UPTEC F 15068

Examensarbete 30 hpDecember 2015

Analysis and visualization of collective motion in football Analysis of youth football using GPS and

visualization of professional football

Emil Rosén

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Analysis and visualization of collective motion infootball

Emil Rosén

Football is one of the biggest sports in the world. Professional teams track theirplayer's positions using GPS (Global Positioning System). This report is divided intotwo parts, both focusing on applying collective motion to football. The goal of the first part was to both see if a set of cheaper GPS units could be usedto analyze the collective motion of a youth football team. 15 football players did twoexperiments and played three versus three football matches against each other whilewearing a GPS. The first experiment measured the player's ability to control the ballwhile the second experiment measured how well they were able to move together asa team. Different measurements were measured from the match and Spearmancorrelations were calculated between measurements from the experiments andmatches. Players which had good ball control also scored more goals in the match andreceived more passes. However, they also took the middle position in the field whichnaturally is a position which receives more passes. Players which were correlatedduring the team experiment were also correlated with team-members in the match.But, this correlation was weak and the experiment should be done again with moreplayers. The GPS did not work well in the team experiment but have potential towork well in experiments done on a normal-sized football field.

The goal of the second part of the report was to visualize collective motion, morespecifically leader-follower relations, in football which can be used as a basis forfurther research. This is done by plotting the player's positions at each time step to auser interface. Between each player, a double pointed arrow is drawn, where eachside of the arrow has a separate color and arrow width. The maximum time lagbetween the between the two players is shown as the "pointiness" of the arrow whilethe color of the arrow show the maximum time lag correlation. The user can changethe 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.

ISSN: 1401-5757, UPTEC F 15068Examinator: Tomas NybergÄmnesgranskare: Thomas SchönHandledare: David Sumpter

Popularvetenskaplig sammanfattning

Fotboll ar en av varldens storsta sporter i varlden. Professionella lag spararspelarnas position och hastighet under traningsmatcher med hjalp utav GPS(Global Positioning System). Darmed kan en manager till exempel se vilkaytor pa planen en spelare tacker eller hur snabbt och ofta de springer ellerspurtar, vilket ocksa mycket forskning inom fotboll ar fokuserad pa. Dockar ju fotboll en lagsport och mindre fokus inom forskningen har lagts pa attanalysera dynamiken inom fotbollslagen.

Ett satt man kan gora detta pa ar att titta pa den kollektiva rorelsen inomett lag. Med kollektiv rorelse i fotboll menar man att spelarnas rorelser intear oberoende utav varandra, utan en spelare bestammer vart hen ska placerasig utifran dess lagkamraters och motstandares position. Mycket forskninghar skett pa kollektiv rorelse inom andra omraden, sa som hur fiskars rorelserberor pa varandra for att skapa dynamiska fiskstim eller hur bin skapar storasvarmar. Ideen med det har projektet ar att anvanda kollektiv rorelse foratt analysera fotbollspelarnas rorelser likt det man gor inom biologin.

Projektet ar uppdelat i tva delar med olika fokus. I den forsta delenanvandes GPS for att spara 10-ar gamla fotbollsspelares positioner pa en fot-bollsplan. Malet med denna del var dels att undersoka ifall en billigare GPS(an de som anvands av professionella lag) kan anvandas for att undersokadenna typ av experiment samt att utfora nagra enkla experiment for attundersoka den kollektiva rorelsen inom laget. 15 fotbollsspelare utforde tvaexperiment samt spelade fyra tre mot tre matcher (pa en liten fotbollsplan)mot varandra. Det forsta experimentet matte deras individuella formaga atthantera boll medan det andra experimentet var ett backlinjeexperiment sommatte deras formaga att rora sig som ett lag. Spelarna rankades inom olikaomraden utifran resultaten fran experimenten och matchen, som till exempelderas bollskicklighet, hur bra de ar pa att rora sig som ett lag, hur mangamal de gjorde, hur snabbt de springer under en match och hur manga pass-ningar de far. Darefter beraknades korrelationer mellan dessa rankningar foratt undersoka ifall spelare som ar bra i ett omrade ar bra eller daliga i ettannat.

Spelare som var bra pa att hantera boll gjorde ocksa mer mal samt fickmer passningar. Dock tog dessa spelare aven mittpositionen i laget vilket aren position som naturligt far mer passar. Darmed ar det inte sakert om dessaspelare faktiskt var battre pa att gora mal eller om det endast berodde pa denposition de hade. Spelare som var korrelarade med andra spelare i backlinje-experimentet var ocksa mer korrelerade med sina lagkamrater nar de hadeboll. Dock utfordes experimenten med endast 15 spelare vilket betyder att

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detta resultat inte ar overtygande och experimentet borde goras om med flerspelare. GPS:erna fungerade inte sarskilt bra i backlinje-experimentet menkan anvandas battre under matcher eller experiment som sker pa en storrefotbollsplan.

