Decomposing the Immeasurable Sport: A deep learning expected … · 2019-06-18 · Equation (1) presents EPV, the expected outcome of the possession given all the spatiotemporal information

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2019ResearchPapersCompetitionPresentedby:

DecomposingtheImmeasurableSport:

Adeeplearningexpectedpossessionvalueframeworkforsoccer

JavierFernándezF.C.Barcelona

[email protected]

LukeBornnSimonFraserUniversity,Sacramento

[email protected]

DanCervone

[email protected]

1. IntroductionWhatistherightwaytothinkaboutanalyticsinsoccer?Isthesportaboutmeasuredeventssuchaspassesandgoals,possessionpercentagesandtraveleddistance,orevenmoreabstractnotionssuchas mistakes (to quote Cruyff, “Soccer is a game of mistakes, whoever makes the fewer wins”)?Analyticalwork to date has focusedprimarily on thesemore isolated aspects of the sport,whilecoaches tend to focus on the tactical interplay of all 22 players on the pitch. Soccer analytics islacking froma comprehensive approach that can start to address performance-related questionsthat are closer to the language of the game. Questions such as:who addsmore value?How andwhere is thisvalueadded?Are the teammatescreating spacesofvalue?Whenandhowshouldabackward pass be taken? How risky is a team attacking strategy? What is a player’s decision-makingprofile?

In order to make an impact on key decision-makers within the sport, soccer analyticsrequires a comprehensive tool to facilitate a continuous cycle of questions and answers withcoaches.Analyticmethodsmustthereforeencapsulateawidesetofactionsofinteresttocoachestoprovide a detailed and flexible interpretation of complex aspects of the game. In this paper wedevelopsuchamodel,measuringandelucidatinginstantaneousvalueonthepitch.Specifically,wequantify the expected outcome at every moment in a possession, driven by a fine-grainedevaluationofthefullspatio-temporalcharacteristicsofthe22playersaswellasthepotentialvalueof ball drives, shots, or passes to any location.While our aim is similar to that of the expectedpossession value (EPV) approach in basketball [1], our focus on soccer necessitates a drasticallydifferentapproachtoaccountforthenuancesofthesport,suchasloosernotionsofpossession,theability of passes and drives to happen at any location, and space-time dependent turnoverevaluation. Moreover, the model is designed in a decoupled way which provides greatinterpretativepowerforbothvisualandquantitativeanalysisofgamesituations.Specifically,deep

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learning-based componentmodels are built to capture the complex intricacies of spatiotemporaltactics, while a high-level stochastic process model fuses each component model together in acohesive,interpretableway.

In thenext sectionwepresent adescriptionof the technical characteristics of themodel,

then through the remainder of the paperwe focus on showcasing several practical applications,coveringhighly detailed evaluations of passing, off-ball value creation anddistribution, andbothteamandplayerleveldecisionmaking.

2. Anexpectedpossessionvalue(EPV)frameworkWedefineexpectedpossessionvalue(EPV)astheexpectedoutcomeofasoccerpossessionbasedonthefullresolutionspatiotemporaldata.EPVisarealnumberinthe[-1,1]range,expressingthelikelihoodof a possession ending in a goal for the attacking team (1) or a goal by the defendingteam(-1)afteranimmediatepossessionregain.SimilarlytotheEPVapproachforbasketball[1,2]ourmodelprovidesaframebyframeestimationoftheoutcomeofthepossession,actingasastocktickerfortheexpectedoutcomeofapossession.Asidefromasharedhigh-levelgoal,however,ourapproach is drastically different, driven by the underlying differences in the two sports. As oneconcreteexample,insoccerwecannotassumethatpassesareplayeddirectlytoaplayer’slocation,as theballcanbeplayed intoopenspace in frontoforbehindthe intendedreceiver;assuch,weneed toconsider the full spaceofpotentialdestination locations.Asanotherexample, there isnotimelimitforsoccerpossessions(asidefromthe45minutehalf),withcomplexandoftenblurreddynamicsbetweenoffenseanddefense.

Figure (1) presents the evolution of the EPV value during a soccer possession in a RealMadrid vs FC Barcelona match during the 2017-2018 La Liga season (seehttps://lukebornn.com/sloan_epv_curve.mp4towatchthefullsequence).Thecurverepresentstheexpectationoutcome(homevs.awaygoal)framebyframe.Weobservethatatthebeginningofthepossession,theEPVreaches-0.09asaconsequenceofhighspatialpressurebytheopponentduringthe build-up. The negative value indicates that in this scenario it is more probable that thedefendingteamregainspossession(andpossiblyscores)thanthepossessionendsinagoalfortheattacking team. Next, a back pass, an often criticized action in soccer, is shown to increaseconsiderablytheEPVvalue(upto0.04)byprovidingbetterconditionstofurtherthepossessionupthepitch.Thewave-shapedcurvealsoprovidesagoodexampleofthecomplexityandfluctuatingnatureofsoccer.TheimagesabovetheEPVcurveshowthevaluedistributionforpassesalongthewholefield,wheretheblueandgreenarrowsindicatethetakenpassandthebestpasspossibletotake,providingaglimpseattheinterpretativepowerofthemodel.

