UPTEC F 15068 Examensarbete 30 hp December 2015 Analysis and visualization of collective motion in football Analysis of youth football using GPS and visualization of professional football Emil Rosén Abstract Analysis and visualization of collective motion in football Emil Rosén Teknisk- naturvetenskaplig fakultet UTH-enheten Football is one of the biggest sports in the world. Professional teams track their player's positions using GPS (Global Positioning System). This report is divided into Besöksadress: two parts, both focusing on applying collective motion to football. Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 The goal of the first part was to both see if a set of cheaper GPS units could be used to analyze the collective motion of a youth football team. 15 football players did two Postadress: experiments and played three versus three football matches against each other while Box 536 751 21 Uppsala wearing a GPS. The first experiment measured the player's ability to control the ball while the second experiment measured how well they were able to move together as Telefon: a team. Different measurements were measured from the match and Spearman 018 – 471 30 03 correlations were calculated between measurements from the experiments and Telefax: matches. Players which had good ball control also scored more goals in the match and 018 – 471 30 00 received more passes. However, they also took the middle position in the field which naturally is a position which receives more passes. Players which were correlated Hemsida: during the team experiment were also correlated with team-members in the match. http://www.teknat.uu.se/student But, this correlation was weak and the experiment should be done again with more players. The GPS did not work well in the team experiment but have potential to work well in experiments done on a normal-sized football field. The goal of the second part of the report was to visualize collective motion, more specifically leader-follower relations, in football which can be used as a basis for further research. This is done by plotting the player's positions at each time step to a user interface. Between each player, a double pointed arrow is drawn, where each side of the arrow has a separate color and arrow width. The maximum time lag between the between the two players is shown as the "pointiness" of the arrow while the color of the arrow show the maximum time lag correlation. The user can change the metrics the correlations are based of. As a compliment to the lagged correlation, a lag score is defined which tell the user how strong the lagged correlation is. Handledare: David Sumpter Ämnesgranskare: Thomas Schön Examinator: Tomas Nyberg ISSN: 1401-5757, UPTEC F 15068 Popul¨arvetenskaplig sammanfattning Fotboll ¨aren av v¨arldensst¨orstasporter i v¨arlden. Professionella lag sp˚arar spelarnas position och hastighet under tr¨aningsmatcher med hj¨alputav GPS (Global Positioning System). D¨armedkan en manager till exempel se vilka ytor p˚aplanen en spelare t¨acker eller hur snabbt och ofta de springer eller spurtar, vilket ocks˚amycket forskning inom fotboll ¨arfokuserad p˚a.Dock ¨arju fotboll en lagsport och mindre fokus inom forskningen har lagts p˚aatt analysera dynamiken inom fotbollslagen. Ett s¨attman kan g¨oradetta p˚a¨aratt titta p˚aden kollektiva r¨orelseninom ett lag. Med kollektiv r¨orelsei fotboll menar man att spelarnas r¨orelserinte ¨aroberoende utav varandra, utan en spelare best¨ammervart hen ska placera sig utifr˚andess lagkamraters och motst˚andaresposition. Mycket forskning har skett p˚akollektiv r¨orelseinom andra omr˚aden,s˚asom hur fiskars r¨orelser beror p˚avarandra f¨oratt skapa dynamiska fiskstim eller hur bin skapar stora sv¨armar. Id´eenmed det h¨arprojektet ¨aratt anv¨andakollektiv r¨orelsef¨or att analysera fotbollspelarnas r¨orelser likt det man g¨orinom biologin. Projektet ¨aruppdelat i tv˚adelar med olika fokus. I den f¨orstadelen anv¨andesGPS f¨oratt sp˚ara10-˚argamla fotbollsspelares positioner p˚aen fot- bollsplan. M˚aletmed denna del var dels att unders¨oka ifall en billigare GPS (¨ande som anv¨andsav professionella lag) kan anv¨andasf¨oratt unders¨oka denna typ av experiment samt att utf¨oran˚agraenkla experiment f¨oratt unders¨oka den kollektiva r¨orelseninom laget. 