Malet med den andra delen av projektet var att visualisera dynamikeni den kollektiva rorelsen fran en fotbollsmatch for att snabbt kunna fa enoverblick och hitta intressanta omraden som borde undersokas mer. Den po-sitionsdata som anvandes var fran en atta mot atta fotbollsmatch spelad avprofessionella spelare och ar av hog kvalitet. Ett anvandargranssnitt utveck-lades i Matlab dar spelarnas positioner var utritade pa en fotbollsplan ochdar anvandaren kan stega fram tiden for att se hur spelarna forflyttar sig.Samt sa undersokts det om det finns sa kallade “ledare-foljare” relationermellan spelare, alltsa om en spelare foljer en annan spelare eller inte. Dettavisualiseras i form utav dubbelsidiga pilar som pekar mellan spelarna. Fargenpa pilarna visar ifall spelarna ar korrelerade eller inte mellan spetsigheten papilen visar hur stort lag det ar mellan spelarna, dar ett stort lag visar pa atten spelare foljer den andra spelarens rorelser fast med en fordrojning, ochdarmed ar en “foljare”. Med detta granssnitt kan det bland annat ses attdet lag som inte har bollen ar betydligt mer korrelerade med varandra an detattackerande laget.

Contents

1 Abbreviations 4

2 Background and introduction 4

3 Analysis of collective motion of a youth football team usingGPS 53.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . 5

3.2.1 GPS units . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.2 Experiment group and location . . . . . . . . . . . . . 53.2.3 Preprocessing of GPS data . . . . . . . . . . . . . . . . 53.2.4 Validation of GPS data . . . . . . . . . . . . . . . . . . 63.2.5 Correlation score . . . . . . . . . . . . . . . . . . . . . 73.2.6 Ball control experiment: Evaluation of player ball control 83.2.7 Line experiment: Evaluation of player team skill . . . . 83.2.8 Match experiment: Evaluation of player match skill . . 10

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3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3.1 GPS validation . . . . . . . . . . . . . . . . . . . . . . 123.3.2 Ball control experiment results . . . . . . . . . . . . . . 133.3.3 Assignment of player ID . . . . . . . . . . . . . . . . . 143.3.4 Line experiment results . . . . . . . . . . . . . . . . . . 153.3.5 Match experiment results . . . . . . . . . . . . . . . . 153.3.6 Correlations between player measurements . . . . . . . 193.3.7 Correlations between team measurements . . . . . . . . 20

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.1 GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.2 Ball control . . . . . . . . . . . . . . . . . . . . . . . . 223.4.3 Line experiment . . . . . . . . . . . . . . . . . . . . . . 233.4.4 Match experiment . . . . . . . . . . . . . . . . . . . . . 23

4 Visualization of collective motion of a professional footballplayers in a eight versus eight match 244.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . 24

4.2.1 Data description . . . . . . . . . . . . . . . . . . . . . 244.2.2 Preprocessing of data . . . . . . . . . . . . . . . . . . . 244.2.3 Time window . . . . . . . . . . . . . . . . . . . . . . . 254.2.4 Time lag correlation . . . . . . . . . . . . . . . . . . . 254.2.5 Lag score . . . . . . . . . . . . . . . . . . . . . . . . . 264.2.6 Implementation . . . . . . . . . . . . . . . . . . . . . . 27

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.1 Maximum time lag . . . . . . . . . . . . . . . . . . . . 284.3.2 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 youthfootball team 32

Appendix B Movie examples showing the visualization 32

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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 fansaround the globe. Modern mathematics and statistics are used by top-levelfootball teams and clubs to improve training and analyse tactics. A largeamount 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 creationof 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 havebeen developed to analyze the follower-leader relationships in for examplebirds [16] but also in social structures such as that in the relationship betweenGDP per capita and democracy [19]. These kind of analysis could be appliedto football to approach the subject from a different angle, but less work havebeen done in this area compared to the more traditional approach.

Some research about collective motion and football show players of op-posing teams have a greater amount of leader-follower interactions than thatbetween team members [14], developing a network based method for quanti-fying the performance of individuals in a team [5] and relationships betweendifferent quantities in a full football match [22, 23]. Other research combinethe areas of biology and football by modeling a football team as a super-organism to find the collective behaviour of the team [3] or analyzing theshapes the team creates during a match [4, 7].

This thesis will focus on the collective motion of football players and isdivided into two parts. The first part focus on analyzing the collective motionin youth football during a match and different exercises, using GPS to gatherposition data. The second part focus on visualizing the collective motion ofprofessional football players.

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3 Analysis of collective motion of a youth

football team using GPS

3.1 Introduction

To be able to analyze the collective motion of football players their positionhave to be recorded. There are three main systems to track the positionsof football players during a match. Image analysis of video footage (such asProZone [13]), using a local positioning system or by mounting GPS receiverson the players (such as GPSports [9]). While these equipment probably workvery well they are also very expensive. Therefore, one goal of the thesis is tosee if a cheaper GPS can work well enough to analyze the collective motionof youth football players.

Additional goals are to see if there are any relationships between somemeasurements from some simple experiments with measurements from asmall three versus three match, as well as to analyze the collective motion ofthe football players during a match.

3.2 Material and methods

3.2.1 GPS units

The GPS units used were the QStarz BT-Q1300ST GPS logger. The GPSunit can log data at 5 Hz, have a 3 m accuracy in the 2D plane and 0.1 m/sspeed accuracy [18].

3.2.2 Experiment group and location

The experiments were carried out on 15 male football players around the ageof 10, who train approximately 3 times each week, on a local football pitch.Each player carried a GPS mounted on their shoulder while participating ineach experiment.

Parent’s written consent as well as the children’s permissions were ob-tained prior to the experiments. The data is stored anonymously.

3.2.3 Preprocessing of GPS data

The geodetic coordinates gained from the GPS units were converted to a 2Dcartesian coordinate system using the flat earth model. Drift points wereremoved and missing data points were filled in if the gap was small enough(< 1 s) using linear interpolation [21]. The data points were rotated so that

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the length and width of the football pitch would be aligned with the X andY axis respectively.

