Making Offensive Play Predictable -Using a Graph Convolutional Network to Understand Defensive Performance in Soccer

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Making'Offensive'Play'Predictable'-'Using'a'Graph'
Convolutional'Network'to'Understand'Defensive'
Performance'in'Soccer'
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Michael(Stöckl,(Thomas(Seidl,(Daniel(Marley(&(Paul(Power(|(Stats(Perform(
(
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1.#Introduction#
1.1#Measuring#defensive#quality#in#soccer#
The!art!of!good!defending!is!to!prevent!something!from!happening!before!it!has!even!happened.!Virgil!Van!
Dijk!is!considered!one!of!the!best!defenders!in!world!soccer!as!he!has!the!ability!to!prevent!a!pass!being!made!
to!an! open!attacker!to!shoot!by!forcing! the! ball!carrier!to!pass!somewhere!else!less!dangerous.!!However,!
while!we!know!this!is!great!defending,!in!today’s!stats,!Van!Dijk!would!not!receive!any!acknowledgement.!!A!
defender’s!contribution!is!simply!measured!by!the!number!of!tackles!or!interceptions!they!make.!But!what!
if!we!were!able!to!measure!actions!that!have!been!prevented!before!they!were!made?!!
!!!
The! aim! of! a! defense! and! a! defender! is! to! make! offensive! play! predictable.! For! example,! Jürgen!Klopp’s!
Liverpool,!press!the!opposition!with!the!aim!of!forcing!them!to!give!the!ball!away!in!specific!areas!of!the!pitch!
by!limiting!the!number!of!passing!options! available!in! dangerous! areas.! !If! the! art! of! good!defending!is!to!
make!play!predictable,!then!it!should!be!measurable.!Given!enough!data,!we!should!be!able!to!predict!where!
a!player!will!pass!the!ball,!the!likelihood!of!that!pass!being!completed!and!whether!this!pass!will!result!in!a!
scoring!opportunity.!It!therefore!stands!that!we!should!be!able!to!measure!if!a!defender!forces!an!attacker!to!
change!their!mind!or!to!prevent!an!attacker!from!even!becoming!an!option.!!!
!
Figure 1 shows a situation from a match between Liverpool vs Bayern Munich in the 2018/19!UEFA!Champions!
League!that!leads!to!Mané!(red!10)!scoring.!!Our!model!identifies!that!Milner!(red!7)!is!the!primary!target!for!
Van!Dijk!(red!4)!in! the! first! instance.!However,!due!to!the!combination!of!Gnabry!(blue!22)! closing! down!
Milner,!Lewandowski!(blue!9)!closing!down!Van! Dijk! and! Mané! making! an!active'run,!behind!the!defence,!
Mané!becomes!both!the!most!likely!receiver!and!a!high!threat!for!scoring.!!This!demonstrates!our!ability!to!
model!how!players!decision!making!is!influenced!and!how!a!situation!can!move!from!low!threat!to!high!threat!
by!the!off-ball!actions!of!attackers!and!defenders.![LINK!TO!VIDEO].!
!
In!this!paper!we!present!a!novel!Graph!Convolutional!Neural!Network!(GNN)!which!is!able!to!deal!with!highly!
unstructured!and!variable!tracking!data!to!make!predictions!in!real!time.!!This!allows!us!to!accurately!model!
defensive!behaviour!and!its!effect!on!attacking!behaviour,!i.e.,!preventing'actions'before'they!have'occurred.!!!
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To!do!this!we!trained!the!following!models:!
- !"#$#%&#'(!Predicts!the!likelihood!of!every!player!becoming!the!pass!receiver!at!any!moment!within!
a!player!possession.!!!
- !)*'#+,(-Predicts!the!probability!of!a!shot!occurring!in!the!next!10!seconds!if!a!pass!was!played!to!
an!attacker.!!!
- !.+//:!Predicts!how! likely! a!pass!would!be!completed!to!each!attacker! off! the! ball! at!any!moment!
within!a!player!possession.!!
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and!introduce!new!defensive!concepts:!
!
- .0+1#'- 2&+%0+3%0%,1:! Using! the! outputs! from! xReceiver! and! xPass! we! infer! how! available! every!
attacker!is!off!the!ball!at!each!frame.!
- 4#5#6/%&#- 789+$,:! We! are! able! to! detect! high! level! defensive! concepts! such! as! ball! and! man!
orientated!defending,!defensive!position!play!and!off!ball!runs.!!
- 4%/':9,%;6- <+9/:! Global! visual! representations! of! defending! teams’! ability! to! disrupt! the!
oppositions!attacking!strategy.!
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=%>:'#-?(-We!train!three!models!(!.+//@-!"#$#%&#'-A-!)*'#+,)!to!better!understand!defensive!and!offensive!
off!the!ball!behaviour,!such!as!8+6B;'%#6,+,#C-C#5#6C%6>,!3+00B;'%#6,+,#C-C#5#6C%6>-and!+$,%&#-;55-3+00-
':6/.!!This!lets!us!better!understand!how!Sadio!Mané!scored!a!1-0!lead!vs!Bayern!Munich!during!Liverpool’s!
way!to!the!UCL!final!in!2017/18.!LINK!TO!VIDEO!
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Related#Work#
#
1.2.1 Dealing#with#unstructured#data#
Tracking!data!is!highly!unstructured!and!can!be!difficult!to!model!due!to!most!machine!learning!techniques!
requiring!tabular!datasets!where!features!are!inserted!in!a!specific!order.!!To!solve!this!ordering!issue!Lucey!
et!al.![1]!presented!the!concept!of!aligning!players!to!a!formation!template![1,!2].!!However,!this!method!has!
several!limitations.!Firstly,!in!soccer,!teams!use!different!formations!so!a!player!at!role!10!for!a!team!using!
433!would!be!very!different!to!a!team!playing!352.!!Therefore,!it!is!difficult!to!compare!predictions!between!
these!players.!!In!addition,!this!method!is!reliant!upon!teams!having!the!same!number!of!players!on!the!pitch!
(11!per!team)!meaning! different! models!have!to!be!learned!when!players!have! been! sent! off!for!example.!!
With!regards!to!real!time!inference!a!further!limitation!is!the!speed!at!which!players!need!to!be!aligned!before!
calculating!features!for!inference.!!"
!
Fernandez![3]!and!Brefeld![4]! use! Convolutional! Neutral!Networks!(CNNs)!on! an! image! representation!of!
tracking! data! to!circumvent! the! ordering/alignment! issue! while! predicting! probabilistic! pitch! control!
surfaces.!!Converting!tracking!data!directly!to!images!is!suboptimal!as!one!gives!up!a!very!low-dimensional!
data! set! and! converts! it! into! a! high-dimensional! sparse! representation.!!Tracking! data! has! an! irregular!
structure!due!to!missing!players!and!a!lack!of!clear!scheme!to!order!players!in!a!sequence!or!frame![19].!Both!
techniques! are! also! time! consuming! and!could! cause! timing! issues! for! feature! generation! in! real-time!
applications.!!Instead!of!using!an!image-based!representation!we!used!Graph!Neural!Networks!(GNNs)!which!
1)!neglects!the!need!for!ordering!features,!2)!can!cope!with!varying!number!of!players!on!the!pitch!and!3)!
learns! local! and! higher! scale! features! directly! from! the! tracking! data.! Horton! applied!a! set-learning!
framework!to!model!passing!in!football!which!is!similar!to!a!simple!graph!(no!edges)![18].!
"
1.2.2 Evaluating#and#Predicting#Future#Actions#in#Sports#
Concepts!such!as!xThreat!and!xPass!are!not!new!with!previous!research!using!tracking!data!to!predict!the!
likelihood!of!a! pass! being!complete!or!a! goal! being! scored! after! a! specific! action![2,! 4,! 6].!! In! addition!to!
measuring!the!value!of!an!action,!the!concept!of!valuing!a!players’!off!ball!position,!has!also!been!investigated!
[2,! 3].! ! Spearman! [9]! also! developed! a! model! to! evaluate! off-ball! scoring! opportunities!in! soccer.! !These!
models!create!a!surface!area!combining!xThreat!and!xPass!values!to!understand!how!dangerous!a!team’s!or!
player’s!current!possession!is!and!also!what!space!they!control.!
!
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! shooting!
performance.!!Ghosting![11,!12]!hallucinated!where!a!team!of!defenders!will!move!to!next!based!on!where!
the!attackers!have! moved,!and! the!ball! is! moving! to.! !This! potentially! provides! useful! tools!to! assess! the!
defensive! strategy! of! teams!by! evaluating! the! difference! in! Expected! Goal! (xG)! or! Possession! Value!(PV)!
compared!to!a!global!baseline.!"
"
2.#Method#
2.1#Data#
To!train!and!validate!the!three!models!(xTransition,!xThreat,!and!xReceiver)!we!used!1,200!games!of!tracking!
data!from!multiple!seasons!of!Top!5!European!football!leagues!sampled!at!10Hz!per!second.!!Tracking!data!
consists!of!(x,! y)! positions!for!each!player!and!the! ball,! the!team!and!player!ids,!time,!half,! and! event!id!at!
each!frame.!!In!total,!the!dataset!consisted!of!one!million!passes!which!was!split!into!a!90/10!train!and!test!
set.!

