Assessing Team Strategy using Spatiotemporal

Assessing Team Strategy using Spatiotemporal Data
Patrick Lucey
Dean Oliver
Disney Research
Pittsburgh, PA, USA
ESPN
Bristol, CT, USA
[email protected]
[email protected]
Peter Carr
Joe Roth
Iain Matthews
Disney Research
Pittsburgh, PA, USA
Disney Research
Pittsburgh, PA, USA
Disney Research
Pittsburgh, PA, USA
[email protected]
[email protected]
[email protected]
ABSTRACT
The Moneyball [14] revolution coincided with a shift in the
way professional sporting organizations handle and utilize
data in terms of decision making processes. Due to the demand for better sports analytics and the improvement in
sensor technology, there has been a plethora of ball and
player tracking information generated within professional
sports for analytical purposes. However, due to the continuous nature of the data and the lack of associated high-8.
level labels to describe it - this rich set of information has[1]
had very limited use especially in the analysis of a team’s
tactics and strategy. In this paper, we give an overview of[2]
the types of analysis currently performed mostly with handlabeled event data and highlight the problems associated
with the influx of spatiotemporal data. By way of exam-[3]
ple, we present an approach which uses an entire season of
ball tracking data from the English Premier League (20102011 season) to reinforce the common held belief that teams[4]
should aim to “win home games and draw away ones”. We
do this by: i) forming a representation of team behavior by
chunking the incoming spatiotemporal signal into a series
of quantized bins, and ii) generate an expectation model of[5]
team behavior based on a code-book of past performances.
We show that home advantage in soccer is partly due to the
conservative strategy of the away team. We also show that[6]
our approach can flag anomalous team behavior which has
many potential applications.
[7]
Categories and Subject Descriptors
[8]
H.4 [Information Systems Applications]: Miscellaneous;[9]
I.2.6 [Learning]: General
Keywords
Sports Analytics; Spatiotemporal Data; Representation
[10]
Permission to make digital or hard copies of all or part of this work for personal or
classroom use is granted without fee provided that copies are not made or distributed
for profit or commercial advantage and that copies bear this notice and the full citation
[11]
on the first page. Copyrights for components of this work owned by others than the
author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or
[12]
republish, to post on servers or to redistribute to lists, requires prior specific permission
and/or a fee. Request permissions from [email protected].
KDD’13, August 11–14, 2013, Chicago, Illinois, USA.
[13]
Copyright is held by the owner/author(s). Publication rights licensed to ACM.
Copyright 2013 ACM 978-1-4503-2174-7/13/08 ...$15.00.
[14]
Canada
9(3)
13
3
1
38%
3
0
4
USA
12(4)
11
8
4
62%
1
0
3
In CVPR, 2009.
[16] W. Lu, J. Ting, K. Murphy, and
Players in Broadcast Sports Vide
Random Fields. In CVPR, 2011.
[17] P. Lucey, A. Bialkowski, P. Carr
I. Matthews. Characterizing Mul
Behavior from Partial Team Tra
the English Premier League. In A
[18] L. Madden. NFL to Follow Army
(a)
(b)Sensors in Attempt to Prevent H
www.forbes.com/sites/lancema
REFERENCES
Figure 1: (a) An example of standard soccer
statisnfl-to-follow-armys-lead-ontics
hand-labeled
event
data which
describe
S. Ali
andbased
M. Shah.on
Floor
Fields for Tracking
in High
-attempt-to-prevent-head-inj
Density
Crowd
Scenes. In ECCV,
2008.
[19]has
R. Masheswaran,
what
happened.
(b) Spatiotemporal
data
the po- Y. Chang, A. H
N. Allen, J. Templon, P. McNally, L. Birnbaum, and
S. Danesis.
the Rebo
tential to describe the where and how, but
as it Destructing
is
K. Hammond. StatsMonkey: A Data-Driven Sports
Tracking Data. In MIT Sloan Sp
a continuous
signal
which is
not associated
with
a
Narrative
Writer. In AAAI
Fall Symposium
Series,
Conference, 2012.
is V.difficult.
2010.fixed event, using this data for analysis
[20]
Morariu and L. Davis. MultiBBC-Sports. Footballers may trial wearing microchips
Recognition in Structured Scena
to monitor health.
[21] T. Moskowitz and L. Wertheim.
www.bbc.co.uk/sport/0/football/21460038, 14 Feb
Hidden Influences Behind How S
2013.
Games Are
Won. Crown Publish
In
his
2003
book
Moneyball
[14],
Michael
Lewis
docuM. Beetz, N. von Hoyningen-Huene, B. Kirchlechner,
[22] NBA Shot Charts. www.nba.com/
mented
how M.
Oakland
A’sM.General
Beane was
S. Gedikli,
F. Siles,
Durus, and
Lames. Manager Billy
[23] D. Oliver. Basketball on Paper: R
ASPOGAMO:
Analysis
able to Automated
effectivelySports
use Game
metrics
derived from hand-crafted
Performance Analysis. Brassey’s
Models.
