Playing Fast Not Loose: Evaluating team-level pace of play in ...located behind the net while in soccer, this results in a turnover for the team in possession. 3.2 - Pace of Play by

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2019ResearchPapersCompetitionPresentedby:

PlayingFastNotLoose:Evaluatingteam-levelpaceofplayinicehockeyusing

spatio-temporalpossessiondataDavidYu*,ChristopherBoucher,LukeBornn,MehrsanJavan

SPORTLOGiQ,Montreal,Quebec,Canada*Email:[email protected]

1. IntroductionPace of play is an important characteristic in ice hockey aswell as other team-invasionsports. While in basketball pace has traditionally been defined as the number ofpossessions per 48minutes, herewe focus on pace andmovementwithin a possession,leveraging the tremendousadvancements in the captureof spatio-temporaldata in teamsports inrecentyears [1].Whilemuchattentionhasbeen focusedonspeedanddistancecovered at the player level, spatio-temporal datasets also allow for more granulardefinitionsof team-level paceof play such asmeasuresof the speedbetween successiveeventsorthespeedofapossessionasawhole.While ice hockey has always been one of the fastest-moving sports, rule and tacticalchangesinthepast15years,suchastheremovaloftherulelimiting2-linepassesandthestricterenforcementofobstruction/holding infractions,haveplaced furtheremphasisonpace.Atthestartofthe2016-17NHLseason,PaulMaurice,headcoachoftheWinnipegJetssaid:

"Thisgameisjustsofastnow...I'veseenfastplayersandI'veseenfastteams,it'sthefirsttimeIthoughtwehadafastleague.Thespeed,tome,istheonethingthat’schangedmorethananything.Ourteam,andtheleagueaswell,isasfastasI’veeverseenit.”[2]

Giventheemphasisonpace inhockey inrecentyears, it issurprisingthatarecentstudyfoundaslightnegativecorrelationbetweenvariousmetricsofforwardattackingpaceandoffensive output such as shots and goals [3]. In this paper we not only explain thiscounterintuitiveresult,butalsoprovidethe firstcomprehensivestudyofpacewithinthesportofhockey,focusingonhowteamsandplayersimpactpaceindifferentregionsoftheice,andtheresultanteffectonotheraspectsofthegame.Ourobjectivesarethreefold:

1. Examinehowpaceofplayvariesacross the surfaceof the rink,betweendifferentperiods, in differentmanpower situations, between different professional leaguesandrinksurfaces,andthroughtimebetweendifferentseasons.

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2. Determinehowpaceprecedingvariouskeyevents(suchasshots,zoneentriesandpasses)impactstheiroutcomes.

3. Quantifyvariationsinpaceofplayattheteamandplayerlevelandprovidemetricstoassesshowwellteamsandplayersattack/defendpace.

Our results show that pace varies considerably, in both expected and unexpectedways,across all of the dimensionswe examined and that pace is not strictly good or bad, butratheradelicaterisk-rewardbalance.

2. Methods

2.1-Dataset

WemakeuseofSPORTLOGiQ’sspatio-temporaldatasetwhichhasbeenusedinanumberofrecentstudiesinicehockey[3,4,5,6].Thedatasetcontainsanaverageof~3650eventspergamewith21primaryeventtypesand89distinctsubtypes.EacheventcontainspreciseX,Yrinkcoordinatesandtimestamps.Furthermore,eacheventislabeledwiththepossessionstatemakingiteasytodeterminewhichteamwasinpossessionatthetimeoftheevent.AnalyseswereperformedonallregularseasonNationalHockeyLeague(NHL),AmericanHockeyLeague(AHL)andSwedishHockeyLeague(SHL)gamesinthe2016-17and2017-18seasons.Foranalysesonthe2018-19season,allregularseasongamesuptoandincludingNovember24,2018havebeenincluded.

2.2-MetricsofPace

Wehaveusedthedistancetravelledandtimeelapsedbetweensuccessivepossessioneventsbythesameteam(i.e.passes,receptions,puckrecoveries)tocalculatevariousdefinitionsofteam-levelpace.Thisincludestotalspeed(ɸT),aswellastheeast-west(ɸEW),north-south(ɸNS),andnorth-only(ɸN)componentsofspeed.Weuseconventionalhockeyterminologyindefiningdirectionswherenorthisthedirectionofattack,andeast-westrepresentsplayacrossthewidthoftherink(Figure1).ɸNdiffersfromɸNSinthatonlyforwardprogressismeasuredandanybackwardprogressisassignedaɸNofzero.Ourstandardterminationcriteriawastoendpossessionsequenceswheneithertheteaminpossessionchanged,themanpowersituationchanged,orastoppageinplayoccurred.Inthesecases,thelasteventinthesequencewasnotincludedinthecalculationofpace.Thisdefinitionofpacemeansthatpossessionsequencesareallowedtocontinueevenifthedefendingteammakesasuccessfuldefensiveplay(e.g.blockedshotorsave)solongastheplayisnotstoppedandtheattackingteamregainspossessionofthesubsequentloosepuck.

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Figure1-Examplepossessionsequenceillustratinghowpaceiscalculatedinthisstudy.P1recoverspuckintheDZ,carriestotheirDZbluelineandmakesanoutletpasstoP2whocarriesintotheOZbeforepassingtoP3foraone-timershot.Theshotissavedandheldforaface-offtherebyterminatingthepossessionsequence.Alleventsinthissequencehave

positiveɸNexceptforthepassfromP2toP3whichhasaɸNofzero.

2.3-ZonalAnalysis

Possessionswerebrokenintosequencesthatoccurredineachofthethreezones(offensive,neutral,defensive).Inadditiontoourstandardterminationcriteria,possessionswerealsoterminatedwhenplaytransitionedbetweenzoneswhilethesameteammaintainedpossession.Whenthisoccurred,pacefromthefinaleventintheprecedingsequencewasassignedtothenextsequenceandthefinaleventwasthensetasthefirsteventofthesubsequentpossessionsequence.