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!
For!learning!a!xThreat!model!only!frames!relating!to!the!moment!of!passing!events!were!considered.!For!the!
xTransition!and!xReceiver!models!we!included!tracking!data!from!not!only!the!individual! passes! but! also!
tracking!data!from!one!half-second!(5!frames)!and!one!second!(10!frames)!before!the!pass.!Including!these!
two!additional! moments! prior! to!each! pass! event! allowed!us!to! achieve! a!semantic!regularization! during!
training!preventing!the! model! to! overfit! to! the! pass!moment! where! players’!movements!already! indicate!
where!the!ball!will!be!played!to!some!degree.!!!
2.2#Graph#Convolutional#Network"
To!represent!the!tracking!data!in! a! well-defined! structure!that!avoids!ordering!issues,!we!used!a!graph.! A!
graph!G(V,!E,!U)!is!defined!by!nodes!V,!edges!E,!and!global!features!U.!In!our!representation,!as!shown!in!
Figure!2,!the!nodes!represent!the!player!and!ball!tracking!data,!and!the!edges!contain!information!about!the!
relationship!between!the!nodes.!No!global!features!were!included!in!this!approach.!The!edges!eij!are!directed!
and!connect!a!sending!node!vi!to!a!receiving'node!vj.!!
!
To!learn!the!relationship!between!the!graph!input!and!outputs,!we! used! a! GNN.!Specifically,!we!apply!the!
spatial!GNN!approach! that! includes!separate!operations,! known! as! blocks,!on! the! edges! and!nodes!of! the!
graph![13].!An!edge!block!is!defined!by!a!neural!network!that!takes!inputs!from!the!edge!features,!sending!
node!features,!receiving!node!features!and!outputs!a!new!edge!embedding.!!!
!
Similarly,!a!node!block!is!defined!by!a!neural!network!that!takes!inputs!from!the!node!features,!aggregated!
sending! edge! features,! aggregated! receiving! edge! features! and! outputs! a! new! node! embedding.! A!
permutation!invariant! function! is!required! to! aggregate! the!sending! and! receiving!edge! features,! e.g.,!the!
mean!or!sum!of!those!features.!We!used!a! similar! GNN! architecture!for!each!of!the!three!models:!an!edge!
block!followed! by! a!node! block.! Each!block! has! a! multilayer! perceptron!(MLP)!with!three! layers! and!the!
number!of!units!in!each!layer!varies!between!each!task.!!
!
Using!an!edge!block!in!the!GNN!allowed!the!network!to!learn!the!relationships!between!different!nodes!for!
each!task.!This!flexibility!is!not!present!in!standard!approaches!such!as!MLPs!or!convolutions,!where!the!
connections!between!inputs!are!defined.!
!
Each!model!outputs!a!prediction!for!each!player!from!the!final!node!block.!!The!prediction!on!each!node!is!
the!likelihood!of!a!player!receiving!the!next!pass!(xReceiver),!the!pass!will!be!completed!(xPass),!and!if!there!
will!be!a!shot!on!goal!within!the!next!10!seconds!(xThreat).!
!
Figure'2:""
Sketch" of" the" graph" representation" used" for" the"
tracking"data.""Individual"players"and"the"ball"are"
shown"as"nodes"in"the"graph"with"directed"edges"
connecting"them."""
"
Individual" players" and" the" ball" are" shown" as"
nodes"in"the"graph"connected"by"directed"edges."
"
Edges" are" weighted" to" allow" the" model" to" learn"
which"nodes"are"on"which"team."""
"