3.2.4 Validation of GPS data

Seven GPS units were placed along a 104 cm long pole with 16 cm betweeneach neighboring GPS. A calibration, running and line experiment (Table 1)was carried out to measure the position accuracy of the GPS at the experi-ment location. The sky was almost completely clear.

Table 1: Description of experiments measuring and validating GPS positionaccuracy

Name DescriptionCalibration The pole was placed for 1 minute on each corner of a

penalty fieldRunning Running around the circumference of the penalty field

twice with the pole perpendicular to the runningdirection

Line Jogging back and forth along one of the widths of thepenalty field four times with the pole perpendicular tothe jogging direction

At each time step the relative position error of the GPS units is given by

Et =2

N(N − 1)

N∑x=1

N∑y=x+1

√(0.16 · (y − x)− |Xx,t −Xy,t|)2 (1)

where Et is the RMSE at time t, Xn,t is the position of GPS n at time t andN is the number of GPS units.

In the line experiment, the GPS units are only moving in one dimension.For each time step, the variance of the position on the axis parallel with thedirection of movement between all GPS units were calculated according to:

V‖, t = var(X‖, t) (2)

If the GPS units would be ideal, V‖, t = 0 for each time step.

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3.2.5 Correlation score

Pearson correlations between players, of some measurement, over several timesegments were compared to each other in this thesis. This was done bydefining and calculating a correlation score for each player using correlationmatrices each calculated over a different time segment. The correlation scoreis higher for players that correlate more than players that do not correlate.

Given a time series of correlation matrices, C = {C1, C2, ..., Ci}, whereCi is a correlation matrix (of some measurement) from time segment i. Eachcorrelation pair Cx1,y1,i1 is compared to all other correlation pairs Cx2,y2,i2 ,where Cx,y,i is the correlation pair between player x and player y for timesegment i (x 6= y). Each time the correlation pair Cx1,y1,i1 has a highercorrelation than correlation pair Cx2,y2,i2 , with 95% significance, the correla-tion score for player x1 is increased by one. This tournament like methodis applied between all correlation pairs from all given time segments. SeeAlgorithm 1.

input : C: Time series of correlation matrices. Each correlationmatrix consist of correlation pairs Cx,y,i between player x andplayer y for time segment i.

output: S: Correlation scores. Consists of elements Sp, which is thecorrelation score for player p

Initialize all scores to 0for each Sp in S do

Sp ← 0end

Compare all correlation pairs Cx1,y1,i1 with all correlation pairsCx2,y2,i2, where Cx,y,i is the correlation pair between player x and y attime segment ifor each Cx1,y1,i1, x1 6= y1 in C do

for each Cx2,y2,i2, x2 6= y2 in C doif Cx1,y1,t1 > Cx2,y2,i2 with 95% confidence then

Sx1 ← Sx1 + 1end

end

endAlgorithm 1: Algorithm which calculates a correlation score for eachplayer given a time series of correlation matrices. The correlation scoreis used for comparing the overall correlation between the different players.

A correlation pair is considered bigger than another correlation pair with

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95% confidence if it is bigger, and the 95% confidence intervals of the twopairs does not overlap. The confidence intervals are calculated using theFisher transformation [12]. A Fisher transformation of a correlation coeffi-cient can be calculated by

zr =1

2ln(1 + r

1− r

)= arctanh(r) (3)

and with inverse

r =e2zr−1

e2zr+1= tanh(zr) (4)

where r is the original correlation coefficient and zr is the transformedcorrelation coefficient. Equation 3 has standard error 1√

N−3 where N is thenumber of samples. The confidence intervals can then be calculated by

r = tanh(arctanh(r)± z1−α/2 ·

1√N − 3

)(5)

with z1−α/2 = 1.96 for a 95% confidence interval.

3.2.6 Ball control experiment: Evaluation of player ball control

Each player did two individual experiments, dribbling and juggling (Table2), to measure their individual skill level at controlling a football. The bestresult for each player was recorded for each experiment.

Table 2: Description of experiments evaluating player ball control

Name Description # AttemptsDribbling Dribble the ball between six

cones as fast as possible2

Juggling Juggle the ball (with their feet)for as many times as possible

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3.2.7 Line experiment: Evaluation of player team skill

The players did a defensive line experiment in groups of six to measure theirability to work as a team. In the experiment, the group was standing besideeach other in a straight line and was asked to run forward as fast as theycould while still retaining the line formation. Occasionally a football coachclapped their hands, indicating that the group had to turn and run in the

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opposite direction. The experiment was repeated four times with differentgroup configurations with each group changing direction 11 times. The play-ers had done the experiment once before so that they would be familiar withit.

The following statistics were measured for each player from the line exper-iment: Speed, reaction time and velocity correlation, measured either whenrunning or when changing direction. A group is defined as running duringtwo seconds after a direction change to two seconds before the next directionchange. A group that is turning, or changing direction is defined as the timespan two seconds before and after a direction change.

Table 3: Description of measurements used to evaluate how well a playerscollaborate with their team members

Name Description Time segmentSpeed Average speed of group while

running2 s after a direction change and2 s before the next directionchange

Reactiontime

Reaction time compared withgroup members while changingdirection

2 s before and after a directionchange

Runcorrelation

Correlation score calculated fromspeed correlation between eachplayer in a group while running.Divided by total participationtime.