Recentwork in socceranalyticshasprovidedpowerfulmodels for inspectingavarietyof

specificgamesituations,includingpassriskandquality[3],attackingshotdanger[4],andoff-ballpositioning inshootingopportunities [5].Whilebeingsuccessful in thespecific task theyresolve,there is no clear path on howwe could join thesemodels together into a more comprehensiveframeworkofanalysis. OtherapproachesmakeuseofMarkovprocessestocorrelatesequenceofeventswithin possession sequenceswith the probability of scoring [6, 7, 8], providing a similaroverall objective of that of EPV but with lower interpretability capabilities than the presented

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model.Here,weproposeadecoupledmodelforEPVthatdecomposesgoalvalueintotheexpectedvaluesofdifferentactionsthatfurtherthepossession,alongwiththeprobabilitiesoftheseactions.Equation (1) presents EPV, the expected outcome of the possession given all the spatiotemporalinformationattimet(𝑇𝑡),asthecompositionofindependentmodelsforthreemaintypesofactions(A): passes (𝜌), shots (𝜍) and ball-drives (𝜕). Different sets of these components are estimatedindependently,suchasthevaluesurfaceforpasses,thevaluesurfaceforball-drives,thelikelihoodofoneoftheseeventstakingplace,andtheexpectationofgoalsforshots.

(1)

Figure1:TheimagebelowrepresentstheexpectedpossessionvalueofapossessionduringaRealMadridvsFCBarcelonamatch,duringthe2017-2018LaLigaseason.ThreespecificsituationsA,B,and C, are highlighted in the three images above, from left to right. Each image presents theexpected value surface if a pass action is performed, with a cool towarm divergent color scale,wherecool(blue)colorsrepresentnegativeEPVandwarm(red)colorsrepresentpositiveEPV.Thedirectionoftheattackgoesfrombottomtotop.Ablueandgreenarrowisshownforeveryimage,representingthetakenpassandthebestpossiblepassaccordingtothemodel,respectively.Yellowandbluecirclesrepresenttheattackinganddefendingteamlocations,respectively,whileagreen

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circlerepresentsthelocationoftheball.Seethislinkhttps://lukebornn.com/sloan_epv_curve.mp4foravideoofthefullsequence.

Passes aremodeled alongside turnovers. Equation 2 presents a further decomposition ofthepassingmodeltoaccountforthesuccessofapassΟ𝜌.

(2)

Figure 2 presents a glance at the interpretative power of this decoupling. Here we can

observehowapassingvaluesurfaceaccountingfortheeffectsofsuccessfulpassingandturnoverscan be decomposed into four other visually interpretable surfaces: the expected pass value, theexpectedturnovervalue,andtheprobabilitiesofbothpassingandturnovertoanygivenlocation.

Figure2:Thecenter-leftimagerepresentstheexpectedvaluesurfaceifapassistakenbytheattackingteamtoeverypossible location.The four imagesat theright represent, from left to rightand top tobottom: thevaluesurfaceofsuccessfulpasses,thepassprobabilitysurface,thevaluesurfaceofturnovers(unsuccessfulpasses)andtheturnoverprobabilitysurface.Yellowandbluecirclesrepresenttheattackinganddefendingteamlocations,respectively,whileagreencirclerepresentsthelocationoftheball.Thedirectionoftheattackgoesfromlefttoright.

Each of the model components is estimated independently through machine learningalgorithms based on a wide set of spatiotemporal features. Pass and turnover probabilities areestimated using logistic regression. Action likelihood ismodeled through a convolutional neuralnetworkontopofpitchcontrolandpitchinfluencesurfacesbasedonarecentstatisticalmodelforpitchcontrol[9].Passandball-drivevalueexpectationarelearnedfromasetofcarefullydesigneddeep neural networks. All the models are carefully tuned and calibrated for accuracy at the

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componentlevelaswellasthejointEPVlevel.Recently,neuralnetworkshavebeenexploredinasimilarcontext[10],byestimatingplayerpositioningandprobabilityofreachingcertainlocationsonthefield,whichisfundamentallydifferentfromtheobjectivesofourapproach.Forthepurposesofthispaperwefocusnotonthetechnicaldetails,butratherthepowerofthedecoupledmodelingframeworkinansweringmanyimportantquestionspreviouslyunansweredbythesocceranalyticscommunity. With an eye towards demonstrating this paper, we place heavy emphasis on thepassing components of themodel, as the shot and goal aspects of themodel are fundamentallyvariantsofexpectedgoalsmodelsandhencealreadywell-studied.ModelswerefittedusingopticaltrackingdataprovidedbySTATSLLC forthe2012-2013PremierLeagueseason,aswellasopticaltrackingdataprovidedbyFootovisionforFCBarcelonamatchesinthe2017-2018and2018-2019LaLigaseason.3. TheroleofcontextwithintheunpredictablesportA critical aspect to properly evaluate soccer situations is to have a clear understanding of theongoingcontext,orwhatteams’andplayers’intentsare.Soccerissodynamicthatsometimesevenmarkingthebestplayerisnotagoodoption,asJohanCruyffwouldsay“thereareveryfewplayerswhoknowwhat todowhen they’renotmarked. So sometimes you tell a player: that attacker isverygood,butdon’tmarkhim”.Mostofthetimethelocationofaneventinspaceandtimealoneisnotsufficienttofullyevaluateitspotentialimpact.Forexample,tocontrolaballinthemidfieldisusuallymoredifficultwhen theopponentdefendswithahigh lineofpressure,but simpler if theopponent is “parking thebus”.Manyof theseexamples flood the tactical analysisof thegame. Intactical analysis, organizedpossessions can be structured theoretically in threephases: build-up,progression and finalization. The build-up is a phasewhere a possession starts to develop fromone’s own half, typically with themajority of the opponent team behind the ball. Once the firstpressurelineorthemidfieldisreached,thepossessionisconsideredtoreachaprogressionphase,wheretheobjectiveistokeepprogressingtowardstheopponentgoal.Then,whenthepossessionreaches zones near the box, the possession enters a finalization stage, where the objective is toscore.Duringthesamepossessionateamcouldreturntoapreviousphase.Whilethesestagescantakemanynamesandforms,theunderlyingideaisthatapossessiongoesthroughdifferentstageswhere the contextual characteristics differ, and are not straightforward to define. Also, for eachstagethecharacteristicsofon-ballandoff-ballactionsmightvary,giventhattheobjectiveofeachphasevariesaswell.

