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MakingOffensivePlayPredictable-UsingaGraphConvolutionalNetworktoUnderstandDefensive

PerformanceinSoccer

MichaelStöckl,ThomasSeidl,DanielMarley&PaulPower|StatsPerform

1.Introduction1.1MeasuringdefensivequalityinsoccerTheartofgooddefendingistopreventsomethingfromhappeningbeforeithasevenhappened.VirgilVanDijkisconsideredoneofthebestdefendersinworldsoccerashehastheabilitytopreventapassbeingmadetoanopenattackertoshootbyforcingtheballcarriertopasssomewhereelselessdangerous.However,whileweknowthisisgreatdefending,intoday’sstats,VanDijkwouldnotreceiveanyacknowledgement.Adefender’scontributionissimplymeasuredbythenumberoftacklesorinterceptionstheymake.Butwhatifwewereabletomeasureactionsthathavebeenpreventedbeforetheyweremade?The aimof a defense and a defender is tomakeoffensive playpredictable. For example, JürgenKlopp’sLiverpool,presstheoppositionwiththeaimofforcingthemtogivetheballawayinspecificareasofthepitchbylimitingthenumberofpassingoptionsavailableindangerousareas. Iftheartofgooddefendingistomakeplaypredictable,thenitshouldbemeasurable.Givenenoughdata,weshouldbeabletopredictwhereaplayerwillpasstheball,thelikelihoodofthatpassbeingcompletedandwhetherthispasswillresultinascoringopportunity.Itthereforestandsthatweshouldbeabletomeasureifadefenderforcesanattackertochangetheirmindortopreventanattackerfromevenbecominganoption.Figure 1 shows a situation from a match between Liverpool vs Bayern Munich in the 2018/19UEFAChampionsLeaguethatleadstoMané(red10)scoring.OurmodelidentifiesthatMilner(red7)istheprimarytargetforVanDijk(red4)inthefirstinstance.However,duetothecombinationofGnabry(blue22)closingdownMilner,Lewandowski(blue9)closingdownVanDijkandManémakinganactiverun,behindthedefence,Manébecomesboththemostlikelyreceiverandahighthreatforscoring.Thisdemonstratesourabilitytomodelhowplayersdecisionmakingisinfluencedandhowasituationcanmovefromlowthreattohighthreatbytheoff-ballactionsofattackersanddefenders.[LINKTOVIDEO].InthispaperwepresentanovelGraphConvolutionalNeuralNetwork(GNN)whichisabletodealwithhighlyunstructuredandvariabletrackingdatatomakepredictionsinrealtime.Thisallowsustoaccuratelymodeldefensivebehaviouranditseffectonattackingbehaviour,i.e.,preventingactionsbeforetheyhaveoccurred.Todothiswetrainedthefollowingmodels:

- xReceiver:Predictsthelikelihoodofeveryplayerbecomingthepassreceiveratanymomentwithinaplayerpossession.

- xThreat:Predictstheprobabilityofashotoccurringinthenext10secondsifapasswasplayedtoanattacker.

- xPass:Predictshowlikelyapasswouldbecompletedtoeachattackerofftheballatanymomentwithinaplayerpossession.

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andintroducenewdefensiveconcepts:

- Player Availability: Using the outputs from xReceiver and xPass we infer how available everyattackerisofftheballateachframe.

- Defensive Impact: We are able to detect high level defensive concepts such as ball and manorientateddefending,defensivepositionplayandoffballruns.

- Disruption Maps: Global visual representations of defending teams’ ability to disrupt theoppositionsattackingstrategy.

Figure1:Wetrainthreemodels(xPass,xReceiver&xThreat)tobetterunderstanddefensiveandoffensiveofftheballbehaviour,suchasman-orientateddefending,ball-orientateddefendingandactiveoffballruns.ThisletsusbetterunderstandhowSadioManéscoreda1-0leadvsBayernMunichduringLiverpool’swaytotheUCLfinalin2017/18.LINKTOVIDEO