International
Journal of
Science inin the value of indistatistics
to exploit
theComputer
inefficiencies
[24] D. Oliver. Guide to the Total Qu
Sport, 8(1), 2009.
espn.go.com/nfl/story/_/id/6
vidual
baseball
players.
Around
the
same
time,
Basketball
P. Carr, Y. Sheikh, and I. Matthews. Monocular
explaining-statistics-totalon
Paper
[24]
was
published
which
outlined
methods
for
Object Detection using 3D Geometric Primitives.
4 August 2011.
2012.valuing player performance in basketball which
is
a
far
more
[25] Opta Sports. www.optasports.co
K. Goldsberry.
CourtVision:
Visual and
challenging
problemNew
because
it isSpatial
a continuous
sport.A. Ess, K. Schindle
[26] team
S. Pellegrini,
Analytics for the NBA. In MIT Sloan Sports Analytics
You’ll
Never
Walk Alone: Model
Due to the popularity and effectiveness of the tools
that
emConference, 2012.
for Multi-Target Tracking. In CV
anated
from these
works,
there
A. Gupta,
P. Srinivasan,
J. Shi,
and L.
Davis.has been enormous interest
[27] M. Perse, M. Kristan, S. Kovacic
Understanding
Videos,
Constructing
Plots: Learning
a last 10 years with
in the field
of sports
analytics
over the
Trajectory-Based Analysis of Co
Visually
Grounded
Storyline
Model
from
Annotated
many organizations (e.g. professional teams, media
groups)
Activity
in Basketball Game. Co
Videos. In CVPR, 2009.
Image
Understanding,
2008.
housing
their
own
analytics
department.
However,
nearly
all
Hawk-Eye. www.hawkeyeinnovations.co.uk.
[28]hand-labeled
Prozone. www.prozonesports.co
of
the
analytical
works
have
dealt
solely
with
D. Henschen. IBM Serves New Tennis Analytics At
[29] B. Siddiquie, Y. Yacoob, and L.
event data
which describes what happened (e.g.
basketball
Wimbledon.
www.informationweek.com/software/
Plays in American Football Vide
business-intelligence/
- rebounds, points scored, assists; football - yards
per carry,
University
of Maryland, 2009.
ibm-serves-new-tennis-analytics-at-wimbl/
tackles,
sacks;
soccer
passes,
shots,
tackles;
–
see Fig-www.sportsvision
[30] SportsVision.
240002528, 23 June 2012.
[31] STATS SportsVU. www.sportvu.
ure 1(a)).
the Understanding
data is in this
A. Hervieu
and P. Once
Bouthemy.
sportsform, most approaches
Statsheet.
www.statsheet.com.
for relevant
dataInfrom
a database,
applying
sportvideoquery
using players
trajectories.
J. Zhang,
L. Shao, then [32]
[33] D. Stracuzzi, A. Fern, K. Ali, R.
L. Zhang,
G. Jones,
Intelligent
Video methods,
basedand
rules
and editors,
standard
statistical
including
reT. Konik, and D. Shapiro. An A
Event Analysis and Understanding. Springer Berlin /
gression
and
optimization.
to
American
Football: From Obs
Heidelberg, 2010.
Video to with
Control in a Simulated
Asand
most
sporting
environments
tend to be dynamic
S. Intille
A. Bobick.
A Framework
for Recognizing
Magazine,
32(2), 2011.
multiple
players
and competing
against
Multi-Agent
Action
fromcontinuously
Visual Evidence.moving
In AAAI,
[34] X. Wei, P. Lucey, S. Morgan, and
1999.each other, simple event statistics do not capture
the
comSweet-Spot: Using Spatiotempor
K. Kim,
Grundmann,
A. Shamir,
plexM.aspects
of the
game.I. Matthews,
To gain an advantage
and over
Predictthe
Shots in Tennis. In M
J. Hodgins, and I. Essa. Motion Fields to Predict Play
Analytics
Conference, 2013.
rest of
the field,
sporting
looked
Evolution
in Dynamic
Sports
Scenes.organizations
In CVPR, 2010. have recently
[35]
C. Xu,can
Y. Zhang,
to employ
commercial
trackingan technologies
which
lo- G. Zhu, Y. Ru
M. Lewis.
Moneyball:
The Art of Winning
Unfair
Q. Huang. Using Webcast Text f
Game.
Norton,
2003.
cate
the position
of the ball and players at each time
instant
Detection in Broadcast. T. Multi
R. Li and R. Chellappa. Group Motion Segmentation
[36] Zonalmarking. www.zonalmarkin
Using a Spatio-Temporal Driving Force Model. In
1.
Shots (on Goal)
Fouls
Corner Kicks
O↵sides
Time of Possession
Yellow Cards
Red Cards
Saves
INTRODUCTION
CVPR, 2010.