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2.3#Features#
All!three!GNN!models! use!the!same!set!of! input!features.!Node!features! include!player!XY!position,!speed,!
acceleration,!angle!of!motion,!distance!and!angle!to!the!attacking!goal,!distance!to!the!ball!carrier,!difference!
in!the!angle!of!motion!to!the!ball!carrier,!and!a!flag!that!indicates!whether!the!player!is!the!ball!carrier.!The!
edge!features!include!a!flag!defining!the!relationship!between!the!two!nodes!(teammate!2,!or!opponent!1),!
the!distance!between!the!two!players,!and!the!difference!in!the!angle!of!motion.!
!
2.4#Training#
We!trained!a!unique!GNN!for!each!of!the!xTransition,!xThreat,!and!xReceiver!models
1
.!!Across!the!different!
tasks,!the!nodes! are! weighted! in! the!loss!calculation!to! stabilize! the! training.!The!nodes! representing! the!
defensive!players!were!masked!out!for!all!models.!During!the!training!of!the!xTransition!and!xThreat!model,!
the! only! players! considered! were! those! that! received! the! pass! or! were! the! intended! receivers.! For! the!
xReceiver!model!the!(intended)!receiver!of!a!pass!has!a!weight!of!1.0!and!all!other!teammates!of!the!ball!
carrier!have!a!weight!of!0.1!to!balance!the!signal!to!background.!
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2.5#Model#Training#Results#
We!compared!the!trained!graph!models!xReceiver,!xPass!and!xThreat!against!respective!baseline!models!we!
trained!earlier.!The!baseline!models!were!MLPs!that!were!based!on!many!handcrafted!features!considering!
the! players’! motion! characteristics! (speed,! acceleration,! moving! direction),! relationships! between! the!
players!shown!by!differences!in!the!motion!features!and!we!also!considered!the!ball!information!(where!it!is!
played!with!which!speed)!as!seen!in![11,!12].!!!
!
The!loss!and!accuracy!of!all!three!GNN!models!were!better!than!or!the!same!as!the!metrics!of!the!respective!
baseline!model.!Whereas!the!accuracy!was!calculated!the!same!for!all!models,!the!logloss!is!not!comparable!
for!the!xReceiver!models.!As!described!above,!the!logloss!of!the!GNN!xReceiver!contains!all!teammates!of!the!
passer,!even!though!most!of!them!with! small! weights*.! However,! the! logloss!for!the!baseline!xReceiver!is!
calculated!only!considering!the!player!a!pass!was!played!to.!In!total,!the!GNN!models!are!better!or!at!least!of!
the!same!quality!as!the!baseline!models!although!much!fewer!handcrafted!features!were!used!since!the!graph!
was! able! to! learn! the! spatial! relationships! between! the! players! on! the! pitch.!!Interestingly! the! baseline!
xReceiver!model!had!the!speed!of!pass,!angle!of!pass!and!distance!to!receiver!calculated!for!the!pass!moment.!
However,! these! features! were! not! included!in! the! GNN.! ! This! indicates! that! the! GNN! is! able! to! learn! the!
complex!dynamic!characteristics!of!football!based!on!the!player!motion!features!at!the!node!level!combined!
with!the!inter-player!motion!dynamics!and!team!identity!at!the!edge.!!This!is!what!allows!us!to!use!a!simpler!
feature!representation!allowing!faster!end!to!end!prediction!(0.05s).!!See!Appendix!A1!for!details.!!
'
Table!1:'Training'metrics'of'the'three'GNN'models'
'
Accuracy'
logloss'
baseline"xPass""
0.85"
0.29"
GNN"xPass""
0.86"
0.28"
baseline"xReceiver""
0.73"
0.70"
GNN"xReceiver""
0.83"
0.07*"
baseline"xThreat"
0.95"
0.16"
GNN"xThreat"
0.95"
0.16"
1
!We!use!a!custom,!pure-TensorFlow!package!based!on!the!DeepMind!graph_nets!library!
[https://github.com/deepmind/graph_nets]!to!train!our!GNNs.!