2.4-SpatialPolygridAnalysis

Wedividedtherinkinto668equalsectionsmeasuring5ft.x5ft.,whichwetermapolygrid(portmanteauofpolygongrid).Wethenassignedthedistancetravelledandtimeelapsedbetweensuccessivepossessioneventsequallytoallcellsthatintersectthepathbetweensuccessivepossessionevents.Onlythestandardterminationconditionswereusedinthisanalysis.Differentialpolygridsweremadebyaligningandsubtractingspeedvaluesbetweentwopolygrids.Incaseswherelimitedsamplesizeproducedhigherlevelsofnoiseinthedifferentialpolygrid,a2DGaussiankernel(σ=0.5)wasappliedtosmooththedatapriorto

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calculatingthedifference.Thistechniquereplaceseachcellinthepolygridwithaweightedaverageofitselfanditsneighbors.Thiswasdoneforteam-levelpolygridswhencomparingteamperformancerelativetoleagueaverage.

2.5-TeamLevelAnalyses

Team-levelanalysesofattackinganddefendingpaceweredoneusingboththezonalandpolygridapproaches.Metricswereonlycalculatedateven-strength5v5fortheNHL.Teamattackingmetricsarecalculatedforwhenateamisinpossession,whileteamdefendingmetricsmeasurethepaceoftheopposingteamwhileagiventeamisdefending.

2.6-PlayerLevelAnalyses

Player-levelanalyseswerecalculatedateven-strength5v5fortheNHLusingonlythezonalapproachduetosmallersamplesizes.Playershadtohaveplayedaminimumof200minutesateven-strength5v5tobeincluded.Twodifferentmetricswerecalculatedattheplayerlevel:

2.6.1-IndividualPlayerPace

Individualplayerpacewascalculatedbylookingatonlypossessioneventsaplayerdirectlyparticipatedin.Forsuccessivepossessionevents,thedistanceandtimecomponentsareassignedequallybetweentheplayersassociatedwiththetwoevents.Forexample,apass-receptionsequencewouldbedividedequallybetweenthepasserandreceiverwhileareception-shotbythesameplayerwouldhavethedistanceandtimeoftheinterveningcarryassignedentirelytothatplayer.

2.6.2-WithorWithoutYou(WOWY)PlusMinus

The“withplayer”metricwascalculatedbyaveragingtheteam’sattackingpaceofallpossessionsequenceswhilethatplayerwasontheice.The“withoutplayer”metricwascalculatedbyaveragingtheteam’sattackingpacewhiletheplayerwasnotontheice.Thelatterwasdoneonlyforgameswhereaplayerwasinthelineuptobetteraccountforplayersthatdidnotplayallgameswithagiventeaminaseason.

3. ExploringPace

3.1-PaceofPlaybyZone

Wefirstdeterminedhowpacevariesbetweentheoffensive(OZ),neutral(NZ)anddefensive(DZ)zonesintheNHLforthe2017-18regularseason.

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Figure2-SpeedbyZoneintheNHLforthe2017-18regularseasonateven-strength(5v5)WefoundthatɸTishighestintheNZandgenerally~10-13%slowerintheOZandDZ.ThehighertotalspeedintheNZisdrivenlargelybydifferencesinɸNSasɸEWspeedisroughlyequalinallzones.PaceofplayisrelativelysimilarbetweentheOZandDZacrossalldirectionswiththeexceptionofɸN.WefindthatɸNintheOZis35%slowerthanDZɸNand43%slowerthanNZɸN.Ouranalysishelpstoexplainsomeofthecounterintuitiveresultsobtainedinpriorstudies.ThesestudieshavefoundthatɸN(alsoreferredtoasforwardattackingordirectpace)displaysaweaknegativecorrelationwithbothoffensiveoutputssuchasshotsandgoalsinhockey[3]aswellaswithteamqualityinEnglishPremierLeaguesoccer[7,8].WebelievethisnegativecorrelationisduetothelargedeclineinɸNasplayenterstheoffensivezonesincethat’swhereshotsandgoalsaregeneratedandiswheregoodteamsspendproportionatelymoreoftheirtime.

Furthermore,thedeclineinɸNintheoffensivezoneshouldbeexpectedsincetherearediminishingreturnsforadvancingforwardinbothicehockeyandsoccer.Inbothsports,advancingforwardalongthesidesoftheplayingsurfaceleadstoprogressivelyworseshootinganglesonnet.Inaddition,bothsportsfurtherdisincentivizeteamsfromadvancingthepuck/ballbeyondthegoalline.Inhockey,thisresultsinthepuckbeinglocatedbehindthenetwhileinsoccer,thisresultsinaturnoverfortheteaminpossession.

3.2-PaceofPlaybyLeague(5v5)

WenextexaminedhowpacevariesbetweentheNHLandtwoofthetopprofessionalleaguesintheworld,theAHLandSHL.

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Figure3-LeaguespeedrelativetotheNHLforthe2017-18regular

seasonateven-strength(5v5)TheAHLisbasedinNorthAmericaandservesastheprimarydevelopmentalleaguefortheNHLandistypicallyrankedas4thor5thbestleagueintheworldaftertheNHL[9].AHLgamesareplayedonthesamesizedrinkastheNHL(200ft.x85ft.).OuranalysisshowsthatɸTis1-2%slowercomparedtotheNHL.TheslowdownismoreapparentintheOZandDZandisprimarilydrivenbyadeclineinɸEWacrossthethreezones.ThisislikelyduetotheslightlylowertalentlevelsintheAHLcomparedtotheNHL.Sincemoretalentedplayerstendtoplaythepuckmoreeast-westandareabletoplayathigherspeedsintheDZandOZwheredefensivepressureisgenerallyhigher.TheSHListhehighestdivisioninSwedishicehockeyandistypicallyrankedas3rdbestleagueintheworldaftertheNHL[9].SHLgamesareplayedoninternationalicerinksthatareconsiderablywider(~13.5ft.or16%),havelongerneutralzones(~8ft.or16%)andagoallinemuchclosertotheblueline(6ft.or9.4%)comparedtoNorthAmericanrinks.