[15] R. Li, R. Chellappa, and S. Zhou. Learning
Multi-Modal Densities on Discriminative Temporal
Interaction Manifold for Group Activity Recognition.
in professional leagues [9, 26, 29, 32]1 - to determine where
and how events happen. Even though there is potentially
an enormous amount of hidden team behavioral information
to mine from such sources, due to the sheer volume as well
as the noisy and variable length of the data, methods which
can adequately represent team behaviors are yet to be developed. The value of this data is limited as little analysis can
be conducted. What compounds the difficulty of this task
is the low-scoring and/or continuous nature of many team
sports (e.g. soccer, hockey, basketball) which makes it very
hard to associate segments of play with high-level behaviors
(e.g. tactics, strategy, style, system, formations). Without
these labels, which essentially give the game context, inferring team strategy or behavior is impossible as there are no
factors to condition against (see Figure 1(b)).
Due to these complexities, there has been no effective
method of utilizing spatiotemporal data in continuous sports.
Having suitable methods which can first develop suitable
representations from imperfect (e.g. noisy or impartial) data,
and then learn team behaviors in an unsupervised or semisupervised manner, as well as recognize and predict future
behaviors would greatly enhance decision making in all areas of the sporting landscape (e.g. coaching, broadcasting,
fantasy-games, video games, betting etc.). We call this the
emerging field of Sports Spatiotemporal Analytics - and we
show an example of this new area of analytics by comparing the strategies of home and away teams in the English
Premier League using ball tracking data.
2.
RELATED WORK
The use of automatic sports analysis systems have recently graduated from the virtual to the real-world. This
is due in part to the popularity of live-sport, the amount
of live-sport being broadcasted, the proliferation of mobile
devices, the rise of second-screen viewing, the amount of
data/statistics being generated for sports, and demand for
in-depth reporting and analysis of sport. Systems which use
match statistics to automatically generate narratives have
already been deployed [2, 33]. Although impressive, these
solutions give a low-level description of match statistics and
notable individual performances without any tactical analysis about factors which contributed to the result. In tennis, IBM Slamtracker [10] provides player analysis by finding
patterns that characterize the best chance a player has to
beat another player from an enormous amount of event labeled data - although no spatiotemporal data (i.e. player or
ball tracking information) has been used in their analysis
yet.
Spatiotemporal data has been used extensively in the visualization of sports action. Examples include vision-based
systems which track baseball pitches for Major League Baseball [31], and ball and players in basketball and soccer [29,
32]. Hawk-Eye deploy vision-based systems which track the
ball in tennis and cricket, and is often used to aid in the
officiating of these matches in addition to providing visu1
As nearly all professional leagues currently forbid the use of
wearable sensors on players, unobtrusive data capture methods such as vision-based systems or armies of human annotators are used to provide player and ball tracking information.
However, this restriction may change soon as monitoring the
health and well-being of players has attracted significant interest lately, especially for concussions in American Football [19], as well as heart issues in soccer [3].
alizations for the television broadcasters [9]. Partial data
sources normally generated by human annotators such as
shot-charts in basketball and ice-hockey are often used for
analysis [23], as well as passing and shot charts in soccer [26]. Recently, ESPN developed a new quarterback rating in American Football called “TotalQBR” [25] which assigns credit or blame to the quarterback depending on a host
of factors such as pass or catch quality, importance in the
match, pass thrown under pressure or not. As these factors
are quite subjective, annotators who are reliable in labeling such variables are used. In terms of strategic analysis,
zonalmarking.net [37] describes a soccer match from a tactical and formation point of view. This approach is very
qualitative and is based solely on the opinion of the analyst.
As the problem of fully automatic multi-agent tracking
from vision-based systems is still an open one, most academic research has centered on the tracking problem [1, 5,
17,27]. The lack of fully automated tracking approaches has
limited team behavioral research to works on limited size
datasets. The first work which looked at using spatiotemporal data for team behavior analysis was conducted over 10
years ago by Intille and Bobick [12]. In this seminal work,
the authors used a probabilistic model to recognize a single
football play from hand annotated player trajectories. Since
then, multiple approaches have centered on recognizing football plays [15, 16, 30, 34], but only on a very small number of
plays (i.e. 50-100). For soccer, Kim et al. [13] used the global
motion of all players in a soccer match to predict where the
play will evolve in the short-term. Beetz et al. [4] proposed
a system which aims to track player and ball positions via
a vision system for the use of automatic analysis of soccer
matches. In basketball, Perse et al. [28] used trajectories of
player movement to recognize three types of team offensive
patterns. Morariu and Davis [21] integrated interval-based
temporal reasoning with probabilistic logical inference to
recognize events in one-on-one basketball. Hervieu et al. [11]
also used player trajectories to recognize low-level team activities using a hierarchical parallel semi-Markov model. In
addition to these works, plenty of work has centered on analyzing broadcast footage of sports for action, activity and
highlight detection [8, 36]2 . The lack of extensive tracking
data to adequately train models has limited the success of
the above research.