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#
#
#
#
=%>:'#-D(-Example!of!how!we!are!able!to!capture!emergent!behaviour.!2BE!show!specific!moments!within!a!
possession!of!Bayern!Munich!(blue!team).!=!shows!frame!level!estimates!for!xReceiver!(low!values:!blue,!high!
values:! red)! for! a! subset! of! offensive! players! throughout! the! possession.! Players! are! identified! by! jersey!
number.! Grey! ellipsoids! show! collective! man! orientated! defending! whereas! orange! ellipsoids! show! ball!
orientated!defending!from!Liverpool!(red!team).!!Green!ellipsoids!show!active!runs!from!the!blue!team.!F7GH-
)I-J74EI-----

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#
3.#Measuring#the#Unmeasurable#
#
We! introduce! a! new! defensive! toolbox,! Defensive' Impact,!which! analytically! determines! how! much! the!
defending!team!disrupts!the!opposition’s!play.!!We!could!measure!this!by!looking!at!where!teams!intercept!
the! ball,! however! as! discussed! in! Section! 1! defending! is! about! preventing' what' hasn’t' happened' yet.! We!
demonstrate! that! the! xReceiver! model! not! only! accurately! predicts! who! will! receive! the!ball! next! at! the!
moment!of!a!pass,!but!when!applied!at!the!frame!level,!captures!human!decision!making.!!We!find!the!model!
can!predict!who!will!receive!the!ball!in!advance!of!a!pass!being!made!and!also!(more!impressively)!when!a!
player!changes!his!mind!and!more!importantly,!why.!Our!xThreat!and!xPass!models!allow!us!to!value!not!just!
what!did!happen!but!what!could!have!happened!or!more!accurately!what!was!prevented!(Figure!3!link!to!
video).!
!
In!the!following!section!we!will!demonstrate!how!we!created!the!features!that!power!Defensive!Impact!and!
the!new!insights!that!are!now!possible!to!be!generated!using!an!example!game!between!Lazio!vs!Juventus!
from!2018/19!Serie!A!season.!
#
3.1#Disruption#Maps#
While!we!are!able!to!create!very!granular!insights!with!Defensive!Impact,!the!ability!to!find!summary!insights!
is!equally!important.!!To!provide!compressed!representations!of!our!insights!we!introduce!Disruption'Maps.''
A!Disruption!Map!is!a!weighted!2d!distribution!that!shows!where!a!team,!positively!or!negatively,!disrupted!
the!opposition’s!off!ball!options.!!To!calculate!a!Disruption!Map,!we!first!generate!a!‘spatial'identity’!(Figure!
4! top! left)! for! each! team! for! their! xReceiver,! xThreat! and! xPass! model! output.! ! This! acts! as! a! global!
representation!of!a! team!(see! Appendix!A2!for!outputs!for!all!teams!in!2018/19!Serie! A! season).! We!then!
calculate!the!same!surface!at!a!game!level!(Figure!4!top!middle)!and!subtract!the!two!surfaces!to!create!the!
Disruption!Map!(Figure!4!top!right).!!This!final!image!reveals!where!the!opposition!disrupts!(or!not!in!some!
cases)!the! opposition’s! normal!strategy/flow
2
.!! We!can!now!use!these!maps!to!determine!which! team! had!
the!biggest!impact!on!their!opposition’s!attacking!style!and!efficiency.!!We!are!also!able!to!break!this!down!
at!a!player!level!to!see!who!was!target!both!on!and!off!the!ball.--
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3.2#Lazio’s#“Stellungsspiel”#-#Defensive#Position#Play""
Despite! Lazio! being! beaten! 1-2,! Juventus’! Giorgio! Chiellini! stated! post! game! "It! was! the! worst! Juventus!
performance!of!the!season!for!the!first!60!minutes”![14].!We!used!our!Disruption!Maps!to!understand!what!
Lazio! did! to! affect! Juventus! so! much! and! which! players! they! targeted! Figure! 4! bottom! shows! Juventus’!
Disruption!Maps!for!the!game.!We!can!clearly!see!Lazio!considerably!decreased!the!xThreat!from!their!left!
side!of!the! penalty! box! (Ronaldo’s!side),!with!a! 10%! decrease! in!Juventus’!xThreat!compared! to! all! other!
Juventus!games!in!that!season.!!In!addition,!we!can!also!see!how!Lazio!increased!the!risk!of!completing!a!pass!
to!any!option!in!the!wide!channels!between!the!touchline!and!six-yard!box!and!in!the!“second!penalty!area”!
outside!the!penalty! area!by!20%.!!These! are! the!most!dangerous!zones!where! shots!and!goals!are!created!
and!the!spaces!that!Juventus’!three!primary!attackers!operate.!!With!regards!to!where!players!were!likely!to!
be!a!target!for!a!pass,!we!can!see!that!xReceiver!was!higher!than!average!around!Lazio’s!penalty!box!however,!
as!discussed,! these! areas!had!a!significantly!higher! risk!of!competition!and!more!importantly! significantly!
lower!probability!of!leading!to!goal!even!if!they!were!completed.!
2
!Disruption!Maps!estimate!tactical!deviation!from!an!average!style,!where!differences!can!be!attributed!to!
opposition!and/or!changes!of!your!own!team’s!tactic!for!a!specific!game.!To!differentiate!between!the!two!
is!out!of!the!scope!of!this!paper.!