InmanyoftheregularmeetingsthattookplacewithtacticalanalystsofFCBarcelonayouthteams during the development of this work, there was a recurrent concept associated with theevolutionofpossessions:passingacrossopponent’spressurelines(orformationlines),oftencalledbreakinglines.Analystsrecognizethepossessiontobeinadifferentcontextdependingonwhethertheballpossession is locatedbehind,between,orbeyondtheopponent’s formation lines.Weusethis concept as a proxy to identify where an action is located (relatively) according to context.Relativelocationsarefoundbyfirstobtainingthedynamiclinesofformationofthedefendingteamateverytimestep.WeapproachthisbyapplyingspectralclusteringtothesetofmeanXcoordinateposition of each defending team player in a fixed 2-second time window. For simplicity ofapplicationwefixthenumberofclusterstobethree,thustheobtainedformationsprovideverticalalignments of three groups: the first pressure line (typically forwards), the second pressure line

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(typicallymidfieldersandwingers)andthethirdpressureline(typicallydefenders).Insomeofthepracticalapplicationspresentedinthispaperwegroupactionsthatweresituatedinaparticularsetofrelativelocations;forexample,behindthefirstpressureline.Forbetterinterpretationwecouldalso loosely assume that actions behind the first pressure line correspond to build-ups, actionslocated between the first and second line correspond to progression phase, and actions locatedbeyondthesecondlinecorrespondtoafinalizationphase.Thisconceptofrelativelocationisusedthroughoutallthesub-modelsofthepresentedEPV-framework,showingtobeanimportantspatialfeature.

Defensive lines are only one contextual aspect of the game. Optical tracking data has

recently enabled studies of other contextual factors as well, such as player motion and ball-interception[11],distancesandanglesbetweenplayersandlocations[12],automaticdetectionofmatch-wideformations[13],andexpert-guidedhandcraftedfeatures[4],amongothers.Weemployasuiteofthesecontextualfactors(suchasmovement,distances,angles,etc.)withinthecomponentmodelstoimproveinterpretabilityandpredictiveability.

4. Value:ThemissingkeytopassanalysisPassing is the most frequent action in soccer, reaching over 800 passes per match on average.Soccer analytics has longed focused on evaluating teams and players based on the total sum ofpasses,theoverallaccuracy,orassists(ararekindofpass).Perhapsthatisoneofthereasonswhythe Spanish national team, 2010World Cup champion, was praised for their “Tiki-taka” style ofplay,atermthathighlightsthehighfrequencyofpasses(shortpassesinparticular).However,thesameSpanishnationalteamwithasimilarstylewasnotsurprisinglydefeatedat2018’sWorldcup,despitereachingover1100passesinthematchwheretheygoteliminated.Hencewhilepassesarea central element of the game, quantitative analysis has shown difficulties in disentangling therelativeimpactofeverypass.Inordertofullyevaluatetheimpactofpasses,asmanyotheractionsinthegame,weneedtofirstunderstandthemanyintentionsthatapassorapasssequencemighthave. Pass sequences can be created to attract an opponent, to open the possession into newpassingorball-drivesituations, topushgradually theopponent toonesideof the fieldandmovethe ball to the other, ormore typically to provoke disorder situations in order to find spaces ofgreater value. In thewords of the renownedorganizingmidfielder XaviHernandez: “I spend theentire90minuteslookingforspaceonthepitch.I’malwaysbetweentheopposition’stwoholdingmidfieldersandthinking:thedefenseishere,soIgettheballandIgotheretowherethespaceis”.

Themodelproposed in thispaperpresentsakeyelement forelevatingpassanalysis: theconceptof value.Thepassmodel, once coupledwith theothermodels, allowsus to evaluate theimpactofpassesanddecision-makingbasedon several factors suchas theexpectedvalueof thesuccessfulpass(reward), theexpectedvalueaddedtothepossession(expectedpassEPVadded),the expected value in case of turnover (risk) and the probabilities of the pass reaching a givenlocation.Thiscanbeevaluatedforeverylocationonthepitchatanygiventime,inrelationwiththequalityofthepossession.

