team sports through video tracking. A special interest has been directed to the use of tracking in sports motion analysis because the kinematical analysis can provide useful information about player performance. For instance, the distance each player covers within the match period can lead to better planned routines and to the evaluation of player performance during a competition. In sports-related applications, there are different constraints and goals in regard to mere academic researches. Achieving reasonable tracking is not enough. The user needs to use the application for long periods with accurate, robust and consistent results throughout different runs. Consider a handball game, which usually lasts 60 min, which accounts for 108,000 frames per camera. There is not a single automated solution that can track or automatically handle all complicated occlusion and serious clutter situations that occur in several key points during a match. Such problematic key points are often particularly 29 interesting moments for the behaviour and movement analysis of players. Some of the most widely used methods to obtain activity profiles and performances of team players are based on visual estimation of the distances covered during sporting matches, and most of the descriptions available were obtained using such approaches (Withers et al. 1982; Bangsbo et al. 1991; Mohr et al. 2003). The core task of these methods involves counting the number of strides taken during each discrete activity. This information is converted into distance, considering the length of an average stride for each type of movement (e.g. standing, walking, jogging and sprinting). Such methods are extremely time consuming and provide low spatial and temporal resolutions; moreover, most of them will not allow a simultaneous analyses of more than one player. Global positioning system (GPS) or radio-frequency technology within sensor– transmitters attached to athletes has also been tried (Hennig and Briehle 2000). However, the results for using such approaches have only been noticed during simulating or training situations, due to restrictions imposed by the handball rules over the use of such devices in official competitions. In Edgecomb and Norton (2006), the measurement of distances covered by players, acquired from a global positioning and a computer-based tracking (CBT) system, relying on a human recorder that mechanically follows player movements on a calibrated miniaturised playing field, was compared during an Australian football game. A separate recorder operating a special computer was required for each tracked player. This recorder tracked such a player continuously from an elevated, midfield position in the stadium and recorded his movements with a conventional mouse or a commercially available pen tablet. According to the authors, distances measured by experienced researchers using the CBT system were as accurate as the results of the GPS technology. Image processing and analysis have also been used for tracking, although the majority of these methods present only partial results. In Ohashi et al. (2002), only a single player was tracked per game. In Iwase and Saito (2004), all players were tracked, but only for short periods. In Toki and Sakurai (2005), all players were tracked for an entire game, but manually (frame-by-frame). The problem of tracking multiple players when occlusion and congestion are involved, especially when a scale must be considered, was addressed in Needham and Boyle (2001) but again, only partial results are reported.

Computer vision techniques have also been adopted in an attempt to develop efficient methods for tracking players during sports matches by Pers and Kovacic (2000) and Pers et al. (2002). Using CCD cameras with wide-angle lenses, mounted on the ceiling of a sports arena, these authors have developed, tested and optimised algorithms based on motion detection, template matching and colour-based tracking in their player’s tracker. The problem of labelling multi-targets was discussed in Nillius et al. (2006) and applied to soccer player tracking. The authors built a track graph describing the interactions between targets, explored the track graph and similarity measurements between the tracks to infer the most likely configuration of paths for all targets. Okuma et al. (2004) suggested a vision system algorithm based on a boosted particle filter for multi-target detection and hockey player tracking. This algorithm combines the strengths of two successful algorithms: it mixes particle filters and the cascaded boosting algorithm from Viola and Jones (2001). According to the authors, the already learnt boosting detector enables the quick identification of players when entering the scene, whereas the particle filter tracking algorithm enables the tracking of individual players. The training process of the boosting detector algorithm involves the selection of a large number of image regions containing the objects of interest (players, referee, etc.) and another set with figures of non-players. For example, Okuma et al. (2004) used a set of 6000 figures of players in different poses and another set of 100 images containing non- player objects in order to train the algorithm for a hockey game. The authors implemented a program for the detection of low-intensity regions (i.e. hockey players) surrounded by high- intensity regions (i.e. rink surface). However, they warned that the data supplied by such a simple script are not ideal for training. In two recent papers, we have proposed another successful approach for dealing with the automatic detection issue of soccer players in the analysis of video sequences. In the first (Figueroa et al. 2006a), we considered the problem of recovering background pixel information in order to segment and track objects in video images. The suggested solution involved a non-parametric morphological labelling operation, which considers light-ing changes and the fact that a given scene may include both slow and fast motion. The segmentation of soccer players has been based on the difference between image sequences and the corresponding background representation recovered. 31

In the second paper (Figueroa et al. 2006b), we introduced a video system (DVideo) as a tracking solution for all players during the entire game. This technique utilised a representation based on the graph theory, with nodes corresponding to the blobs obtained by image segmentation and with edges, weighted using the information on blob trajectory in the image sequence, representing the distance between nodes. A novel approach for treating occlusions involving the split of segmented blobs based on morphological operators was presented, as well as backward and forward transversals of the graph to maximise the number of frames tracked automatically. The method automatically located players in 94% of the frames processed, with a relative error of only 1.4% of the covered extension. When the automatic tracking failed, a user interface was available to complete the trajectories manually. The results for the distances covered by soccer players and other kinematical variables obtained using this approach were reported in Barros et al. (2007). The algorithms proposed in Figueroa et al. (2006a, 2006b) can automatically provide good accuracy in the segmentation of regions containing the candidate players (blobs). Furthermore, the use of graphs (Figueroa et al. 2004; Nillius et al. 2006) has proven very effective in solving players trajectory correspondence issues from one frame to the next. However, the application of morpho-logical segmentation steps to all frames, especially when splitting the blobs using (forward traversal) direct and reverse (backward traversal) directions, makes the algorithm time consuming. The present paper proposes and evaluates a new method for tracking handball players based on an automatically trained boosting algorithm. The method integrates the powerful algorithms proposed in Figueroa et al. (2006a, 2006b) with the advantages of the boosting detector (Okuma et al. 2004). The text is organised in two main sections. In the first one, we theoretically describe the basics of the suggested method and its implementation. In Section 2, the experiments for evaluating the method are described. The following evaluations were conducted: (1) evaluation of measurement uncertainty; (2) evaluation of the boosting detector training; (3) evaluation of detection rates; (4) evaluation of automatically tracked trajectories and (5) analysis of the distances covered by handball players during official games using the suggested method. 32

2. Description of the proposed method

2.1 Data acquisition and camera calibration

One male and one female match of a Brazilian regional handball championship, for players under 21 years old,

Figure 1 Synchronised cameras views used for tracking and measurement. were filmed with two digital video cameras (JVC GR-DVL 9500), which were installed at elevated positions on the bleacher. Each camera covered little more than a half of the field as shown in Figure 1. After recording, the video sequences were transferred to the PC and stored as an AVI file format (30 frames/s, with an image resolution of 720 × 480 and 24 bit colour resolution). The cameras were calibrated using the field’s known dimensions. These parameters and the position of the players in the video sequences were used to reconstruct the 2D coordinates of each player using the direct linear transformation method, as described in Figueroa et al. (2003).

2.2 Training of the boosting detector algorithm

The traditional boosting detector algorithm, introduced by Viola and Jones (2001), uses a cascade of AdaBoost classifiers, with a very low false negative rate, a decreasing rate of false positives and an increasing complexity per cascade level, in order to decide if a given rectangular region of the image matches the object of interest or not.

Consider that for each coordinate (x, y)of the image, there is a rectangle R w,h (x, y)with (x, y) as its top-left pixel, width w and height h. At any given run of the boosting detector algorithm, w and h are fixed. Consider that each rectangle is initially marked as a positive example (i.e. it contains the object of interest). The first cascade level has the most simple (and fastest) classifier. It can be applied over the entire image very quickly and unmark examples that are clearly negative. As every classifier has a low false negative rate, most or all positive examples will remain marked. Likewise, as it is a simple classifier, many negative examples will remain marked. The next cascade level uses a more complex (and slower) classifier, but it will be applied over fewer examples. After the last cascade level is applied over the remaining marked examples, hopefully, only the positive examples will remain. The boosting detector algorithm is usually applied many times over the image, using rectangles of different sizes (but with same aspect ratio), to detect objects of different scales. AdaBoost is a statistical technique to improve (hence the name boost) the classification power of weak classifiers, h t, to build a strong classifier

 T  = α H x)( sign ∑ htt x ,)(  t=1 

where at is a weight associated to each weak classifier. A weak classifier is a simple learning algorithm with the classification ratio over 50% for the binary classification problem (decided between is or is-not). Decision tree algorithms such as C4.5 (Quinlan 1993) are popular choices for weak classifiers. Many times a simple stump classifier, i.e. a tree consisting of only the root node, is enough.

The data for the training algorithm are presented as ( x 1, y 1) . . . ( x m, y m), where x i ∈ X is an instance of the input (e.g. a numeric descriptor extracted from a rectangular region of the image) and y i ∈ Y, Y = {- 1.1}, specifies the class of the input (e.g. player or not player). There is a weight, D t(i), associated to each training datum ( x i, y i) and a time t. The weight is used by the algorithm to emphasise inputs that are more difficult to classify. AdaBoost calls a weak classifier repeatedly in a series of rounds (t = 1, . . . ,T). The basic AdaBoost algorithm (Schapire 2002) is as follows: 34

1 Initialise D i)( = . t m

For t = 1 . . . T

• Train the weak learner using the data and D 1, resulting in h t : X →ℜ.

• Choose an αt ∈ ℜ. • Update the weights:

D i)( exp( −α hy (x )) = t tit i Dt+1 i)( , Zt

where Z is a normalisation factor, so that D + i)( = .1 t ∑i t 1 The output is the strong classifier H( x ) For the binary classification problem, usually

1 1− ε  a = ln  t , t  ε  2  t 

ε where t is the classification error. The bigger the T, the more complex the classifier becomes. The boosting detector algorithm uses an integral representation of the image that allows quickly extracting useful numeric descriptors. The integral image representation takes each pixel as the sum of the intensities of the upper left pixels, i.e. II (x,y) = xI y ),','( ∑ ≤ ',' ≤ yyxx where II (x, y) represents the integral image and xI y ),','( is the original image. The descriptors are calculated from integral image features as those of Figure 2. If Sj is the sum of the intensities of the pixels within a given rectangle, the value of the descriptor is

N x = B S , where B is 1 if it is a white rectangle and -1 otherwise. i ∑ j jj j 35

Figure 2 Integral image features (a) - (d)

Using the integral image representation, the descriptor of Figure 3(a) can be calculated with as few as six additions or subtractions. Figure 3(c) shows the integral image feature applied over an image.

Figure 3 Integral image feature applied over an image. (a) A rectangular region of the image. (b) A typical feature, where the sum of the intensities of the pixels on the white rectangle is subtracted from the sum of the dark rectangle. (c) The region with the feature overlaid.

The boosting detector algorithm was trained to detect handball players on the court, using a cascaded classifier with 21 layers at most. All image regions extracted from the video frames were scaled to a resolution of 6 × 15 pixels. The bounding rectangle of each region is adjusted so that all regions have the same aspect ratio. The training sets were obtained using either manual or automatic selection of figures. 36

2.2.1 Training boosting detector using manually selected figures

The group of manually selected figures of handball players for training the boosting detector used up to 5000 figures. This was identified as the manual (M) training group and was subdivided into six subgroups, for evaluating the effects of the large number of positive figures in the training. These subgroups were designated as M100, M200, M500, M1000, M2000 and M5000, based on the number of figures used for training. Each figure was selected by an operator as a bounded rectangular box around the player. Non-handball- player sub-windowswere also used to train the detector; these were generated from a set of 2869 image regions containing non-player objects (court and spectators). They were obtained by automatically extracting rectangles of different sizes, but with the same aspect ratio 2:5, from images of the court with no players in it. The number of regions is enough considering that the videos were shot on the same court. All figures were scaled to 6 × 15 pixels. 37

2.2.2 Training boosting detector using automatically selected figures

This second training group consisted of up to 15,000 figures, automatically chosen by morphological segmentation of blobs in a video sequence of a handball game. This group (A) was also divided into subgroups, with the eight automatically selected groups identified as A100, A200, A500, A1000, A2000, A5000, A10000 and A15000, also based on the number of figures used for training. The figures of the smaller groups were drawn from the A15000 group. The same non-handball-player sub-windows were used. The morphological segmentation method used in the automatic selection of figures (blobs) in order to train the boosting detector, represented in Figure 4, consists of (a) Loading the video sequence. (b) Definition of image boundaries by an operator in the first sequence frame. (c) Background extraction by applying a median filter to the pixels of a set of consecutive frames, thus, regularly updating the background image of those frames, with the intensity of each background pixel calculated as the mean of the most likely repeated intensities of such set of frames. (d) Calculation of the difference between the image in the current frame and that corresponding to the extracted background. (e) Image binarisation by thresholding. (f) Morphological filtering (opening and closing) in order to eliminate noise. Labelling of the connected pixels and definition of the corresponding regions as blobs, using watershed operator. This morphological oper-ation defines a skeleton using zones of influence of the signal regional minima (the set of points with a given value m, such that its external boundary points are strictly greater than m). This skeleton constitutes the boundary of the zones of influence of the regional minima considered.

As it can be seen in Figure 4(f), the morphological segmentation provides a set of blobs, each containing at least one player. In order to avoid training the model with blobs containing more than one player, only those blobs smaller than a predefined size are used. Considering the fact that the figures required by the boosting detector algorithm have to be rectangles with a fixed aspect ratio, a correct bounding rectangle replaces the blob. Blobs are rejected if their scale does not match the scale expected for a handball player at its region on the image. This is done automatically using the homography between the image of the court and a virtual representation of the court with official dimensions.

Figure 4 Steps of morphological segmentation. (a) Load the video sequence; (b) definition of image boundaries; (c) background extraction; (d) difference between the current frame and background; (e) image binarisation and (f) morphological filtering and labeling.

Figure 5 shows the output of morphological segmentation and the input used in the boosting detector algorithm. All training sessions involved figures selected during the first half-time of the game, whereas the detection and tracking procedures were evaluated during the second half.

Figure 5 On the left, automatic segmentation; on the right, automatically generated positive examples for boosting detector training.

2.3 Boosting detector

When running the boosting detector, we limit the multiple scale searches to regions where each scale is possible. As we have done during training, we used the homography between the image of the court and a virtual representation of the court with official dimensions in order for this to be automatically done.