It is clear from the overview given above, that there exists a major disparity in resources between industry and
academia to deal with this problem domain. Sporting organizations receive large volumes of spatiotemporal data from
third-party vendors but often lack the computational skills
or resources to make use of it. Research groups on the otherhand, have the necessary analysis tools can not access these
large data repositories due to the proprietary nature of commercial tracking systems. Recently however, due to the potential payoff, some industry groups are investing in analytical people with these skill sets, or have teamed up with
research groups to help facilitate a solution. The release of
STATS Sports VU data [32] to some research groups has
enabled interesting analysis of shots and rebounding in the
NBA [7, 20]. In tennis, Wei et al. [35] used ball and player
tracking information to predict shots using data from the
2012 Australian Open. For soccer, researchers have charac2
These works only capture a portion of the field, making
group analysis very difficult as all active players are rarely
present in the all frames.
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Team
Man Utd
Chelsea
Man City
Arsenal
Tottenham
Liverpool
Everton
Fulham
Aston Villa
Sunderland
West Brom
Newcastle
Stoke City
Bolton
Blackburn
Wigan
Wolves
Birmingham
Blackpool
West Ham
SUM
AVG(per game)
W
18
14
13
11
9
12
9
8
8
7
8
6
10
10
7
5
8
6
5
5
179
0.47
D
1
3
4
4
9
4
7
7
7
5
6
8
4
5
7
8
4
8
5
5
111
0.29
L
0
2
2
4
1
3
3
4
4
7
5
5
5
4
5
6
7
5
9
9
90
0.24
Home
P
GF
55
49
45
39
43
34
37
33
36
30
40
37
34
31
31
30
31
26
26
25
30
30
26
41
34
31
35
34
28
22
23
22
28
30
26
19
20
30
20
24
648
617
1.71
1.62
SF
347
379
306
350
383
319
321
307
273
287
329
300
298
311
254
290
256
231
296
325
6162
16.2
GA
12
13
12
15
19
14
23
23
19
27
30
27
18
24
16
34
30
22
37
31
446
1.17
SA
191
233
216
154
228
220
227
262
263
243
237
250
256
256
259
227
266
324
297
317
4926
13.0
W
5
7
8
8
7
5
4
3
4
5
4
5
3
2
4
4
3
2
5
2
90
0.24
D
10
5
4
7
5
3
8
9
5
6
5
5
3
5
3
7
3
7
4
7
111
0.29
L
4
7
7
4
7
11
7
7
10
8
10
9
13
12
12
8
13
10
10
10
179
0.47
Away
P
GF
25
29
26
30
28
26
31
39
26
25
18
22
20
20
18
19
17
22
21
20
17
26
20
15
12
15
11
18
15
24
19
18
12
16
13
18
19
25
13
19
381
446
1.00
1.17
SF
272
367
240
305
274
266
259
245
233
246
273
209
186
261
200
221
205
174
240
250
4926
13.0
GA
25
20
21
28
27
30
22
20
40
29
41
30
30
32
43
27
36
36
41
39
617
1.62
SA
271
208
298
251
339
270
279
271
340
311
297
256
294
346
360
284
306
362
441
378
6162
16.2
Table 1: Table showing the statistics for the home and away performances for each team in the 2010 EPL
season: (left columns) home matches (right columns) away columns (Key: W = wins, D = draws, L = losses,
P = points (3 for a win, 1 for a draw, 0 for a loss), GF = goals for, SF = shots for, GA = goals against,
SA = shots against).
terized team behaviors in the English Premier League using
ball-motion information across an entire season using OPTA
data [18]. In this paper, we extend this method to explain
that the home advantage in soccer is due to the conservative
strategy that away teams use (or more aggressive approach
of the home team) which reinforces the commonly held belief that teams aim to win their home games and draw their
away ones.
3.
CASE STUDY:
HOME ADVANTAGE IN SOCCER
3.1
“Win at Home and Draw Away”
In a recent book [22], Moskowitz and Wertheim highlight
that the home advantage exists in all professional sports (i.e.
teams win more at home than away). The authors hypothesized that referees play a significant role by giving home
teams favorable calls at critical moments. They then quantitatively showed this in baseball through the use of pitch
tracking data. For soccer, hand-labeled event statistics such
as the amount of injury time, number of yellow cards and
number of penalties awarded to reinforce their hypothesis.
As soccer is a very tactical game, we hypothesize that the
strategy of the home and away teams also plays a role in
explaining the home advantage.
A great case study of home advantage is the 2010-2011
English Premier League soccer season. In that season, the
home team earned an average 1.71 points out of a total 3
points per match. This is in stark contrast with the away
team, which earned only 1.00 points per game: a rather
large discrepancy, especially considering that teams play every other team both at home and away so that any talent
disparities apply to both home and away averages. In terms
of shooting and passing proficiency, there was no significant difference between teams at home and away (10.01%
vs 9.05% for shooting and 73.46% vs 72.99% for passing see the bottom row in Table 1).
However, there is a large difference between the amount of
shots (16.2 vs 13.0) and goals scored (1.62 vs 1.17) at home
and away. An illuminating example is the league champions
for that season, Manchester United (see top row in Table 1).
At home, they were unbeaten (winning 18 and drawing 1),
but away from home they only won 5 games, drew 10 and
lost 4. The telling statistic is that at home they scored 49
goals from 347 shots, compared to only 29 goals from 272
shots away from home. Comparatively, the opposition at
home games only scored a paltry 12 goals from 191 shots
while at away games they scored 25 goals from 271 shots.