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PaceintheSHLisconsiderablyslowerinboththeDZandOZbutisfasterintheNZ.ThesechangesarelargelydrivenbychangesintheɸNSratherthanɸEWwhichremainrelativelysimilartotheNHL.ThehigherNZɸNSintheSHLcanlikelybeattributedtothemuchlongerandwiderNZwhichlimitstheabilityofdefenderstoapplyNZpressureandallowsattackerstoprogressforwardsrelativelyunchallenged.ThisiscorroboratedbythefactthatthenumberofNZpassespergameintheSHLis14%lowerthantheNHLandthelowestamongthethreeprofessionalleaguesstudied(AppendixTable1).IntheDZandOZ,comparablylowerdefensivepressureintheSHLcausedbytheextrawidthallowsplayerstocarrythepuckmore.ThiseffectivelylowerstheɸTsincequickpassesarenotrequiredformaintainingpossessionliketheyareintheNHLandAHL.ThisissupportedbythefactthattheSHLleadsallleaguesinOZandDZpuckonstickpossessiontime(AppendixTable1).TakentogetherthelargedifferencesinpaceweseebetweenNHL/AHLandSHLarelikelyduetothedifferentrinkdimensionsfavouringdifferingstylesofplayratherthandifferencesinplayerability.TheselargedifferencesinpacebetweenhockeyplayedonInternationalsurfacesandNorthAmericansurfaceslikelycontributetotheadjustmenttimeneededforplayerstransitioningbetweenEuropeanandNorthAmericanprofessionalleagues.

3.3-PaceofPlaybySeason(NHL5v5)

Threeyearsago,theheadcoachoftheWinnipegJetsstatedthattheNHLgameisasfastashe’severseenit.It’sworthexamininghowpaceofplayhaschangedsincethattimeandwhetherpaceofplayhascontinuedtoincrease.Relativetothe2016-17season,pacehasincreasedslightlyintheNHLoverthelastthreeyearswithlargestincreasesoccurringintheNZ(Figure4).TheincreaseintheNZisdrivenmorebyanincreaseinɸEWalongwithamoremodestincreaseinɸNS.HigherɸEWislikelydriveninpartbya3-4%increaseineast-westpassesintheNZoverthatsameperiod(AppendixTable2).

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Figure4-Paceofplayacrossseasonsrelativetothe2016-17

NHLregularseasonateven-strength(5v5)

3.4-PaceofPlaybyPeriod

Wealsoexploredhowpacevariesbetweenperiodsinregulationtime.Inicehockey,thetwoteambenchesarelocatedoneithersideoftheredlineandteamschangeendsaftereveryperiod.Thiscreatesasituationwhereateamdefendsthegoalclosertotheirbenchinthe1stand3rdperiodsandfurtherfromtheirbenchinthe2ndperiod.The‘longchange’inthe2ndperiodhasbeenshowntoincreasegoalscoringrateswiththeproposedrationalebeingthatthelongchangemakesitmoredifficultfortireddefendersstuckintheirownDZtochange[10,11].Wedon’tseeevidenceforthe‘tireddefenders’hypothesisinouranalysisofpaceat5v5(Figure5).TotalspeedintheOZisactuallylowestinthe2ndperiod,notwhatwe’dexpectifteamswithpossessionintheOZaretakingadvantageoftireddefenders.Rather,weseeanuptickinDZpaceinthe2ndperioddrivenprimarilybya~7%increaseinɸN.WebelievethisincreaseinDZɸNinthe2ndperiodisduetoteamsmovingthepuckforwardquicklytoeithercatchopposingteamsoffguardonbadchangesorpreventingthemfromchangingalltogether.Indeed,wefindthe2ndperiodhasthelowestnumbersofeast-westDZpassesandcontrolledexits,andthehighestnumberofforwardstretchpasses,whichislikelyresponsibleforthelowerɸEWandhigherɸNintheDZ(AppendixTable3).HigherDZandNZɸNinthe2ndperiodleadstoa~35%increaseinoddmanrushes(1-on-0,2-on-1,3-on-1,3-on-2)whichlikelycontributestotheincreasedscoringrates(AppendixTable3).

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Figure5-Paceofplaybetweenperiodsinthe2017-18NHLregularseasonateven-strength(5v5).Periods2and3arebenchmarkedrelativetoPeriod1.

WealsoobserveaprogressivedeclineinɸEWinallthreezonesfromthe1stto3rdperiods.Thiseffectisobservedevenafteradjustingforcloseortiedscoredifferentials(datanotshown).WebelievetheslightdeclineinɸEWmaybeattributedtomorecautious,risk-averseplayasthegameprogressesthoughthishypothesisbearsfurtherexamination.

3.5-PaceofPlaybyManpowerSituation

WenextexaminedhowpacevariesacrossdifferentmanpowersituationsintheNHL(Figure6).Totalspeedislowerinallzonesat4v4thoughtheincreaseinɸNSintheNZwithcorrespondingdecreasesintheOZandDZissimilartotheSHLandmaybecausedbyareductionindefensivepressureinallzonesduetodecreasedplayerdensity.

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Figure6-Paceofplayatdifferentmanpowersrelativetoeven-strength

(5v5)forthe2017-18NHLregularseasonAt3v3,allformsofpacearesloweracrossallzones.IntheNHL,3v3isplayedonlyinsudden-deathovertimeandteamsaretypicallydeliberatelyslowingdownandplayingmorecautiouslysinceturnoverscanoftenleadtoahighdangercounterattackfortheopposingteam.Onthepowerplayat5v4and5v3,weobservealargedeclineinDZpaceconsistentwiththeslowingdownofplayastheteamonthepowerplayregroupsaftertheopposingteamclearstheirzone.IntheNZandOZ,paceisfasteronthepowerplaydrivenlargelybeanincreaseinɸEWasteamstrytobreakdowndefensesanddrawthegoalieoutofpositionwithcross-icepasses.

3.6-PaceofPlayAcrosstheRink(Polygrid)

Toobtainamoregranularviewintohowpacevariesacrosstherink,wedividedtherinkinto668equalsectionsmeasuring5ftx5ft.Wethenassignedthedistancetravelledandtimeelapsedbetweensuccessivepossessioneventsequallytoallgridsectionsonthepath

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betweentheseevents.Weusedthepolygridapproachtoexaminehowvariousmetricsofpacevarybetween5v5and5v4manpowersituations(Figure7).

Figure7-Paceofplayacrossthesurfaceoftherinkinthe2017-18NHLregularseason.Left:Even-strength(5v5)Center:Powerplay(5v4)Right:5v5-5v4difference(blue:

fasterat5v5;red:fasterat5v4).Allunitsareinft/s.Theresultsshowthatpaceisnon-uniformlydistributedacrossthelengthandwidthoftherink.Forexample,theeffectofhockey’soffsiderulecanbeclearlyseenattheoffensivebluelinewithamarkeddeclineinbothɸNandɸNSandapeakinɸEW.Wealsomeasureddifferencesinpacebetweeneven-strength(5v5)andpowerplay(5v4)situations.Whilepaceonthepowerplayincreasesinlargesectionsoftheoffensivezone(red),itdeclinesbyasimilarmagnitude(blue)inthedefensivehalf.Resultsfromthepolygridanalysisareconsistentwiththedifferencesbetween5v5and5v4speedshowninthezonalanalysisbutprovideamuchmoregranularviewofhowpacevarieswithineachzone.