15 fotbollsspelare utf¨ordetv˚a experiment samt spelade fyra tre mot tre matcher (p˚aen liten fotbollsplan) mot varandra. Det f¨orstaexperimentet m¨attederas individuella f¨orm˚agaatt hantera boll medan det andra experimentet var ett backlinjeexperiment som m¨attederas f¨orm˚agaatt r¨orasig som ett lag. Spelarna rankades inom olika omr˚adenutifr˚anresultaten fr˚anexperimenten och matchen, som till exempel deras bollskicklighet, hur bra de ¨arp˚aatt r¨orasig som ett lag, hur m˚anga m˚alde gjorde, hur snabbt de springer under en match och hur m˚angapass- ningar de f˚ar. D¨arefterber¨aknadeskorrelationer mellan dessa rankningar f¨or att unders¨oka ifall spelare som ¨arbra i ett omr˚ade¨arbra eller d˚aligai ett annat. Spelare som var bra p˚aatt hantera boll gjorde ocks˚amer m˚alsamt fick mer passningar. Dock tog dessa spelare ¨aven mittpositionen i laget vilket ¨ar en position som naturligt f˚armer passar. D¨armed¨ardet inte s¨akert om dessa spelare faktiskt var b¨attrep˚aatt g¨oram˚aleller om det endast berodde p˚aden position de hade. Spelare som var korrelarade med andra spelare i backlinje- experimentet var ocks˚amer korrelerade med sina lagkamrater n¨arde hade boll. Dock utf¨ordesexperimenten med endast 15 spelare vilket betyder att 1 detta resultat inte ¨ar¨overtygande och experimentet borde g¨orasom med fler spelare. GPS:erna fungerade inte s¨arskiltbra i backlinje-experimentet men kan anv¨andasb¨attreunder matcher eller experiment som sker p˚aen st¨orre fotbollsplan. M˚aletmed den andra delen av projektet var att visualisera dynamiken i den kollektiva r¨orelsenfr˚anen fotbollsmatch f¨oratt snabbt kunna f˚aen ¨overblick och hitta intressanta omr˚adensom borde unders¨okas mer. Den po- sitionsdata som anv¨andesvar fr˚anen ˚attamot ˚attafotbollsmatch spelad av professionella spelare och ¨arav h¨ogkvalitet. Ett anv¨andargr¨anssnitt utveck- lades i Matlab d¨arspelarnas positioner var utritade p˚aen fotbollsplan och d¨aranv¨andarenkan stega fram tiden f¨oratt se hur spelarna f¨orflyttarsig. Samt s˚aunders¨oktsdet om det finns s˚akallade “ledare-f¨oljare"relationer mellan spelare, allts˚aom en spelare f¨oljeren annan spelare eller inte. Detta visualiseras i form utav dubbelsidiga pilar som pekar mellan spelarna. F¨argen p˚apilarna visar ifall spelarna ¨arkorrelerade eller inte mellan spetsigheten p˚a pilen visar hur stort lag det ¨armellan spelarna, d¨arett stort lag visar p˚aatt en spelare f¨oljerden andra spelarens r¨orelserfast med en f¨ordr¨ojning,och d¨armed¨aren “f¨oljare". Med detta gr¨anssnittkan det bland annat ses att det lag som inte har bollen ¨arbetydligt mer korrelerade med varandra ¨andet attackerande laget. Contents 1 Abbreviations 4 2 Background and introduction 4 3 Analysis of collective motion of a youth football team using GPS 5 3.1 Introduction . 5 3.2 Material and methods . 5 3.2.1 GPS units . 5 3.2.2 Experiment group and location . 5 3.2.3 Preprocessing of GPS data . 5 3.2.4 Validation of GPS data . 6 3.2.5 Correlation score . 7 3.2.6 Ball control experiment: Evaluation of player ball control 8 3.2.7 Line experiment: Evaluation of player team skill . 8 3.2.8 Match experiment: Evaluation of player match skill . 10 2 3.3 Results . 12 3.3.1 GPS validation . 12 3.3.2 Ball control experiment results . 13 3.3.3 Assignment of player ID . 14 3.3.4 Line experiment results . 15 3.3.5 Match experiment results . 15 3.3.6 Correlations between player measurements . 19 3.3.7 Correlations between team measurements . 20 3.4 Discussion . 21 3.4.1 GPS . 21 3.4.2 Ball control . 22 3.4.3 Line experiment . 23 3.4.4 Match experiment . 23 4 Visualization of collective motion of a professional football players in a eight versus eight match 24 4.1 Introduction . 24 4.2 Materials and methods . 24 4.2.1 Data description . 24 4.2.2 Preprocessing of data . 24 4.2.3 Time window . 25 4.2.4 Time lag correlation . 25 4.2.5 Lag score . 26 4.2.6 Implementation . 27 4.3 Results . 27 4.3.1 Maximum time lag . 28 4.3.2 Voronoi Regions . 30 4.4 Discussion . 30 5 Conclusions 31 6 Future Outlook 32 Appendices 32 Appendix A Movie examples of collective motion of a youth football team 32 Appendix B Movie examples showing the visualization 32 3 1 Abbreviations • GPS - Global Positioning System • GUI - Graphical User Interface • RMSE - Root mean squared error • STD - Standard Deviation 2 Background and introduction Football is one of the worlds biggest and most popular sports with million fans around the globe. Modern mathematics and statistics are used by top-level football teams and clubs to improve training and analyse tactics. A large amount of research have been directed into areas such as player's run per- formance in various speed intervals, distance covered, team ball possession, team pass rate, correlations between training exercises and in the creation of heat maps which show which areas certain players covers during a match [2, 6, 10, 17, 20]. In the area of collective motion and behaviour, models and methods have been developed to analyze the follower-leader relationships in for example birds [16] but also in social structures such as that in the relationship between GDP per capita and democracy [19]. These kind of analysis could be applied to football to approach the subject from a different angle, but less work have been done in this area compared to the more traditional approach.