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RelatedWork

1.2.1 DealingwithunstructureddataTrackingdataishighlyunstructuredandcanbedifficulttomodelduetomostmachinelearningtechniquesrequiringtabulardatasetswherefeaturesareinsertedinaspecificorder.TosolvethisorderingissueLuceyetal.[1]presentedtheconceptofaligningplayerstoaformationtemplate[1,2].However,thismethodhasseverallimitations.Firstly,insoccer,teamsusedifferentformationssoaplayeratrole10forateamusing433wouldbeverydifferenttoateamplaying352.Therefore,itisdifficulttocomparepredictionsbetweentheseplayers.Inaddition,thismethodisreliantuponteamshavingthesamenumberofplayersonthepitch(11perteam)meaningdifferentmodelshavetobelearnedwhenplayershavebeensentoffforexample.Withregardstorealtimeinferenceafurtherlimitationisthespeedatwhichplayersneedtobealignedbeforecalculatingfeaturesforinference.Fernandez[3]andBrefeld[4]useConvolutionalNeutralNetworks(CNNs)onanimagerepresentationoftracking data to circumvent the ordering/alignment issue while predicting probabilistic pitch controlsurfaces.Convertingtrackingdatadirectlytoimagesissuboptimalasonegivesupaverylow-dimensionaldata set and converts it into a high-dimensional sparse representation. Tracking data has an irregularstructureduetomissingplayersandalackofclearschemetoorderplayersinasequenceorframe[19].Bothtechniques are also time consuming and could cause timing issues for feature generation in real-timeapplications.Insteadofusinganimage-basedrepresentationweusedGraphNeuralNetworks(GNNs)which1)neglectstheneedfororderingfeatures,2)cancopewithvaryingnumberofplayersonthepitchand3)learns local and higher scale features directly from the tracking data. Horton applied a set-learningframeworktomodelpassinginfootballwhichissimilartoasimplegraph(noedges)[18].1.2.2 EvaluatingandPredictingFutureActionsinSportsConceptssuchasxThreatandxPassarenotnewwithpreviousresearchusingtrackingdatatopredictthelikelihoodofapassbeingcompleteoragoalbeingscoredafteraspecificaction [2,4,6]. Inaddition tomeasuringthevalueofanaction,theconceptofvaluingaplayers’offballposition,hasalsobeeninvestigated[2,3]. Spearman [9] alsodevelopedamodel to evaluateoff-ball scoringopportunities in soccer. ThesemodelscreateasurfaceareacombiningxThreatandxPassvaluestounderstandhowdangerousateam’sorplayer’scurrentpossessionisandalsowhatspacetheycontrol.Wei [7, 8] modelled the probability of where the next action will go in tennis and soccer. Franks [10]predicted defensive match ups and measured the influence of defenders on the offenses shootingperformance.Ghosting[11,12]hallucinatedwhereateamofdefenderswillmovetonextbasedonwheretheattackershavemoved,and theball ismoving to. Thispotentiallyprovidesuseful tools toassess thedefensive strategyof teamsbyevaluating thedifference inExpectedGoal (xG)orPossessionValue (PV)comparedtoaglobalbaseline.2.Method

2.1DataTotrainandvalidatethethreemodels(xTransition,xThreat,andxReceiver)weused1,200gamesoftrackingdatafrommultipleseasonsofTop5Europeanfootballleaguessampledat10Hzpersecond.Trackingdataconsistsof(x,y)positionsforeachplayerandtheball,theteamandplayerids,time,half,andeventidateachframe.Intotal,thedatasetconsistedofonemillionpasseswhichwassplitintoa90/10trainandtestset.

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ForlearningaxThreatmodelonlyframesrelatingtothemomentofpassingeventswereconsidered.ForthexTransitionandxReceivermodelsweincludedtrackingdatafromnotonlytheindividualpassesbutalsotrackingdatafromonehalf-second(5frames)andonesecond(10frames)beforethepass.Includingthesetwoadditionalmomentsprior toeachpasseventallowedustoachieveasemanticregularizationduringtrainingpreventingthemodel tooverfit to thepassmomentwhereplayers’movementsalready indicatewheretheballwillbeplayedtosomedegree.