4. ImpactofPace

4.1-PacePrecedingZoneEntries

PastresearchinicehockeyhasshownthatcontrolledentriesintotheOZresultinmorefavourableoutcomesthandump-inentries[12].However,evenamongcontrolledentries,notallareofequalvalue.SPORTLOGiQeventdatatrackstheskaterdifferentialsforeverycontrolledentry.Hereweusedthepercentageofentrieswithashotongoalafteraswellas

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theshootingpercentageofshotstakenwithin5secondsfollowingazoneentrytoclassifyentriesintohigh,mid,low,andverylowdanger(Table1).Noticethatnotalloddmanrushes(whereattackersoutnumberdefenders)arehighdangerwith3-on-2entrieshavingafarlowerchanceofscoringthanothertypesofoddmanentries.WecalculatedɸTofalleventsinthepossessionsequenceprecedinganentryandfoundthathigherdangerentriesoccuratahigherpace.ɸTprecedinghighdangerentriesisapproximately13%fasterthanthatprecedingdump-ins.Thedatapresentedisforthe2017-18NHLregularseasonbuttheresultsareapplicabletotheAHLandSHL(AppendixTable4).

EntryType ShotafterEntry% Shooting% EntryClass ɸT(ft/s)

1-on-0 66.6% 26.2%

3-on-1 48.8% 25.5%

2-on-1 43.7% 22.0%

HighDanger

24.3

3-on-2 31.5% 10.4%

1-on-1 29.9% 8.8%

2-on-2 26.2% 7.1%

MediumDanger

23.4

3-on-3 20.8% 5.2%

1-on-2 21.3% 4.8%

2-on-3 21.6% 4.6%

LowDanger

22.5

dump-in 1.1% 6.2%VeryLowDanger

21.6

Table1-Paceofplayprecedingzoneentriesateven-strength(5v5)intheNHLforthe2017-18regularseason.

4.2-PacePrecedingShots

WemeasuredɸTinthe5seconds.precedingnon-deflectedshotattemptsateven-strength(5v5)inthe2017-18NHLregularseason(Figure8).Weexcludedalldeflectedshotsduetotheinherentrandomnessofoutcomesresultingfromdeflections.Shotsweredividedintoquintilesbythepre-shotɸT.Averagepre-shotspeedvariedfrom10ft/sto42ft/sbetweenthelowestandhighestɸTquintiles.Trueshootingpercentage,whichisdefinedasthenumberofgoalsdividedbythetotalshotattempts,increasesfrom2.9%-4.1%,anincreaseof38%comparingthelowesttohighestɸTquintiles.AverageshotdistanceremainsfairlyconstantbetweenɸTquintiles(37-40ft.)suggestingthatthepaceofpre-shotmovement,andnotshotdistance,isthedeterminingfactorinincreasedshotquality.

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Figure8-Effectoftotalspeedprecedingashotonshotdistanceaswellastheshootingpercentageinthe2017-18NHLregularseason(5v5).Trueshootingpercentageis

calculatedasgoalsdividedbytotalshotattempts.

TheseresultsaregenerallyapplicableintheAHLandSHL(AppendixTable5).Sincepacehasbeenshowntoimprovetoshotqualityindependentlyofshotlocation,webelievethatexpectedgoalsmodelsshouldincorporatepre-shotpaceasafeature.

4.3-EffectofPassSpeedonReceptionSuccess

SPORTLOGiQeventdatacontainsthecoordinatesandtimestampsforallpassesandreceptions.Receptionscanbeclassifiedasfailedifthepasstouchesthereceiver’sbladebuttheyfailtogainpossession.Weexaminedtheeffectofpassspeedonreceptionoutcomeforalleven-strength5v5passesintheNHLduringthe2017-18NHLseason(0.50million).WeusedSPORTLOGiQpasstypestoaccountforvariabilityinpasslength,angleanddifficulty.Asidefrompassestotheslot,failedreceptionsfromallotherpasstypesoccuratsignificantlyhigherspeedsthansuccessfulreceptions(Figure9).

Figure9-Effectofpassspeedsonreceptionoutcomesforvariouspasstypes.Successful

receptionsaregreenwhilefailedreceptionsarered.

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5. TeamandPlayerEffects

5.1-Team-levelPace(Zonal)

Weexaminedteam-levelpaceusingboththezonalandpolygridmethods.Webenchmarkedagiventeam’sattackinganddefendingpacerelativetotheleagueaverage.Analyseswereperformedforthe2016-17and2017-18NHLregularseason(Figure10).

Figure10-Zonalanalysisoftotalspeedbyteaminthe2017-18NHLregularseason.Top:TeamAttackingvs.NHLAverage.Bottom:TeamDefendingvs.NHLAverage

Zonalanalysisshowsthatteamsvaryintheirabilitiestoattackordefendpaceindifferentzones.Whileattacking,teamslikeChicago(CHI)andLosAngeles(LAK)wereconsistentlyfasterthanleagueaverageinallthreezoneswhileotherslikeArizona(ARI)andWinnipeg(WPG)wereconsistentlyslower.Theseteamsaretheexceptionsincemostteamswerefasterinsomezonesandslowerinothers.Forexample,Nashville(NSH)hadthelowestDZɸTandthehighestOZɸTofanyteamintheNHL.Whiledefending,someteamsconsistentlygaveupmore(e.g.ARI,CHI,MTL)orless(CAR,LAK)pacethroughallzonesthoughonceagain,mostteamsdisplayvariabilitybetweendifferentzones.DifferencesinteamattackinganddefendingspeedrelativetoleagueaveragearesomewhatrepeatableacrossseasonsintheNHL(AppendixFigures1and2)

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5.2-Team-levelPace(Polygrid)