2.4 Tracking using the DVideo system

In order to compare the performance of the automatically trained boosting detector with that of the original DVideo segmentation procedures, the results of the two methods were introduced into the DVideo system and submitted to identical tracking procedures, which can be summarised as follows:

(1) Manual frame-by-frame tracking (done by humans) assumed to provide true trajectories and used to compare the results of the next two conditions (manual tracking). (2) Automatic tracking using the blobs detected by a boosting detector trained with 15,000 automatically selected Figures (A15000, boosting tracking). (3) Automatic tracking using the original DVideo algorithm with morphological segmentation, fol-lowed by the split of blobs using graphs in forward and reverse directions (DVideo tracking). 40

Graphs were then developed from the set of blobs obtained during the detection (boosting tracking) and segmentation (DVideo tracking) steps, so that nodes represent blobs, whereas edges indicate the distance among these blobs. Therefore, each node of the graph stores the spatial information of a blob, whereas the edges convey the temporal information related to the dependence of blobs. The tracking of each player is performed by minimal path searching through the graph. In addition to indicating the distance between blobs, the edges of the graph are weighted for information such as velocity, orientation and blob colour. In each step of the tracking method, the true 2D coordinates of the players on the court are reconstructed using calibration parameters and image coordinates. Figure 6 presents a flowchart of the overall processing.

Figure 6 Flowchart of the overall processing. 41

3. Results and discussion

3.1 Evaluation of measurement uncertainty

In order to estimate uncertainties in the determination of court positions, 22 points were measured manually, 10 times each, and the results were compared to the expected values. The mean 2D position of each point over the 10 repetitions was calculated, with the expected position obtained by direct measurement. Figure 7 shows the results of mean ± standard deviation of the distances between observed and expected positions in the different regions of the court.

Figure 7 Representation of uncertainties to measure and reconstruct positions (n=10) in 22 positions of the handball court. Mean ± standard deviation. Values are in metres.

The mean uncertainty involved in the determination of a position is 0.20 m. Considering that the field-of-view of each camera covers approximately half of the court (20 × 20 m), the relative uncertainty is less than 1%, and can be considered as acceptable.

3.2 Evaluation of boosting tracking

In this section, we have analysed the time spent in the manual and automatic selection of figures for the training of the boosting detector (selection time), as well as, the time spent in manual and automatic training (training time). These procedures were executed on a Pentium 4 PC (3.0 GHz, 2 GB RAM) running on Microsoft Windows XP.

3.2.1 Evaluation of selection and training times

Manual selection involved approximately 1250 figures per hour, or 0.35 figures per second. Of course, this process is extremely tedious and time consuming. The use of automatic selection of figures using the morphological segmentation algorithm suggested in this paper dealt with approximately 24 figures (blobs) per second. The training time required for using these figures is shown in Figure 8.

Figure 8 Manual (M) and automatic (A) training times of the boosting detector for handball players localisation. The number beside the letter M or A indicates how many figures were used for training.

In both manual and automatic training times, the increase of figures (blobs) initially increased the training time, although later on the time decreased. The time required to train the boosting detector was maximal with the use of 1000 figures, for both manual and automatic training. One possible explanation for this is that, for our application, the cascaded boosting detector algorithm converges more rapidly when a larger number of figures are used for training. In general, the time required for training with manually selected figures is less than that with the automatically selected ones, due to the better quality of the manual selection. Interestingly enough, the time required for training the boosting detector algorithm with 15,000 automatically selected figures is almost the same as that with the use of 100 manually selected figures.

3.2.2 Evaluation of detection using manual and morphological segmentation training

The effect of using manual and automatic training on the boosting detector and varying of the number of figures used in training can be analysed in Figure 9. It is important to emphasise that the algorithm was trained during the first period of a game, whereas detection was tested during the second period of that same game. The larger the number of figures (blobs) used for training, the smaller the accumulated error in detection, regardless of training kind. The relationship between the number of images analysed and the accumulated error is approximately linear. This information can be useful in planning the number of figures that are necessary for the training process. Those periods in the sequence with non-linear behaviour between variables were analysed and revealed that game dynamics may have a slight effect on results. The transition phase, as players pass from defence to attack, as well as player agglomeration or simple pauses in the game may result an increase or decrease in the detection rate. 44

Figure 9 Accumulated error of the boosting detector in function of the number of images analysed for manual (M) and automatic (A) training, with different sizes of training set. Errors in pixels.

Figure 10 shows the percentage of successful detection as a function of the number of figures used for manual and automatic training. In general, the manual training provides better results than that using automatic selection if the number of figures remained constant. Such better results were to be expected and can be explained by those situations in which the automatic selection of figures introduces false positive figures during training, a problem avoided by the manual selection. The training using automatic morphological segmentation has achieved the highest detection rate (82%) with the use of 15,000 figures. 45

Figure 10 Percentage of successful detection for manual and automatic trainning

3.3 Evaluation of tracking

Figure 11 shows the x-coordinate (main court direction) of the trajectory of a single player as a function of the frames analysed for 3 min, using manual tracking, boosting tracking and DVideo tracking. Figure 12 shows the y-coordinate for the same situations. Data were filtered using a third-order Butterworth digital filter.

Figure 11 Motion of one player (x-coordinate) in function of frames analysed over 3min by manual, boosting and Dvideo tracking 46

Figure 12 Motion of one player (y-coordinate) in function of the frames analysed over 3min by manual, boosting and Dvideo tracking.

In both figures, the curves present a similar shape revealing similarity of results when using different tracking conditions. Table 1 allows the quantitative comparison of the trajectories of four players tracked during the same 3 min of the game. The mean percentage of the absolute difference from the manual measurements and that segmented by the DVideo system was 2.2% and the maximal percentage error reached was 7.8%. The booting tracking presented better results considering both the mean percentage differences (1.8%) and the maximal error (3.6%). It is, however, necessary to remember that the filter can affect the three sets of data differently; therefore, these results should be carefully analysed. The percentage of frames automatically tracked was 67% with the DVideo tracking and 84% with the boosting tracking. This result can be considered a great advance regarding the manual and current automated methods applied to handball matches. Better results were previously obtained when the same system was used to analyse soccer players, with mean of 94% with automatic tracking (Barros et al. 2007). The reduction observed here is probably related to the peculiarities of handball games. Further improvements can probably be achieved by positioning cameras in both sides of the court or at the ceiling, as suggested by Pers and Kovacic (2000). 47

3.4 Results of distances covered by handball players

Figure 13 presents the trajectories of six players over the first halt-time (30 min). Player 4 was replaced by player number 8 and, therefore, their trajectories were merged. The representation allows individual and collective analyses by the team staff about the tactical performances of players. For instance, the defensive and offensive team strategies can be identified by the team staff considering the region of the pitch that has been most frequently visited. The results in Table 1 showed that the tracking of player 7 was particularly difficult using the DVideo tracking. One possible explanation can be found looking at Figure 14, which shows that such a player has the pivot function in the team, therefore always playing in a region of great congestion, in the middle or behind the opposite defence. Figure 14 presents the distances covered by outline players of both teams in the first and second half of the match. It is important to emphasise that this kind of simultaneous results for all outline players, during the whole game, obtained not in simulated but in actual competition condition, was not found within the literature. Furthermore, the distances covered provide useful information about the physical performance of players and it can be used for better planning the training process. Table 1 Distances covered by six players during 5 min of game calculated from the data obtained by manual, boosting and Dvideo tracking. The percentage differences from Dvideo and boosting tracking compared to manual tracking are indicated in brackets.

Player Distance covered (m) number Manual Dvideo Boosting tracking Tracking Tracking 2 440.4 436.5 (-0.8%) 440.8 (0.1%) 3 447.3 454.7 (1.6%) 432.5 (-3.3%) 4 381.4 378.3 (-0.6%) 390.8 (2.1%) 5 325.5 318.3 (-1.6%) 341.8 (3.6%) 6 367.2 370.6 (0.7%) 367.0 (0.0%) 7 435.2 470.2 (7.8%) 443.2 (1.8%)

Figure 13 Trajectories of handball players in the first half-time (30 min). Defence on the right side.

Figure 14 Distances covered by players of teams A and B in the first and second half-times of a handball game. 49

4. Conclusions

In this paper, we have evaluated and compared the use of a boosting detector, the publicly available OpenCV implementation, in the task of tracking, for a long period, handball players in official matches, with no controlled environment or lighting. The mean uncertainty to determine absolute position in the handball court using the suggested vision system is 0.20 m and the relative uncertainties are less than 1% and can be considered acceptable. The use of automatic selection of figures using the morphological segmentation algorithm proposed in this paper dealt with approximately 24 figures (blobs) per second as opposed to 0.3 figures per second provided by manual selection. The increment of figures in the training process did not cause always the increment in training time, as could be expected, because greater and better set of figures given for training will provoke a faster convergence of the cascade boosting detector algorithm. The time spent for automatically training the boosting detector algorithm with 15,000 figures is almost the same needed for training using 100 manually selected figures. The larger the number of figures (blobs) used for training, smaller will be the accumulated error in detection, regardless of training kind, and the relationship between the number of images analysed and accumulated error is approximately linear. The highest successful detection rate (82%) was provided by the boosting detector trained with automatic morphological segmentation using 15,000 figures. The use of automatic morphological segmentation showed to be a fast and efficient method for training the boosting detector. The percentage of frames automatically tracked was 67% with the DVideo tracking and 84% with the boosting tracking. The complication factor of the boosting algorithm is training and building the appropriate training set. To address this question, we used a boosting detector trained for the above situation to track a female handball match, recorded on a different day under distinct camera and illumination conditions with players using uniforms with different luminance and colour patterns. This experiment held an average detection rate of 74% (compared to a 5-min manually detailed sequence). As expected, the accuracy decreases, as the training is no longer specialised for the game conditions, 50 nevertheless, this shows the incredible potential of the application of cross-training boosting detectors. Although these results can be considered a great advance compared to manual methods, further developments are required due to the large number of frames to be manually measured or corrected. Official sports events pose a series of difficulties for the use of computer vision. Most of the time, there are severe restrictions on where you can place your cameras. Additionally, there is no control over the colours or patterns of uniforms and equipment used by athletes. In the examples we used in this paper, it is very difficult for a human to distinguish between two different teams. The strength against variation in the video quality is also something not entirely explored within the literature, and deserves a lot of further work. Additionally, little is described on the computer vision literature regarding the qualitative nature of the algorithms failures, and how to proceed in a real system when they eventually occur. In sports analysis, this means human intervention, and not all errors are treated equally. New methodologies to measure accuracy and false negatives have to be developed in order to take this into account.

CAPÍTULO 3: COVERED DISTANCES OF HANDBALL PLAYERS OBTAINED BY AN AUTOMATIC TRACKING METHOD

Neste capítulo apresentamos o artigo “Covered distances of hanball players obtained by an automatic tracking method.”, apresentado no 25° Congresso da Sociedade Internacional de Biomecânica do Esporte ISBS em Ouro Preto no ano de 2007 (Russomanno et al, 2007). O objetivo principal desse trabalho foi propor um método de obtenção das distâncias percorridas por jogadores de handball e suas velocidades durante um jogo utilizando uma nova abordagem baseada no rastreamento automático descrito no método de Figueroa et al. (2006a, 2006b) e o detector Adaboost (Okuma, 2004). Esse trabalho mostra uma possibilidade de aplicação do método de rastreamento automático apresentado no capítulo 2, e apresenta uma forma de avaliar o desempenho de atletas durante uma partida de handebol utilizando um novo método de rastreamento, visando obter as variáveis relativas às distâncias percorridas dos jogadores nos dois períodos do jogo e às faixas de velocidade em que esses atletas permanecem ao longo de uma partida oficial. Os resultados obtidos nesse trabalho são importantes para a avaliação de desempenho da equipe e do desempenho individual de cada jogador e para o planejamento da equipe em uma temporada de jogos ou ao longo de um campeonato, fornecendo dados precisos sobre o posicionamento de cada jogador ao longo de uma partida de handebol.

COVERED DISTANCES OF HANDBALL PLAYER OBTAINED BY AN AUTOMATIC TRACKING METHOD

Tiago G. Russomanno 1, Milton S. Misuta 1, Rafael P. Menezes 1, Bruno C. Brandão 2, Pascual J. Figueroa 2, Neucimar J. Leite 2, Siome K. Goldestein 2, Ricardo M. L. Barros 1 1Laboratory of Instrumentation for Biomechanics – College of Physical Education – University of Campinas – Campinas – Brazil 2Institute of Computing – University of Campinas – Campinas - Brazil

The aim of this work is to obtain the distances covered by handball players and their velocities during a match using a new approach based on automatic tracking method described in Figueroa et. al. (2006a, 2006b) and the Adaboost detector (Okuma, 2004). A whole game of a Brazilian regional handball championship for players under age of 21 was recorded. Applying the mentioned automatic tracking, the accumulated covered distances and the velocities were calculated for all the players. The results of average covered distances ( ±SD) in the 1 st and 2 nd halves were 2199( ±230) and 2453( ±214). The results of covered distances and the velocities allow individual and collective analyses of the players by the team staff. The proposed method revealed to be a powerful tool to improve physical analysis of the handball players.

KEY WORDS: automatic tracking, handball, biomechanics, covered distance

1. Introduction

Tracking players in team sports has been conducted with many different purposes. Special interest has been devoted to tracking sport players automatically focusing the motion analysis of the game and the players. The distance covered by players during a match can be used for better planning of subsequent training periods and also to evaluate the player performance during competitions. A tracking method based on an automatic video was presented in Figueroa et al. (2006). The method provides automatically the soccer players position in function of time in 94% of the processed frames. The relative error was 1.4% in the determination of the covered distance. An interface was used to complete the trajectories manually when automatic tracking fails. This system was developed in the Laboratory of Instrumentation in Biomechanics of the State University of Campinas (Brazil) and it was denominated DVideo. 53

Another solution based on computer vision techniques was used with the purpose of developing efficient methods for tracking players in sports (Pers and Kovacic, 2000; Pers et al. , 2002; Kristan et al., 2006). Using CCD cameras with wide-angle lenses mounted to the ceiling of a sports hall, these authors developed, tested and optimized different algorithms for players tracking. In Okuma et al. (2004), the authors proposed a vision system based on a Boosted Particle Filter for multitarget detection and tracking hockey players. The algorithm combines the strengths of two successful algorithms: mixture particle filters and cascaded Adaboost algorithm of Viola and Jones (2001). According to the authors, the learned Adaboost proposal distribution allows to detect quickly players who are entering the scene, while the filtering process enables to keep tracking the individual players. Considering advantages and drawbacks of previously mentioned approaches, this paper aims to obtain the distances covered by handball players and the velocities during all the match using a new approach based on an automatic tracking method described in Figueroa et al. (2006a, 2006b) and the Adaboost detector (Okuma, 2004).