In soccer, there is the commonly held belief that team should
aim to win their home games and draw their away ones. If
you skim down Table 1, you will find that: i) all teams won
more home games (except for Blackpool who won the same
amount), ii) all teams score more goals at home (except Arsenal and Blackburn), iii) all teams had more shots at home
compared to away, and iv) all teams gained more points at
home. These event statistics tell us what has occurred, in
the rest of the paper we use spatiotemporal data to help
explain where and why this occurred. Before we detail the
method, we first describe the data.
3.2
Ball Tracking and Event Data
Due to the difficulty associated with accurately tracking
players and the ball, data containing this information is still
scarce. Most of the data collected is via an army of human
annotators who label all actions that occur around the ball
- which they call ball actions. The F24 soccer data feed collected for the English Premier League (EPL) by Opta [26]
is a good example of this. The F24 data is a time coded
feed that lists all player action events within the game with
a player, team, event type, minute and second for each action. Each event has a series of qualifiers describing it. This
ing
partial
team
tracings.
Wethe
show
this
framing
the
and
Sycara
proposed
another
recognizing
algorithm
that
hardness
of
single
and
multi-agent
plan
recognition,
and
hardness
ofthe
single
and
multi-agent
plan
recognition,
and
ically
changed
structures
of
groups
ofbythe
agents,
Sukthan
solve
MAPR
problems
in
the
model
using
abeing
first-cut
approach,
provided
that
ateam
fully
observed
team
trace
and
aplaybook
li-en4another
3and
ement
over
fixedwindows
windows
ically
changed
structures
of
groups
of
agents,
Sukthankar
with
aconnection
new
model,
revealing
the
distinction
between
the
coded
dynamic
team
membership
to
prune
thethe
size
of
the
acking
information
(?;
solve
MAPR
in
model
a first-cut
ap
5using
4problems
hardness
of
single
multi-agent
plan
recognition,
and
new
statistics
including
spatial
location
events
gencated
the
between
agents,
to
track
sue
by
representing
behavior
asof
aaovercome
spatio-temporal
ocand
Sycara
proposed
recognizing
algorithm
that
en
I(X
as
spatio-temporal
ocIn
this
paper,
we
propose
ano
method
to
overcome
this
isment
over
fixed
cation
of
events
gen5team
sue
by
representing
team
behavior
asas
ato
spatio-temporal
ocverifying
such
analysis
(?;
?).
This
is
despite
use
of
proach,
provided
that
aateam
fully
observed
team
trace
and
aoc•by
Characterize
team
tactics
as
function
of
the
size.
a aspatio-temporal
ocdespite
the
use being
of
plan
library.
Banerjee
et
al.
proposed
formalize
MAPR
solve
MAPR
problems
in
the
model
using
aadynamfirst-cut
aper
tracking
information
(?;
In
this
paper,
we
propose
aspatial
method
to
isment
over
fixed
windows
nts.
By
analyzing
aamatch
coded
the
dynamic
membership
to prune
the
sizeand
ofand
the
•humans
Characterize
team
tactics
as
ameans
function
of
the
playbook
and
often
unreliable
as
there
are
quantitative
of
cupancy
map
based
on
ball
movement
over
fixed
windows
solve
MAPR
problems
in
the
model
using
a this
first-cut
apnew
statistics
including
location
of
events
being
gensue
representing
behavior
ainput
spatio-temporal
hardness
of
single
and
multi-agent
plan
recognition,
an
4of
problem
as
a5single
team
identification
task.
proach,
provided
that
fully
observed
team
trace
and
alili5multi-agent
solve
MAPR
problems
in
theobserved
model
using
first-cut
ap
•
Show
that
teams
have
unique
playing
styles,
despite
havcoded
the
dynamic
team
membership
to
prune
the
size
of
the
5
and
Sycara
proposed
another
recognizing
algorithm
that
6
solve
MAPR
problems
in
the
model
using
a
first-cut
aphardness
of
and
plan
recognition,
proach,
provided
that
a
fully
observed
team
trace
and
a
liand
Sycara
proposed
another
recognizing
algorithm
that
enbrary
of
full
team
plans
were
given
as
(?).
proach,
provided
that
a
fully
team
trace
a
l
ents.
By
analyzing
match
ically
changed
structures
groups
of
agents,
Sukthankar
plan
library.
Banerjee
et
al.
proposed
to
formalize
MAPR
solve
MAPR
problems
in
the
model
using
a
first-cut
aperated
by
(?)
and
player
tracking
information
(?;
cupancy
map
based
on
ball
movement
over
fixed
windows
coded
the
dynamic
team
membership
to
prune
the
size
of
th
6
•
Automatically
analyze
an
unseen
match
in
terms
of
tacsue
by
representing
team
behavior
as
a
spatio-temporal
ocover
fixed
windows
6Banerjee
cupancy
map
based
on
ball
movement
over
fixed
windows
ts.