Figure3presentstheprobabilityofpassesbeingcompletedagainstthegaininEPVofthe

possessionafterthepass istaken(EPVadded),wheresizeandcolorbothrepresenttheexpectedEPV added at themoment of the pass (the difference between the expected EPV added and the

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current EPV). From this image we can identify several characteristics of passes in soccer. Thebiggest fractionofpasses are createdwithhighprobabilityof success, lowexpectationof addingvalue to the possession and ultimately end up adding or subtracting little value from thepossession.Passeswithhighlikelihoodofaddingvalue(bigyellowcircles)tendmoretobefailedand subtract value from the possession, butwhen successful they can addmore value than lessambitiouspasses.

The decoupled nature of the model allows us to inspect the decision-making process ofindividual situations,which canbeuseful forprofiling a player’s passing tendencies, evaluate offball positioning or analyze opponentmarking, amongmany others. Figure 4 shows the expectedpass value surface in a specific game situation. Here we can observe three concepts related todecision-making: high reward passes, low risk passes, and risk-reward balanced passes. The redarrowsshowingthetwopasseswithhighestreward,i.e.thetwoactionsthatwouldmaximizethequality of the possession if successful, disregarding the consequences of a turnover. These arereward-drivenpasses.Thecyanarrowshowsthepassthatminimizestheturnoverexpectedvalue,corresponding to the pass that assumes the least risk among all the possible. The green arrowshowsthebestpassexpectedvalueconsideringbothpassingsuccessandturnoverrisk.

Figure3:PassprobabilityagainstEPVaddedforallthepassesinFCBarcelonamatchesinthe2017-2018LaLigaseason.ColorandsizeofthecirclerepresenttheexpectedEPVaddedpriortothepassattempt.

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Figure4:The imagepresents the expectedpass value surface in a specific game situation, using a cool towarmdivergentcolorscale,wherecool(blue)colorsrepresentlowerEPVandwarm(red)colorsrepresenthigherEPV.Yellowandbluecirclesrepresenttheattackinganddefendingteamlocations,respectively,whileagreencirclerepresentsthelocationoftheball.Thethreecoloredlinesrepresentpotentialpasses.Theredlines represent the two passes providing the biggest reward, the green line the best pass based on theexpectedpasssurface,andthecyanlinerepresentsthepasswithlowerturnoverexpectedvalue.

4.1 Evolvingpass-mapsOne of themost popular visualizations in soccer is the pass-map visualization, consisting of theaverage locationofeveryplayeronthe field,aplayercirclesizeaccordingto frequencyofpassestakenbytheplayer,andlinesbetweenplayerswithsizeandcolorrelatedtofrequencyofpasses.Moresophisticatedversionsofpass-mapsassigncolorbasedonmodelsofthecontributionoftheplayer to attacks ending in a shot. While pass-maps are great tools to understand frequency ofpassesbetweenpairsofplayers, they fail torecognizewhether thosepassesaddedorsubtractedvalueandthedistributionofthosepasses.Weintroducehereanevolvedversionofpass-mapsthatincorporatesEPV-relatedmetrics,inordertobetterevaluatepassingquality.

Figure5presentsapass-mapforallpassesdepartingfromRakiticinasingleFCBarcelonamatch in La Liga season 2017-2018. Just one player is shown for simplicity. This pass-mapintroducesseveralconcepts.Playersarelocatedattheirmeanlocationforallthereceivingpasses.

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Thesizeofaplayer’scirclesisproportionaltothemeanpitchcontroltheyhadwhenthepasswastaken,wheresmallersizesrepresentlowerspacecontrol,thushighpressureontheplayer.HerewecanseethecentraldefendersarereceivingballsfromRakiticwithlowpressure,whilethewingersandforwardsareunderconsiderablyhigherpressure(Suarezinparticular).ThecolorofthelinesandcirclesisgivenbytheEPVaddedmetric(althoughanyotherEPVmetriccouldbeused)ofthepasses in consideration. Circles are coloredwith themeanEPV addedby passes received by theplayer(exceptforRakitic).Thecolorsofthelinesshoulddeservespecialattention.Sincepassesinsoccervarysomuchaccording tocontext,coloringbasedonasolesummarystatisticsuchas themeanormedianEPVaddedwillprovideaconsiderablelossofinformation.Inordertogetacloserviewintothepassingdistribution,arrowsaredividedintothreeequallysizedblocks.Eachblockiscoloredaccording to theEPVaddedof thepasses in thepercentile25,50and75 respectivelyofeachcorrespondingdistributionofpassesbetweenplayers.Havingthis,wecanobservethatwhilepasses to Suarez incorporate awide range of results (from0.01 to 0.12), the top 25%of passeswhere of great value. Also, we can observe that the top 25% of passes to Piqué (typically backpasses)managed to provide above 0.05 EPV added. The plot also shows the average location ofeachpressure linewhenpassesbyRakiticwhereperformed, thus the locationsof the teammatesalso provide an average location according to average formation line, providing a grasp of therelativepositioningoftheplayers.Moredetailedinformationcanbeobtainedfromtheplotwhenfilteringforspecificsituations,forexample,passesbehindthefirstpressureline.4.2 Passingreliesoncontext