Figure11-Polygridanalysisoftotalspeedbyteaminthe2017-18NHLSeason.Lefthandsideoftherinkistheteam’sDZandrighthandsideistheteam’sOZforbothattackingand

defendingpolygrids.Allunitsareinft/s.Wealsoexploredvariationinpaceattheteam-levelusingthepolygridapproach.Thisallowedustoobtainamoregranularviewofwhatareasoftheiceateamismostorleasteffectiveatgeneratingorpreventingpace(Figure11).Whiletheoverallresultsofthepolygridanalysislargelycorroboratesthosefoundinthezonalanalysis,weareabletodiscernpatternswithinzonesthatwouldotherwisebemissed.Forexample,whileattacking,someteamsshowasymmetryinDZɸTwithfasterpaceoneithertheleft(LAK,VAN)orright(CAR,CHI)sideoftheice.Someteamsarealsomuchslower(NSH,ANA)orfaster(CHI,VAN)aroundtheirownnetintheDZandthiscorrelateswellwiththeteam’stendencytoperformcontrolledbreakouts(NSH-1st;ANA-5th;CHI-28th;VAN-30th)whichslowdownthepaceofDZexits.ThereisalsoconsiderablevariationinattackingpacewithintheOZwheresometeamshavemuchhigher(ANA)orlower(TOR)pacealongtheOZblueline.PaceinthisregionoftheiceisprimarilyduetopossessionmaintainingEWpassesbetweendefencemanandlikelydoeslittletocontributetohigherdangerscoringchances.Someteamsarealsofasteralongtheboards(CHI,TOR)whileothersappeartoplaywithhigherpacethroughouttheentireOZ(NSH,LAK).Onthedefensiveside,teamsalsoexhibitdifferencesinwheretheyaremosteffectiveatslowingdowntheiropponents.Forexample,LAKisveryeffectiveatslowingdownteamsaroundtheopposingteam’snet,thengiveuppacethroughmostoftheNZ,buttheneffectivelyslowdownpaceacrosslargeswathesoftheirownDZ.

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Webelievethatteam-leveldifferentialpolygridsareausefulwaytovisualizeattackinganddefendingtendencies.DifferentialpolygridsforallremainingNHLteamsforthe2017-18seasoncanbefoundinAppendixFigure3.

5.3-Player-levelPace(Zonal)

Attheplayerlevelwechosetoexaminebothindividualplayerpace(forpossessioneventsthatplayerwasdirectlyinvolvedin)aswellasWOWYplus-minus(on/offsplitsofteam-levelattackingpace)usingthezonalapproach(Figure12).Forindividualspeed,wenoticedthatdefencemanweremuchslowerthanforwardsintheDZwhiletheoppositewastrueintheOZ(AppendixFigure4).Thisdiscrepancyislikelyduetothevaryingamountsofdefensivepressureappliedbytheopposingteamonforwardsanddefencemaninthesetwozones.Assuch,individualplayerpacemetricswereadjustedforteam,position,andzoneforallanalyses.Adjustingforteam-differenceswasdonetobringindividualplayerpaceanalysesinlinewithWOWY(whichbydefinitionisteam-adjusted)thoughteam-adjustedmetricswillpenalizeplayersplayingonfasterteamsandviceversa.

Figure12-ComparisonofIndividualandWOWYspeedforConnorMcDavid(EDM)and

JaromirJagr(CGY)inthe2017-18NHLregularseason.ConnorMcDavidisconsideredbymanytobethefastestandmostdynamicplayerintheNHLtoday[13].JaromirJagrisoneoftheall-timegreats,havingaccumulatedthe2ndmostcareerpointsintheNHLafterWayneGretzky.However,Jagrwas45yearsoldinthe2017-18NHLseasonmakinghimbyfartheoldestplayerinaleaguegettingyoungerandfastereveryyear.ExaminingpaceforthesetwoforwardsusingboththeIndividualandWOWYmethodsshowsMcDavidtobeoneofthefastestandJagrtobetheslowestplayerintheNHLintheOZ.ThereisgoodcorrespondencebetweentheIndividualandWOWYmetrics,thoughthedifferencesaretypicallymagnifiedforindividualpacecomparedtotheWOWYpace.Thisistobeexpectedsinceindividualpaceshouldbelessaffectedbythequalityofyourline-matescomparedtoWOWYpace.

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ComparisonsofɸTtotheɸEWandɸNScomponentsshowthatConnorMcDaviddrivespaceprimarilythroughhigherspeedsinthenorth-southdirectionwhichisconsistentwiththeevaluationofmosthockeyexperts[13].Thetopandbottom20playersforeachzoneforthe2017-18NHLregularseason,rankedbytotalspeedWOWYdifference,aregiveninthe(AppendixTables6-11)

6. DiscussionWeprovidethefirstcomprehensivereviewofteam-levelpaceinicehockeyshowinghowpacevariesindifferentareasoftheice,betweenleagues(andrinksurfaces),acrossseasons,betweenperiods,andwhenmanpowersituationschange.Furthermore,wedemonstratehowpaceimpactstheoutcomesofkeyevents.Ourfindingssuggestthatincreasedteam-levelpaceisbeneficial,butperhapsonlyuptoacertainpoint.Higherpacecancreatebreakdownsindefensivestructureandleadtobothhigherdangerzoneentriesandimprovedshotquality.Ontheotherhand,ourpassreceptionanalysisshowsthatveryhighpassspeedscanleadtomoreturnovers.Finally,weshowthatteamsandplayersvaryintheirabilitytoattackanddefendpaceindifferentzonesandareasoftheicesurface.Futureworkattheplayer-levelwilluseanadjustedplus-minusmodeltoaccountfortheeffectsofteammatesandoppositiononaplayer’sperformance.Ouranalysisalsosuggeststhatforwardattackingpace(ɸN),whichiscurrentlythemostwidelyusedmetricofteam-levelpaceinbothhockeyandsoccer[3,7,8],isnotanidealmetricformeasuringeitheroffensiveoutputorteamquality.ThisisbecauseɸNdeclinesbyalargeamountasplayprogressesclosertotheopponent’sgoal.ɸNmayserveasausefultooltogaugeteam-levelpaceinthedefensiveandneutralzonesbutwebelievethatɸTorperhapsɸEWarebettermetricsonceplayhasenteredtheoffensivezoneoroffensivethird.Takentogether,ourresultsdemonstratethatmeasuresofteam-levelpacederivedfromspatio-temporaleventdataareinformativemetricsinicehockeyandmayproveusefulinotherteam-invasionsports.Definingthepaceofplayasthespeedofonthepuckactionsratherthanasetofplayertrajectoriesisabetterestimateofteam-levelpaceasitimplicitlycapturesgamecontext.Usingthisdefinition,ourapproachcanbeeasilyextendedtoothersportsandleagueswherenoplayertrackingdataisavailable.Futureworkwillexploreteam-levelpaceinothersportslikesoccer,basketball,rugbyorhandballtoseeifsimilarpatternsexist.