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!
!
!
=%>:'#-KL- - Top!row!shows! how! Disruption!Maps! are! composed;!they! are! the!difference! between-+- Team!
Identity!and!a!Game!Identity;!Bottom!row!shows!Juventus’!Disruption!Maps!for!xReceiver,!xPass,!and!xThreat!
!
To!re-emphasise!how!poor!Juventus’!performance!was!viewed,!the!German!football!magazine!Kicker!stated!
in!the!first!half,!“Cristiano! Ronaldo! was! out! of! the! game,!and!Dybala!also!failed!to!give! momentum! to! the!
Bianconeri's!offense.”! [14].! !Our! player! Disruption! Maps!back!this! up! (Figure!5).!Ronaldo’s! probability! of!
receiving!a!pass!was!below!average!across!the!pitch!in!first!half!especially!in!right!channels.!This!marginally!
improved!in!the!second!half!but!only!in!the!deep!right!channel.!!His!threat!didn’t!exist!in!the!first!half!(Figure!
5!lower!left)!however,!he!took!up!dangerous!positions!on!the!left!channel.!But,!as!shown!in!his!second!half!
xReceiver!Disruption!Map!(Figure!5!upper!right)!he!was!never!viewed!as!a!good!option!to!pass!to.!
!
Dybala!took!up!significantly!more!dangerous!positions!on!the!left!of!the!penalty!area!and!around!the!penalty!
spot.!!The!risk!of!completing!the!pass!was!significantly!lower!as!well!indicating!he!took!both!threatening!and!
low! risk! positions! in! attacking! areas.! ! However,! he! was! rarely! viewed! as! a! realistic! passing! option! (low!
xReceiver)!with!him!only!being!above!average!on!the!left!flank!and!the!middle!of!the!pitch.!!This!is!the!critical!
insight!we!are!now!able!to!surface!compared!to!other!methods.!!We!are!not!just!able!to!measure!if!a!player!
is!in!a!good!position!(high!threat/low!risk),!we!can!measure!if!they!are!a!realistic!option!to!receive!the!ball.!!
To!understand!why!Dybala!was!not!a!viable!option!despite!his!good!positioning!we!need!to!go!a!deeper!level!
of!analysis!which!is!out!of!scope!for!this!paper.!

9
!
!
=%>:'#-M(-Player!xReceiver!and!xThreat!Disruption!Maps!by!half:!Left!Ronaldo,!Right!Dybala.!Blue!areas!are!
below!average!values!whereas!red!indicates!above!average!regions.-
-
4.#Going#Deeper#–#Measuring#Decision#Making!
#
A!primary! defensive! tactic!in!soccer!is!to!target! key! players!in!possession.!!These!may! be!players!who!are!
important!to!the!team’s!build!up!or!conversely!players!who!are!more!likely!to!give!the!ball!away!and!cause!
transition!moments.!!Targeting!can!happen!in!three!ways,!ball'orientated'where!defenders! will!specifically!
target!the!player!in!possession!through!pressure;!man!orientated,!where!the!ball!carrier!is!not!targeted!but!
their!passing!options!are;!or!a!combination!of!both!with!the!aim!of!either!causing!a!transition!or!for!the!ball!
to!be!played!to!a!less!dangerous!area![16]!(Figure!3).!
!
These!high-level!complex!coaching!concepts! are!incredibly!difficult!to!capture!and!rely! on!domain!experts!
watching!hours!of!video!to!find!and!analyze.!!However,!by!using!the!output!from!the!xReceiver!model,!we!can!
create!a!detector! to! find!these!moments!by! simply! finding!when! the! primary! target!changes!for! the! ball!
carrier.!!We!define!the!primary!target!as!the!attacker!with!the!highest!xReceiver!value!at!each!frame.!!If!there!
is!a!change!in!the!primary!target,!we!make!an!assumption!that!a!proactive!action!has!occurred.!This!could!be!
a!run!from!a!supporting!attacker,!the!player!in!possession!moving!with!the!ball!or!a!defender(s)!actions.!
!
An!obvious! next! step! could!be! to! train! a!model! to! predict!these!situations.! ! However,!these!labels! do! not!
currently!exist!and!to!ask!a!set!of!domain!experts!to!annotate!thousands!of!examples!would!be!highly!time!
consuming!and!expensive.!!Instead,!we!used!a!programmatic!labelling!functions!approach![17]!and!asked!a!
domain! expert! to! identify! simple! functions! that! capture! the! expected! behaviour! of! players! for! different!
defensive!contexts!(see!Appendix!A3!for!a!sample).!!Based!on!observing!our!initial!detected!moments!with!a!
domain!expert,!we!defined!three!defensive!and!two!attacking!situations!(Table!3).!
!
!
!