2. Methods

A whole game of a Brazilian regional handball championship for players under age of 21 was recorded by two digital video cameras (JVC GR-DVL 9500), which were installed at bleachers in elevated positions. Each one them covering approximately one half of the court, but with an overlap for certain areas (Figure 15). After recording, the video sequences were transferred to a PC and stored in AVI file format (30 frames/s, with image resolution of 720x480 pixels). The cameras were calibrated using the court’s known dimensions and the 2D coordinates of player’s positions, which was reconstructed according to procedures described in Figueroa et. al.(2006) The novel approach presented in this work to obtain the kinematical variables is based on the automatic tracking method presented by Figueroa et al. (2006a, 2006b) and also on Adaboost classifier. The first one consists in the tracking using a representation based on graph theory and the other one consists in the detection of the players. After measuring the player’s positions in the video sequences, the 2D coordinates of the players related to the court game are reconstructed using an image-object transformation method (Direct Linear Transformation).

Figure 15 A) image of the players; B) image of the court without the players; C) Image segmentation results; D) Automatic tracking results.

Applying the mentioned automatic tracking method, all players were tracked in the whole match. The covered distance was calculated as the accumulated sum of the player’s displacement between two successive time sample (0.016s). Using the time-position curve obtained for each player, the time-velocity curve was numerically derived. According to this new curve the spent time of each player was classified in five types of movements based on the work proposed by Misuta (2004): standing - displacements with velocities from 0 to 0.2 m/s; walking - displacements with velocities from 0.2 to 2 m/s; jogging - displacements with velocities from 2 to 4 m/s; running - displacements with velocities from 4 to 6 m/s and sprinting - displacements with velocities higher than 6 m/s. The players were then classified in six positional groups: right backcourt player (RB), left backcourt player (LB), center backcourt player (CB), left wing player (WP), right wing player (RW) and pivot (P).

3. Results

The average results of covered distances and the time spent in each one of the types of movements were presented considering only the players that participated in the whole match (n=9 players). The results of covered distances by the players in function of time are shown in the figure 16. This representation distinguishes between individual player’s performances. As noticed in this match, the right wing player (RW) of the team A and B had a better performance than other players during the whole match. It is also possible to recognize specific situations of the game. For example, the curves of all players presented a little plateau around the minute 22 for team A and B (Figure 16). This means that the reduction of the average velocities and this is caused by specifics situations as many sequences of free throws and finalizations with a 7-meters throw.

Team A Team B 6 6

RW 5 WP / CB 5 RW LB / WP RB / LB CB / RB 4 P 4 P

3 3 [Km] [Km]

2 2

1 1

0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 [minutes] [minutes] Figure 16 The accumulated covered distances by the players of the teams A and B. The players are identified as right backcourt player (RB), Left backcourt player (LB), Centre backcourt player (CB), Left wing player (WP), right wing player (RW) and Pivot (P). The respective players CB, RB (team A) and CB (team B) were substituted during the game.

The results of average covered distances (±SD) in the 1 st and 2 nd halves were, respectively, 2199m (±230m) and 2453m (±214m) considering only the players that took part of the whole match (n=9 players). The shortest and the longest covered distance in the 1st half was respectively 1845m and 2506m and in the 2nd half was 2018m and 2693m.

Team A 0-0.2 m/s Team B 0-0.2 m/s 80 0.2-2 m/s 80 0.2-2 m/s 2-4 m/s 2-4 m/s 70 4-6 m/s 70 4-6 m/s 6-10 m/s 6-10 m/s 60 60

50 50

40 40

30 30 [percentage time] [percentage [percentagetime] 20 20

10 10

0 0 WP *CB *RB RW LB P RW *CB LB RB WP P

Figure 17 Percentage of time spent in each type of movement during the game. The following players CB, RB (team A) and CB (team B) were substituted during the game. The results of the percentage of time spent in each one of the types of movements are shown in figure 17. The time averages spent by team A were: standing (840 seconds / 25%), walking (2280 seconds / 67%), jogging (180 seconds / 6%), running (7.2 seconds / 0.2%) and sprinting (zero / 0%). The results for team B were: standing (780 seconds / 24%), walking (2400 seconds / 70%), jogging (180 seconds / 5%), running (4.8 seconds / 0.1%) and sprinting (zero / 0%).

4. Discussion

In this paper, we presented the results referent to the covered distances in function of time and the percent of time spent in each type of movement for all of the outline players. These were obtained by an automatic tracking method. The automatic tracking method applied to the soccer by Figueroa (2006) was 94% automatic against 75% as presented in this work. This difference can be related to some of the following aspects: reduction of the match space in function of the size of the court and number of players; a great number of occlusions caused by great number of players during attack and defence. For a better player tracking aiming to increase the automatic tracking, more cameras should be used in the other side of the court. The results of average covered distance presented in this paper (4653m) are close to the one obtained by Pers et al. (2002) in a controlled game (4800m). The similarities and differences can be explained by the methodological differences among the studies, such as, the method used to obtain the covered distances. The percentage time spent in each type of movement was presented by Pers et al. (2002) as follows: 37% walking(velocities lower than 1.4 m/s); 31% light running( velocities between 1.4 and 3 m/s); 25% running (velocities between 3 and 5.2 m/s); 7% high speed running (velocities higher than 5.2 m/s). Comparing these results to the ones obtained by the method exposed in this paper, the differences noticed may have a relationship with the technical level and age of the players.

5. Conclusion

In this paper, the covered distances by handball players and the velocities in percentage time spent in five different types of movements were obtained using a novel and accurate video-based automatic tracking method. The representation allows individual and collective analyses of the players by the team staff. Furthermore, the distances covered give useful information about the physical performance of the players. The proposed method revealed a powerful tool to improve physical analysis of the game.

Acknowledgement Supported by Fapesp (00/01293-1, 00/07258-3 and 05/53262-6), Capes and CNPq.

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Capítulo 4: MEASUREMENT OF PERFORMANCE IN COMBINED EVENTS

Neste capítulo apresentamos o artigo “Measurement of performance in combined events”. Esse artigo é parte uma evolução do trabalho “Performance comparison in combined events” (Freitas & Russomanno, 2008), apresentado em 2008 durante o “First Joint International Pré-Olympic Conference of Sport Science” em Nanjing na China. As provas combinadas existem desde a Grécia antiga, uma das primeiras provas combinadas a serem disputadas era o pentatlo (corrida, salto, lançamento de disco, lançamento de dardo e luta). Atualmente o decatlo, é a prova que consagra seu campeão como o atleta mais completo. Mas o decatlo não é a única competição de provas combinadas. Podemos listar outras provas famosas como as corridas de aventura e triatlos, ou outras menos conhecidas como o pentatlo moderno, Gigatlon e o Multiatlon. Em todas essas provas o objetivo é achar o atleta mais completo, para isso é necessária a existência de um modelo de pontuação que permita comparar o desempenho em todos os eventos de modo uniforme. Para isso foram desenvolvidas tabelas de pontuação para cada uma das provas do decatlo e também para outras provas combinadas do atletismo, como o heptatlo. A idéia por trás das tabelas de pontuação do decatlo é bastante sofisticada. No entanto alguns autores (Westera, 2006) argumentam que essas tabelas têm um viés, propondo alguns métodos para corrigi-las. Mesmo assim, até hoje, ninguém discutiu o ponto principal do problema nas tabelas de pontuação do decatlo que é a diferença entre a pontuação individual, uma vez que a pontuação final é soma dos pontos obtidos em cada prova (combinação linear). O objetivo do trabalho é apresentar um novo método de pontuação que permita avaliar homogeneamente o desempenho dos atletas do decatlo, o método apresentado nesse artigo utiliza uma função logaritmo espelhado normalizado que facilita a livre escolha do gradiente (velocidade de crescimento) de acordo com as necessidades da competição. O método é simples, interpretável, uniforme em todos os eventos e pode ser utilizado para outras provas combinadas além do decatlo.

MEASUREMENT OF PERFORMANCE IN COMBINED EVENTS

Tiago Guedes Russomanno, Cezar Augusto de Freitas Anselmo e René Brenzikofer University of Campinas

Abstract Combined events exist since ancient Greeks, where the pentathlon (running, jumping, discus throwing, javelin throwing and wrestling) was disputed. Nowadays, the decathlon, composed by ten events contested in two days, considered its champion as the all-round athlete. Decathlon is not the only competition disputed in a “combined events” way. We can list the famous adventure races and triathlons, as well as some less known, like modern pentathlon, Gigathlon and Multiathlon. In all these competitions, if the all- roundness is the objective, it’s necessary to use a scoring model allowing compare performances in all events through a uniform manner. For this purpose, scoring tables have been developed for each of the events (in decathlon and other combined events in Athletics, like heptathlon). Despite of this, non athletics combined events also use the sum of times in each event to determine it’s champion, just allowing time scale measured events to be disputed (or including subjective scores or using non continuous and non progressive scores). The idea behind the scoring tables used in athletics combined events is quite sophisticated; however, [1] argues it appears to be cursed with unacceptable bias, proposing some methods to correct them. Even so, until nowadays, nobody has been discussing that the difference among the individual scores is in fact the soul of the subject, once the final score is the sum (linear combination) of events scores. Our method uses a normalized mirrored-logarithmic function which facilitates the free choice of its gradient (growth speed) according to competition needs. In addition, it allows comparison of amateur and professional individuals, once it uses a robust reference point unlike average point, and it turns possible the use of scoring tables in competitions not globally disputed, for which top 100 lists could be corrupted by poor performances. The method is simple, interpretable, and uniform over the events and enjoys the properties requested in Westera (2006) and Trkal (2007). Its purpose is not to compete with the proposals presented by Westera (2006), but to popularize the use of scoring tables theory in competitions out of world of Athletics. To emphasize this, the method has been used successfully in Multiathlon since 2003, objectively comparing events so different like athletics, swimming, cycling, apnea, climbing, canoeing, skating, archery and weight lifting. Keywords: combined events, multi-events, performance comparison, scoring tables, decathlon, triathlon, multiathlon 63

1. Introduction

The decathlon is one of the combined events in athletics that make up the Olympic athletics program together with the heptathlon. It consists of 10 separate events held on 2 consecutive days. Being performed on the first day: 100 m running, long jump (LJ), shot- put (SP), high jump (HJ), and 400 m running; on the second day: 110 m hurdles, discus throw (DT), pole-vault (PV), javelin (JT) and 1500 m running. The track events are measured in minutes and seconds and the field events (distances or heights) in meters and centimeters. Basically for each one of the events measured in time and distance the athletes are awarded by score point in a given table provided by the IAAF. Since the creation of combined events by ancient Greeks humankind tries to find one way to measure the performance of athletes in different events with the purpose of knowing which athlete is the best one. The modern combined events, such as the pentathlon and the decathlon, as we know them nowadays, started being considered as an olympic event at the 5th Olympic Games, in Stockholm (Sweden), and the original sequence of events was confirmed at the 1914 IAAF Congress, remaining unchanged since then. Nowadays the decathlon is still referred as the ultimate athletic competition. But somehow, we have competitions of combined events, such as triathlon, Gigathlon and Multiathlon, which purpose also tries point the best athlete in the world. The men and women who take part of such events are challenged to combine their best physical aspects and skills in order to be the best athlete. Regarding the decathlon, the basic idea is to determine the all round athlete. In order to achieve that, a well-founded scoring model is necessary to combine the performances at disciplines in a total score. If the objective is the all-roundness, it is necessary to use a scoring model that allows comparing performances in all events through a uniform manner. In athletics, scoring tables have been developed for each one of the events. Although, non athletics combined events also use the sum of times in each event to determine it is champion, just allowing time scale measured events to be disputed (or to include subjective scores or using non continuous and non progressive scores). The idea behind the scoring tables used in decathlon is quite sophisticated. On the other hand, these tables have been the subject of extended discussions about their fairness and validity. In first place, because the 64 points awarded for each event are based on a table that uses an IAAF formulae which are not readily available (Cox & Dunn, 2002). Secondly, the use of tables can lead to possible error in the data transferring (it occurs often in IAAF site). The truncations of the point’s award are another source of error that is even worse than the rounded points. Another item to consider is the amount of paper that the tables use for each event with a worse approximation, for example from 10 to 10 seconds in the 1500 m. In some occasions amendments have been made; however, Westera (2006) argues that it appears to be cursed with unacceptable bias, proposing some methods to correct them. Even so, until nowadays, nobody has discussed that the difference among the individual scores is in fact the soul of the subject, once the final score is the sum (linear combination) of events scores. The aim of our work is to purpose a new method to evaluate and measure performance in combined events based on a normalized mirrored-logarithmic function which facilities the free choice of its gradient (growth speed) according competition needs.

2. Model to evaluate performance

Models which set points to performances in sports need to satisfy some requirements, in order to minimize the chance of inverting positions of the athletes’ ranks. The first table developed for being used in combined events was linear in performance and dates of 1884. Find below some requirements that are used to select good models (requirements “a” to “d” are the most important ones) based on model proposed by Viktor Trkal in 1982(see appendix): a) Models should be performance increasing. It means that, the larger the performance is, the more points will be obtained. b) Models should be progressive (increasing gradient), because the larger a performance is, smaller the chances to supplant it. In other words, an improvement in a higher performance has to be more awarded than an equivalent improvement in a lower performance. 65

c) Models should be continuous to allow quantifying even small improvements in a certain performance, therefore reducing the possibility of ties. d) If all events have the same importance, models should provide a uniform base of comparison in all of them. In this way, could be required that models set approximately the same score to performances equally proportional to the record in each event. e) In combined events is not required that models measure singular performances. It may sound strange but models are used to compare performances in different events. Once the intention is to attribute scores in a reasonable scale then we need to use parameters like energetic demand or caloric intake. f) Models need to be easily interpretable; allowing calculating scores along the competition, is this way, helping athletes and coaches in its tactics. g) In general, final score is computed by adding scores obtained in each event. It means that the final score is a linear combination of partial scores. This requirement, together with requirements d) and e), allow observing an interesting property, discussed ahead (Figure 20). In order to illustrate the difficulty in selecting a good model, we can think about the simplest one: consider only two athletes and that the champion is the one who has more wins. A generalization of this model, when there are more than two athletes, is the sum of the positions from each competitor in each event. In this way, the champion clearly would be considered the one who has the smallest sum (similar to Formula 1 scores). Both of these models fail in three of the four more important requirements: a), b) and c). We can think in a model as a mathematical function, like a curve. So, for searching a model, we can start by setting the growth velocity of the curve. Find below some examples:

mb (1.1a) or − 1 log b m , (1.1b)

Where m denotes the athlete’s performance and b controls the growth velocity of the curve. Before we go ahead, we need to define two types of events: “the-larger-the-better” ones 66

(the higher the performance is, the larger the score, as in long jump) and “the-smaller-the- better” ones (the lower the performance is, the larger is the score, as in 100 meters sprint). If we set b>1, it becomes clear that Equation (1.1a) is ideal for events that are the larger the better ones, while Equation (1.1b) fits to the smaller the better events.