By
analyzing
a
match
new
statistics
including
spatial
location
of
events
being
genr,nts.
tracking
information
(?;
•
Characterize
team
tactics
as
a
function
of
the
pla
size.
brary
of
full
team
plans
were
given
as
input
(?).
proach,
provided
that
a
fully
observed
team
trace
and
a
li5
sue
by
representing
team
behavior
as
a
spatio-temporal
ocverifying
such
analysis
(?;
?).
This
is
despite
the
use
of
fent
events
being
genplan
library.
et
al.
proposed
to
formalize
MAPR
nt
over
fixed
windows
6
of
time,
which
we
call
play-segments.
By
analyzing
a
match
with
a
new
model,
revealing
the
distinction
between
the
erated
by
humans
(?)
and
player
tracking
information
(?;
By
analyzing
a match
cupancy
map
based
on
ball
movement
over
fixed
windows
6problems
we
can
characterize
the
solve
MAPR
in
the
model
using
a
first-cut
•
Characterize
team
tactics
as
a
function
of
th
7
size.
proach,
provided
that
a
fully
observed
team
trace
and
a
liproach,
provided
that
a
fully
observed
team
trace
and
a
lia
brary
of
full
team
plans
were
given
as
input
(?).
coded
the
dynamic
team
membership
to
prune
the
size
of
•
Show
that
teams
have
unique
playing
styles,
despite
plan
library.
Banerjee
et
al.
proposed
to
formalize
MAPR
ing
partial
team
tracings.
We
show
this
by
framing
the
solve
MAPR
problems
in
the
model
using
a
first-cut
ap7
and
Sycara
proposed
another
recognizing
algorithm
that
enbrary
of
full
plans
were
given
as
input
(?).
proach,
provided
that
a
fully
observed
team
trace
and
a
li7 team
proach,
provided
that
a
fully
observed
team
trace
and
a
licoded
the
dynamic
team
membership
to
prune
the
size
of
the
?)
being
generated.
of
time,
which
we
call
play-segments.
By
analyzing
a
match
brary
of
full
team
plans
were
given
as
input
(?).
plan
library.
Banerjee
et
al.
proposed
to
formalize
MAP
s,
we
can
characterize
the
with
a
new
model,
revealing
the
distinction
between
the
•
Automatically
analyze
an
unseen
match
in
terms
of
taccupancy
map
based
on
ball
movement
over
fixed
windows
od
to
overcome
this
istics.
6
of
time,
which
we
call
play-segments.
By
analyzing
a
match
s.
By
analyzing
a
match
erated
by
humans
(?)
and
player
tracking
information
(?;
7awere
size.
7 10plans
we
can
characterize
the
10
new
statistics
including
spatial
location
of we
events
being
genbrary
of
full
team
plans
given
as
input
(?).
cupancy
map
based
oncall
ball
movement
over
fixed
windows
with
adynamic
new
model,
revealing
the
distinction
between
asofas
aof
playbook
of
play-segments,
can
characterize
the
ng
information
?)
being
generated.
time,
which
we
play-segments.
By
analyzing
a match
proach,
provided
that
fully
observed
team
trace
and
By
analyzing
a (?;
match
size.
hardness
single
and
multi-agent
plan
recognition,
and
s,
we
can
characterize
the
ws
for
tactical
analysis
of
brary
of
were
given
asdistinction
input
(?).
method
to
overcome
this
isbrary
of
full
team
plans
were
given
as
input
(?).
10
plan
library.
Banerjee
et observed
al.
proposed
to(?).
formalize
MA
ing
partial
team
tracings.
We
show
this
by
framin
provided
that
fully
team
trace
and
a the
li-ath
coded
the
team
membership
to
prune
the
size
of
the
Show
that
teams
have
unique
playing
styles,
despite
hav5 proach,
×
4
10
×
15team
×model,
12 plans
with
new
model,
revealing
the
distinction
the
brary
of
full
team
were
given
as
input
problem
as
aof
team
identification
task.
as
ateam
playbook
of
play-segments,
we
can
characterize
theand
with
a8full
new
revealing
the
between
7a 10
planbrary
library.
Banerjee
et
al.
proposed
to
formalize
MAPR
of
full
plans
were
given
as
input
(?).
In
this
paper,
we
propose
a tracking
method
toinformation
overcome
this
isReference
tics.
time,
which
we
call
play-segments.
By
analyzing
abetween
match
for
tactical
analysis
of
10
hardness
of
single
and
multi-agent
plan
recognition,
•this
Show
that
teams
have
unique
playing
styles,
despite
hav15
as
as
aa•as
playbook
play-segments,
we
can
characterize
the
ssws
afor
spatio-temporal
oc?)
being
generated.
can
characterize
the
English
Premier
League
Ball
Action
Data
by
humans
(?)
and
player
(?;
ofof
time,
which
we
call
play-segments.