2 s after a direction change and2 s before the next directionchange

Turncorrelation

Correlation score calculated fromspeed correlation between eachplayer in a group while changingdirection. Divided by totalparticipation time.

2 s before and after a directionchange

3.2.7.1 Calculation of correlations scores for the line experiment

To be able to determine which player’s correlate more with their group mem-bers over the entire experiment a correlation score is calculated according toAlgorithm 1. To calculate the correlation score, Pearson correlations betweeneach player’s velocity were calculated (Equation 6) for two scenarios: Whenthe players are running and when they are changing direction. This gives

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a correlation matrix for each group and for each time segment for the twodifferent scenarios. The matrices were converted to absolute valued matricesby applying the absolute value to each element. This way the player’s whichdo not correlate at all would get low scores while those who correlate eitherpositively or negatively would get a high correlation score.

The equation used to calculate a correlation matrix was:

Ci = abs(corr(Vi, Vi)) (6)

where abs(A) = [|ak,l|] is a function that returns the absolute value foreach element ak,l in generic matrix or vector A. The function corr(A,B)calculates the Pearson correlations between all elements in two generic vectorsA and B. Vi is a vector of the velocities of all players for time interval i andCi is the resulting (absolute valued) correlation matrix between all player’svelocity for time interval i.

These series of correlation matrices were used to calculate a correlationscore for each player and each scenario. The correlation scores were normal-ized by weighting the score gained from a correlation matrix by the lengthof that time span and finally divided by the total amount of time for thatscenario.

The GPS units does not directly give a velocity, they only measure theplayers speed. But since the players are only moving in one dimension andthe direction of their movement is known the velocity is easily derived. Thevelocity was used for the correlation calculations because in the deviationsof the player’s position were too small compared to the accuracy of the GPSwhile the measured speed had higher deviation (compared to the GPS accu-racy of the measured speed).

3.2.8 Match experiment: Evaluation of player match skill

Five matches, with three versus three players (no goalkeeper), were playedwith different group configurations so that each player got to play at leastone match (small pitch ≈ 26 × 14 meters, small goals 0.8 meters wide and0.6 meters high). The starting formation of each team was with two playersplaced at each corner of their side of the pitch and one player in front oftheir goal (Figure 1). Each team composition was chosen by a coach, but theindividual positions were chosen by the players. The teams were chosen sothat the their skill level would be on a similar level by choosing each groupso that their combined rank from the dribbling and juggling experiment (seeFigure 4) would be on the same level between the groups.

If the ball went out of bounds or if a team scored a goal each playerhad to return to their starting position and a player chosen by the coach

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would start with the ball. Each player started with the ball an equal amountof times. During each match a commentary was recorded stating whichplayer who currently is possessing the ball, if the ball went out, if a goal wasscored or if the match was otherwise paused. Each match was between 3to 5 minutes long. The following parameters were measured for each player:Number of received and successfully made passes, number of interceptions,ball possession, position in team formation, number of goals scored, speedand correlation between the player’s movement (Table 4).

Table 4: Description of player statistics measured during a match and thenormalization method used for each measurement.

Name Description NormalizationPasses received Number of received passes Divided by team ball

possession timePasses made Number of successful

passesDivided by team ballpossession time

Interceptions Number of time a playerbroke an opponent’s attack

Divided by opponent ballpossession time

Ball possession Amount of time possessingthe ball

Divided by team ballpossession time

Formation Position in team formation(Wing or center)

N / A

Goals scored Number of goals scored Divided by total timeplayer was playing actively

Speed Average speed Only measured when aplayer was actively playing

Corr, team(Attacking)

Correlation score withteammates while attacking

Divided by team ballpossession time

Corr, team(Defending)

Correlation score withteammates while defending

Divided by opponent ballpossession time

Corr, opponent(Defending)

Correlation score withopponents while defending

Divided by opponent ballpossession time

3.2.8.1 Calculation of correlation scores for the match experiment

The correlation scores for the match experiment are calculated analogouslyto the correlation scores from the line experiment (Section 3.2.7.1) but withthe difference that rather than using the velocities, the player’s position along

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the X-axis (axis parallel to the pitch) were used, and the correlations werecalculated when a team was either attacking or defending.

A team is defined as attacking if they have possession over the ball forfour consecutive seconds or longer while a defending team is the opposingteam in that scenario.

Figure 1: Three versus three pitch, with the X-axis parallel with the pitchlength and the Y-axis parallel with the pitch width. Yellow and blue circlesare the starting position for the yellow and blue team respectively. Pitchsize: ≈ 26× 14 meters.

3.3 Results

3.3.1 GPS validation

The mean and standard deviation was calculated from the time series oferrors given by equations 1 and 2 (Figure 2). The mean error was calculatedto E = 1.2 for the relative GPS experiment and slightly lower for the lineexperiment. This is a smaller error than the accuracy of 3m given by thespecification of the GPS (Section 3.2.1).

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Figure 2: Mean error and standard deviation of the relative position errorof the GPS units for a GPS validation experiment(blue). Mean error andstandard deviation of the the position parallel to the direction of movementfor a line (one dimensional) GPS validation experiment(red).

3.3.2 Ball control experiment results

Players which do well in one of the two ball control experiments (dribblingand juggling) also seem to do well in the other ball control experiment, witha Spearman rank correlation of ≈ 0.8(p < 0.01) (Figure 3). Those playersseem to have better control over the ball in general. The ranking were appliedso that skilled players have low rank, i.e descending order for the jugglingexperiment and ascending order for the dribbling experiment.