Another fact that must be clear is that events are in different scales (for example, it is easier to achieve 60 m in javelin throw than jump 60 m in the pole vault). Thus the scales must be normalized. One way to do this is by comparing the performances with a reference value, like the world record for the event. Then we get:

(m / r ) b (1.2a) or − 1 log(b m / r ) , (1.2b)

Where r is the record for the event, where the ratio is inverted to keep the signal of the gradient of each curve (requirement b). This choice satisfies, somehow, requirement d). Finally, for purely aesthetic matters, it can be use integer scores like 989 and 1253 instead scores 0.989 or 1.253. We can achieve that by including in the model a multiplicative factor R (in general R=1000):

R( m / r ) b (1.3a) or − R(1 logb ( m / r )) . (1.3b)

It is clear that R value does not impact the score ordering. We will adopt Equation (1.3b). The justification for this choice will become clear throughout the text. Once the requirements b), c) and d) (partially) set the behavior of the model in a singular event, we need to analyze their ability to measure performances in different events 67 in a uniform way. So we can ask: who should be considered the winner between two athletes when the first one is ten percent better than the other in one event while the second one is ten percent better than the first one in another event? If the competition involves only these two events and each event has the same weight, it is counter-intuitive not awarding them a tie. To verify this, let be Pi the score obtained in event i, which record is given by ri and mij the athlete’s performance j at event I, i is 1 or 2 and j is A or B labeling the athletes.

According this, we can set m1A = 1.1 m1B and m2B = 1.1 m2A . Thus,

m  1.1 m  =−1A =− 1 B PmR1( 1 A ) 1log b  R 1log b   , r1   r 1 

m   = − 1B P1( m 1 B ) R  1 log b    , r1  

m   = − 2 A P2( m 2 A ) R  1 log b    and r2  

m  1.1 m  =−2B =− 2 A PmR2( 2 B ) 1 log b  R 1 log b   . r2   r 2 

= + Set Pj Pm11() j Pm 22 ( j ) the athlete’s total score j at two events. So,

1.1 m   m  =−1B +− 2 A PAR() 1logb  R 1log b   r1   r 2  and

m  1.1 m  =−1B +− 2 A PBR() 1logb  R 1log b   r1   r 2  are the scores of each athlete and 68

PA()− PB () = 1.1m   m   m  1.1 m   −1B +− 2 A −− 1 B +− 2 A  = R1logb  R 1log b   R 1log b   R 1log b   r1   r 2   r 1   r 2           m11B− 111.1 m B + 1.1 mm 2 AA − 2 = Rlogb log b   log b  log b    r  r   r2   r 2   mm1.1  1.1 mm   11BB+ 22 AA = Rlogb  log b    rr11  rr 22   ()()()+ = −+ = = Rlogb (1/1.1) log b (1.1) R log bbb (1) log (1.1) log (1.1) R log b (1) 0. (1.4) As we can see in the examples, this property also ensures that the world recorder holders in each event obtain the same amount of points in their respective events, due to the fact we have used r in Equation (1.2). Until now we have been supposing that the events are the smaller the better (once b>1). If we plot Equation (1.3b) for the larger the better events, we get in contradiction with requirement a). So it’s necessary to find a way to correct this through an equivalent curve. If there exists a constant k such that P(m) = P(k-m) at neighborhood of m=r , we ensure that requirement a) is valid for two types of events in this neighborhood. It is easily see that k= 2r, so Equation (1.3) can be rewritten as

  ()()− + − 1−t  () = −  2r 1 t m 1  (1.5) P m R1 log b  ,   r  where P is the score (points) earned, R is a reference value (1000), b is the growth of the scoring curve, r is the event record for each category, m is the mark (individual performance) and t is the nature of event (1 or 0), the index t sets the nature of the events (t=1 to the-smaller-the-better events, usually measured in units of time, and t=0 to the larger-the-better events, usually measured in distance units). It can also be shown that for two performances m1 e m2, we have P() mP− () mP = () mP − () m the-smaller-the-better 1 the-smaller-the-better 2 the-larger-the-better 2 the-larger-t he-better 1 (1.6) .

What about the choice of b value? Until now all properties of equations (1.3b) and (1.5) does not depend on this parameter. So, we can freely set a value (since this value is the same for all events). One suggestion is to use a value that allows distinguishing, in a determined event, performances with small differences among them, like as one centimeter in shot put or one centesimal in 400 m sprint. 70

3. The current scoring method

At no time it was implicit the number of events for which the model is valid. Indeed, it can be used both in heptathlon, equivalent to decathlon female, as in the triathlon (a non IAAF sport). For the sake of comparison, we will use the decathlon, the most notorious competition of combined events and the heptathlon a female combined event, both are official competition of the IAAF and are Olympic events. The current scoring tables (see appendix) used for the combined events of athletics are the result of years of evolution. They are a great progress compared to the linear model or the model of positions. In order to compare the scores of events in the decathlon in a same graph (Figure 18) we must normalize the marks, as it is done in equations (1.2a) and (1.2b).

Scoring in all ten decathlon events

100m LJ 400m SP 110mH HJ 1500m DT PV JT

scoring

500 1000 1500 2000

0.6 0.8 1.0 1.2 1.4 m (standardized) Figure 18 Score curves of the decathlon for the 10 events using the IAAF ranking method.

In Figure 18 it is noticeable that performances, equally proportional to the record in each event, have different scores. Indeed, the own record (vertical gray line) has a score that changes according to the event. But the most important fact is that the curves have 71 different gradients. This means that one advantage proportionally higher in two performances is going to capture scores in different amounts, according to the scoring curve gradient. The same kind of behavior we can be observed for heptathlon curves, as showed in figure 19 indeed, the own record (vertical gray line) has a score that changes according to the event.

Scoring in all seven heptathlon events

100mH 200m HJ scoring 800m SP LJ JT 500 1000 1500 2000

0.6 0.8 1.0 1.2 1.4

m (standardized)

Figure 19 Score Curves of the heptathlon for the 7 events using the IAAF ranking method.

Figure 20 illustrates the model (1.5) applied to the 10 events of the decathlon. Note that we only have 2 curves (continuous lines) and that they are mirroring from one of another around the record. One fact for that usually is not given attention is that the final score is the accumulated sum of scores in each event (requirement g). This means that the score curves do not need to be the same and that only their respective gradients need to be the same instead. 72

In order to illustrate this fact, take a look in Figure 20. Consider that the model is represented by the green curve (for the-smaller-the-better events) and replace the red curve by the blue dashed one (for the-larger-the-better events). So, for two performances named m1 and m2 we have

*− * = Pthe-larger-the-better() mP 2 the-larger-the-better () m 1 −− −= (Pthe-larger-the-better ())( mkP 2 the-larger-the-better ()) mk 1 − Pthe-larger-the-better( mP 2 ) the-larger-the-better ( m 1 ), (1.7) where P* denotes the original model translated by k at the larger the better events. This property ensures properties (1.4) and (1.6).

Proposed model

all the-small-the-best events all the-larger-the-best events scoring 800 1000 1200 1400

an alternative scoring

0.6 0.8 1.0 1.2 1.4

m (standardized)

Figure 20 Score curves for the proposed method to evaluate performance in combined events.

4. Results

The results shown are based on the top 100 results of all time of the decathlon updated in 2010 at the IAAF website. Here we can see the difficulty of building scoring tables. Table 2 shows the top 10 positions using IAAF scoring tables (appendix) and Equation (1.5). Both models agree in the first 3 positions, with disagreements in 4 th , 5 th , 7 th , 8 th , 9 th and 10 th .

Table 2 Comparison of the two models for the first ten places of the top 100 of all time in the decathlon.

IAAF rank 1 2 3 4 5 6 7 8 9 10

Eq. (1.5) rank 1 2 3 5 4 6 12 9 7 8

In table 3 we compared the top 10 positions for top 100 results of all time in female heptathlon updated in 2010 at the IAAF website using IAAF scoring tables(appendix) and Equation (1.5) and we can see the same consequence for this comparison. Both models agree in the first 5 positions, with disagreements in 6 th , 7 th , 8 th , 9 th , and 10 th as shown in table 2.

Table 3 Comparison of the two models for the first ten places of the top 100 of all time in the female heptathlon. IAAF 1 2 3 4 5 6 7 8 9 10

rank

Eq. (1.5) 1 2 3 4 5 7 8 6 10 9 rank

Now, let’s consider just the comparison between the results of the 4 th and 5 th athletes for the decathlon of all times, as shown in Table 4.

Table 4 Comparison of the performance between the results of the 4th and 5th athletes for the decathlon of all times updated in 2010 in the IAAF website. Score T* is the points awarded by the athletes without truncation, Score IAAF is the points awarded based on the decathlon tables and Score Eq 1.5 is the points awarded based on the model proposed in this work.

Athletes Tomáš Dvorák year 2000 Roman Šebrle year 2004 Classification 4th (according IAAF) 5th (according IAAF) Event Performance Score T* Score IAAF Score eq 1.5 Performance Score T* Score IAAF Score eq 1.5 Winner 100m 10.54s 966.32 966 909.33 10.85s 894.87 894 881.81 4th Long Jump 8.03m 1068.83 1068 907.10 7.84m 1020.38 1020 889.00 4th Shot put 16.68m 893.75 893 766.70 16.36m 873.97 873 756.48 4th High jump 2.09m 887.39 887 869.84 2.12m 915.74 915 880.03 5th 400m 48.36s 892.27 892 892.43 48.36s 892.27 892 892.43 tie 110m 13.89s 989.25 989 927.59 14.05s 968.56 968 916.71 4th Discus throw 47.89m 827.04 827 712.59 48.72m 844.26 844 720.48 5th Pole Vault 4.85m 865.10 865 818.94 5.00m 910.91 910 838.31 5th Javelin 67.21m 847.38 847 738.19 70.52m 897.80 897 762.72 5th 1500m 4:42.33 min 666.19 666 700.74 4:40.01 min 680.73 680 708.57 5th Total 8903.50 8900 8243.50 8899.50 8893 8246.50

Analyzing the data of the decathlon showed in tables 2 and 4 and considering only the number of wins (discrete model), the champion would be the 5 th placed athlete, not in accordance to the IAAF model. Furthermore, if we consider how the performance of an athlete, in each event, is higher/lower in comparison to the respective performance of their opponent (ratio of efficiencies), we can conclude that the average performance of the 5 th placed is 0.2% more efficient than the respective performance for the 4 th placed, agreeing with the results expressed by Equation (1.5) model. However, if we look at the top 100 results from the decathlon following the model in use by IAAF and evaluate their accumulated scores with and without the truncation, we noticed a change in the results of 17 athletes. Table 4 shows some of these changes (inversions), demonstrating that they are not rare (more than 17% of the all). As shown in a case in which the athlete is displaced from 2 positions in the top 100 of all time (the 62 th one).

Table 5 Inversions in position due to the truncation of scores awarded in the decathlon for the top 100 of all time updated in 2010 IAAF website. Real 13° 12° 37° 36° 40° 41° 49° 48° 64° 62° position 8830.1 8830.5 8737.0 8739.4 8733.7 8734 8712.2 8713.4 8682.2 8682.5 Truncated 12° 13° 36° 37° 39° 40° 48° 49° 62° 63° position 8825 8824 8733 8732 8730 8730 8709 8707 8677 8676

As it was demonstrated in the above tables for the data of decathlon and to evaluate the effect of the method proposed in this paper, we also tested the following equation (1.5) with the heptathlon. For comparison of the marks achieved by the heptathlon athletes, we show in table 5 the 9 th and 10 th place of all time.

Table 6 Comparison of the performance between the results of the 9th and 10th athlete for the heptathlon of all time updated in 2010 IAAF website. IAAF 100mH LJ SP HJ 200m JT 800m Score Score Position IAAF Eq 1.5

9th 13”18 6.68 14.19 1.94 22”98 49.90 2’12”12 7001 5987.67 10th 13”11 6.63 14.84 1.93 23”65 51.62 2’12”67 6985 5989.09

winner 10th 9th 10th 9th 9th 10th 9th 9th 10th

Once again if we compare both models we come to the same results demonstrated in table 4. Furthermore, if we also look at the top 100 results from the heptathlon following the model used by IAAF and evaluate their accumulated scores with and without the truncation, we notice a change in the results of 58 athletes.

5. Discussion

As we can see the proposed model did not change the top 3 athletes in the top 100 of all time for both events (Decathlon and Heptathlon), basically because their performance are much higher than the others athletes, however if we take a look back at table 1, we can observe that the results of the top 10 athletes are affected by our method, that is confirmed in table 3 by the comparison between the 4 th and 5 th places and in table 5 by the comparison of 9 th and 10 th places in the heptathlon. Regardless the model used, it is important to consider fitting the mathematical precision. If, when calculating the score in an event, we just cut its values (truncation), this cut is able to spread an error enough to change the results of a competition at the end. Notice that we are not suggesting building score tables with 2 or 3 decimals to be used in the events, but that the final result takes into account the precision needed instead. Otherwise, it’s possible to make a change by 10 points (one point for each event) in the result of one athlete. It may seen that the cutting (truncation) it is not unfair, once the change reduces all performance results. Our method corrects the bias that exists in the actual IAAF score table model that can be seen in table 5. Furthermore our formula is easy to use, interpretable and uniform over the events and is available for use, different from the IAAF formulae which are not readily available (Cox & Dunn, 2002). This slight changes in position based on truncation made by the use of scoring tables do not have a great effect in all time top list, but this same bias can affect on national round or maybe in Olympic and World championship rounds deciding who will or will not represent a country. The sources of error generated by the IAAF score model not only cause the problem of changing positions by the truncation but also lead to errors generated by typing the marks as can been see in the IAAF website and the use of tables instead of a computer systems to compute the marks and to evaluate the results and the points awarded. Based on these findings the proposed method uses a normalized mirrored- logarithmic function which facilitates the free choice of its gradient according to competition needs. It can be used even in amateur competitions, where top athletes lists 77 may not be available. The method can also be used to identify strengths and weaknesses in athletes because it can be used as a tool to evaluate performance not only in the combined events but also in other activities and basic fundamentals of sports to evaluate athletes. The method is uniform over the events and enjoys the properties requested in Westera (2006) and Trkal (2007). Its purpose is not to compete with the proposals presented in Westera (2006) but to popularize the use of scoring tables theory and to present a homogenous system for evaluation performance in decathlon and in competitions out of world of Athletics.