10
!
Table!3:'Defensive'off'ball'contexts'and'their'definitions'as'defined'by'the'domain'expert.'
!
#
#
4.1#Ronaldo:#Null#and#Void#
We!can! see! from! the! Disruption! Maps!that! in! the! first!half! Lazio! were! able!to! nullify! Ronaldo! as!a! viable!
passing!option.!However,!how!did!they!do!this?!!Using! our!Defensive!Impact!toolbox,!we!can!now!assess!if!
Ronaldo!was!targeted!when!in!possession!(ball!orientated!defending)!and!out!of!possession!(man!orientated!
defending).!!In!addition,!we!can!assess!if!Ronaldo!made!any!active!runs!to!become!more!available!for!a!team!
mate.!!!
-
4.1.1 Targeting#the#Supply#Line#
To!understand!why!Ronaldo!went!missing!in!the!first!half,!we!identified!the!primary!players!who!pass!the!
ball!to!Ronaldo!from!the!last!5!games!(Table!5).!We!chose!the!last!5!games!as!this!is!how!opposition!scouts!
would!do!it.!!!We!measured!how!often!Ronaldo!was!identified!as!a!primary!target!for!these!players!(Table!6).!!
We!clearly! see! that! the!relationship!between!Matuidi! and! Ronaldo!is! heavily!targeted,!with! Ronaldo! only!
being!considered!an!option!for!Matuidi!once!during!the!Lazio!match.!We!also!see!the!difference!in!Ronaldo’s!
performance!between!the!first!and!second!half,!with!Ronaldo!only!being!identified!5!times!in!the!first!and!8!
times!in!the!second.!!This!further!supports!the!observations!in!Kicker.!!
!
4.1.2 Targeting#Ronaldo#in#Possession#
Ronaldo! was! targeted! 8! times! in! the! game! when! in! possession! with! Lazio! applying! both! ball! and! man!
orientated!defending.!!Figure!6!(right)!shows!a!primary!example!of!how!Lazio!closed!down!Ronaldo’s!options!
by!applying!pressure!to!Ronaldo!as! he! carried! the! ball!and!also!applying! pressure! to! his! primary! targets;!
Matuidi!(red!14)!and!Sandro!(red!12).!!We!can!see!how!Sandro!made!an!active!run!to!become!the!primary!
target!and!how!Correa!(blue!11)!attempted!to!apply!man!orientated!pressure.!!However,!the!defensive!run!
of!Luis!Alberto!(blue!10)!to!press!Ronaldo!was!responsible!for!the!decrease!in!Sandro’s!xReceiver!value.!!!At!
the!same!time! Matuidi! (red! 14)!became!the!most!likely!receiver!(xR!0.98),!however,! due! to! the! combined!
pressure!of!Milinković-Savić! (blue!21)!and!Parolo!(blue! 16)!his!xPass!was!only!0.66,! meaning! there!was!a!
high!chance!of!a!transition.!
!
!
!
!
!
Situations'
Definition'
Ball"orientated"defending"
Defender"moves"closer"to"the"ball"carrier"at"high"speed"to"increase"the"chance"of"the"
ball"being"given"away"or"pass"to"less"dangerous"area.'
Man"orientated"defending"
Defender"moves"closer"to"the"primary"target"to"reduce"the"probability"of"them"being"a"
receiver.'
Ball"and"man"orientated"
defending"
Combination"of"the"previous"two.'
Active"off"Ball"Runs"
An"attacker"moves"at"high"speed"to"increase"their"probability"of"being"a"receiver.'

11
!
Table!5.'Top'3'passers'who'started'the'game'from'the'previous'5'matches'
'
'
-
-
-
'
'
'
Table!6.'Ronaldo’s'availability'for'his'three'primary'suppliers'
-
-
!
!
!
-
-
Table!7.'The'availability'of'Ronaldo’s'three'primary'suppliers'when'he'is'in'possession'
-
!
Option'
Ronaldo'In'Possession'!
First'Half!
Ronaldo'In'Possession'!
Second'Half'
Paulo"Dybala"
4"
4"
Blaise"Matuidi"
2"
1"
Alex"Sandro"
3"
6"
!
We!have!demonstrated!how!effective!Lazio’s!defensive!play!was!in!nullifying!Ronaldo!and!how!they!did!it.!
The!other!aspect! we! can!examine!is! if! Ronaldo!actively!tried! to! make! himself!available.!! Ronaldo! made! 7!
active!runs!(Figure!6!Right!F%6N-,;-J%C#;)!however!only!3!were!attacking!forward!runs.!!If!we!compare!this!
to!Lazio’s!forwards,!Immobile!and!Luis!Alberto!(Figure!7!Left),!we!see!they!were!more!dangerous!with!their!
runs.!!Figure!6!(Left)!shows!an!example!of!Ronaldo!making!an!active!run!into!the!penalty!area!to!become!a!
primary! target! for! Douglas! Costa.! ! When! Costa! received! the! ball! Ronaldo! only! had! an! xReceiver! of! 0.22.!!
However,!as!we!follow!his!run,!we!can!see!him!becoming!the!primary!target!at!the!edge!of!the!penalty!area.!!
Interestingly,!the!plot!reveals!he!was!always!in!a!highly!threatening!position!for!the!entirety!of!the!move!by!
playing!on!the!shoulder!of!the!last!defender.!
Passer'
Pass'Total'
Games'Played'Together'
Pass'Per'90'
Alex"Sandro"
31"
4"
7.23"
Matuidi"
22"
4"
5.31"
Dybala"
22"
4"
5.29"
Supplier'
Ronaldo'Target'!
First'Half'
Ronaldo'Target'!
Second'Half'
Paulo"Dybala"
1"
5"
Blaise"Matuidi"
1"
0"
Alex"Sandro"
3"
3"