18


Acknowledgements

TheauthorswouldliketothankYiZhouforhelpwithgraphicdesignandEvinKeane,NickCzuzoj-Shulman,MattPerri,andSamGregoryforhelpfuldiscussionsandcomments.

References[1]J.GudmundssonandM.Horton,“Spatio-TemporalAnalysisofTeamSports,”ACM

ComputSurv,vol.50,no.2,pp.22:1–22:34,Apr.2017.[2]M.Clinton,“Nospeedlimit,”NHL.com,05-Oct-2016.[Online].Available:

https://www.nhl.com/jets/news/speed-is-the-name-of-the-game/c-282406734.[Accessed:03-Dec-2018].

[3]R.M.Silva,J.Davis,andT.B.Swartz,“Theevaluationofpaceofplayinhockey,”J.SportsAnal.,vol.4,no.2,pp.145–151,Jan.2018.

[4]N.Mehrasa,Y.Zhong,F.Tung,L.Bornn,andG.Mori,“DeepLearningofPlayerTrajectoryRepresentationsforTeamActivityAnalysis,”presentedattheMITSloanSportsAnalyticsConference,2018,p.8.

[5]O.Schulte,Z.Zhao,M.Javan,andP.Desaulniers,“Apples-to-Apples:ClusteringandRankingNHLPlayersUsingLocationInformationandScoringImpact,”presentedattheMITSloanSportsAnalyticsConference,2017,p.14.

[6]G.LiuandO.Schulte,“DeepReinforcementLearninginIceHockeyforContext-AwarePlayerEvaluation,”inProceedingsoftheTwenty-SeventhInternationalJointConferenceonArtificialIntelligence,Stockholm,Sweden,2018,pp.3442–3448.

[7]J.Harkins,“Introducingapossessionsframework,”OptaSportsPro.[Online].Available:https://www.optasportspro.com/about/optapro-blog/posts/2016/blog-introducing-a-possessions-framework/.[Accessed:03-Dec-2018].

[8]D.Alexander,“Sequencingunmaskingtruecreativeforces,”EnglishPremierLeague.[Online].Available:http://www.premierleague.com/news/489392.[Accessed:03-Dec-2018].

[9]G.Desjardin,“ProjectingJuniorHockeyPlayersandTranslatingPerformancetotheNHL,”BehindtheNet.[Online].Available:http://www.behindthenet.ca/projecting_to_nhl.php.[Accessed:04-Dec-2018].

[10]S.Pettigrew,“Testingtwocommonadagesaboutwhengoalsarescored,”RinkStats.[Online].Available:http://rinkstats.com/2013/06/testing-two-common-adages-about-when.[Accessed:04-Dec-2018].

[11]S.Pettigrew,“HowTheLong-ChangeOTCouldCutNHLShootoutsByAThird,”stephenpettigrew.[Online].Available:https://stephenpettigrew.kinja.com/how-the-long-change-ot-could-cut-nhl-shootouts-by-a-th-1542328902.[Accessed:09-Dec-2018].

[12]E.Tulsky,G.Detweiler,R.Spencer,andC.Sznajder,“UsingZoneEntryDataToSeparateOffensive,Neutral,AndDefensiveZonePerformance,”presentedattheMITSloan

19


SportsAnalyticsConference,2013,p.6.[13]K.Campbell,“Yeah,ConnorMcDavidgotfasteroverthesummer.Andhe’snotfinished

yet,”TheHockeyNews,13-Oct-2017.

20


Appendix

League SeasonDZ

PassesDZTime(min.)

NZPasses

NZTime(min.)

OZPasses

OZTime(min.)

NHL 2017-18 352.5 12.6 115.0 5.4 250.0 8.9

AHL 2017-18 323.0 11.5 103.1 4.8 223.2 8.0

SHL 2017-18 327.6 12.7 98.5 4.8 239.0 9.2AppendixTable1-ComparisonofpassingandpossessiontimebyzoneintheNHL/AHL/SHL

(even-strength-5v5).Passmetricsincludebothsuccessfulandfailedattemptsandareaveragedpergame.Zonepossessiontimemetricsarealsoaveragedpergame.

League Season Manpower EW>10ft.Passes EW>15ft.Passes

NHL 2016-17 5v5 47.9 39.8

NHL 2017-18 5v5 49.1 40.7

NHL 2018-19 5v5 49.7 41.3

AppendixTable2-Neutralzoneeast-westpassingtendencybyseasonintheNHL(even-strength-5v5).Successfulpasseswithgreaterthan10or15ftofEWdistancewerecounted.PassesmusthavebothoriginatedinandbeenreceivedintheNZ.Metricsareaveragedper60minutes.

League Season Period DZControlled

Exits DZD2DPasses

DZStretchPasses

OddManRushes

NHL 2017-18 1 21.6 44.1 11.8 2.65

NHL 2017-18 2 18.6 37.3 12.7 3.49

NHL 2017-18 3 21.2 39.8 11.5 2.44

AHL 2017-18 1 19.9 41.7 10.3 2.84

AHL 2017-18 2 17.1 35 10.5 3.55

AHL 2017-18 3 19.1 37.1 9.8 2.52

SHL 2017-18 1 19.6 46 10.9 2.04

SHL 2017-18 2 16.5 38.7 12.4 2.57

SHL 2017-18 3 19.2 42 11.2 1.42

21


AppendixTable3-DefensiveZoneTendenciesandOddManRushesbyPeriod.Allmetricsarereportedaspergameaverages.

League AHL SHL

EntryType

ShotafterEntry%

Shooting% Speed(ft/s)ShotafterEntry%

Shooting% Speed(ft/s)

1-on-0 69.1% 24.3% 69.6% 24.1%

3-on-1 47.5% 25.1% 42.5% 33.3%

2-on-1 45.3% 20.4%

23.8

41.5% 17.8%

23.9

3-on-2 30.4% 8.8% 29.2% 10.5%

1-on-1 32.6% 8.9% 27.0% 6.2%

2-on-2 26.9% 6.3%

22.7

24.3% 6.2%

23.1

3-on-3 19.9% 5.5% 20.2% 5.1%

1-on-2 20.7% 4.2% 18.0% 4.6%

2-on-3 20.5% 4.0%

22.2

19.5% 3.3%

22.5

dump-in 1.1% 8.5% 21.3 0.8% 9.7% 21.6AppendixTable4-Paceofplayprecedingcontrolledanddump-inentriesfortheAHLandSHLwithpercentofentrieswithashotongoalandshootingpercentofshotstakenwithin5secondsof

entry.