2.2GraphConvolutionalNetworkTorepresentthetrackingdatainawell-definedstructurethatavoidsorderingissues,weusedagraph.AgraphG(V,E,U) isdefinedbynodesV,edgesE,andglobalfeaturesU.Inourrepresentation,asshowninFigure2,thenodesrepresenttheplayerandballtrackingdata,andtheedgescontaininformationabouttherelationshipbetweenthenodes.Noglobalfeatureswereincludedinthisapproach.Theedgeseijaredirectedandconnectasendingnodevitoareceivingnodevj.Tolearntherelationshipbetweenthegraphinputandoutputs,weusedaGNN.Specifically,weapplythespatialGNNapproachthat includesseparateoperations,knownasblocks,ontheedgesandnodesof thegraph[13].Anedgeblockisdefinedbyaneuralnetworkthattakesinputsfromtheedgefeatures,sendingnodefeatures,receivingnodefeaturesandoutputsanewedgeembedding.Similarly,anodeblockisdefinedbyaneuralnetworkthattakesinputsfromthenodefeatures,aggregatedsending edge features, aggregated receiving edge features and outputs a new node embedding. Apermutation invariant function isrequiredtoaggregatethesendingandreceivingedge features,e.g., themeanorsumofthosefeatures.WeusedasimilarGNNarchitectureforeachofthethreemodels:anedgeblock followedbyanodeblock.Eachblockhasamultilayerperceptron(MLP)with three layersandthenumberofunitsineachlayervariesbetweeneachtask.UsinganedgeblockintheGNNallowedthenetworktolearntherelationshipsbetweendifferentnodesforeachtask.ThisflexibilityisnotpresentinstandardapproachessuchasMLPsorconvolutions,wheretheconnectionsbetweeninputsaredefined.Eachmodeloutputsapredictionforeachplayerfromthefinalnodeblock.Thepredictiononeachnodeisthelikelihoodofaplayerreceivingthenextpass(xReceiver),thepasswillbecompleted(xPass),andiftherewillbeashotongoalwithinthenext10seconds(xThreat).

Figure2:Sketchof the graph representationused for thetrackingdata.Individualplayersandtheballareshownasnodesinthegraphwithdirectededgesconnectingthem.Individual players and the ball are shown asnodesinthegraphconnectedbydirectededges.Edgesareweighted to allow themodel to learnwhichnodesareonwhichteam.

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2.3FeaturesAllthreeGNNmodelsusethesamesetofinputfeatures.NodefeaturesincludeplayerXYposition,speed,acceleration,angleofmotion,distanceandangletotheattackinggoal,distancetotheballcarrier,differenceintheangleofmotiontotheballcarrier,andaflagthatindicateswhethertheplayeristheballcarrier.Theedgefeaturesincludeaflagdefiningtherelationshipbetweenthetwonodes(teammate2,oropponent1),thedistancebetweenthetwoplayers,andthedifferenceintheangleofmotion.2.4TrainingWetrainedauniqueGNNforeachofthexTransition,xThreat,andxReceivermodels1.Acrossthedifferenttasks, thenodesareweightedinthe losscalculationtostabilizethetraining.Thenodesrepresentingthedefensiveplayersweremaskedoutforallmodels.DuringthetrainingofthexTransitionandxThreatmodel,the only players consideredwere those that received the pass or were the intended receivers. For thexReceivermodelthe(intended)receiverofapasshasaweightof1.0andallotherteammatesoftheballcarrierhaveaweightof0.1tobalancethesignaltobackground.2.5ModelTrainingResultsWecomparedthetrainedgraphmodelsxReceiver,xPassandxThreatagainstrespectivebaselinemodelswetrainedearlier.ThebaselinemodelswereMLPsthatwerebasedonmanyhandcraftedfeaturesconsideringthe players’ motion characteristics (speed, acceleration, moving direction), relationships between theplayersshownbydifferencesinthemotionfeaturesandwealsoconsideredtheballinformation(whereitisplayedwithwhichspeed)asseenin[11,12].ThelossandaccuracyofallthreeGNNmodelswerebetterthanorthesameasthemetricsoftherespectivebaselinemodel.Whereastheaccuracywascalculatedthesameforallmodels,theloglossisnotcomparableforthexReceivermodels.Asdescribedabove,theloglossoftheGNNxReceivercontainsallteammatesofthepasser,eventhoughmostofthemwithsmallweights*.However,theloglossforthebaselinexReceiveriscalculatedonlyconsideringtheplayerapasswasplayedto.Intotal,theGNNmodelsarebetteroratleastofthesamequalityasthebaselinemodelsalthoughmuchfewerhandcraftedfeatureswereusedsincethegraphwas able to learn the spatial relationships between the players on the pitch. Interestingly the baselinexReceivermodelhadthespeedofpass,angleofpassanddistancetoreceivercalculatedforthepassmoment.However, these featureswerenot included in theGNN. This indicates that theGNN is able to learn thecomplexdynamiccharacteristicsoffootballbasedontheplayermotionfeaturesatthenodelevelcombinedwiththeinter-playermotiondynamicsandteamidentityattheedge.Thisiswhatallowsustouseasimplerfeaturerepresentationallowingfasterendtoendprediction(0.05s).SeeAppendixA1fordetails.Table1:TrainingmetricsofthethreeGNNmodels

Accuracy loglossbaselinexPass 0.85 0.29GNNxPass 0.86 0.28

baselinexReceiver 0.73 0.70GNNxReceiver 0.83 0.07*baselinexThreat 0.95 0.16GNNxThreat 0.95 0.16

1Weuseacustom,pure-TensorFlowpackagebasedontheDeepMindgraph_netslibrary[https://github.com/deepmind/graph_nets]totrainourGNNs.

