Post on 04-Jun-2018
DevelopingaData-DrivenPlayerRankinginSoccerUsingPredic8veModelWeights
JoelBrooks Ma>hewKerr JohnGu>agMassachuse>sIns8tuteofTechnology
Mo8va8on• TeamsthisyearinLaLigaarespendingover$3billionontheirplayers
• Howdoteamsevaluateaplayer’sworth?
• Quan8ta8vemetricscanhelpjus8fysubjec8veevalua8ons,andprovidenewinsightintonon-obviousplayercontribu8ons
Imagesource:h>p://espn.go.com/sports/soccer/news/_/id/5580467/european-football-ea8ng-itself2
PassingContribu8onsonOffense
• Passingstrategyisakeycomponentofoveralloffensivesuccess
• Wefocusedspecificallyonthecontribu8onofspecificpassesonoffense
• Passestellyoualotabouthowmuchanindividualplayercontributesonoffenseoutsideofgoalsandassists
3
Howtorankplayersfrompasses?
7
Loca8onsofPassesWithinaPossession
DistributedLoca8onFeatureRepresenta8on
Howtorankplayersfrompasses?
8
SupervisedLinearModelforPredic8ngShots
Loca8onsofPassesWithinaPossession
DistributedLoca8onFeatureRepresenta8on
Howtorankplayersfrompasses?
9
SupervisedLinearModelforPredic8ngShots
PassValueMeasurementBasedonModelWeights
Loca8onsofPassesWithinaPossession
DistributedLoca8onFeatureRepresenta8on
Howtorankplayersfrompasses?
10
SupervisedLinearModelforPredic8ngShots
PassValueMeasurementBasedonModelWeights
Loca8onsofPassesWithinaPossession
DistributedLoca8onFeatureRepresenta8on
Thedata
• (x,y)coordinatesofallpassoriginsanddes8na8onsfromthe2012-2013LaLigaseason
• >300,000passes• 380games• >500players
11
Imagesource:h>ps://flic.kr/p/nvVaHM
SparsePassLoca8onRepresenta8on
DEFENSE OFFENSE
Origin(zone10) =[0,0,0,0,0,0,0,0,0, ,0,0,0,0,0,0,0,0]Des8na8on(zone14) =[0,0,0,0,0,0,0,0,0,0,0,0,0, ,0,0,0,0]
14
DensePassLoca8onRepresenta8on
DEFENSE OFFENSE
15
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]Des8na8on(zone14)=[0,0,0,0,0,0,0,0,0,0, ,0,0, ,0,0,0,0]
PassLoca8onRepresenta8onFormula• Representapassloca8onlas:
• Eachelementofris:
• d(l,zi)istheEuclideandistancebetweenlandthecenterofzoneI• ciisanindicatorvariablethatis1ifiisoneoftheNclosestzones,0
otherwise• Inprac8ceN=2seemtoleadtothebestresults
16
DensePassLoca8onRepresenta8on
DEFENSE OFFENSE
17
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]Des8na8on(zone14)=[0,0,0,0,0,0,0,0,0,0, ,0,0, ,0,0,0,0]
FeatureVectorforaPossession
• Foreachpassinthepossessionwithanoriginloanddes8na8onld:1. Computerloandrld,
thevectorrepresenta8onsofthepassoriginanddes8na8on
20
FeatureVectorforaPossession
• Foreachpassinthepossessionwithanoriginloanddes8na8onld:1. Computerloandrld,
thevectorrepresenta8onsofthepassoriginanddes8na8on
22
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]
Des8na8on(zone14) =[0,0,0,0,0,0,0,
0,0,0, ,0,0, ,0,0,0,0]
FeatureVectorforaPossession
• Foreachpassinthepossessionwithanoriginloanddes8na8onld:1. Computerloandrld,the
vectorrepresenta8onsofthepassoriginanddes8na8on
2. ComputethematrixRlod=rloxrld,theouterproductoftheoriginanddes8na8onrepresenta8ons
23
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]
Des8na8on(zone14) =[0,0,0,0,0,0,0,
0,0,0, ,0,0, ,0,0,0,0]
FeatureVectorforaPossession
• Foreachpassinthepossessionwithanoriginloanddes8na8onld:1. Computerloandrld,the
vectorrepresenta8onsofthepassoriginanddes8na8on
2. ComputethematrixRlod=rloxrld,theouterproductoftheoriginanddes8na8onrepresenta8ons
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0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 .32 0 0
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]
Des8na8on(zone14) =[0,0,0,0,0,0,0,
0,0,0, ,0,0, ,0,0,0,0]
Origin-Des8na8onOuterProduct(10,14)=
......