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Figure 3: Juggling versus dribbling Spearman ranking for players partici-pating in a ball control experiment. The result for the worst and best playerfor each measurement is noted in a parenthesis next to the rank. Skilledplayers have low rank.

3.3.3 Assignment of player ID

Each players was given an ID ordered after their combined performance in thetwo ball control experiments between 15 players by combining the rank fromboth experiments. The player with the lowest combined rank was denotedas having player ID 1, the next lowest as having player ID 2, and so on untilthe player which had the highest combined rank were given ID 15 (Figure4).

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Figure 4: Combined Spearman ranking from a dribbling(blue) and jug-gling(red) ball control experiment for 15 players. Players were given an IDdepending on their combined rank from these two experiments with the playerwith the lowest combined rank given ID 1 and the one with the highest com-bined rank given ID 15. Skilled players have low rank.

3.3.4 Line experiment results

No Spearman correlations with at least 95% confidence were found eitherbetween the measurements from the line experiment or between the lineexperiment and the ball control experiment.

3.3.5 Match experiment results

There were several correlations between the measurements from the matchcontrol experiment that correlated with each other and with the ball controland line experiment.

3.3.5.1 Ball control

Passes made correlated with ball possession with a correlation of≈ 0.75(p < 0.01)and ball possession correlated with scored goals at ≈ 0.52(p < 0.05). Ballpossession, passes received, passes made and goals scored correlated with thedribbling experiment positively with correlations between≈ [0.59, 0.89](p < 0.02)(Figure 5), and (to a lower degree) with the juggling experiment.

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Figure 5: Spearman ranked ball possession versus passes made, (a) scoredgoals (b) and dribbling time (c) as well as passes received versus dribblingtime (d), for players participating in a match and a dribbling experiment.The result for the worst and best player for each measurement is noted in aparenthesis next to the rank. Skilled players have low rank.

3.3.5.2 Player formation and ball control

Player’s position in the team formation correlate positively with dribbling,juggling, ball possession and passes received, i.e players which have a centerposition also receive more passes and are better at dribbling and juggling(Figure 6). The player’s position in each team were not enforced so it seemlike that players that are good at dribbling and juggling also take the centerposition. Players which have a center position also get more passes andpossesses the ball for more time compared to their team members. See Figure7 for an example of a pass chain from the match.

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Figure 6: Passes received and ball possession Spearman rank for each playerparticipating in a match. Each player’s position in their team formationis noted in parenthesis next to their player ID as C, a center player, orW, a wing player. Players with a high amount of received passes and ballpossession have low rank.

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Figure 7: One of the longer passing chains recorded from a three versusthree match. The center player (blue) acts as an intermediate player wherethe two wing players (yellow) does rarely pass the ball to each other. Thenumbers indicate the order of the passes where number one is the first passwhile the arrows indicate the direction of the pass.

3.3.5.3 Line experiment and scored goals

A negative correlation were found between the Spearman rank the turncorrelation from the line experiment and the number of scored goals with≈ −0.52(p < 0.05). The players which correlated with each other the leastwhile turning during the line experiment also scored more goals in general(Figure 8d).

3.3.5.4 Correlations between players in a match and in the lineexperiment

Players that correlated with their team members while defending also cor-relate with their opponents while defending with a Spearman correlation of≈ 0.61(p < 0.02). Players that correlated while team members correlatedwith the player’s speed rank (0.74(p < 0.01)). Players which also correlatedwith team members while attacking also correlate with each other while run-ning in the line experiment (≈ 0.58(p < 0.05)) (Figure 8a, 8b, 8c).

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Figure 8: Spearman rank between different measurements for players par-ticipating in a match and a line experiment. The figure show: Players thatcorrelate with their team members while attacking versus player speed duringmatch (a) and correlation while running in the line experiment (b), playersthat correlate with their team versus opponents while defending (c), playersthat correlate with each other while changing direction in the line experimentversus scored goals during match (d). The results for the lowest and highestranked player for each measurement is noted in a parenthesis next to theirrank. The ranking is applied in descending order.

3.3.6 Correlations between player measurements

The Spearman’s rank correlation between all measurement from the threeexperiments are shown in Figure 9. Correlations with significance lower than95% were removed.

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Figure 9: Spearman correlations with at least 95% significance betweenmeasured and derived values from three different football experiments fordifferent players. Red indicates a positive correlation while blue is negative.

3.3.7 Correlations between team measurements

The average of each player’s measurements for the three experiments werecalculated for every team from the five matches in the match experiment.Two teams consisted of exactly the same members so there were nine differentteams in the five matches. The Spearman correlation were calculated for thedribbling, juggling, number of interceptions, goals scored, opponent scoredgoals, speed, correlation with team members while attacking and defendingand correlation with opponents while defending (Figure 10). Correlations

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with significance less than 95% were removed.From this figure it is seen that teams that had players that were good

at juggling also had players good at dribbling (≈ 0.68(p < 0.05)). Howeverno significant correlation between the number of scored goals and opponentscored goals were found.

Teams with fast players correlated with teams which had a high corre-lation with each other while attacking (≈ 0.75(p < 0.02)) while they cor-related negatively with teams that had a high correlation while defending(≈ −0.7(p < 0.05)).

Figure 10: Spearman correlations with at least 95% significance betweenmeasured and derived values from five football matches and nine differentteams. Red indicates a positive correlation while blue is negative.

3.4 Discussion

3.4.1 GPS

One of the goals of these experiments was to see how well this particularGPS, and in extension other GPS with similar capabilities, in reality would

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work to measure position data and calculate correlations between footballplayers movement.