12
-
=%>:'#-OL-F#5,(-Example!of!Ronaldo!(7)!making!an!active!off!ball!run!to!become!the!most!likely!receiver.!!His!
trail!shows!both!how!dangerous!his!run!was!and!how!his!xReceiver!increased.!"%>*,(-Ronaldo!being!targeted!
with!combined!man!orientated!and!ball!orientated!defending.!LINK!TO!VIDEO!!!
#
-
=%>:'#-PL-Active! Run! Maps! for! Lazio’s!(Ciro!Immobile!and!Luis! Alberto)!and! Juventus’! (Paulo! Dybala!and!
Christiano!Ronaldo)!main!attackers.--!

13
"
4.#Summary#
#
We!proposed!a!novel!GNN!architecture!that!allows!to!deal!with!unstructured!data.!The!GNN!allows!us!to!
directly!learn!from!a!lightweight!feature!representation!the!collective!behaviour!of!the!soccer!players!on!the!
pitch.!!This!circumvents!the!need!to!order!players!and!for!heavy!feature!crafting!which!allows!us!to!apply!an!
end-to-end!inference!pipeline!in!real-time!applications.!
!
Based!on!the!model!outputs,!we!introduced!Defensive!Impact,!a!toolbox!to!measure!the!influence!of!defensive!
strategy! on! the! opposition! at! a! team! and! player! level.! ! Disruption! Maps! create! a! compact! visual!
representation!of!a!team’s!effect!on!the!opposition’s!xThreat,!xPass!and!xReceiver!values!compared!to!their!
global!overage.! ! It! allows! users! to! determine! where! a! defence! has!been! successful! or!struggled! based! on!
reducing/increasing!an!opposition’s!threat,!pass!risk!and!player!availability.!!
!
We!were!able!to!identify!different!defensive!styles!(man!and!ball!orientated!defending)!and!off!ball!runs.!!Due!
to!the!lack!of!labelled!data!we!utilised!a!task!programming!approach!–!creating!labelling!functions!based!on!
a!domain!expert’s!insights.!Moving!forward!an!active!learning!approach!where!labels!are!generated,!trained!
against!and!then!assessed!would!be!a!recommended!next!step.!!
!
This!research!enables!the!evaluation!of!defensive!behaviour!and!provides!tools!and!insights!for!coaches!and!
fans!to!engage!with.!!
!
!
"
"
" "