InSection3wedetailedtheideaofcontextualizingactionsbasedontherelativelocationaccordingtothemeanpositionofpressurelinesatagiventime.Here,weleveragethatconcepttoprovideacontextualized view into the passing performance of a set of players in a givenmatch. Figure 6presents a comparison of the value added through passing between relative locations for twocentraldefenders(SergioRamosandGerardPiqué)andtwomidfielders(LukaModricandSergioBusquets) for a FC Barcelona vs RealMadridmatch, in La Liga season 2018-2019. Each columngroupspassestakenfromtheredcoloredareashownonthefirstrow.Eachofthefourareas(thatwecallZ1,Z2,Z3andZ4)representthespacebetweentheowngoalandthefirstpressureline(Z1),thespacebetweenthe firstpressure lineandthesecond(Z2), thespacebetweenthesecondandthethirdpressureline(Z3)andthespacebetweenthethirdpressurelineandtheopponentsgoal(Z4). Notice that these zones are not predefined but they move dynamically according to theopponent’slocationateverytimestep.EachplotshowsastackedbarchartrepresentingthesameconceptasarrowsinSection4.1.Thatis,thedistributionofpassesissplitintothreeequallysizedgroups(favoringthetopincaseofnotexactdivisionby3)andcoloredaccordingtotheEPVaddedafterthepass.Thex-axis locationsrepresentthedestinationof thepass, indicating if itkeepstheballinthecurrentrelativezoneorgoesbackorforwardtoanyotherzone.

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Figure5:Pass-mapforallpassesofRakiticina2017-18FCBarcelonamatch.Circlesarelocatedinthemeanpass destination location for every other player, and located in themean pass origin location for Rakitic.Circle size is related to the pitch control the player hadwhenmaking the pass,where smallermeans lessspace(higherpressure).Thecolorofthecirclesrepresentthemeanaddedvalueofthosepasses.Thelinesaresplit into three equally sized blocks. Each block (starting from Rakitic) is colored by the added valueassociatedwiththepercentile25,50and75inthedistributionofpassesbetweenthosetwoplayers.Thegrayareasrepresentthespacebetweenthemeanpressurelinesoftheopponent.

Let’sanalyzethis figurecolumnbycolumn.Foractionsbehindthe firstpressure line(Z1)weobservenopassesfromthemidfielder(Modric)andtwodifferentpasstendenciesfromcentraldefenders(RamosandPiqué).Ramoshadahighertendencytoovercomethefirstlineofpressuretowards thesecondbut thisresultedmostof the time ina lossofvalue for thepossession.Piquéshowedahighertendencytokeeppossessionvaluebypassingbehindthe firstpressure line,butalsoattemptstoovercomethefirstandthesecondpressure line.Histhreeattemptstoovercomethefirstlineofpressuresuccessfullyaddedvaluetothepossession.Thesecondcolumnrepresentspassesstartingbetweenthefirstandsecondpressureline,typicallyduringtheprogressionphaseof the possession. For the central defenders, we observe again two different tendencies. PiquépassedbacktoZ1twiceasmuchasRamos,bothwiththetendencyoflosinganaverageof0.01EPVin theirpossessionwhenpassingbehindthis line.Whenkeeping theball inZ2Piquéwasable toincrease theEPVof thepossessionwhilevalues forRamos in thatzonewereconsiderably lower,providingahint fordifferent typesofpressurereceivedbyeachteam.Regardingthemidfielders,wecanseetheneedforanalyzingthedistributionofpassesinsteadofjumpingdirectlytosummarystatistics. For both midfielders, two thirds of the passes subtracted or added little EPV to thepossession, however, the last third of passes where able to add value to the possession.

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Remarkably, Busquets was able to provide two passes beyond the defenders back adding aconsiderableamountofvalue.Forpassesstartingbetweenthefirstandsecondline(Z3)wehavedifferentsituations.Here, thecontributionofcentraldefenderswasvery lowforRamosandnon-existentforPiqué.Ramoswasnotabletoaddvaluethroughpassingwhileremaininginthiszone,however his presence in this zone adds more information to the match analysis regarding thetendencyofthedefendertocontributewiththeattack.Forbothmidfielderspasseswithinthesamezonepresentedaconsistentlossofvalue,whichshowsthedifficultyofaddingvalueintherelativezone in soccerwhere the highest pressure is found.Remarkably, backpasses to Z2 found addedvalueinthethirdofthecasesforbothModricandBusquets,butsubtractedvaluewhentheywentbacktoZ1,showingagainthechangingnatureofsocceraccordingtocontext.4.3 Therisk-rewarddichotomy

Thepassingcomponentofthemodelallowstoderivetwoimportantconceptsforpassanalysis:riskand reward. The risk of a pass can be approached from the perspective of the possession anddefinedastheprobabilityoftheopponentscoringincaseofthepassendinginturnover.Thismightbeamoreaccuraterepresentationofriskthantheprobabilityofturnover,assometurnoversaremuchmorecostlythanothers.RiskcanthenberepresentedbytheturnoverEPVofagivenpass.Similarly,wecandefinerewardastheexpectationofvalueofacurrentpossessiongiventhepassissuccessful,whichcanberepresentedbythepassEPVcomponent.Theanalysisofriskandrewardcan provide helpful information for analyzing the passing profiles of teams and players. Theanalysis of passes is usually approached by quantifying the ratio of successful and unsuccessfulpasses, and pass probability is used to evaluate the difficulty of completing that pass. However,thesetwostatisticsareinsufficienttounderstandmorefinegrainedcharacteristicsofpassing,suchasthetrade-offbetweenlowerorhigherpassprobabilityandhigherorlowerreward.