AHL SHL

SpeedQuintile

TrueShooting%

ShotDistance(ft.)

Speed(ft/s)

TrueShooting%

ShotDistance(ft.)

Speed(ft/s)

1 3.15% 39.8 9.5 2.68% 38.6 10.3

2 3.27% 41.4 18.5 2.93% 40.8 18.7

3 3.43% 42.3 23.3 3.22% 41.5 23.8

4 3.99% 40.8 27.8 3.30% 40.3 28.8

5 4.32% 39.8 42.1 3.42% 39.1 42.8 AppendixTable5-Paceprecedingashotinthe2017-18regularseasonfordifferentleagues.

22


AppendixFigure1-SeasonoverSeasonDifferencesinTotalSpeedfor(TeamAttackingvs.NHL

Average).Top:2017-18SeasonBottom:2016-17Season

AppendixFigure2-SeasonoverSeasonDifferencesinTotalSpeedfor(TeamDefendingvs.NHL

Average).Top:2017-18SeasonBottom:2016-17Season

23


AppendixFigure3-Team-levelɸTpolygridsfortheremaining23NHLteamsforthe2017-18NHL

Season.Attackingpaceonrightanddefendingpaceonleft.Allunitsinft/s.

24




25




26




27


AppendixFigure4-Individualplayerpacebyplayerpositionandzone.

AppendixTable6-Top20playersbytotalspeedWOWY%differenceintheoffensivezoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% SJS JoeThornton F 643 9.0% 15.9% 3.4% 3.4% WPG PaulStastny F 256 8.0% 11.1% 7.0% 9.3% OTT MarkStone F 877 7.9% 8.5% 7.6% 5.2% VAN BrendanLeipsic F 201 7.8% 10.1% 6.4% 6.6% PHI ClaudeGiroux F 1,217 7.7% 8.9% 6.5% 3.6% OTT DerickBrassard F 832 7.5% 9.7% 6.9% 1.1% PHI SeanCouturier F 1,238 7.3% 7.5% 7.1% 3.5% BUF ZachBogosian D 303 6.7% 9.6% 4.4% 9.8% SJS JoePavelski F 1,200 6.3% 10.6% 2.9% 5.7% EDM ConnorMcDavid F 1,327 6.2% 3.0% 9.0% 12.7% ARI DerekStepan F 1,171 6.1% 5.9% 5.7% 5.2% DAL JamieBenn F 1,168 5.5% 6.5% 5.2% 5.5% BUF JasonPominville F 1,022 5.5% 8.5% 3.1% 4.2% VGK ReillySmith F 885 5.4% 5.0% 6.1% 11.5% WPG NikolajEhlers F 1,090 5.3% 5.4% 5.8% 4.7% DAL TylerSeguin F 1,219 5.3% 6.8% 4.4% 3.6% CGY MichealFerland F 994 5.1% 6.3% 4.9% 8.2% SJS PaulMartin D 204 5.1% 3.7% 6.1% 2.5% PHI TravisKonecny F 1,036 5.0% 2.9% 6.3% 8.0% VGK WilliamKarlsson F 1,135 5.0% 4.8% 5.6% 10.9% AppendixTable7-Bottom20playersbytotalspeedWOWY%differenceintheoffensivezoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% PIT RileySheahan F 868 -7.0% -7.8% -6.3% -6.1% MTL ByronFroese F 492 -7.1% -2.9% -10.9% -10.8%

28


COL NailYakupov F 507 -7.1% -10.0% -5.3% -2.8% MTL DanielCarr F 418 -7.3% -2.4% -10.9% -12.3% BUF JordanNolan F 658 -7.3% -5.4% -7.9% -5.2% PHI JordanWeal F 772 -7.3% -7.5% -7.0% -5.2% TOR AustonMatthews F 930 -7.3% -6.2% -7.1% -4.8% DAL GemelSmith F 422 -7.5% -9.9% -6.0% -5.2% BOS TimSchaller F 908 -7.7% -6.4% -8.6% -7.8% ARI BradRichardson F 927 -8.2% -7.5% -8.1% -6.4% VGK RyanReaves F 206 -8.2% -7.7% -8.1% -12.1% BOS NoelAcciari F 676 -8.3% -7.9% -7.8% -7.3% STL OskarSundqvist F 377 -8.4% -7.0% -9.6% -5.3% BUF JacobJosefson F 376 -8.7% -3.0% -12.9% -10.5% VGK P.E.Bellemare F 706 -8.8% -8.1% -9.5% -13.8% PHI TaylorLeier F 351 -9.2% -9.8% -8.5% -8.5% CBJ MarkLetestu F 206 -9.6% -8.7% -9.7% -1.2% VGK TomasNosek F 628 -10.0% -9.8% -10.2% -13.9% VGK WilliamCarrier F 323 -12.0% -11.7% -12.0% -17.2% CGY JaromirJagr F 249 -13.7% -15.8% -11.3% -10.6% AppendixTable8-Top20playersbytotalspeedWOWY%differenceintheneutralzoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% TOR KasperiKapanen F 377 5.2% 6.5% 4.6% 3.6% EDM BrandonDavidson D 346 4.8% 8.7% 2.4% 1.4% WPG PaulStastny F 256 4.8% 4.4% 4.9% 3.4% TBL J.T.Miller F 266 4.7% 13.7% -0.1% 3.6% VGK TomasTatar F 250 4.6% 6.4% 4.5% 4.6% EDM AdamLarsson D 1,169 4.6% 6.9% 3.3% 5.5% NSH KevinFiala F 992 4.4% 11.2% 0.6% 1.5% EDM LeonDraisaitl F 1,114 4.3% 4.7% 3.8% 3.0% BOS AndersBjork F 335 4.3% 7.5% 3.3% 0.2% PHI SeanCouturier F 1,238 4.2% 6.9% 2.8% 5.0% NJD BenLovejoy D 744 4.1% 6.2% 2.6% 3.9% NSH KyleTurris F 847 4.1% 8.2% 1.8% 5.4% CGY CurtisLazar F 605 3.9% 2.6% 4.5% 8.7% LAK KevinGravel D 206 3.8% 8.7% 0.8% -2.3%