6. Conclusion

Despite the results found in this article and pointed out flaws in the current decathlon scoring system, any change only can be done by the IAAF. The aim of this work was to show a way to evaluate and measure performance of the athletes in a uniform manner respecting the basic premise of the all round athlete. The acceptance of this method depends on the popularization of the scoring table’s theory and the discussion over individual performance, once the final score is the sum (linear combination) of events scores. The method has been successfully used in Multiathlon (currently consisting of 40 events in one day), comparing events as different as athletics, swimming, cycling, climbing, apnea and archery.

Acknowledgements

Thanks to the University of Campinas and district hall of Barão Geraldo for the support and realization of Multiathlon, which made possible the development of this work, and the collaboration of Conceição Aparecida Geremias, José Ribamar Macedo Costa and Carolina Usuda Tanoue. 79

CAPÍTULO 5: ANÁLISE DESCRITIVA DA ENERGIA MECÂNICA DO SALTO COM VARA DA MELHOR ATLETA BRASILEIRA.

Neste capítulo apresentamos o artigo “Análise descritiva da energia mecânica do salto com vara feminino da melhor atleta brasileira” a ser submetido à revista Sports Biomechanics. Este artigo faz parte de uma série de trabalhos realizados pelo Laboratório de Instrumentação para Biomecânica da Unicamp, que em conjunto com o Comitê Olímpico Brasileiro no ano de 2007 e 2008 e com apoio da Confederação Brasileira de Atletismo realizou uma serie de avaliações biomecânicas dos atletas brasileiros em competições de atletismo que faziam parte da preparação desses atletas para as olimpíadas de Pequim em 2008. Partes dessas avaliações foram apresentadas na forma de um relatório aos técnicos de cada modalidade e, em particular, os dados do salto com vara foram apresentados no 27° International Conference on Biomechanics in Sports (2009) no trabalho “3D Kinematical analysis of Brazilian female pole vaulters”. Porém neste capítulo em especial temos como foco a atleta Fabiana Murer que em junho de 2008 durante o troféu Brasil de atletismo bateu o recorde Sul americano do salto com vara feminino. O objetivo desse trabalho foi descrever a biomecânica do salto com vara da atleta brasileira e comparar com as melhores atletas da modalidade quanto a energia mecânica do salto com vara. Para o cálculo da energia mecânica do salto com vara foram utilizados os dados cinemáticos tridimensionais obtidos durante as finais do salto com vara no XXVII troféu Brasil de atletismo em 2008. A velocidade de aproximação da atleta durante seus 11 saltos teve um CV 1,2%, com uma velocidade média de take-off de of 7,72 m/s ± 0,20 m/s. A altura máxima atingida pelo centro de massa da atleta mostrou correlação significativa com a energia Final total (r= 0,82, P<0,01). O E_Gain da atleta brasileira foi de 1,18 ± 0,87 J/Kg, enquanto para as atletas durante a final do salto com vara feminino em Sydney foi de 5,74 ±1,63 J/Kg. Apesar dos baixos valores de E_gain a atleta apresenta altos valores de E_Initial e E_Final, com valores médios, respectivamente de 45,96 ± 0,82 J / kg e 47,14 ± 80

0,71 J / kg. Diferentemente das outras atletas ela apresenta um Grip mais alto, que lhe confere uma vantagem técnica em relação as outras saltadoras. Quando comparada com outras saltadoras com vara que figuram na elite da modalidade, a atleta brasileira está entre as mais velozes, o que lhe confere resultados expressivos no circuito mundial e a coloca entre as 5 melhores atletas atuais na modalidade. 81

ANÁLISE DESCRITIVA DA ENERGIA MECÂNICA DO SALTO COM VARA DA MELHOR ATLETA BRASILEIRA

TIAGO G. RUSSOMANNO, NATALIA ROSETTO, MILTON S. MISUTA, RENÉ BRENZIKOFER, RICARDO M. L. BARROS Faculdade de Educação Física, Unicamp

Resumo

O salto com vara é uma das modalidades mais técnicas no atletismo e um bom conhecimento da mecânica por trás dessa modalidade é essencial para a melhora no desempenho dos saltadores e para compreensão da modalidade, principalmente para atletas de alto nível. Recentemente o salto com vara feminino brasileiro alcançou resultados que o colocam entre as melhores atletas do mundo, contudo não existem dados sobre a biomecânica do salto com vara de tal atleta. O objetivo desse estudo é descrever a biomecânica do salto com vara da atleta brasileira e confrontar com as melhores atletas da modalidade focando na energia mecânica do salto com vara. Para o cálculo da energia mecânica do salto com vara foram utilizados os dados cinemáticos tridimensionais obtidos durante as finais do salto com vara no XXVII troféu Brasil de atletismo em 2008. A velocidade de aproximação da atleta durante seus 11 saltos teve um CV 1,2%, com uma velocidade média de take-off de of 7,72 m/s ± 0,20 m/s. A altura máxima atingida pelo centro de massa da atleta mostrou correlação significativa com a energia Final total (r= 0,82, P<0,01). O E_Gain da atleta brasileira foi de 1,18 ± 0,87 J/kg, enquanto para as atletas durante a final do salto com vara feminino em Sydney foi de 5,74 ±1,63 J/kg. Apesar dos baixos valores de E_gain a atleta apresenta altos valores de E_Initial e E_Final, com valores médios, respectivamente de 45,96 ± 0,82 J/kg e 47,14 ± 0,71 J/kg. Diferentemente das outras atletas ela apresenta um Grip mais alto, que lhe confere uma vantagem técnica em relação as outras saltadoras. Quando comparada com outras saltadoras com vara que figuram na elite da modalidade, a atleta brasileira é uma das mais velozes, com altos valores de E_Final e E_Initial, o que lhe confere resultados expressivos no circuito mundial e a coloca entre as 5 melhores atletas atuais na modalidade.

1. Introdução

O salto com vara é uma das modalidades mais técnicas do atletismo e vem sendo estudado na biomecânica, principalmente a partir da década de 60, onde as primeiras varas de fibras de vidro e colchões de espuma foram introduzidos na modalidade o que ocasionou uma melhora significativa nos recordes alcançados pelos atletas. A média de progressão do recorde passou de 1,63 cm por ano para 3,97 cm por ano com a introdução das varas de fibra de vidro (Anderson, 1997). Basicamente a modalidade consiste em saltar sobre um sarrafo utilizando uma vara flexível. Uma das principais diferenças entre o salto com vara e as outras modalidades de salto no atletismo, é que a transferência da energia de aproximação no início do salto acontece sem diminuição da energia total e podendo ocorrer em alguns casos um ganho de energia (Arampatzis et al. 1997). Em todas as outras modalidades de salto (salto em altura, salto triplo e salto em distância) ocorre uma grande redução da energia total do atleta durante a fase de transição da corrida para impulsão (Brüggemann et al., 1997). Essa diferença na transferência da energia total do atleta está relacionada à elasticidade da vara (Ekevad et al., 1997). Arampatizis et al. (1997) encontraram uma correlação alta entre a energia mecânica máxima do atleta no salto com vara e a altura máxima do centro de massa de saltadores com vara do sexo masculino durante o Campeonato Mundial de Atletismo em Atenas em 1997. Nesse estudo foram analisadas as trocas energéticas entre o saltador e a vara com objetivo de fornecer uma explicação para a altura alcançada. A importância das trocas energéticas no desempenho de saltadores de vara foi estudada por diversos autores, sendo considerado um aspecto relevante para os estudos biomecânicos da modalidade segundo (Arampatizis et al.,1999; Schade et al., 2000) . Angulo-Kinzler et al. (1994) avaliaram o desempenho de 8 atletas do salto com vara durante os jogos Olímpicos de Barcelona (1992), os autores calcularam o momento angular total dos atletas com o intuito de explicar as vantagens obtidas nos saltos pelos atletas campeões. Também se verificou que a altura do grip era um bom indicador de desempenho no salto. Além disso, os autores argumentaram que o posicionamento adiantado dos 83 quadris, bem como a aproximação do centro de massa do saltador com o sarrafo no momento de soltura da vara podem ser indicadores favoráveis para um bom salto. Schade et al. (2004) compararam a energia mecânica entre saltadores de elite do sexo masculino e feminino durante as Olimpíadas de Sydney em 2000, encontrando valores superiores de energia inicial, energia no momento de máxima deformação da vara e energia final para saltadores do sexo masculino. Concluíram que a técnica feminina de salto não é uma projeção da técnica masculina, mas sim uma nova forma de interagir com a vara flexível e com grande potencial de melhora nas marcas alcançadas. Estudo semelhante foi conduzido durante o Campeonato Mundial de Helsinque em 2005(Schade et al. 2005) e divulgado posteriormente com o objetivo de fornecer dados biomecânicos de atletas de elite no salto com vara e melhorar o conhecimento em relação aos aspectos biomecânicos da modalidade, nesse estudo foram avaliados os finalistas do sexo masculino e feminino. Frere et al. (2010) apresentaram uma revisão sobre a mecânica do salto com vara e apontaram as principais variáveis que influenciam o desempenho na modalidade durante as fases de aproximação, take-off, suporte da vara (penetração) e fase de vôo. Os autores afirmam que é fundamental um maior entendimento e compreensão da mecânica do salto com vara, pois se trata de uma modalidade complexa com vários fatores relacionados, que podem influenciar o desempenho durante um salto, dos quais se destacam a velocidade do atleta, energia potencial e cinética, energia elástica armazenada na vara, força e torque aplicados pelo atleta e o próprio design da vara. Vale ressaltar que existem poucos estudos na literatura que analisam saltadores de vara em competição, principalmente atletas do sexo feminino. Diferentemente do salto com vara masculino, o feminino somente se tornou modalidade olímpica no ano 2000, durante os jogos de Sydney. Apesar do começo tardio, o salto com vara feminino teve uma evolução considerável nos recordes da modalidade em um período tão curto de tempo, basta observar as marcas mundiais alcançadas pelas atletas 4,45m (1996) e 5,06m (2009). 84

Recentemente, uma das atletas brasileiras alcançou resultados em nível internacional no salto com vara feminino, constando entre as melhores atletas do ranking da IAAF (2° colocação IAAF, 2008), contudo não existem estudos biomecânicos realizados com tal atleta, o que justifica o desenvolvimento de estudos que descrevam a biomecânica do salto com vara feminino dessa atleta. O objetivo desse estudo é descrever a biomecânica do salto com vara da atleta brasileira Fabiana Murer e confrontar os dados obtidos com as melhores atletas da modalidade focando na energia mecânica do salto; descrever a mecânica do salto da atleta brasileira durante uma competição oficial; confrontar as variáveis e resultados com as atletas que figuram entre as 10 melhores do ranking da IAAF, tendo como foco a energia mecânica do salto com vara;

2. Metodologia

2.1 Participante Um total de 11 saltos da melhor atleta do Brasil e campeã da prova foram escolhidos para análise biomecânica, com saltos variando de 4,30m a 4,91m. Os dados foram coletados durante a final do salto com vara feminino no “XXVII Troféu Brasil Caixa de Atletismo” em São Paulo, Brasil em 2008.

2.2 Coleta de dados Os saltos foram gravados por 4 câmeras Basler (modelo A602fc), posicionadas ao lado direito do corredor da pista de aproximação, nas seguintes posições: duas câmeras para registrar os últimos metros da corrida de aproximação e o momento de máxima deformação da vara e outras duas para a fase de passagem sobre o sarrafo. As 4 câmeras foram conectadas e sincronizadas por hardware (genlock) através do mesmo computador com a frequência de amostragem de 100 Hz. Para cada um dos saltos da atleta foi registrada uma sequência de vídeo em cada uma das 4 câmeras.

2.3 Calibração Para a calibração utilizou-se um mastro de 5 m de altura com 9 marcadores distribuídos ao longo do mastro com distâncias conhecidas entre eles. O mastro foi registrado pelas 4 câmeras (sincronizadas) durante o processo de calibração que consistiu em posicionar verticalmente o mastro em 6 pontos pré-determinados. Esses pontos foram medidos diretamente no chão formando um referencial ao longo do corredor de aproximação em uma pista de atletismo certificada pela IAAF (classe I), totalizando um volume de calibração de 8m x 1,20m x 5m, com o sistema de referência tendo a origem localizado no nível da pista, na vertical do ponto mais profundo da caixa de encaixe. A acurácia na determinação das coordenadas espaciais na calibração foi melhor que 1 cm.

2.4 Medição As sequências de vídeo obtidas para cada um dos saltos foram medidas utilizando o sistema Dvideow (Figueroa et al. 2003). Digitalizaram-se na tela 18 pontos anatômicos de interesse, definindo 12 segmentos corporais da atleta: cabeça, tronco, braços, antebraços, coxas, pernas e pés ( Hanavan ,1964 ). As coordenadas tridimensionais dos 18 pontos de interesse foram calculadas utilizando o método DLT (Abdel-Aziz e Karara, 1971). Os dados cinemáticos foram suavizados por um filtro digital butterwotrh de 3ª ordem com uma freqüência de corte de 6 Hz para cada um dos pontos do modelo.

2.5 Análise dos dados A partir do conjunto de coordenadas suavizadas calculou-se a trajetória do centro de massa (CM) da saltadora, por meio do modelo proposto por Zatsiorsky e Seluyanov (1990), para cada um dos 11 saltos realizados pela atleta. A energia total do centro de massa da atleta ao longo do tempo foi calculada como a soma da energia potencial mais a energia cinética, conforme a equação 1: mv (t) 2 E ()()t = mgH t + CM Eq(1) CM CM 2 -2 onde, m é a massa da atleta, g é a aceleração da gravidade (g= 9,81 ms ), H CM (t) é a altura do centro de massa da atleta e v CM (t) é a velocidade do centro de massa da atleta em função do tempo t. A velocidade do centro de massa da atleta foi calculada através da derivada temporal da curva de posição do centro de massa. Os parâmetros energéticos foram calculados para a comparação das variáveis mecânicas em momentos pré-determinados do salto de acordo com estrutura de fases desenvolvida por Arampatzis et al. (1997). Neste trabalho também dividimos o salto em 4 fases distintas para análise de variáveis de descrição com objetivo de determinar avaliar o desempenho da atleta, sendo assim foram definidos os 4 momentos conforme ilustrado na figura 25: 87

1-Momento Inicial: caracterizada pela fase de corrida de aproximação do atleta, na qual foi calculada a velocidade média de aproximação da atleta (V) nos 10 metros finais da corrida. 2-Momento de Takeoff (TO): caracterizada pelo momento de impulsão do atleta em sua última passada, na fase de TO foram consideradas as variáveis de altura do grip no momento de takeoff (GHTO), Distância do takeoff (DTO), Velocidade de takeoff (VTO). • Altura do Grip no momento de takeoff (GHTO): distância vertical entre a ponta do pé de impulsão da atleta no momento de takeoff e o grip superior, conforme a figura 21; • Distância do takeoff (DTO): distância horizontal entre a ponta do pé de impulsão da atleta no momento de takeoff e a caixa de encaixe, conforme a figura 22; • Velocidade de takeoff (VTO): velocidade do centro de massa da atleta no momento de takeoff;

Figure 21 Altura do Grip no momento de takeoff (GHTO).