Figure (7) presents four images comparing the difference between reward and risk of apass, and the associated pass probability, for all the passes in FC Barcelonamatches in La Ligaseason17/18,foralltheplayersandthreeotherdifferentplayers:Marc-AndréTerStegen,SamuelUmtiti and Sergio Busquets. From the general distribution of passes we can observe that lowerprobabilitypassesarenotnecessarilyassociatedwithlowerreward.Infact, forpassprobabilitiesbetween70%and90%thereisahighsetofpasseswithahighpositivebalanceofrewardandrisk.Forlowerpassingprobabilitiestheamountofcaseswithnegativebalanceofrewardandriskstartstoincreaseconsiderably,asitcouldbeexpected.TerStegenshowsanotabledifferencewithotherfield players such as Umtiti and Busquets, by taking frequently high probability passes with abalancedriskandreward.WecanclearlyobservetheFCBarcelonatendencyofstartingbuild-upsfromthegoalkeeperandtoopenspacestoprovideahighprobabilityandlowerriskpass.Incasethe passes would have lower probabilities and less risk, we would evidence long-ball actions.Umtiti,acentraldefender,usuallytakessecurepasses(between92%and100%probability) thathaveabalancedriskandrewardratio.Thiscoincideswiththeexpectationforcentraldefenderstoprefer lower reward passes that are more secure and with less turnover values, given theassociateddangerwith theirpositionon the field.Noticeable,Umtitialsopresentsseveralpasseswith a positive difference between reward and risk addingmore than 0.05 EPV, highlighting hisknowncontributionwiththepossessionduringtheprogressionphase.Busquets,onhisside,showsa remarkable amount of passeswithhigh expectation of adding value (even above0.1EPV) at awiderangeofpassingprobabilities.Ananalysisinthispassdistributionwouldprovideinterestingfeedback for opponent scouting by noticing that a defensive mid-fielder like Busquets has a

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remarked tendency to attempt high reward passes with different probability levels, which isunusualforplayersinthisposition,andmightbecomearelevantskilltocounter.

Figure 6: The image presents the distribution of EPV added for passes between relative zones for fourdifferentplayersinaFCBarcelonavsRealMadridmatchofLaLigaseason2018-2019.Columnsgrouppassestaken from three relativezones:behind the firstpressure line (Z1),between the first andsecondpressureline (Z2) and between the second and third pressure line (Z3). The stacked bar charts represent thefrequencyofpassesandaresplit into threeequallysizedgroups.Frombottomto top thecolorof thebarscorrespondtotheEPVaddedoftheactionsatpercentile25,50and75respectively.X-axisinthebarchartsrepresent thedestinationof thepass, includinga fourthzone(Z4)correspondingto thespacebetweenthethirdpressurelineandtheopponentsgoal.Thedirectionoftheattackgoesfromlefttoright.

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(a) Allplayers (b)Marc-AndréTerStegen

(c)Allplayers (d)SergioBusquets

Figure7:ThefigurepresentsfourimagescomparingthepassprobabilityandthedifferencebetweenrewardandriskforallthepassesinFCBarcelonamatchesinLaLigaseason17/18,foralltheplayersandthreeotherdifferentplayers.Reward is representedby theEPVafterapassandriskby theEPVaftera turnover.ThecolorandsizeofdotsrepresenttheexpectationofEPVaddedbythepass.

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5. Distillingoff-ballvaluecreationWhileon-ballactionstendtocapturemostoftheattentioninsocceranalytics,thevalueofoff-ballactions (whatplayersdowhen theydon’thave theball) is stillyet in its first steps.Thedifferentvaluesurfacesprovidedbythemodelallowsustoinspectthequalityofpositioningofteammatesduringthematchandacrossactions,eveniftheydidn’tendupreceivingtheball.Inthissectionwefirstpresentthedistributionofoff-ballvalueacrossdifferentsoccerpositions,andthenwepresentadetailedinspectionintothesurfaceofoff-ballvaluegenerationbyindividualplayers.5.1 Off-balldemandsaccordingtopositionsThedynamicnatureofsoccermakesdifficulttheassigningoffixedpositionsforplayers.Dependingonthesituation,asupposeddefender likeJordiAlbacanactasawinger,orapivot likeBusquetscantemporarilyassumetheroleofanattackingmidfielder.However,takingabroadperspectivewecanmake the assumption that there are specific demands by positionwhen it comes to off-ballmovements and positioning. In Figure (8) we compare the off-ball value of three different EPVmetrics for defenders,midfielders and forwards. Off-ball value is calculated every time a pass istakenandevery1secondofball-drives,takingintoconsiderationallthe10teammatesineachcase(notjusttheplayerreceivingthepass).

The firstmetric is expected EPV added,wherewe can see defenders being positioned inlocationswithlowexpectedlossofvalueandlowexpectedgainofvalue.Thedistributionwidensformidfielderstoa[-0.1,0.1]rangeofexpectedEPVadded.Forwardsshowahighertendencytomove towards locations of higher value,which is consistentwith themobility demanded of thatrole. The second metric compares the difference between the reward of a pass (pass expectedvalue)andtherisk(turnoverexpectedvalue).Herewecanseeagainthatforwardstendtohaveawiderdistributionfavoringmoreextremerewardandriskconditions.Midfielderstendtocontrolmore their positioning into less risky passing situations but are still able to reach high valuelocations.Defenderstendtokeeppositionswithslightadditionofvaluebutreducingconsiderablytobeplacedinlocationswithhighriskofturnover.Thethirdcolumnpresentsthepassprobabilityfor off-ball positioning. Here the tendencies presented in the other two cases are maintained.Forwards, however, present a considerably wide distribution reaching very low passingprobabilities, which shows the high pressure put upon them. Surprisingly forwards are able togenerate as much and even more off-ball value than the other two positions, presenting aconsiderablylowerprobabilityofsuccessfullyreceivingtheball.