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Figure3:Exampleofhowweareabletocaptureemergentbehaviour.A-EshowspecificmomentswithinapossessionofBayernMunich(blueteam).FshowsframelevelestimatesforxReceiver(lowvalues:blue,highvalues: red) for a subsetof offensiveplayers throughout thepossession.Players are identifiedby jerseynumber. Grey ellipsoids show collectiveman orientated defendingwhereas orange ellipsoids show ballorientateddefendingfromLiverpool(redteam).Greenellipsoidsshowactiverunsfromtheblueteam.LINKTOVIDEO

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3.MeasuringtheUnmeasurableWe introduce a new defensive toolbox,Defensive Impact, which analytically determines howmuch thedefendingteamdisruptstheopposition’splay.Wecouldmeasurethisbylookingatwhereteamsinterceptthe ball, however as discussed in Section 1 defending is aboutpreventingwhat hasn’t happened yet.Wedemonstrate that the xReceivermodelnot only accuratelypredictswhowill receive theball next at themomentofapass,butwhenappliedattheframelevel,captureshumandecisionmaking.Wefindthemodelcanpredictwhowillreceivetheballinadvanceofapassbeingmadeandalso(moreimpressively)whenaplayerchangeshismindandmoreimportantly,why.OurxThreatandxPassmodelsallowustovaluenotjustwhatdidhappenbutwhatcouldhavehappenedormoreaccuratelywhatwasprevented(Figure3linktovideo).InthefollowingsectionwewilldemonstratehowwecreatedthefeaturesthatpowerDefensiveImpactandthenewinsightsthatarenowpossibletobegeneratedusinganexamplegamebetweenLaziovsJuventusfrom2018/19SerieAseason.3.1DisruptionMapsWhileweareabletocreateverygranularinsightswithDefensiveImpact,theabilitytofindsummaryinsightsisequallyimportant.ToprovidecompressedrepresentationsofourinsightsweintroduceDisruptionMaps.ADisruptionMapisaweighted2ddistributionthatshowswhereateam,positivelyornegatively,disruptedtheopposition’soffballoptions.TocalculateaDisruptionMap,wefirstgeneratea‘spatialidentity’(Figure4 top left) for each team for their xReceiver, xThreat and xPass model output. This acts as a globalrepresentationofateam(seeAppendixA2foroutputsforallteamsin2018/19SerieAseason).Wethencalculatethesamesurfaceatagamelevel(Figure4topmiddle)andsubtractthetwosurfacestocreatetheDisruptionMap(Figure4topright).Thisfinalimagerevealswheretheoppositiondisrupts(ornotinsomecases)theopposition’snormalstrategy/flow2.Wecannowusethesemapstodeterminewhichteamhadthebiggestimpactontheiropposition’sattackingstyleandefficiency.Wearealsoabletobreakthisdownataplayerleveltoseewhowastargetbothonandofftheball.3.2Lazio’s“Stellungsspiel”-DefensivePositionPlayDespite Lazio being beaten 1-2, Juventus’ Giorgio Chiellini stated post game "Itwas theworst Juventusperformanceoftheseasonforthefirst60minutes”[14].WeusedourDisruptionMapstounderstandwhatLazio did to affect Juventus somuch andwhich players they targeted Figure 4 bottom shows Juventus’DisruptionMapsforthegame.WecanclearlyseeLazioconsiderablydecreasedthexThreatfromtheirleftsideofthepenaltybox(Ronaldo’sside),witha10%decreaseinJuventus’xThreatcomparedtoallotherJuventusgamesinthatseason.Inaddition,wecanalsoseehowLazioincreasedtheriskofcompletingapasstoanyoptioninthewidechannelsbetweenthetouchlineandsix-yardboxandinthe“secondpenaltyarea”outsidethepenaltyareaby20%.ThesearethemostdangerouszoneswhereshotsandgoalsarecreatedandthespacesthatJuventus’threeprimaryattackersoperate.Withregardstowhereplayerswerelikelytobeatargetforapass,wecanseethatxReceiverwashigherthanaveragearoundLazio’spenaltyboxhowever,asdiscussed,theseareashadasignificantlyhigherriskofcompetitionandmoreimportantlysignificantlylowerprobabilityofleadingtogoaleveniftheywerecompleted.