Figure 22 Distância do takeoff (DTO).

3-Momento de deformação da vara: caracterizada pelo momento de máxima deformação da vara, quando foi calculado o comprimento da Corda da Vara (MPB). • Corda da Vara (MPB): distância entre o grip superior e o encaixe da vara no momento de máxima deformação da vara, conforme figura 23;

Figure 23 Corda de Vara (MPB).

4- Momento de passagem sobre o sarrafo: caracterizado pela máxima altura do centro de massa do atleta (HCM), essa fase é precedida por dois momentos, um primeiro que é caracterizado pela retificação da vara (GHPE), e um segundo momento onde o atleta perde o contato com a vara (PR). • Retificação da vara (GHPE): momento no qual a vara retorna à sua forma retificada após a máxima deformação, neste instante é medido a altura do grip, conforme figura 24;

Figure 24 Retificação da vara (GHPE).

Uma vez obtidos essas variáveis o coeficiente de deformação da vara (%MPB) é calculado como a relação de encurtamento da corda da vara pela equação (2).

%MPB = (1-(MPB/GHPE)) X 100. Eq. (2)

As variáveis de energia mecânica foram definidas da seguinte forma, conforme ilustradas na figura (25): - A energia Inicial (E_Initial) : energia mecânica total da atleta na metade da última fase de vôo da passada de takeoff. - Energia Final (E_Final): energia total do atleta no momento de máxima altura do centro de massa. - Decréscimo de Energia (E_Decrease): diferença entre E_Initial da atleta e a energia total do atleta no momento de máxima deformação da vara (E_MPB). - Crescimento de Energia (E_Increase): diferença entre E_Final da atleta e E_MPB. -Ganho de energia (E_Gain): diferença entre E_Final da atleta e E_Initial da atleta.

V = velocidade de aproximação HCM VTO = velocidade de takeoff DTO = distância do takeoff GHTO = altura do grip no takeoff PR = soltura da vara PR GHPE = retificação da vara MPB = corda da vara HCM = altura máxima do CM

GHPE

GHTO

MPB V VTO

DTO

Figure 25 Esquema ilustrando as variáveis calculadas nos 4 momentos definidos para o salto com vara e o cálculo da energia total da saltadora com vara (adaptado de de Arampatziz et al. (1997).

A figura 26 apresenta as curvas de energia mecânica representadas pelas curvas de energia total, energia cinética e energia potencial do salto com vara da atleta Fabiana Murer, caracterizando as quatro fases de cálculo de energia mecânica e os quatro momentos para análise das curvas de energia mecânica do salto com vara. O primeiro momento (1) esta relacionado com o Decréscimo de Energia (E_Decrease) logo após o momento de takeoff da atleta, o segundo momento (2) é representado pela região de mínimo na curva de energia total caracterizando o momento de máxima deformação da vara (E_MPB), o terceiro momento (3) é a fase de crescimento da curva de energia total, relacionado ao Crescimento de Energia (E_Increase) e a quarto momento (4) é a fase onde a atleta solta a vara (PR), que no salto com vara feminino é caracterizado por um platô na curva de energia total, diferentemente do salto com vara masculino.

Figure 26 Curvas de energia mecânica do centro de massa característica do salto com vara feminino.

Para avaliar as qualidades técnicas da atleta, as variáveis obtidas nesse trabalho foram confrontadas com variáveis de mesma natureza de outras atletas em outros dois estudos sobre a biomecânica do salto com vara, especialmente os trabalhos de Schade et al. (2004 e 2005) tendo como um dos objetivos identificar possíveis semelhanças e diferenças ou possíveis vantagens técnicas entre os saltos da atleta brasileira e os saltos das outras atletas de nível internacional. 92

2.6 Estatística Um teste estatístico de Mann-Whitney (P<0.05) foi realizado para avaliar as médias das alturas saltadas pelas atletas em ambos os eventos para fim de comparação das variáveis calculadas. Também foi calculada a correlação de Pearson entre altura máxima do centro de massa da atleta e a energia final total da atleta em cada um dos saltos, com significância P<0,01. 93

3. Resultados

3.1 Individual da atleta brasileira A altura dos saltos (n=11) realizados pela atleta, durante a competição variou de 4,30m a 4,91m, são saltos de qualidade que estão qualificados entre os melhores saltos da temporada. A tabela 7 apresenta dados das variáveis relacionadas aos 11 saltos analisados da atleta e parâmetros individuais, incluindo as tentativas mal sucedidas e ordenadas em ordem decrescente. Os dados apresentados são referentes à velocidade média de aproximação, velocidade de takeoff e parâmetros de energia mecânica total da atleta durante os saltos. A altura máxima do centro de massa da atleta mostrou correlação significante com a energia final total da atleta (r=0,82, P<0,01).

Table 7 Dados descritivos de E_Initial, E_Final, E_Decrease, E_Increase , E_Gain, V, VTO e HCM da atleta Fabiana Murer durante o Troféu Brasil de atletismo. Sarrafo 4,91# 4,8 4,8# 4,8# 4,71 4,71# 4,71# 4,6 4,5 4,4 4,3 (m) E_Initial 45,92 45,32 46,85 46,87 46,51 46,86 46,56 45,64 45,3 44,17 45,56 (J/kg) E_Final 47,48 47,91 47,84 47,82 47,22 47,92 46,08 47,05 46,38 46,77 46,12 (J/kg) E_Decreas 18,77 19,31 19,59 20,48 19,79 19,08 17,93 18,30 17,66 15,59 16,48 e (J/kg) E_Increase 20,33 21,9 20,58 21,43 20,5 20,14 17,45 19,71 18,74 18,19 17,04 (J/kg) E_Gain 1,56 2,59 0,99 0,95 0,71 1,06 -0,48 1,41 1,08 2,6 0,56 (J/kg) V (m/s) 8,43 8,46 8,53 8,40 8,62 8,48 8,3 8,38 8,35 8,23 8,35 VTO (m/s) 7,81 7,86 7,64 7,90 7,84 8,03 7,37 7,78 7,75 7,44 7,52 HCM (m) 4,7 4,74 4,72 4,74 4,80 4,71 4,59 4,68 4,56 4,54 4,51 # salto em que atleta derrubou o sarrafo

A velocidade média de aproximação (V) da atleta no trecho final (10m) de corrida em seus 11 saltos durante o Troféu Brasil 2008 foi de 8,41 ± 0,10 m/s, com coeficiente de variação CV =1,2%. A velocidade de takeoff média foi de 7,72 ± 0,20 m/s. As variáveis de energia cinética total média inicial e final foram respectivamente de 45,96 ±0,82 J/kg e 47,14 ±0,71 J/kg. Já as variáveis de decréscimo e crescimento de energia foram 18,45 ±1,39 J/kg e 19,63 ±1,51 J/kg. O ganho de energia da atleta apresentou um valor menor da ordem de 1,18 ±0,83 J/kg. 94

Os valores médios de energia inicial, decréscimo de energia, crescimento de energia e energia muscular encontrados por Schade et. al. (2004) foram respectivamente 42,25J/kg, 13,10 ± 1,48 J/kg, 18,84 ± 1,48J/kg e 5,74 ±1,63 J/kg para as atletas do salto com vara feminino durante a final da competição.

3.2 Dados descritivos

A tabela 8 apresenta dados referentes à altura do grip da atleta brasileira (Fabiana Murer) em diferentes alturas e os dados do grip de outras atletas em alturas semelhantes, os valores são referentes aos dados coletados no mundial de 2005(*relatório IAAF). Table 8 Valores do grip (m) para comparação entre as saltadoras com vara no mundial de 2005 e os dados da saltadora Fabiana Murer em 2008.

Ano Sarrafo(m) Atleta Grip (m) 2008 4,30 Fabiana 4,28 2005* 4,35 Hingst 4,14

Agirre 4,22 Ellis 4,06

Rogoswska 4,22

2008 4,40 Fabiana 4,29 2005* 4,50 Gao 4,26

Polnova 4,04 Hamackova 4,29

2008 4,50 Fabiana 4,34

2005* 4,60 Pyrek 4,24 2008 Fabiana 4,38 2005* 5,01 Isinbayeva 4,37

2008 4,71 Fabiana 4,38

*relatório 2005 IAAF 95

A tabela 9 mostra os valores do comprimento da corda da vara e o coeficiente de deformação da vara utilizada pela atleta brasileira em três diferentes alturas saltadas (4,40m, 4,50m, 4,60m) em comparação com outras atletas com a mesma altura do sarrafo, nos jogos olímpicos de 2000 e no Mundial de 2005. Os valores menores encontrados para o comprimento da corda nos saltos durante os jogos olímpicos de 2000 estão relacionados ao tipo de vara utilizado pelas atletas nessa época.

Table 9 Comprimento da corda da vara no momento de máxima deformação da vara e coeficiente de deformação da vara para diferentes atletas. Ano Atleta Sarrafo(m) Comprimento da Corda MPB(m) %MPB 2000* Pyrek 4,40 0,78 18,8 2008 Fabiana 4,40 3,46 19,35 2000* Flosadottir 4,50 0,89 20,6 2005** Polnova 4,50 3,02 25,2 2008 Fabiana 4,50 3,36 22,5 2000* Dragila 4,60 1,10 26,0 2005** Pyrek 4,60 3,33 21,6 2008 Fabiana 4,60 3,27 25,3 * Journal of sport science, 2004, 22, 835-842; ** relatório 2005 IAAF.

A tabela10 apresenta as velocidades médias de aproximação da atleta brasileira em 4 diferentes alturas (4,50m, 4,60m, 4,71m, 4,80m)no troféu Brasil de 2008 e as velocidades médias de aproximação da atleta Yelena Isinbayeva em saltos com 4 diferentes alturas(4,50m, 4,60m, 4,70m, 5,01m) no mundial de 2005. A velocidade média (V) da atleta brasileira durante a competição em 2008 foi de 8,41 ± 0,10 m/s(n=11), enquanto a velocidade média da atleta Yelena Isinbayeva no Mundial de 2005 foi de 8,40 ± 0,09m/s(n=4). Table 10 Valores de velocidade média de aproximação entre as atletas Fabiana Mures e Yelena Isinbayeva. Ano Atleta Sarrafo(m) Velocidade(m/s) 2008 Fabiana 4,50 8,35 4,60 8,38 4,71 8,62 4,80 8,46 2005* Isinbayeva 4,50 8,33 4,60 8,49 4,70 8,47 5,01 8,31 * Relatório 2005 IAAF 96

4. Discussão e implicações

O presente estudo mostrou resultados inéditos da atleta brasileira. Os resultados apresentados são importantes, pois ajudam a compreender qualitativamente e quantitativamente melhor a modalidade do salto com vara feminino por meio dos dados obtidos por uma de suas principais representantes e fornece dados sobre uma das melhores atletas da modalidade (2ª ranking da IAAF 2008). Tendo em vista os resultados encontrados, podemos destacar que a atleta apresenta características diferenciadas em sua corrida de aproximação, na regularidade de sua velocidade de aproximação, na posição da sua mão no grip da vara, bem como seus parâmetros energéticos em relação a outras atletas que figuram entre as 10 melhores do ranking internacional durante a última década. Algumas dessas características encontradas como a E_gain podem futuramente influenciar a técnica da atleta e consequentemente em mudanças no resultado da atleta. Baseado nos dados encontrados na literatura em Schade et al.(2004, 2005) e nos resultados desse trabalho podemos avaliar variáveis importantes para o salto com vara feminino. Na tabela 10 podemos ver que as velocidades médias de aproximação da atleta Yelena Isibayeva e da atleta brasileira (2ª ranking da IAAF 2008), são muitos próximas, mesmo em diferentes alturas, o que confirma o nível de desempenho da atleta brasileira, se comparada com a melhor atleta do mundo e recordista mundial e olímpica na prova. Podemos verificar que a variabilidade da velocidade de aproximação da atleta em seus 11 saltos no troféu Brasil 2008 apresentou um coeficiente de variação de CV =1,2%, esse baixo valor de variação indica que a atleta já tem uma técnica de corrida de aproximação bem desenvolvida. Outra variável importante é a velocidade de takeoff da atleta, no caso a velocidade de takeoff média foi de 7,72 ± 0,20 m/s, um valor também muito estável com pouca variação, indicando também que atleta é muito veloz na sua fase de impulsão, com um decréscimo na velocidade horizontal do centro de massa de 0,69 m/s. Outros trabalhos (McGinnis, 1987, Gros and Kunkel, 1990 e Angulo-Kinzler et al., 1994) reportaram até 2 m/s de decréscimo na velocidade horizontal do centro de massa. 97