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Figure 8: A kernel density estimation for the off-ball value of three different EPV metrics comparingdefenders(blue),midfielders(red)andforwards(blue).ThefirstmetricisexpectedEPVaddedofpasstothatplayer.Thesecondmetricsisthedifferencebetweentheexpectedvalueofasuccessfulpass(reward)andtheexpectedvalueofturnover(risk).Thethirdmetricshowsthepassprobabilityofsuccess.

5.2 BeyondlocationheatmapsA common visualization in soccer analytics is player’s location distribution on the field, whichbasically shows where the player was located or took actions during the match. However, theplayer being in a certain location says little about the contribution of the player to the game, inparticular when it comes to off-ball positioning. An intuition for this can be extracted from thedistancetraveledmetricoftenusedinTVbroadcasts,wheredistancestendtovarylittlefromoneplayer to another, independently from their performance in the match. The question we areinterestedininspectinghereis:whatwasthevalueoftheplayerwheninagivenlocationacrossthematch?Figure(9)presentsthevaluesurfaceoftwoEPVmetricsfortheoff-balllocationofseveralplayersacrossthemostrecentFCBarcelonavsRealMadridmatchinthe2018-2019LaLigaseason.ThefirstrowpresentstheexpectedEPVafterapasstothatplayer(ifapasswastobetaken)andthesecondrowtheexpectedadditionofvalueto thepossession incaseofpassingtothatplayer.Wecanobservedifferentsituationshere.FortwostrikerslikeSuarezandBenzemawecanseeinthefirstrowtheirtendencytogobackfromtheirforwardpositiontobeavailabletoreceivetheballandcontributewiththeprogressionof thepossession.SuarezshowsatendencytobackupmorethanBenzema.Whenobservingthesecondrowwecanseethatbothplayerswerelessabletobepositioned into locations that would increase the value of the possession. Moreover, when theywenttothesidesofthefield,theexpectedadditionofvaluewasfrequentlynegative.Thenexttwocolumns compare Arturo Vidal and Toni Kroos. Vidal remained located compactly in locationsnearbythemidfield.HoweverhewasabletobeconsistentlylocatedinareasofpositiveEPVadded.InthecaseofToniKroosthefirstrowshowshispivotingskillacrossthefield,withtendencytotheleftlane.However,thevalueaddeddistribution,showninthesecondrow,presentsamoredispersedistribution of positive and negative value addition. Through careful consideration of context,specificsituations,orcoaches’specificdemandsforplayers,theoff-ballvaluesurfacescanprovidehelpfulinsightsaboutthequalityofthepositioningofplayers.Fromadefensiveperspectiveitcouldalsoprovidehintsforopponentteamtacticalscouting,inordertoidentifylocationsandsituationswhereaplayerismorelikelytobelocatedtoincreasethelikelihoodofthepossessionendinginagoal.

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Figure9:The imagepresents thedistributionofvalue inoff-ballpositioning for twoEPVmetricsand fourdifferentplayersinaFCBarcelonavsRealMadrid,LaLigaseason2018-2019match.ThefirstrowshowstheexpectedEPV ifapasswas taken towards thatplayer(i.e.overallvalue),while thesecondrowsshowstheexpectedadditionofvaluetothepossessionifthatpasswastaken(i.e.differenceinvaluebefore/afterpass).

6. DecisionmakinganalysisThehighlydetailed informationabout thestateofapossessionthat thismodel isable toprovidecanbe applieddirectly to decision-making analysis at the teamor individual player level. Figure(10)presentsapossessionduringaRealMadridvsFCBarcelonamatch,wherewecanobservetheframe by frame evolution of the possession EPV and the expected value of the best and worstpossible actions at any given time.We evaluate EPV for three different types of actions: passes,shots and ball-drives, at the moment the action is beginning. Ball-drives are split into discreteactions every quarter of second. This is done for simplicity of representation, although theevaluationofEPVcouldbeperformedoneveryframeavailable.Duringthetimebetweenapassora shot being taken until it reaches its destination (the first touch or ball out) the EPV is notcalculated,sowesticktotheinstanceswheretheballisinpossessionofoneplayer.Theyellowandred curve present the EPV for the best, second best and worst action to take. Since the modelprovidescontinuoussurfacesforthepassingandballdrivescomponents,aswellasfortheactionslikelihood,thesetofpossibleactionsistheoreticallyinfinite.Tosimplifythisanalysiswediscretizethepossiblesetofactionsbyselectingthebestpasslocationforeveryteammate,thelocationoftheplayer in thenextsecondaccordingtohisvelocity for theball-drivecomponent,andtheeventofshootingfromthecurrentlocation.