By
analyzing
a
match
tactical
analysis
of
hardness
of
single
and
multi-agent
plan
recognition,
and
behavior
of
each
team
which
allows
for
tactical
analysis
of
15
as
as
a
playbook
of
play-segments,
we
can
characterize
the
15
brary
of
full
team
plans
were
given
as
input
(?).
to
overcome
this
is- • erated
In
paper,
we
propose
a
method
to
overcome
this
isewe
can
characterize
the
•
Show
that
teams
have
unique
playing
styles,
despi
solve
MAPR
problems
in
the
model
using
a
first-cut
apws
for
tactical
analysis
eethod
efficacy
and
usability
of
with
a
new
model,
revealing
the
distinction
between
Show
the
utilization
of
this
approach
on
an
iPad,
which
ior
as
a
spatio-temporal
ocproblem
as
team
identification
task.
library.
Banerjee
eta10
al.
proposed
to
formalize
MAPR
brary
of
full
team
plans
were
given
as Ball
input
(?).
1 plan
English
Premier
League
Ball
Action
Data
15
ing
partial
team
tracings.
show
this
bythe
framing
thehardness
15
Allen,
N.;
Templon,
J.;Data
McNally,
behavior
of
each
team
which
allows
for
tactical
analysis
of
single
and
multi-agent
plan
recognition,
and
hardness
single
and
multi-agent
plan
recognition,
and
20
sue
by
representing
team
behavior
asBall
aWe
spatio-temporal
oc•ofproblems
Show
that
teams
have
unique
playing
styles,
new
revealing
the
distinction
between
the
as
amodel,
playbook
of
play-segments,
we
can
characterize
the
English
Premier
League
Action
English
Premier
League
Ball
Action
Data
behavior
ofof
each
team
which
allows
for
tactical
of
efficacy
and
usability
ofwith?) abeing
solve
MAPR
problems
in
the
model
using
aanalysis
first-cut
apIn
this
paper,
we
propose
aallows
method
to
overcome
this
ising
team
tracings.
We
show
this
framing
the
20
over
fixed
windows
as
agenerated.
playbook
ofpartial
play-segments,
we
can
characterize
slish
for
analysis
English
Premier
League
Data
solve
MAPR
in
the
model
using
aiPad,
first-cut
apaas
team’s
performance.
We
show
the
efficacy
and
usability
of
behavior
of
each
team
which
for
tactical
analysis
Show
the
utilization
of
this
approach
on
an
which
55
×
5
×
48
10
10
×
815
8
15
15
×
×
12
12
5•×
5
5×
4a×
545×
4
510
×English
×
4
5
10
4
×
5
×
10
45×
8model,
4
10
510
×
4
8
10
×
8
4×
15
×
10
4×
4
10
15
8×
×
15
10
84
10
12
×
8revealing
15
10
15
×20
8
12
15
×
12
8×
×
15
8
×
12
8×
15
12
15
×
12
×
15
12
×
12
×
12
12
•as
Automatically
an
unseen
match
in
terms
of
tacand
usability
of
sue
by
representing
team
behavior
as
aAction
spatio-temporal
oc15
English
Premier
League
Ball
Action
Data
2
refficacy
as
atactical
spatio-temporal
ocing
partial
team
tracings.
We
show
this
byRefere
frami
References
Referenc
Referenc
Refer
Refe
Ref
R
ohe
overcome
this
is-windows
20
Hammond,
K.
2010.
StatsMonkey
hardness
of
single
and
multi-agent
plan
recognition,
for
tactical
analysis
of
with
new
the
distinction
between
the
20
proach,
provided
that
aaanalyze
fully
observed
team
trace
and
aby
lient
efficacy
and
usability
of
Premier
League
soc25We
Premier
League
Ball
Action
Data
shows
it’s
viability
to
be
used
for
amateur
level
use.
vement
over
fixed
a
team’s
performance.
We
show
the
efficacy
and
usability
of
solve
MAPR
problems
in
the
model
using
a
first-cut
ap
problem
as
team
identification
task.
cupancy
map
based
on
ball
movement
over
fixed
windows
ing
partial
team
tracings.
show
this
by
fR
behavior
of
each
team
which
allows
for
tactical
analysis
solve
MAPR
problems
in
the
model
using
a
first-cut
ap25
hardness
of
single
and
multi-agent
plan
recognition,
and
25
English
Premier
League
Ball
Action
Data
English
Premier
League
Ball
Action
Data
Problem
Formulation
a
team’s
performance.
We
show
the
efficacy
and
usability
of
•
Automatically
analyze
an
unseen
match
in
terms
oJ.PTJM
sue
by
representing
team
behavior
as
a
spatio-temporal
ocglish
Premier
League
socIn
this
paper,
we
propose
aWe
tofor
overcome
this
is-windows
proach,
that
fully
observed
team
trace
and
li20be
To
behavior
ofprovided
each
team
which
allows
tactical
analysis
of
.efficacy
ByPremier
analyzing
aocmatch
11it’s
1provided
13a1hardness
1 111
1 1solve
11
proach,
that
aa25fully
observed
team
trace
and
aDo
liproblem
as
amethod
team
identification
task.
English
Premier
League
Ball
Action
Data
our
method
on
thebased
2010-2011
English
Premier
League
socNarrative
Writer.