2DisruptionMapsestimatetacticaldeviationfromanaveragestyle,wheredifferencescanbeattributedtooppositionand/orchangesofyourownteam’stacticforaspecificgame.Todifferentiatebetweenthetwoisoutofthescopeofthispaper.

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Figure4. ToprowshowshowDisruptionMapsarecomposed; theyare thedifferencebetweenaTeamIdentityandaGameIdentity;BottomrowshowsJuventus’DisruptionMapsforxReceiver,xPass,andxThreatTore-emphasisehowpoorJuventus’performancewasviewed,theGermanfootballmagazineKickerstatedinthefirsthalf,“CristianoRonaldowasoutofthegame,andDybalaalsofailedtogivemomentumtotheBianconeri'soffense.” [14]. OurplayerDisruptionMapsbackthisup(Figure5).Ronaldo’sprobabilityofreceivingapasswasbelowaverageacrossthepitchinfirsthalfespeciallyinrightchannels.Thismarginallyimprovedinthesecondhalfbutonlyinthedeeprightchannel.Histhreatdidn’texistinthefirsthalf(Figure5lowerleft)however,hetookupdangerouspositionsontheleftchannel.But,asshowninhissecondhalfxReceiverDisruptionMap(Figure5upperright)hewasneverviewedasagoodoptiontopassto.Dybalatookupsignificantlymoredangerouspositionsontheleftofthepenaltyareaandaroundthepenaltyspot.Theriskofcompletingthepasswassignificantlyloweraswellindicatinghetookboththreateningandlow risk positions in attacking areas. However, hewas rarely viewed as a realistic passing option (lowxReceiver)withhimonlybeingaboveaverageontheleftflankandthemiddleofthepitch.Thisisthecriticalinsightwearenowabletosurfacecomparedtoothermethods.Wearenotjustabletomeasureifaplayerisinagoodposition(highthreat/lowrisk),wecanmeasureiftheyarearealisticoptiontoreceivetheball.TounderstandwhyDybalawasnotaviableoptiondespitehisgoodpositioningweneedtogoadeeperlevelofanalysiswhichisoutofscopeforthispaper.

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Figure5:PlayerxReceiverandxThreatDisruptionMapsbyhalf:LeftRonaldo,RightDybala.Blueareasarebelowaveragevalueswhereasredindicatesaboveaverageregions.4.GoingDeeper–MeasuringDecisionMakingAprimarydefensivetacticinsocceristotargetkeyplayersinpossession.Thesemaybeplayerswhoareimportanttotheteam’sbuilduporconverselyplayerswhoaremorelikelytogivetheballawayandcausetransitionmoments.Targetingcanhappeninthreeways,ballorientatedwheredefenderswillspecificallytargettheplayerinpossessionthroughpressure;manorientated,wheretheballcarrierisnottargetedbuttheirpassingoptionsare;oracombinationofbothwiththeaimofeithercausingatransitionorfortheballtobeplayedtoalessdangerousarea[16](Figure3).Thesehigh-levelcomplexcoachingconceptsareincrediblydifficulttocaptureandrelyondomainexpertswatchinghoursofvideotofindandanalyze.However,byusingtheoutputfromthexReceivermodel,wecancreateadetector to find thesemomentsby simply findingwhen theprimary target changes for theballcarrier.WedefinetheprimarytargetastheattackerwiththehighestxReceivervalueateachframe.Ifthereisachangeintheprimarytarget,wemakeanassumptionthataproactiveactionhasoccurred.Thiscouldbearunfromasupportingattacker,theplayerinpossessionmovingwiththeballoradefender(s)actions.Anobviousnextstepcouldbetotrainamodeltopredict thesesituations. However, these labelsdonotcurrentlyexistandtoaskasetofdomainexpertstoannotatethousandsofexampleswouldbehighlytimeconsumingandexpensive.Instead,weusedaprogrammaticlabellingfunctionsapproach[17]andaskedadomain expert to identify simple functions that capture the expected behaviour of players for differentdefensivecontexts(seeAppendixA3forasample).Basedonobservingourinitialdetectedmomentswithadomainexpert,wedefinedthreedefensiveandtwoattackingsituations(Table3).