A altura máxima do centro de massa da atleta mostrou correlação significante com a E_Final (r= 0,82, P<0,01), o que corresponde com os dados de Schade et al.(2004) que encontrou (r=0,86, P<0,01) na final feminina e (r= 0,88, P<0,01) para a final masculina nas Olimpíadas de Sydney em 2000 e Arampatzis et al.(1997) para a final masculina do Campeonato Mundial de Atenas em 1997. Também observamos que a energia total da atleta brasileira permaneceu constante entre GHPE e PR, fato que foi observado por Schade et al. (2004) para as atletas finalistas do sexo feminino das olimpíadas de 2000, enquanto para os atletas finalistas do sexo masculino observou-se um leve crescimento na mesma fase em conseqüência do trabalho muscular diferenciado executado pelos atletas do sexo masculino. Em relação à altura do grip no momento de máxima extensão da vara (tabela 8) podemos verificar que os valores medidos para a atleta brasileira estão acima dos valores médios encontrados na literatura. Isso se deve principalmente a forma diferenciada da atleta brasileira em ter um grip mais alto, que lhe confere uma vantagem em relação às outras. Esses valores diferenciados na altura do grip podem ser um indicativo de vantagem técnica da atleta em relação a outras saltadoras. Angulo-Kinzler et al. (1994) verificou também em atletas do sexo masculino, que uma maior altura do grip juntamente com uma melhor utilização do momento angular pelo saltador é um bom indicador de desempenho do saltador com vara, confirmando os achados nesse estudo. Os valores de comprimento de corda da vara durante o momento de máxima deformação da vara são maiores dos que das outras atletas, apesar da %MPB dela ser melhor se comparado com outras atletas (tabela 9). Também pode ser observado que os valores de corda para os dados das Olimpíadas de Sydney em Schade et al. (2004) são menores devido à técnica utilizada pelas saltadoras com vara feminino na época e pelo tipo de vara utilizado. É importante notar que apesar da corda da vara da atleta brasileira ser bem maior que das outras atletas em Schade et al.(2004,2005), seu aproveitamento %MPB é muito similar. Isso se deve principalmente a altura do grip, que compensa essa diferença no comprimento da corda da vara no momento de máxima deformação da vara e do tipo de vara utilizado pela atleta brasileira. Deve-se destacar que a corda da vara serve como um indicador de aproveitamento da energia elástica da vara e quanto da energia cinética inicial 98 proveniente da corrida de aproximação foi de fato aplicada para deformar a vara. A interpretação e a avaliação desse parâmetro podem indicar que a atleta não usou todo o potencial elástico da vara ou que os níveis de energia aplicados sobre a vara estão abaixo dos valores de melhor aproveitamento da energia de restituição da vara. Contudo essa informação técnica depende muito do tipo de vara que a atleta esta utilizando (lenta ou rápida) e em nenhum dos trabalhos citados essa informação foi utilizada (Russomanno et al. 2009). Em relação aos parâmetros de energia mecânica total do salto com vara o objetivo principal do saltador é alcançar o maior nível de E_Final possível, para isso a energia gerada durante a corrida de aproximação deve ser transferida para a vara em forma de energia elástica. A respeito dessa troca de energia entre atleta e vara o salto pode ser dividido em duas fases delimitadas pelo momento de máxima deformação da vara (Arampatzis et al. 1997). Na primeira fase, o atleta transfere energia para a vara enquanto na segunda fase a energia é transferida de volta para o atleta. Além disso, o atleta pode fornecer energia adicional ao sistema através de trabalho muscular (Arampatzis et al. 1999) . Esse trabalho muscular pode levar a uma deformação adicional da vara (energia adicional é armazenada na vara) com um aumento da energia mecânica total do atleta (Arampatzis et al. 2002). Sendo assim a elasticidade (flexibilidade) da vara desempenha um papel importante em toda a cadeia de transferência de energia durante o salto. A vara ajuda a reduzir a perda de energia que ocorre durante o encaixe da vara e o takeoff (Linthorne, 2000) assim como facilita ao atleta fornecer energia adicional ao sistema saltador-vara durante a fase em que o saltador adiciona energia através de trabalho muscular sobre a vara (Ekevad e Lunderg, 1995,1997; Arampatzis et al., 1999). O atleta emprega força muscular sobre a vara numa tentativa de adicionar ou acumular mais energia elástica na vara, além da energia cinética acumulada previamente pela corrida de aproximação. No caso da saltadora brasileira esses valores de E_Gain adicionados na cadeia energética da vara são menores se comparados com outras atletas. O valor médio da saltadora brasileira foi de 1,18 ± 0,87 J/kg, enquanto o valor médio para atletas nas olimpíadas de Sydney foi de 5,74 ±1,63 J/kg (Schade et al. 2004). Podemos verificar claramente uma desvantagem da atleta brasileira em fornecer E_Gain durante a 99 fase de acumulo de energia sobre a vara. Essa diferença de valores pode ser um fator determinante para a melhoria do desempenho da saltadora em obter marcas superiores às atuais. Possivelmente uma deficiência na técnica pode ser a causa desses valores baixos de E_Gain, uma explicação para esse fato pode estar relacionada com a posição dos membros inferiores da atleta observados no momento de penetração do salto, logo após a perda de contato com o solo onde a atleta esta pendurada na vara. Nessa fase a atleta tem que rodar em torno do eixo de seu quadril e dos seus ombros para projetar seu corpo para cima. Contudo o movimento retardado do quadril pode vir a gerar menos energia muscular sobre a vara, o que explicaria o fato dos valores da saltadora com vara brasileira serem inferiores ao das saltadoras com vara da final olímpica de 2000 (Schade et al. 2004). Esse fator pode representar um potencial de desenvolvimento da atleta em busca de melhor técnica e de melhores resultados. Uma vez identificado essa deficiência é possível que isso aumente E_Gain da atleta durante o salto, fato que não foi verificado nesse estudo. Contudo apesar dos baixos valores E_Gain , a atleta apresenta altos valores de E_Initial e E_Final alcançando valores médios respectivamente de 45,96 ±0,82 J/kg e 47,14 ±0,71 J/kg se comparados com outras atletas e também apresenta uma regularidade nas variáveis avaliadas que indica uma consistência da técnica da atleta, como pode ser observado na tabela 7. Verificamos que em todos os saltos válidos, em que atleta ultrapassou o sarrafo o valor de E_Final foi sempre superior ao E_Initial. Nós casos onde isso não ocorre, são nas tentativas falhas (1° tentativa de 4,71m e na 1° e 2° tentativa de 4,80m), possivelmente nessas 3 tentativas a atleta percebeu algo diferente e antes de finalizar o salto desistiu, o que ocasionou em uma redução na E_Final. De acordo com a regularidade das variáveis de velocidade, podemos verificar que a atleta apresenta um padrão técnico de movimento estável para saltos em diferentes alturas e com valores altos de E_initial. Também apresenta um diferencial em relação às outras atletas, obtendo uma posição mais alta do grip, o que lhe dá uma vantagem em relação às outras atletas tanto no salto como no %MPB (coeficiente de deformação da vara). Os desvios padrão confirmam a regularidade da atleta em relação a essas variáveis, em outras modalidades esportivas como a canoagem a redução da variabilidade e a 100 estabilização de variáveis indicam um aumento da habilidade e do nível de excelência dos atletas de elite (Hunter, 2009). Fato que é confirmado pelos dados da atleta brasileira no salto com vara indicando o nível de excelência e a regularidade da atleta, fato que confirma a sua posição no ranking atual da IAAF.

5. Conclusões Quando comparada com outras atletas de elite do salto com vara, a atleta brasileira se destaca como uma das mais velozes conforme os resultados observados, apresentando valores altos de E_Final e E_Initial e apresenta um diferencial na posição do grip, diferença essa que consequentemente a coloca entre as 5 melhores atletas do mundo atualmente. Os resultados desse estudo são relevantes para o salto com vara brasileiro e mundial, pois fornecem informações importantes sobre a biomecânica do salto com vara feminino. Contudo um acompanhamento em um maior número de provas seria necessário para avaliar a evolução da técnica do salto com vara feminino e encontrar variáveis determinantes na prova, bem como o tipo de vara utilizado por essas atletas.

Agradecimentos

Ao COB e CBAt que tornaram possível a realização desse trabalho, a FAPESP e CAPES pelo suporte financeiro e em especialmente ao Élson Miranda técnico da atleta Fabiana Murer por todo seu interesse e sua disponibilidade em discutir os resultados e fornecer dados sobre sua atleta e sobre as competições em que participaram, a Fabiana Murer que sempre foi receptiva e interessada nos resultados apresentados nesse trabalho.

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CAPÍTULO 6: CONCLUSÕES E POSSIBILIDADES FUTURAS

Neste trabalho apresentamos três diferentes ferramentas de análise de desempenho de atletas baseadas na utilização de recursos computacionais e métodos biomecânicos e aplicadas em três diferentes modalidades: handebol (modalidade coletiva), provas combinadas e salto com vara (modalidades individuais). Nos capítulos 2 e 3 apresentamos um sistema de rastreamento automático para modalidades coletivas (quadra/campo) que foi implementado e testado para o handebol. Os resultados obtidos foram promissores para utilização do Adaboost, com uma taxa de detecção de 82% para um conjunto de treinamento com 15000 imagens, demonstrando que a utilização de segmentação morfológica automática é um modo rápido e eficiente para treinar um detector Boosting . O rastreamento automático alcançado neste trabalho foi de 84%, demonstrando o potencial para utilização desse algoritmo para modalidades coletivas, com a vantagem de não ser necessário controlar o ambiente ou a iluminação. Os resultados do rastreamento automático permitiram avaliar o desempenho individualizado dos jogadores de handebol a partir do cálculo da distância percorrida e o percentual de tempo gasto em cada uma das cinco faixas de velocidade. Esse tipo de análise é umas das formas de avaliar o desempenho de uma equipe ou o desempenho individual de cada atleta. O método de rastreamento apresentado neste trabalho se mostrou uma ferramenta poderosa para a análise de desempenho de atletas de handebol. Deve-se destacar que tal método pode vir a ser utilizado em outras modalidades esportivas, dada a versatilidade do algoritmo de detecção e a possibilidade de acrescentar outros algoritmos de rastreamento para melhorar o percentual de automatização e a velocidade de rastreamento, podendo futuramente fornecer dados em tempo quase-real. No capítulo 4 apresentamos uma nova proposta de pontuação para provas combinadas através de um modelo uniforme para variáveis medidas em tempo e distância, cujo objetivo é avaliar e mensurar o desempenho de atletas de uma forma uniforme. O modelo apresentado permite avaliar o desempenho dos competidores não só em provas de 102 atletismo, mas também em outras diferentes modalidades (natação, ciclismo, escalada, etc) servindo como forma de controle em treinamentos ou mesmo em processos de seleção de novos talentos. O sistema de pontuação ainda permite que possamos mudar o coeficiente de crescimento das curvas “ b” (caso seja necessário) para privilegiar uma prova em relação a outra, sendo mais versátil do que os atuais modelos de pontuação em provas combinadas. Podendo também ser utilizado para o ranqueamento de atletas em testes físicos, teste de habilidades, testes de aptidão motora ou qualquer outro tipo de teste que se queira classificar desempenhos. Estudos futuros podem se utilizar de tal método para comparar o desempenho de atletas em tarefas específicas ou fundamentos esportivos a fim de criar um sistema único de comparação de desempenho de atletas ou de selecionar novos talentos esportivos. No capítulo 5 apresentamos uma análise cinemática tridimensional da melhor saltadora com vara do Brasil e que ocupa atualmente o 2º lugar no ranking da IAAF (2010). Por meio desse tipo de análise foi possível determinar e estudar uma série de variáveis importantes para a modalidade (velocidade de aproximação, velocidade de takeoff, distância de takeoff, parâmetros de energia mecânica) e munido dessas informações avaliarem o desempenho da atleta. Vale destacar que esse método pode ser utilizado nas mais diversas modalidades esportivas. O tema principal deste trabalho foi obter informações que pudessem ajudar a compreender a biomecânica do salto com vara e a possibilidade de avaliar o desempenho da atleta, comparando os seus resultados com os resultados de outras atletas de elite do salto com vara encontrados na literatura. Podemos destacar que a atleta brasileira é uma das mais velozes conforme os resultados observados, apresenta valores altos de E_Final e E_Initial e com um grip diferenciado, que possivelmente é um fator que a coloca entre as melhores atletas do mundo atualmente. Os resultados desse estudo são relevantes para o salto com vara brasileiro e mundial, pois fornecem informações importantes sobre a biomecânica do salto com vara feminino. Contudo estudos futuros devem ser realizados com um acompanhamento em um número maior de provas, com objetivo de avaliar a evolução do desempenho da atleta buscando encontrar variáveis determinantes na prova, bem como a realização de um estudo especifico que leve em consideração o tipo de vara utilizado por essas atletas e seus respectivos desempenhos. 103

O presente trabalho ao longo desses quatro capítulos apresentou contribuições originais para área de esportes principalmente em biomecânica através do desenvolvimento de ferramentas de análise de desempenho de atletas baseadas em métodos de computação (visão computacional e processamento de imagens) e em análise cinemática 3D aplicados em três diferentes modalidades esportivas e com potencial de ser utilizada nas mais diversas modalidades (coletivas ou individuais), permitindo a avaliação de atletas individualmente e coletivamente por profissionais ligados a área de esporte. As contribuições apresentadas são de domínio público e podem ser utilizadas tanto em atletas profissionais como amadores com a possibilidade de integração entrem as três ferramentas (sistema de rastreamento automático, sistema de pontuação, análise cinemática 3D) apresentadas nesse trabalho a critério de quem for utilizá-la. Estudos futuros poderão realizar análises integradas dos atletas através dos métodos apresentados nesse trabalho.

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GLOSSÁRIO

Adaboost: short for Adaptive Boosting, is a machine learning algorithm, formulated by Yoav Freund and Robert Schapire. It is a meta-algorithm, and can be used in conjunction with many other learning algorithms to improve their performance. AdaBoost is adaptive in the sense that subsequent classifiers built are tweaked in favor of those instances misclassified by previous classifiers.

Blobs: refers to visual modules that are aimed at detecting points and/or regions in the image that are either brighter or darker than the surrounding.

Boosting: is a machine learning meta-algorithm for performing supervised learning. Boosting is based on the question posed by Kearns: can a set of weak learners create a single strong learner? A weak learner is defined to be a classifier which is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification.

Frames: Quadros em uma seqüência de imagens de vídeo

Finta: é um termo usado para designar um ou vários movimentos que tendem a "ludibriar", enganar um adversário, quando se está participando de competições ou jogos esportivos. O objetivo é fazer com que o adversário acredite em uma ação, que não acontecerá, levando-o a tomar postura, posição ou atitude ineficiente diante do ataque.

Graphs Theory: is the study of graphs , mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected , meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another.

Grip: Empunhadura do atleta na vara, posição em que a mão do atleta se encontra. Particle filter: also known as Sequential Monte Carlo methods (SMC), are sophisticated model estimation techniques based on simulation. Particle filters have important applications in econometrics and in other fields.

Truncation: is the term for limiting the number of digits right of the decimal point.

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Visão computacional: é a ciência e tecnologia das máquinas que enxergam. Ela desenvolve teoria e tecnologia para a construção de sistemas artificiais que obtém informação de imagens ou quaisquer dados multi-dimensionais. Exemplos de aplicações incluem o controle de processos (como robôs industriais ou veículos autônomos), detecção de eventos, organização de informação, modelagem de objetos ou ambientes e interação (atrelado a interação homem-computador).

Takeoff: Momento em que o atleta perde o contato com o solo na impulsão para um salto.

Fase de aproximação: Fase em que o atleta adquire velocidade para realizar o salto.