FeatureVectorforaPossession
• Foreachpassinthepossessionwithanoriginloanddes8na8onld:1. Computerloandrld,the
vectorrepresenta8onsofthepassoriginanddes8na8on
2. ComputethematrixRlod=rloxrld,theouterproductoftheoriginanddes8na8onrepresenta8ons
25
Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]
Des8na8on(zone14) =[0,0,0,0,0,0,0,
0,0,0, ,0,0, ,0,0,0,0]
R(7,11)= * =R(7,11)= * =R(7,14)= * =R(10,11)= * =R(10,14)= * =
Origin-Des8na8onOuterProduct(10,14)=
FeatureVectorforaPossession• Foreachpassinthe
possessionwithanoriginloanddes8na8onld:1. Computerloandrld,the
vectorrepresenta8onsofthepassoriginanddes8na8on
2. ComputethematrixRlod=rloxrld,theouterproductoftheoriginanddes8na8onrepresenta8ons
3. Constructthefeaturevectoras: [rlo,rld,fla>en(Rlod)]
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Origin(zone10) =[0,0,0,0,0,0, ,0,0, ,0,0,0,0,0,0,0,0]
Des8na8on(zone14) =[0,0,0,0,0,0,0,
0,0,0, ,0,0, ,0,0,0,0]
R(7,11)= * =R(7,11)= * =R(7,14)= * =R(10,11)= * =R(10,14)= * =
Origin-Des8na8onOuterProduct(10,14)=
FeatureVectorforaPossession
• 18origin+18des8na8on+324origin-des8na8onpairfeatures=360features
• Thefeaturevectorforapossessionistheaverageofthefeaturevectorsforeachindividualpass
• Eachfeaturevectorisassignedalabel:– +1ifthepossessionendedinashot– -1otherwise
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ExperimentalOverview• Usedthefirst80%ofgames
inthe2012-2013seasonasatrainingset
• Evaluatedthemodelonthefinal20%
• TrainedaL2-regularizedSVMmodelfindingthewthatminimizes:
• ClassspecificcostparametersCkchosenwith5-foldcrossvalida8on
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False Positive RateTr
ue P
ositi
ve R
ate
ROC Curve for Shot Predition Model (AUC = .79)
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AUC=0.79
TopModelWeights
14 − 1816 − 14
9 − 1415 − 14
18 − 168 − 15
18 − 1414 − 13
14 − DT5 − 14
−0.015
−0.010
−0.005
0
0.005
0.010
0.015
0.020
Feature
Relat
ive F
eatu
re W
eight
DEFENSE OFFENSE
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14 − 1816 − 14
9 − 1415 − 14
18 − 168 − 15
18 − 1414 − 13
14 − DT5 − 14
−0.015
−0.010
−0.005
0
0.005
0.010
0.015
0.020
Feature
Relat
ive F
eatu
re W
eight
TopModelWeights
DEFENSE OFFENSE
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14 − 1816 − 14
9 − 1415 − 14
18 − 168 − 15
18 − 1414 − 13
14 − DT5 − 14
−0.015
−0.010
−0.005
0
0.005
0.010
0.015
0.020
Feature
Relat
ive F
eatu
re W
eight
TopModelWeights
DEFENSE OFFENSE
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ModelWeightsàPassValueMetric
• Weightsprovideaconceptualmaptowhichloca8onsleadtoshots
• Eachpasshasthreerelevantmodelweights– Origin– Des8na8on– Origin-Des8na8onpair
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PassShotValue(PSV)
• PassShotValue(PSV)iscomputedforapasswithorigininzoneiandades8na8oninzonejas:
• Sumofthemodelweightsforthecorrespondingorigin,des8na8on,andorigin-des8na8onpair,respec8vely
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PassShotValue(PSV)
• PassShotValue(PSV)iscomputedforapasswithorigininzoneiandades8na8oninzonejas:
• Sumofthemodelweightsforthecorrespondingorigin,des8na8on,andorigin-des8na8onpair,respec8vely
• e.g.:
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PSVasaPlayerMetric
• Foreveryplayer,computethePSVforeverycompletedpassinwhichtheywerethedistributor
• Averagethesevaluesovertheen8recourseoftheseason
• Limitedanalysistoplayerswith>200completedpasses– ~350players
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TopPlayersbyAveragePSV
Offense Midfield Defense
TopGoalScorers TopPlayersbyAssists
Correla8on:ρ=0.27,p<0.05
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Conclusion• Theloca8onsofpassescanpredictwhetherapossessionendsinashot
• Therela8onshipbetweenpassloca8onandshotscanbeusedtounderstandtheoffensivevalueofindividualpasses
• AveragePSVseparatesplayersbyposi8on,andseemstocorrelatewellwithoffensiveabilitywithineachposi8on
• Almosteveryotherpopularsportiscollec8ngloca8onsofevents,soasimilarmethodologycouldbeapplied
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Conclusion• Theloca8onsofpassescanpredictwhetherapossessionendsinashot
• Therela8onshipbetweenpassloca8onandshotscanbeusedtounderstandtheoffensivevalueofindividualpasses
• AveragePSVseparatesplayersbyposi8on,andseemstocorrelatewellwithoffensiveabilitywithineachposi8on
• Almosteveryotherpopularsportiscollec8ngloca8onsofevents,soasimilarmethodologycouldbeapplied
45Ques8ons?