While the GPS did perform as advertised and in line with previous find-ings [16], they did not work well in the line experiment. The players whichhave the biggest trouble at keeping the line intact still kept within the errormarginal of the GPS, hence it was not possible to determine which playersand groups were good or bad at keeping the line intact by studying the GPSpositions.

The GPS were accurate enough to measure the player’s general positionsin a match. The GPS might not be able to accurately measure a playerdribbling past another player or an interception, but is accurate enough tomeasure the general movement of the players on the pitch. The matches inthe experiment were small three versus three matches so there were a lot ofclose interaction between players, thereby using these GPS might not havebeen optimal for this particular set up. They would probably work better ona normal sized football field with more players since close interactions wouldnormally only include a few of the players at a time.

3.4.2 Ball control

While giving each player a few more attempts at the dribbling and jug-gling experiment and increasing the number of participating players wouldbe preferable, the data gathered was enough to determine that a player goodat dribbling was also good at juggling and vice versa (which is not really asurprising result) (Figure 4). That dribbling and juggling correlate with eachother is in line with previous findings [8].

Players which were good at the ball control experiment also got betterresults during the match. They have a higher ball possession, make andreceive more passes and they score more goals (Figure 5). This is similar toprevious findings, where players good at dribbling were also good at offense inone versus one matches, but no significant correlation was found for playersgood at juggling and one versus one match skills [8].

However, they also take the center position in the team and it is seen thatsuch players receives more passes and have a higher ball possession (Figure 6).But is the only reason they receive more passes because they have the centerposition, because players pass the ball to players they think are skilled orbecause these players actually are better at positioning themselves and thusreceive more successful passes? Since one goal of the experiment was to see ifthe ball control experiment would be good indicators to match performancethis dependency should be removed.

Currently these results show that players with good ball control might

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be better at playing an actual match, or it might be because they take thecenter position. In a future match experiment the player’s positions in theteam should be predetermined and should change throughout the match toremove this dependency.

3.4.3 Line experiment

The line experiment might be able to predict how well player’s in a matchwill correlate with each other, as seen in Figure 8b. It is not far fetched tobelieve that players which are good at correlating in one of the experimentsalso is in the other. However, the significance of the correlation is low so thecorrelation found might not be relevant.

For some reason, players that correlate while changing directions alsoscore less goals (Figure 8d). Why this is the case is unknown, since it is hardto find a logical link between the two measurements. This correlation is notvery strong as well so there is a high possibility that there is no correlationbetween the two.

Since all measurements from the line experiment have low significancemore tests with more players would have to be done to see if there actuallyare any significant correlations between the line experiment and the othertwo experiments.

3.4.4 Match experiment

No significant correlation was found between teams with high ball controland teams that scored many goals (Figure 10) although individual playerswho had high ball control did score more goals (Figure 5b). However onlyfive matches were played so we can only say that we didn’t find a significantcorrelation not that there is none. More matches should be played to eitherfind out the answer.

Players with high speed did correlate also did correlate more with theirteam while attacking both individually and as a team (Figure 5a, Figure10). The same is said for players that correlate well with team members andopponents while defending (Figure 5c, Figure 10). Teams that correlatedwhile defending did not correlate while attacking (Figure 10). One explana-tion for this might be that some players are more offensive (correlate whileattacking) and some players are more defensive (correlate while defending)although there are no results to back this claim.

See Appendix A for video examples of correlating players.

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4 Visualization of collective motion of a pro-

fessional football players in a eight versus

eight match

4.1 Introduction

The goal of this part of thesis was to implement a visualization tool that couldbe used to observe the collective motion behaviour of players and the ball ina football match. The collective motion focused on in this implementationis leader-follower relationships[14, 16], where one player is following anotherplayer.

In addition, Voronoi regions of the players were implemented into theGUI. A Voronoi region is the region around a point which is closer to the pointthan any other point in the space. Thus a football players Voronoi region isthe region which is closer to the player than to the other players and is animportant concept in football. For example, a team would want to increasethe area of their own Voronoi regions while decreasing their opponents [11].

A data set of a professional football match is used as an example to showthe visualization.

4.2 Materials and methods

4.2.1 Data description

The data used for the visualization was a public data set with sensor datafrom a 8 versus 8 football match in Nuremberg Stadium, Germany using alocal wireless positioning system[1]. The sensors were placed on both feet ofeach football player, the judge and also in the ball. The sensors placed onthe players and the judge recorded data at 200Hz while the sensor placed inthe ball recorded data at 2000Hz. Each sensor recorded the current time, itsposition, magnitude and direction of speed as well as direction and magnitudeof their acceleration.

The match was carried out on a half sized football pitch (≈ 70 × 50meters). Two periods were played, each being 30 minutes long.

4.2.2 Preprocessing of data

The data was rotated 90 degrees so that the horizontal axis (X-axis) wouldbe parallel with the pitch. Linear interpolation was used to align data points

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to even 1/25s intervals, and then downsampled to 25 Hz. Missing data pointswere filled in using linear interpolation if the gap was small enough (< 1s)[21].

The senor data from each foot were averaged to a single data point, ratherthan two, for each player.

4.2.3 Time window

The match was divided into rectangular time windows of length Ti. Timewindows of any length can be used. Shorter time windows use less samplesand are therefore more prone to noise and are less reliable. Using a longertime window is more reliable, but if the time window is too long it won’t beable to find dynamic correlations that change too quickly over time.