Fase de takeoff: Momento em que o atleta impulsiona para saltar transferindo parte da velocidade horizontal para velocidade vertical.

Fase de suporte da vara: Momento em que atleta após a penetração no salto e impulsão esta realizando o movimento de pêndula na vara sem contato com o solo.

Fase de vôo: Fase em que a atleta não tem mais contato com a vara.

Corda da vara: distância entre o grip superior e o encaixe da vara no momento de máxima deformação da vara 113

ANEXOS The development of combined event scoring tables and implications for the training of decathletes By Viktor Trkal

Development of the Present Tables

At the end of the 1970s, the athletics movement applied considerable pressure for a review of the 1962 tables. The feeling was that they were becoming increasingly unfair for evaluations and comparisons of disciplines. There were two reasons for this demand. Firstly, hitherto the tables were meant to be used as a points system in combined events and for comparing the performances of various athletes in various disciplines. Improved, more intensive methods of preparing athletes, changes in technique (e.g. the use of a different method of jumping over the crossbar in the high jump) and the use of different materials for the manufacture of vaulting poles contributed to radical changes to performances in some events and thereby did away with the equivalence that had previously existed. For example, the evaluation of Daley Thompson's pole vault of 5.10m (not an exceptional performance these days) was 1075 points, which in these tables was equivalent to running the 100m in 9.99 seconds! Secondly, by following Ulbrich's principle, the scoring tables used for the runs were progressive while for the technical disciplines they were regressive. This was not to the liking of many people as it seemed hardly sensible for an athlete who, for example, in the high jump achieves performances of around 1.60m to receive more points for an improvement of 5cm than the same improvement at around the 2.00m level. The first to try and prepare new tables was Bob Sparks, Chairman of the International Association of Statisticians, whose unfinished draft was accepted by an Extraordinary IAAF Congress in Rome in 1981. These tables were very progressive and, because of the extreme disagreement voiced by combined event athletes and their trainers, the IAAF Council withdrew them before the end of 1981 and commissioned the Technical Committee to draw up a new proposal. At the next meeting of the Committee, on the occasion of the European Championships in Milan (1982), I was tasked with leading a working group that was to try to find an acceptable solution. After studying all hitherto unused proposals and suggestions regarding the current tables and discussing the matter personally with Dr Ulbrich, I proposed to the working group, which agreed, that the new tables should be developed according to the following nine principles: 1. The tables should only be used for combined events. 2. The results in different disciplines that are evaluated with approximately the same point value should be comparable as far as the quality and difficulty of achieving these results are concerned. 3. The tables in all disciplines should be: a. a modification of current tables b. linear in all disciplines c. very slightly progressive in all disciplines 114

4. The tables must be usable with combined events for beginners and juniors as well as top-class athletes. 5. There will be separate tables for men and women. 6. The tables must be based on decathlon statistics, taking into account the statistics of specialist athletes in the individual disciplines. 7. The tables should be usable now and in the future. 8. The sum of points scored by world-class athletes should remain approximately the same. 9. As far as possible, the tables should eliminate the possibility that an athlete specializing in one discipline is able to acquire sufficient points in that discipline to overcome a low scores in weaker disciplines and beat more versatile, all-round athletes. It was decided that work on variations to meet the conditions in no. 3 would be carried out by sub-groups of 1 to 3 persons. I personally took responsibility for 3-c. My starting point was the idea that athletic performance is physical work. This is represented primarily by kinetic energy of the given system, irrespective of whether a run, jump, or throw is involved. Speed v is to the second power in all cases, and this indirectly implies a progressive form for the necessary curve. The American J Gerry Purdy, PhD., has published two articles on the evaluation of performances in athletics, and I studied these. Using statistical data from the countries then included in the IAAF's AA and A groups on the disciplines of combined events, I elaborated a variation that became known as the Czechoslovak proposal. The tables were slightly progressive in all disciplines with slight variations in climb rate for the curves of the different disciplines. I respected the weight of the decathlete (men) or heptathlete (women), especially in the longer runs. The Technical Committee assessed a number of other proposals from Portugal, the USA, East Germany, West Germany, Hungary, Sweden, and Czechoslovakia. On the recommendation of the working group, the committee approved a modified version of the Czechoslovak proposal, while respecting some suggestions from Hungary, West Germany, and Sweden, which it recommended for discussion at the 1984 IAAF Congress in Los Angeles. The Congress adopted the tables for use in men's and women's combined event competitions from 1985. Since then no modifications have been made. The 2001 IAAF Congress in Edmonton approved the inclusion of the women's decathlon among the disciplines, for which world records are kept and approved supplementary tables for the disciplines expanding the heptathlon into a decathlon for women. I am convinced that even if it is never possible to evaluate equivalent performances in individual performances absolutely precisely, the current system of evaluation is the fairest of all those used in athletics so far. The tables guarantee that an athlete's performance will be fairly assessed as a set of points taking into account his/her possibilities from the aspect of physical proportions (i.e. weight and height).

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Practical Implications What are the implications of the IAAF Combined Event Scoring Tables now in use for the preparation for the combined events and in particular the decathlon? Because the tables are based on the theoretical requirement that kinetic energy exerted by the athlete is responsible for the performance (the work), it is necessary in training to emphasize primarily the speed element of preparation. It is also important to control an athletes' weight, so that an optimal balance, in terms of strength, agility and coordination, can be found in the ability to cope with the disciplines. It is down to the art of trainers and their support teams to find the optimal condition for each athlete, along with the best possible management of techniques in the individual disciplines. When trying to make the correct choice of training strategy, it is important to realize that the decathlon is a combination of technically different disciplines, and, therefore physiologically different training approaches are required. Besides the sprint disciplines, there are jumps and throws, and the 1500m assumes a special position. At the level performance between 6000 and 8000 points, it should be taken into account that to gain 50 points, a decathlete has to improve on average as shown in Table 1. A successful performance may depend on the choice of training strategy preferring mobile features in disciplines where the athlete of average weight is likely to make an impact (jumps, sprints), and, on how to cope, in this situation, with the shot put and the throws, so that the necessary power training does not work too much to the detriment of performance in the 1500m. This means placing an emphasis on the correct technical management of the throwing and jumping disciplines.

100m LJ SP HJ 400m 110mH D PV J 1500m 0.25 22 82 5-6 1.20 0.53 2.45 17-18 3.30 7-8 Sec cm cm cm sec sec m cm m sec

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IAAF Scoring Tables for Combined

Events

Ideal Scoring Tables for Athletics events do not exist, for opinions vary considerably between statisticians as to their basis and method of construction. The Tables in use up to 1985 (1962 Men and 1971 Women) had served the IAAF well, but the sport evolved, with progress in certain events (1500m, Pole Vault, Women's High Jump), putting them out of step with other events on the Tables. This caused rumblings of discontent by the early 1970s and finally, in 1982, a Working Group of the Technical Committee under the leadership of Dr. Viktor Trkal concluded that a new table should be established and should be exclusively for use in combined events competitions. To this end, the new tables were to be based mainly on statistics from combined events competitions, while paying due regard to statistics from individual events. Based on these studies, a set of tables accepted by the Working Group, approved by the Technical Committee and passed by the Los Angeles Congress in August 1984, was printed in 1985. In 1998, a new edition was printed after the Athens Congress agreed in 1997 to measure the long throws to the nearest centimetre. The IAAF also took this opportunity to include the tables for the indoor events which are not part of the Men's Decathlon and the Heptatlon for Women. The 2004 edition takes accounts of some important rule changes from the 2001 Edmonton Congress, such as the consequences of the creation of the Decathlon for women (in addition to the traditional Heptathlon which even remains for the moment the official event in the Championships). This decision meant that the IAAF needed to create a new version of the Scoring Tables incorporating 100m, Discus Throw, Pole Vault, 400m and 1500m for women. This reprinted version includes some updates in the text but no changes in the scoring tables.

HOW TO USE THE TABLES

There are separate tables for all the events in the men's decathlon and pentathlon and the women's heptathlon. The score for any performance on the track or in the field can be read off in the appropriate table. In many events, all possible times or distances are not given in the table. In such cases, the score for the nearest lesser performances should be read.

For example:

In the men's 1500m, there is no entry for a time of 4:10.25. The nearest slower time given in the table is 4:10.37 for a score of 879 points.

In the women's shot put there is no entry for a distance of 13.12m. The nearer shorter distance given in the table is 13.11 for a score of 735 points.

TIMING

Two methods of timekeeping shall be recognised as official (IAAF Rule 165):

·fully automatic electrical timing, to 1/100th of a second; ·hand timing, to 1/10th of a second; in this case, use the "Manual Timing" Tables. 117

HOW TO SCORE A COMPETITION

Combined events can be scored by a pre-programmed computer or manually.

When scoring manually it is important to use a system which helps to minimise the chances of error. Further, a standardised system makes it much easier for subsequent readers to check. Examples of normal scoring sheets for decathlon and heptathlon are shown on the next page. This arrangement with vertical additions and a record of the score after each event improves accuracy. Forms can be pre-drawn or pre-printed. Another assistance to accuracy is the entry of the score additions in a different coloured pen. EXAMPLES OF DECATHLON AND HEPTATHLON SCORE SHEETS

DECATHLON - WORLD CHAMPIONSHIPS EDMONTON, 6/7 AUGUST 2001

NAME Tomáš DVORÁK Erki NOOL Dean MACEY

NUMBER 255 328 437

COUNTRY CZE EST GBR

Result Score Result Score Result Score

100m 10.62 947 10.60 952 10.72 924

PLACE/TOTAL 2 947 1 952 3 924

LONG JUMP 8.07 1079 7.63 967 7.59 957

PLACE/TOTAL 1 2026 2 1919 3 1881

SHOT PUT 16.57 886 14.90 784 15.41 815

PLACE/TOTAL 1 2912 2 2703 3 2696

HIGH JUMP 2.00 803 2.03 831 2.15 944

PLACE/TOTAL 1 3715 3 3534 2 3640

400m 47.74 922 46.23 997 46.21 998

PLACE/TOTAL 2 4637 3 4531 1 4638

110m HURDLES 13.80 1000 14.40 924 14.34 931

PLACE/TOTAL 1 5637 3 5455 2 5569

DISCUS THROW 45.51 777 43.40 734 46.96 807

PLACE/TOTAL 1 6414 3 6189 2 6376

POLE VAULT 5.00 910 5.40 1035 4.70 819

PLACE/TOTAL 1 7324 2 7224 3 7195

JAVELIN THROW 68.53 867 67.01 844 54.61 657

PLACE/TOTAL 1 8191 2 8068 3 7852

1500m 4:35.13 711 4:29.58 747 4:29.05 751

FINAL TOTAL 8902 8815 8603

FINAL PLACE 1 2 3

HEPTATHLON-WORLD CHAMPIONSHIPS EDMONTON, 4/5 AUGUST 2001

NAME Yelena PROKHOROVA Natalya SAZANOVICH Sheila BURRELL

NUMBER 697 70 810

COUNTRY RUS BLR USA

Result Score Result Score Result Score

100mH 13.77 1011 13.29 1081 13.05 1117

PLACE/TOTAL 6 1011 3 1081 2 1117

HIGH JUMP 1.88 1080 1.76 928 1.67 818

PLACE/TOTAL 2 2091 4 2009 8 1935

SHOT PUT 13.15 737 15.90 921 12.87 719

PLACE/TOTAL 2 2828 1 2930 10 2654

200m 23.73 1007 23.87 993 22.92 1087

PLACE/TOTAL 2 3835 1 3923 4 3741

LONG JUMP 6.61 1043 6.50 1007 6.45 991

PLACE/TOTAL 2 4878 1 4930 3 4732

JAVELIN THROW 50.73 874 46.72 797 48.74 836

PLACE/TOTAL 1 5752 2 5727 3 5568

800m 2:11.53 942 2:20.87 812 2:14.24 904

FINAL TOTAL 6694 6539 6472

FINAL PLACE 1 2 3

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FORMULAE FOR IAAF COMBINED EVENTS SCORING SYSTEM

For a given performance, the point score (P) is calculated using one of the following equations:

Track events P=a*(b - T)**c [where Tis Time in seconds ; e.g. 10.43 for 100 metres] Jumps P=a*(M - b)**c [where M is Measurement in centimetres ; e.g. 808 for "LJ".] Throws P=a*(D - b)**c [where D is Distance in metres ; e.g. 16.69 for Shot] a, b and c are parameters whose values are listed below. * is the mathematical sign meaning "multiplied by ", and ** is the mathematical sign meaning "raised to the power of". Note: The value of P (points) must be rounded down to a whole number after calculation (e.g. 123.999 becomes 123).

PARAMETERS (constants for each event)

MEN'S EVENTS a b c

100m (auto) 25.4347 18.00 1.81 200m (auto) 5.8425 38.00 1.81 400m (auto) 1.53775 82.00 1.81 1500m 0.03768 480.00 1.85 110mH (auto) 5.74352 28.50 1.92 High Jump 0.8465 75.00 1.42 Pole Vault 0.2797 100.00 1.35 Long Jump 0.14354 220.00 1.40 Shot 51.39 1.50 1.05 Discus 12.91 4.00 1.10 Javelin 10.14 7.00 1.08

(Indoors) 60m (auto) 58.0150 11.50 1.81 1000m 0.08713 305.50 1.85 60mH (auto) 20.5173 15.50 1.92 WOMEN'S EVENTS a b c

200m (auto) 4.99087 42.50 1.81 800m (auto) 0.11193 254.00 1.88 100mH (auto) 9.23076 26.70 1.835 High Jump 1.84523 75.00 1.348 Long Jump 0.188807 210.00 1.41 Shot 56.0211 1.50 1.05 Javelin 15.9803 3.80 1.04

(Decathlon) 100m (auto) 17.8570 21.0 1.81 400m (auto) 1.34285 91.7 1.81 1500m 0.02883 535 1.88 Pole Vault 0.44125 100 1.35 Discus 12.3311 3.00 1.10

(Indoors) 60mH (auto) 20.0479 17.00 1.835 119

NOTE: Points for manual times in events up to 400 metres are calculated either by adding the standard adjustment factor to the time (i.e. 0.24 sec. for events below 400 metres, 0.14 sec. for 400 metres) or by subtracting the factor from the "b" parameter. There are no adjustments for events above 400 metres.

Example (100m Men): 10.40 (auto) for 100m is calculated as P=25.4347*(18.00 - 10.40)**1.81 = 999 10.4 (manual) for 100m is calculated either as P=25.4347*(18.00 - 10.64)**1.81 = 942 or as P=25.4347*(17.76 - 10.4)**1.81 = 942