Below this plotwe canobserve fivedifferent situations along thepossession. First,whenSergiRobertodecides to produce a ball-drive, having a current EPVof 0.04, there are twootherpassingoptionsavailablethatwouldincreaseEPVupto0.082inthebestcase.Hechoosestodriveandthentheintensepressurefromthreedifferentplayerscomingfromoppositedirections,startsdecreasing the EPV considerably down to 0.11. In this case themodel is considering that thereexists a high chance that Real Madrid will regain the possession after integrating the full set ofpossibleactions.AtthatpointthemodelconsidersthattheworstpossibleactiontotakewillresultinanEPVslightlylowerthanthecurrentatthattime,whichisleveragedbythehighprobabilityof

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turnoverinapossibleactiontheplayercouldtakefromhere.Sergiisabletoselectthesecondbestactionwhich is apassback to Iniesta.Herewe cannotice a limitationof themodel and trackingdata:thebestoptionconsideredbythemodelatthistimeisapassforwardtoRakitic,butthedata(andhencethemodel)lacksbodyorientationinformationtounderstandthattherequiredbodyrotationtomakethatpassmakesitmoredifficultthanitseems(whichcanbeintuitivelyunderstoodfromobservational analysis). The back-pass to Iniesta reaches an EPV value near to the second bestaction suggested by themodel. Afterwards, Iniesta passes to Alba,who progressesmanymetersthroughalongball-driveandfinallypassestoMessiasshowninthethirdimage.Here,Messihastwo forward passes that themodel recognize as the best possible, better than keeping the ball.Noticethemodel is trainedtoobtaintheexpectedresult foreveryactiononanaverageplayerofthePremierLeagueandSpanishLeague(thedatausedfortraining),butdoesnothaveindividualplayerinformation.Mostsurely,incaseofhavinganindividualizedeffectforMessikeepingtheball,that model would increase the expectation of ball-drive for the player in that situation. Messidecides to pass down to Iniestawhich reduces the expectation of possession, due to an intensepressure received by the player, who passes the ball back to Messi few meters into the box,increasing up to 0.082 the possession EPV. At this point, shown by the fourth image,Messi hasseveralhighvaluepasses inside theboxbutchooses todriveandgetspushedoutsideof theboxand reduces its passing, shooting and driving opportunities, which, again, drops the possessionvalue,reachinganegativevalueof-0.034.MessichoosestocrosstheballandPaulinhoreceivesanaerialpassandtakesaheader togoalasshown in the last image.Here, thebestandsecondbestaction coincide with the possession EPV. These actions are shooting or keeping the ball in thatlocation.

From this frame by frame evaluation of a possession we can grasp a piece of the

interpretation power of themodel for decisionmaking. Beyond specific possessions, there are awide set ofmetrics that canbederived from this informationwith simple calculations.One is toidentify actions of players that increased or decreased the possession EPV above or below athreshold,rapidlysegmentingactionsofvalue.Theseactionscanbefilteredaccordingtotheactiontype, field location, opponent relative location, and any other contextual variable that can beassociated from the frame by frame evaluation of the possession. From here, is also possible tohighlightthekindofactionsthatarebetterexploitedbythedifferentteamsinacompetition.Themodelwouldalsoallowonetoquicklyidentifysituationswheretherewasahighriskoflosingtheballandtheopponentproducingdanger.Wecanthenstudythedistributionofdecisionsmadeinthese different situations. Regarding individual player decision-making evaluation, we couldidentify not only the total value added or lost by players, but also what kind of actions andsituationsproducethatadditionorloss.AnotherpossibleapplicationofdetailedEPVcurvesduringapossessionistheidentificationofpossessionplateaus,whichwedefineaswindowsoftimewherethe possession is stabilized in a certainmoment of the possessionwithout variation, beyond themany actions that could take place in between. For example, in soccer it is typical that in thefinalizationstagetheballgetspassedfromonesidetoanotherwithoutbeingabletoovercomeanadditionallineorshoot,norbeingforcedtomovebacktoprogressionorbuild-phasestages.Afteridentifying these plateaus, it becomes straightforward to extract actions that produces the jumpbetweenoneplateautoanother.

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Figure10:ImageontoppresentstheevolutionofEPVintimeforapossessionsequenceinaRealMadridvsFC Barcelona match in the 2017-2018 La Liga season. Four different curves are presented showing thepossessionEPV,andtheEPVforthebest,secondbestandworstactiontotakeaccordingtothemodel.Below,the five images represent snapshots of thematch video in different situations. The set of possible actionsconsideredincludespasses,shotsandball-drives.

DiscussionWehavepresentedamodelthatisabletoprovideaframebyframequantificationoftheexpectedvalue of any soccer possession (EPV). Furthermore, themodel captures awide set of positional,motionandcontextualfeatures,andtherelativevalueofanylocationonthefield,addressingakeyfeatureofthissport:understandingplayerinteractioninspace.BeyondthequantitativeadvantagesofacomprehensivemetricsuchasEPV,thedecouplednatureofthemodelallowsforanin-depthvisualandquantitativeinterpretationofanysituation,makingitpossibletolookintotheblack-boxof complexmachine learningmodels,while taking advantage of their generalization power. ThisEPVframeworkforsocceropensthedoorforawidesetofapplicationsinsocceranalytics,coveringplayer-level and team-level performance evaluation, detailed decision-making analysis, effectivequeryingofvalueactions,evaluationofoff-ballcontribution,andmanyothers.

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Decomposing the Immeasurable Sport: A deep learning expected … · 2019-06-18 · Equation (1) presents EPV, the expected outcome of the possession given all the spatiotemporal information