In this thesis the length of the time window was set to Ti = 5 seconds sinceit seemed like this time window worked well for observing overall patterns.

4.2.4 Time lag correlation

Time lagged correlations between each player’s data points were calculatedfor all time windows in the match[16, 19]. During every such time window,the correlation between the player’s X and Y positions (axis parallel andperpendicular to the pitch respectively), speed and direction was calculatedas for all time lags t = [0, Tlag]:

Ci,t = corr(Pi,0, Pi,t) (7)

where Ci,t is the correlation matrix between all players parameters fortime interval i and time lag t. The function corr(A, B) calculates the Pearsoncorrelation between all of the player’s parameters in two matrices A and B,with parameters as columns and data points as rows. Pi,t is a matrix withall player’s parameters as columns and with all data points as rows, for timeinterval i. The data points in the matrix Pi,t are shifted t seconds to thefuture compared to Pi,0.

Since the data points are shifted compared to each other, if the currenttime window is on an edge, the non-shifted and shifted data points on bothedges won’t match up with any shifted and non-shifted data points respec-tively. For this reason, calculating lag correlations with a lag of Tlag secondswould remove 2 · Tlag seconds worth of data. This is not a problem whenanalyzing an entire 30 minute long match. But if analyzing short scenarios,the time lag can’t be too big because of this reason.

The return matrices Ci,0 are normal symmetrical correlation matricesbetween all parameters for each player. However, the matrix Ci,t, for t > 0,is no longer symmetrical due to the time lag. Row A and column B from the

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matrix with lag t would return the correlation between the current values Aand the future values of B.

For every time window and row in the correlation matrix a function c(t)is defined which return the correlation at time lag t. The maximum time lagcorrelation is defined as ‖c‖∞ and the maximum time lag, Tmax, is defined asthe the smallest time lag, t, which satisfy c(t) = ‖c‖∞[16]. If Tmax > 0 thenthat means that the parameter stored at column B is following the parameterin row A, with lag Tmax, since future values of B correlate with the currentvalues of A the most at that point (Figure 11).

Tlag = 2 seconds for this report because football players should rarelybase their movement on older position data.

Figure 11: Example of a time lagged correlation curve. There is a max-imum correlation with a time lag of 1 second (maximum time lag), wherethe correlation is 0.8 (maximum time lag correlation). The area below themaximum lag correlation, above the correlation curve and to the left of themaximum time lag is the lag score.

4.2.5 Lag score

As a supplement of measuring the leader-follower behaviour a lag score wasdefined(8) and calculated for each player. The lag score is calculated fromthe maximum time lag, by calculating the area above the time lag correlationcurve but which is below the maximum time lag correlation (Figure 11). This

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gives a measurement of how strong the leader-follower relationship is. Forexample, if the maximum time lag would be high but the lag score be verylow, the leader-follower relationship can be considered as weak.

For every time window and row in the correlation matrix the lag score iscalculated with the following equation:

S = ‖c‖∞ −∫ Tmax

0

c(t)dt (8)

where S is the lag score and c(t) is the correlation between two parame-ters, A and B, where B is shifted to the future compare to A, with time lagt. c(t) is defined on the interval [0, Tlag]. Tmax is the smallest time lag, t,which satisfy c(t) = ‖c‖∞.

4.2.6 Implementation

Matlab was used for implementation, using Matlabs built in graphical userinterface system: GUIDE[15]. The implementation is divided into two parts:

1. Precalculate the correlations for a preset time window function and apreset time lag

2. Render the match in the GUI

The precalculation stage only has to be run once for a given data set, timelag and window function. In the precalculation stage the maximum time lagand lag score are calculated for every time window in the match, and storedin a file.

After the calculation stage a user may load the stored file using the GUIand observe different parts of the match without the need of additional com-plex calculations.

Since the maximum time lag is calculated for every time window the cor-relations will change abruptly between two subsequent time windows. Linearinterpolation is therefore used to calculate intermediate values of the max-imum time lag, maximum time lag correlation and lag score between twosubsequent time windows. This way the GUI will show a gradual changesrather than sudden abrupt changes. However caution must be taken, espe-cially if the size of the time windows are big, since the values shown betweenthe interpolation points might not be the true values at that point.

4.3 Results

Figure 12 show the implemented GUI. The GUI show the pitch as well asall players and the ball in the center frame. Each yellow and red circle in

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the frame are players from team yellow and red respectively. The blue circleis the ball. The size of the circle of a player show their correlation with theball, with bigger circles showing a bigger correlation. A player which havepossession over the ball have a smaller black dot in the middle of their circle.

The scrollbar below the frame is used to advance, and show, the currenttime in the match. The menu options above and beside the match frame areused to show maximum time lag between players, which parameters are usedfor the correlations and different Voronoi regions.

Figure 12: Visualization GUI showing players from a foot ball match. Theyellow and red circles are players from team yellow and red respectively. Theblue circle is the ball. Players with bigger circles have a higher correlationwith the ball in the Y-axis .The light blue lines show the Voronoi regions ofthe yellow players, excluding the yellow goal keeper.

4.3.1 Maximum time lag

The correlation as well as the maximum time lag between the players canbe shown by connecting players with an edge. The edge is a double pointedarrow, where the pointedness of the arrow represent the maximum time lagbetween the players and the color of the edge show the magnitude and signof the correlation.

If the correlation is positive between two players the edge will be green,with green edges showing a high magnitude while darker green edges show a

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lower magnitude. Negative correlations are shown analogously but using thecolor blue instead.