14
"
5.#References#
#
[1]!Xinyu!W.,!Long!S.,!Lucey,!P.,!Morgan,!S.,!&!Sridharan,!S..!Large-scale!analysis!of!formations!in!soccer.!In!
Digital!Image!Computing:!Techniques!and!Applications!(DICTA),!2013!International!Conference!on,!
pages!1–8.!IEEE,!2013.!
[2]!Power,!P.,!Ruiz,!H.,!Wei,!X.,!&!Lucey,!P.!(2017).!“Not!all!passes!are!created!equal:”!Objectively!measuring!
the!risk!and!reward!of!passes!in!soccer!from!tracking!data.!Proceedings'of'the'ACM'SIGKDD'
International'Conference'on'Knowledge'Discovery'and'Data'Mining.!
[3]!Fernández,!J.,!&!Bornn,!L.!(2020).!SoccerMap:!A!Deep!Learning!Architecture!for!Visually-Interpretable!
Analysis!in!Soccer.!European'Conference'on'Machine'Learning'and'Principles'and'Practice'of'Knowledge'
Discovery'in'Databases'(ECML-PKDD).!
[4]!Brefeld,!U.,!Lasek,!J.,!&!Mair,!S.!(2019).!Probabilistic!movement!models!and!zones!of!control.!Machine'
Learning,!108(1),!127–147.!https://doi.org/10.1007/s10994-018-5725-1!
[5]!Kim,!K.,!Grundmann,!M.,!Shamir,!A.,!Matthews,!I.,!Hodgins,!J.,!&!Essa,!I.!(2010).!Motion!fields!to!predict!
play!evolution!in!dynamic!sport!scenes.!Proceedings'of'the'IEEE'Computer'Society'Conference'on'
Computer'Vision'and'Pattern'Recognition,!840–847!
[6]!Cervone,!D.,!D’amour,!A.,!Bornn,!L.,!&!Goldsberry,!K.!(2014).!POINTWISE:!Predicting!Points!and!Valuing!
Decisions!in!Real!Time!with!NBA!Optical!Tracking!Data.!MIT'Sloan'Sports'Analytics'Conference.!
[7]!Wei,!X.,!Lucey,!P.,!Morgan,!S.,!Reid,!M.,!&!Sridharan,!S.!(2016).!“The!Thin!Edge!of!the!Wedge”:!Accurately!
Predicting!Shot!Outcomes!in!Tennis!using!Style!and!Context!Priors.!MIT'Sloan'Sports'Analytics'
Conference.!
[8]!Wei,!X.,!Lucey,!P.,!Vidas,!S.,!Morgan,!S.,!&!Sridharan,!S.!(2015).!Forecasting!events!using!an!augmented!
hidden!conditional!random!field.!Lecture'Notes'in'Computer'Science'(Including'Subseries'Lecture'Notes'
in'Artificial'Intelligence'and'Lecture'Notes'in'Bioinformatics),!9006,!569–582.!
https://doi.org/10.1007/978-3-319-16817-3_37!
[9]!Spearman,!W.!(2019).!Beyond!Expected!Goals.!MIT'Sloan'Sports'Analytics'Conference.!
[10]!Franks,!A.,!Miller,!A.,!Bornn,!L.,!&!Goldsberry,!K.!(2015).!Counterpoints:!Advanced!Defensive!Metrics!
for!NBA!Basketball.!MIT'Sloan'Sports'Analytics'Conference.!!
[11]!Seidl,!T.,!Cherukumudi,!A.,!Hartnett,!A.,!Carr,!P.,!&!Lucey,!P.!(2018).!Bhostgusters:!Realtime!Interactive!
Play!Sketching!with!Synthesized!NBA!Defenses.!MIT'Sloan'Sports'Analytics'Conference.!
[12]!Le,!H.!M.,!Carr,!P.,!Yue,!Y.,!&!Lucey,!P.!(2017).!Data!Driven!Ghosting!using!Deep!Imitation!Learning.!MIT'
Sloan'Sports'Analytics'Conference.!
[13]!Battaglia,!P,!et!al.!(2018).!Relational!inductive!biases,!deep!learning,!and!graph!networks.!'
[14]!https://www.espn.com/soccer/report?gameId=522613!!
[15]!https://www.kicker.de/lazio-gegen-juventus-2019-serie-a-4509058/spielbericht!(in German)!
[16]!https://spielverlagerung.com/2014/07/07/counterpressing-variations/
[17]!Sun,!J.!J.,!Kennedy,!A.,!Eric,!Z.,!Yue,!Y.,!&!Perona,!P.!(2020).!Task!Programming:!Learning!Data!Efficient!
Behavior!Representations.!arXiv'Preprint,!(2011.13917).!
[18]!Horton,!M.!(2020).!Learning!Feature!Representations!from!Football!Tracking.!MIT'Sloan'Sports'
Analytics'Conference.!
[19]!Mehrasa,!N.,!Zhong,!Y.,!Tung,!F.,!Bornn,!L.,!Mori,!G.!(2018)!Deep!Learning!of!Player!Trajectory!
Representations!for!Team!Activity!Analysis.!MIT'Sloan'Sports'Analytics'Conference!
#

15
A. Appendix#
#
#A1.#Speed#of#Inference#
Our!three!GNN!models!use!the!same!features!and!the!number!of!features!is!rather!small!as!described!above.!
This!raised!our!interest!whether!these!models!are!applicable!in!real-time!or!at!least!close!to!real-time.!We!
ran!a!test!how!long!the! feature! engineering! (custom! python! code)! and!a!GNN!model!inference!of!a!single!
frame!take!on!an!off-the-shelf!notebook
3
,!respectively.!Table!2!shows!that!on!average!the!whole!process!from!
crafting!the!features!until!the!inference!of!the!model!is!made!took!less!than!0.05s!for!one!tracking!timestamp!
on!our!test!notebook.!This!enables!us!to!use!our!GNN!models!nearly!in!real-time.!!
!
!
Table!A.1:'Speed'tests'how'long'feature'crafting'and'the'model'inference'takes'in'seconds'[s];'descriptive'results'
of'1000'attempts'
!
=#+,:'#-$'+5,%6>-Q/R!
765#'#6$#-Q/R!
);,+0-Q/R!
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!
-
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3
MacBookPro with a 2.3 GHz Intel Core i5 processor and 16GB RAM

16
#
#
A2.#Spatial#identity#maps#for#all#teams#from#Serie#A#season#2018/19#ordered#by#league#table#
#
#
=%>:'#-2L?(-SSpatial!Identity!for!xReceiver”!for!all!teams!from!Serie!A!2018/19.!Teams!playing!from!left!to!
right.- -

17
-
-
-
#
-
=%>:'#-2LT(-SSpatial!Identity!for!xPass”!for!all!teams!from!Serie!A!2018/19.!Teams!playing!from!left!to!right.
- -

18
-
-
#
-
=%>:'#-2LD(-SSpatial!Identity!for!xThreat”!for!all!teams!from!Serie!A!2018/19.!Teams!playing!from!left!to!
right.- -

19
#
A3.#Sample#pseudo#code#for#a#programmatic#labelling#function#
#
Based!on!discussions!with!domain!experts!the!task!of!identifying!man!orientated!defending!was!translated!
into!the!following!pseudo!code:!
!
“Defender!moves!closer!to!the!primary!target!to!reduce!the!probability!of!them!being!a!receiver.”!
!
=%>:'#-2LK(-Pseudo!code!for!programmatic!labelling!of!man'orientated'defending.-