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Table3:Defensiveoffballcontextsandtheirdefinitionsasdefinedbythedomainexpert.

4.1Ronaldo:NullandVoidWecansee fromtheDisruptionMapsthat in the firsthalfLaziowereable tonullifyRonaldoasaviablepassingoption.However,howdidtheydothis?UsingourDefensiveImpacttoolbox,wecannowassessifRonaldowastargetedwheninpossession(ballorientateddefending)andoutofpossession(manorientateddefending).Inaddition,wecanassessifRonaldomadeanyactiverunstobecomemoreavailableforateammate.4.1.1 TargetingtheSupplyLineTounderstandwhyRonaldowentmissinginthefirsthalf,weidentifiedtheprimaryplayerswhopasstheballtoRonaldofromthelast5games(Table5).Wechosethelast5gamesasthisishowoppositionscoutswoulddoit.WemeasuredhowoftenRonaldowasidentifiedasaprimarytargetfortheseplayers(Table6).WeclearlyseethattherelationshipbetweenMatuidiandRonaldoisheavilytargeted,withRonaldoonlybeingconsideredanoptionforMatuidionceduringtheLaziomatch.WealsoseethedifferenceinRonaldo’sperformancebetweenthefirstandsecondhalf,withRonaldoonlybeingidentified5timesinthefirstand8timesinthesecond.ThisfurthersupportstheobservationsinKicker.4.1.2 TargetingRonaldoinPossession

Ronaldo was targeted 8 times in the gamewhen in possession with Lazio applying both ball andmanorientateddefending.Figure6(right)showsaprimaryexampleofhowLaziocloseddownRonaldo’soptionsbyapplyingpressuretoRonaldoashecarriedtheballandalsoapplyingpressuretohisprimarytargets;Matuidi(red14)andSandro(red12).WecanseehowSandromadeanactiveruntobecometheprimarytargetandhowCorrea(blue11)attemptedtoapplymanorientatedpressure.However,thedefensiverunofLuisAlberto(blue10)topressRonaldowasresponsibleforthedecreaseinSandro’sxReceivervalue.AtthesametimeMatuidi(red14)becamethemostlikelyreceiver(xR0.98),however,duetothecombinedpressureofMilinković-Savić(blue21)andParolo(blue16)hisxPasswasonly0.66,meaningtherewasahighchanceofatransition.

Situations Definition

Ballorientateddefending Defendermovesclosertotheballcarrierathighspeedtoincreasethechanceoftheballbeinggivenawayorpasstolessdangerousarea.

Manorientateddefending Defendermovesclosertotheprimarytargettoreducetheprobabilityofthembeingareceiver.

Ballandmanorientateddefending Combinationoftheprevioustwo.

ActiveoffBallRuns Anattackermovesathighspeedtoincreasetheirprobabilityofbeingareceiver.

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Table5.Top3passerswhostartedthegamefromtheprevious5matches

Table6.Ronaldo’savailabilityforhisthreeprimarysuppliers

Table7.TheavailabilityofRonaldo’sthreeprimarysupplierswhenheisinpossession

Option RonaldoInPossessionFirstHalf

RonaldoInPossessionSecondHalf

PauloDybala 4 4BlaiseMatuidi 2 1AlexSandro 3 6

WehavedemonstratedhoweffectiveLazio’sdefensiveplaywasinnullifyingRonaldoandhowtheydidit.Theotheraspectwecanexamineis ifRonaldoactivelytriedtomakehimselfavailable. Ronaldomade7activeruns(Figure6RightLinktoVideo)howeveronly3wereattackingforwardruns.IfwecomparethistoLazio’sforwards,ImmobileandLuisAlberto(Figure7Left),weseetheyweremoredangerouswiththeirruns.Figure6(Left)showsanexampleofRonaldomakinganactiverunintothepenaltyareatobecomeaprimary target forDouglasCosta. WhenCosta received theballRonaldoonlyhadanxReceiverof0.22.However,aswefollowhisrun,wecanseehimbecomingtheprimarytargetattheedgeofthepenaltyarea.Interestingly,theplotrevealshewasalwaysinahighlythreateningpositionfortheentiretyofthemovebyplayingontheshoulderofthelastdefender.