The more pointy an edge is, the bigger the maximum time lag is. Forexample, if an edge is pointing from player A toward player B, that meansplayer A is following player B (if the correlation also is high). If the edgewould not be pointy player A would not be following player B. If the edgepoints at both players they both would follow each other.

The GUI can be changed to show the lag score (Section 4.2.5) betweenthe players, rather than maximum time lag, by choosing Score rather thanDelay under the section Lag Type. A higher lag score gives a more pointyedge.

By changing the radio buttons under the sections Origin and Target cor-relations between the following parameters can be shown, the player’s andballs position along the X and Y-axis, speed (|v|) and direction (angle). Dif-ferent parameters for Origin and Target can be chosen. For example if Xis ticked under Origin and Y under Target, the part of the edge closest toplayer B would show the correlation between the X position of player A andY position of player B. If the edge would be pointing from player A to playerB it would mean that the X position of player A is following the Y positionof player B.

In Figure 13 the maximum time lag correlations are shown for players ofthe yellow team (excluding the goal keeper).

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Figure 13: Visualization GUI showing collaborative motion between playersin a team from a foot ball match. The yellow and red circles are players fromteam yellow and red respectively. The blue circle is the ball. Players withbigger circles have a higher correlation with the ball in the X-axis. The edgesconnecting the yellow players show their correlation and maximum time lagwith each other in the X-axis. Light green edges represent a high positivecorrelation while darker edges represent a correlation closer to zero. Theedges are double pointed arrows with variable width depending on how bigthe time lag is between the players. A pointy edge pointing from player A toplayer B mean player A is following player B.

4.3.2 Voronoi Regions

The Voronoi regions for the players can be shown in the GUI by ticking theAll, Yellow or Red Voronoi boxes which show the regions for all, yellow or redplayers respectively (excluding goal keepers). The red and yellow goalkeeperas well as the ball can be included if the corresponding box is ticked in aswell. For example, Figure 12 show the Voronoi regions for the yellow team.

4.4 Discussion

The implemented GUI works well for observing the entire match and quicklychange which parameters or players which should looked closer to at the

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given moment. This eases the process of finding interesting scenarios whichare interesting to analyse further and to make humans understand the data.For example, the GUI can be used to see in which scenarios the players aremore correlated than in other scenarios and which players are more correlatedwith whom and how it changes over time. See Appendix B for exampleobservations.

However, in football, the ball is probably the most important object andit’s position and velocity change the overall state and response from theplayers directly. In the current state the GUI is not able to remove the effectthe ball has on the players, i.e even the players would be correlating witheach other they all might just be following the ball rather than each other.For this reason, in a future version of the GUI, a user should be able toremove the influence of the ball from the player-player correlations.

5 Conclusions

The conclusion of this project is that the GPS do work, if the experimentsare set up in the correct way. For example, doing the experiment on moreplayers on a bigger pitch would work better since the GPS error would notbe as significant as in a smaller three versus three match.

It was found that players which performed well in the ball control exper-iment also seemed to have better ball control in the match and scored moregoals. However, these players also took the center position in the team, aposition which correlated positively with the number of received passes andball possession. Also, not significant correlation between the final match re-sults and any other parameter was found so it is not certain if having playerswith good ball control actually improve the team’s performance. This wouldnot have been a problem if the player’s positions were predetermined. Tomake the data more reliable in general more than 15 players should havebeen used for the experiments and the players should have played more andlonger matches. If so we would be able to find out if there actually is anyrelationship between the line experiment and the collective motion in thematch.

The visualization tool works well for observing the collective motion be-tween the players and the ball but it is also a tool that can be developed muchmore. In the next version of the GUI the ability to remove the influence ofthe ball to the players movements should be implemented so that the playerrelationships can be studied more directly.

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6 Future Outlook

There are countless experiments that can be done using GPS and footballplayers to further analyze the connections between different statistics andfind training exercises that prepare players for a match. Some ideas:

1. Correlations between players movement and the intersections of Voronoiregions could be analyzed to see if players which follow these regionsreceive more passes or not.

2. See if different players in a full size team correlate differently than theirteam members depending on their position.

3. Measuring maximum time lag between position correlations during amatch or the line experiment to see if some players assume leader-followpositions.

4. Letting two players run each running on one out of two perpendicularlines, where one player’s goal is to get as far away from the other playeras possible while the other has to follow. Can be done with the chasedplayer having run with and without a ball.

The visualization tool is a start to a deeper analysis of collective motionin football. The data set used for the visualization is a good data set to alsoperform some analysis like those done on the youth football team. Otherthan that it is a tool that can be developed with many more features whichwould help users to observe specific scenarios or show the collective motionbetween agents from something entirely different than football.

Appendix A Movie examples of collective mo-

tion of a youth football team

This video show the GPS positions of the football players during the match.The correlations between the player’s movements are also shown.

Link: https://www.youtube.com/my_videos?o=U

Appendix B Movie examples showing the vi-

sualization

From time 0.00 to 1.04 the yellow team is defending and is an example of adefending team having a high correlation.

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Link: https://youtu.be/dRLr-lBR2-YFrom time 0.00 to 1.04 the red team is attacking and is an example of anattacking team being less correlated.

Link: https://youtu.be/vAosLGGLXyUAt time 0.19 there is an example of an attacking team getting more correlatedas they begin to advance.

Link: https://youtu.be/B_i98WdH0Pk

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