PHI Shayne

Gostisbehere D 1,296 3.8% 6.6% 2.9% 0.7% OTT MikeHoffman F 1,165 3.8% 10.9% 0.6% -2.6%

29


PHI ClaudeGiroux F 1,217 3.6% 7.4% 2.0% 3.2% PHI IvanProvorov D 1,504 3.6% 3.7% 3.8% 5.2% CGY KrisVersteeg F 234 3.5% 6.5% 2.5% 2.1% DET LukeWitkowski F 209 3.5% -0.4% 5.1% 9.8% AppendixTable9-Bottom20playersbytotalspeedWOWY%differenceintheneutralzoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% NSH AustinWatson F 733 -4.5% -7.0% -3.2% -1.6% VGK P.E.Bellemare F 706 -4.5% -9.2% -1.9% -0.4% NSH ColtonSissons F 901 -4.5% -7.2% -2.7% -1.8% CAR JoshJooris F 292 -4.6% -9.5% -0.9% -1.0% TBL AnthonyCirelli F 209 -4.6% -15.9% 1.3% 2.9% ANA LoganShaw F 385 -4.8% -6.3% -3.7% -7.3% DAL JasonDickinson F 227 -4.8% -10.6% -1.9% 1.5%

OTT AlexandreBurrows F 664 -4.8% -9.3% -3.1% -4.4%

ARI JakobChychrun D 862 -5.0% -3.8% -5.3% -4.8% MIN ZackMitchell F 224 -5.0% -9.7% -3.3% -5.2% STL VladimirSobotka F 1,112 -5.1% -6.4% -4.6% -2.5% VGK RyanReaves F 206 -5.1% -10.7% -2.9% -2.2% NYR NealPionk D 508 -5.1% -9.1% -3.1% -5.1% CGY SeanMonahan F 1,012 -5.2% -4.7% -5.3% -5.9% BUF JoshGorges D 439 -5.2% -8.4% -3.3% 0.5% ARI BradRichardson F 927 -5.3% -7.4% -4.1% -1.8% LAK TobiasRieder F 250 -5.3% -5.3% -5.1% -5.2% LAK MarianGaborik F 357 -5.7% -9.0% -4.3% -5.3% TBL AdamErne F 228 -5.9% -11.2% -3.4% -6.8% NSH MiikkaSalomaki F 558 -6.1% -9.4% -3.9% -1.4% AppendixTable10-Top20playersbytotalspeedWOWY%differenceinthedefensivezoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% NYR RyanSproul D 243 7.2% 8.8% 6.4% 6.0% CHI ErikGustafsson D 574 6.8% 7.6% 6.9% 8.4% WPG JoeMorrow D 248 6.7% 6.6% 7.7% 5.3% MIN JaredSpurgeon D 1,100 6.1% 6.4% 6.0% 6.4% WPG TobyEnstrom D 685 5.8% 9.0% 2.1% -0.7% MIN RyanSuter D 1,522 4.5% 5.3% 4.7% 5.1% WSH ChristianDjoos D 839 4.5% 9.2% 1.2% 0.8% LAK JeffCarter F 332 4.4% 4.4% 4.9% 6.0%

30


TBL BraydonCoburn D 966 4.4% 5.5% 2.9% 3.5% TBL AndrejSustr D 540 4.4% 5.3% 2.7% 3.2% PHI ClaudeGiroux F 1,217 4.3% 7.2% 3.6% 3.5% WPG DustinByfuglien D 1,296 4.1% 4.0% 4.0% 2.6% BUF MarcoScandella D 1,487 4.1% 5.3% 2.2% 2.3% PHI SeanCouturier F 1,238 3.8% 6.5% 3.3% 3.2% CBJ M.Hannikainen F 256 3.5% 1.6% 4.2% 3.7% STL AlexPietrangelo D 1,495 3.4% 4.4% 2.6% 3.4% OTT BenHarpur D 535 3.4% 2.5% 4.5% 5.7% BOS DavidPastrnak F 1,149 3.4% 3.0% 3.9% 3.9% COL MarkBarberio D 664 3.3% 1.1% 4.3% 4.0% TOR MorganRielly D 1,297 3.1% 1.5% 4.5% 5.2% AppendixTable11-Bottom20playersbytotalspeedWOWY%differenceinthedefensivezoneteam playername position toimin ɸT% ɸEW% ɸNS% ɸN% TOR DominicMoore F 448 -7.4% -4.8% -9.7% -11.5% NSH YannickWeber D 534 -7.5% -5.7% -9.5% -11.1% CGY JaromirJagr F 249 -7.7% -5.4% -7.9% -4.8% PIT GregMcKegg F 204 -7.7% -10.3% -6.2% -4.9% BUF NicholasBaptiste F 292 -7.8% -9.3% -7.2% -7.9% PHI JordanWeal F 772 -7.9% -7.1% -9.3% -10.5% BUF KyleOkposo F 974 -7.9% -8.6% -7.4% -7.6% DAL JasonDickinson F 227 -7.9% -5.8% -10.3% -10.2% TBL AntonStralman D 1,370 -8.0% -9.5% -6.5% -8.0% PHI DaleWeise F 465 -8.2% -6.6% -10.3% -13.6% FLA MaximMamin F 268 -8.7% -5.0% -11.7% -13.3% CGY KrisVersteeg F 234 -9.0% -8.2% -8.3% -8.1% COL SamuelGirard D 1,013 -9.0% -10.9% -7.6% -7.7% VAN A.Burmistrov F 248 -9.1% -9.0% -9.3% -10.6% NSH MiikkaSalomaki F 558 -9.2% -7.4% -10.7% -13.1% NSH RyanHartman F 257 -9.5% -8.3% -10.5% -13.3% EDM EricGryba D 278 -9.6% -12.9% -6.1% -4.1% NSH AustinWatson F 733 -9.7% -8.6% -10.8% -13.3% NSH ColtonSissons F 901 -9.9% -8.8% -10.9% -13.0% TBL AnthonyCirelli F 209 -10.2% -16.0% -6.7% -8.8%

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