Passer PassTotal GamesPlayedTogether PassPer90

AlexSandro 31 4 7.23

Matuidi 22 4 5.31Dybala 22 4 5.29

Supplier RonaldoTargetFirstHalf

RonaldoTargetSecondHalf

PauloDybala 1 5BlaiseMatuidi 1 0AlexSandro 3 3

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Figure6.Left:ExampleofRonaldo(7)makinganactiveoffballruntobecomethemostlikelyreceiver.HistrailshowsbothhowdangeroushisrunwasandhowhisxReceiverincreased.Right:Ronaldobeingtargetedwithcombinedmanorientatedandballorientateddefending.LINKTOVIDEO

Figure7.ActiveRunMapsforLazio’s(CiroImmobileandLuisAlberto)andJuventus’(PauloDybalaandChristianoRonaldo)mainattackers.

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4.SummaryWeproposedanovelGNNarchitecturethatallowstodealwithunstructureddata.TheGNNallowsustodirectlylearnfromalightweightfeaturerepresentationthecollectivebehaviourofthesoccerplayersonthepitch.Thiscircumventstheneedtoorderplayersandforheavyfeaturecraftingwhichallowsustoapplyanend-to-endinferencepipelineinreal-timeapplications.Basedonthemodeloutputs,weintroducedDefensiveImpact,atoolboxtomeasuretheinfluenceofdefensivestrategy on the opposition at a team and player level. Disruption Maps create a compact visualrepresentationofateam’seffectontheopposition’sxThreat,xPassandxReceivervaluescomparedtotheirglobaloverage. Itallowsusers todeterminewhereadefencehasbeensuccessfulorstruggledbasedonreducing/increasinganopposition’sthreat,passriskandplayeravailability.Wewereabletoidentifydifferentdefensivestyles(manandballorientateddefending)andoffballruns.Duetothelackoflabelleddataweutilisedataskprogrammingapproach–creatinglabellingfunctionsbasedonadomainexpert’sinsights.Movingforwardanactivelearningapproachwherelabelsaregenerated,trainedagainstandthenassessedwouldbearecommendednextstep.Thisresearchenablestheevaluationofdefensivebehaviourandprovidestoolsandinsightsforcoachesandfanstoengagewith.

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RepresentationsforTeamActivityAnalysis.MITSloanSportsAnalyticsConference

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A. AppendixA1.SpeedofInferenceOurthreeGNNmodelsusethesamefeaturesandthenumberoffeaturesisrathersmallasdescribedabove.Thisraisedourinterestwhetherthesemodelsareapplicableinreal-timeoratleastclosetoreal-time.Weranatesthowlongthefeatureengineering(custompythoncode)andaGNNmodelinferenceofasingleframetakeonanoff-the-shelfnotebook3,respectively.Table2showsthatonaveragethewholeprocessfromcraftingthefeaturesuntiltheinferenceofthemodelismadetooklessthan0.05sforonetrackingtimestamponourtestnotebook.ThisenablesustouseourGNNmodelsnearlyinreal-time.TableA.1:Speedtestshowlongfeaturecraftingandthemodelinferencetakesinseconds[s];descriptiveresultsof1000attempts

Featurecrafting(s) Inference(s) Total(s)mean(s) 0.044 0.001 0.045

std 0.004 0.0002 0.006

min 0.038 0.0007 0.04

max 0.068 0.0029 0.08

3 MacBookPro with a 2.3 GHz Intel Core i5 processor and 16GB RAM

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A2.SpatialidentitymapsforallteamsfromSerieAseason2018/19orderedbyleaguetable

FigureA.1:“SpatialIdentityforxReceiver”forallteamsfromSerieA2018/19.Teamsplayingfromlefttoright.

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FigureA.2:“SpatialIdentityforxPass”forallteamsfromSerieA2018/19.Teamsplayingfromlefttoright.

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FigureA.3:“SpatialIdentityforxThreat”forallteamsfromSerieA2018/19.Teamsplayingfromlefttoright.

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A3.SamplepseudocodeforaprogrammaticlabellingfunctionBasedondiscussionswithdomainexpertsthetaskofidentifyingmanorientateddefendingwastranslatedintothefollowingpseudocode:“Defendermovesclosertotheprimarytargettoreducetheprobabilityofthembeingareceiver.”

FigureA.4:Pseudocodeforprogrammaticlabellingofmanorientateddefending.