In
AAAI
Fall
Sym
a team’s
performance.
show
the
efficacy
and
usability
of
25
and
usability
of
shows
viability
to
used
for
amateur
level
use.
cupancy
map
on
ball
movement
over
fixed
Allen,
Allen,
N.;
N.;
Templo
Temp
Allen,
Allen,
Allen,
Allen,
N.;
Allen,
N.;
Allen,
N.;
Templon,
Allen,
Allen,
N.;
Templon,
Templon,
N.;
N.;
Allen,
N.;
Templon,
Allen,
Templon,
Templon,
N.;
N.;
J.;
Templon,
N.;
Templon,
J.;
McNally,
Templon,
J.;
N.;
McNally
Templon
J.;
McNally
J.;
Temp
J.;
McN
J.;
Mc
M
problem
as
team
identification
task.
ish
League
soc30
Problem
Formulation
tics.
MAPR
problems
in
the
model
using
a
first-cut
of
single
and
multi-agent
plan
recognition,
and
patio-temporal
ement
over
fixed
windows
English
Premier
League
Ball
Action
Data
Problem
Formulation
To
D
ficacy
and
usability
brary
of
full
team
plans
were
given
as
input
(?).
glish
Premier
League
soc30
30
our
method
on
the
2010-2011
English
Premier
League
socments.
By
analyzing
aof
match
proach,
provided
that
a
fully
observed
team
trace
and
a
l
Problem
Formulation
of
time,
which
we
call
play-segments.
By
analyzing
a
match
English
Premier
League
Ball
Action
Data
problem
as
a team
identification
task.
aproach,
team’s
performance.
We
show
the
efficacy
and
usability
25
solve
problems
in
the
model
using
aBy
first-cut
approvided
that
aanalyze
fully
team
trace
and
a2of
our
method
on
the
2010-2011
English
League
soc2 2tics.
25li22
2 2 222
Problem
Formulation
Problem
Formulation
sueMAPR
by
representing
team
behavior
aobserved
spatio-temporal
occupancy
map
based
on,show
ball
movement
over
fixed
Hammond,
Hammond,
K.
K.
201
2SS
Hammond,
Hammond,
Hammond,
Hammond,
Hammond,
K.Hammond,
Hammond,
K.
K.
2010.
Hammond,
2010.
K.
Hammond,
2010.
K.
K.K.
StatsMonkey:
2010.
2010.
2010.
K.
K.
StatsMonke
2010.
StatsMonk
2010.
K.
2010.
StatsMo
StatsM
K.
Stats
Stat
201
20
30Problem
9
13 30
1windows
17Hammond,
team’s
performance.
We
the
efficacy
and
usability
Avrahami-Zilberbrand,
D.;
Banerje
brary
of
full
team
plans
were
given
asHammond,
input
(?).
brary
of
full
team
plans
were
given
asPremier
input
(?).
The
of
paper
describes
the
method
of
doing
this,
inof242solve
data.
our
method
on
the
2010-2011
English
Premier
League
socan
unseen
match
in
terms
tacFormulation
we
can
of
time,
which
analyzing
aof
match
shPremier
Premier
League
socproblems
in
the
model
using
aof
first-cut
aptatrest
,,cer
tas
,,data.
t2•the
, ttAutomatically
tAutomatically
tProblem
twe
t9as
proach,
provided
that
aanalyze
fully
observed
team
and
ver
fixed
windows
Problem
Formulation
ents.
Bycharacterize
analyzing
a the
match
0our
1method
3,, ton
4,, tthe
5,,t2010-2011
6,,ttcall
7, ttplay-segments.
8, ,tanalyze
hnts,
League
soccer
data.
Formulation
brary
of
full
team
plans
were
given
as2010.
input
(?).
33
3t2•
3 The
333 3MAPR
3
33
30
Automatically
an
unseen
match
in
terms
rest
of
the
paper
describes
the
method
doing
this,
in
as
atime,
playbook
of
play-segments,
we
can
characterize
the
•full
an
unseen
match
in353terms
of
tacNarrative
Narrative
Writer.
Writer.
IF
Narrative
Narrative
Narrative
Narrative
Narrative
Writer.
Narrative
Writer.
Narrative
Writer.
Narrative
Writer.
Narrative
In
Writer.
Writer.
Narrative
AAAI
Writer.
In
Intrace
Writer.
AAAI
Writer.
AAAI
In
In
Fall
In
Writer.
AAAI
In
AAAI
Writer.
AAAI
Fall
Fall
Sympo
AAAI
In
InFall
AA
Sym
AA
Sym
Fa
In
Fa
we
can
characterize
the
English
Premier
League
socLyle,
J.Narrative
Multi-Agent
Plan
Re
t
,
t
,
,
t
,
t
,
t
,
t
,
t
,
t
,
t
t
t
,
cer
proach,
provided
that
a
fully
observed
team
trace
and
a
licupancy
map
based
on
ball
movement
over
fixed
windows
•
Show
the
utilization
of
this
approach
on
an
iPad,
which
Problem
Formulation
of
which
we
call
play-segments.
By
analyzing
a
match
brary
of
team
plans
were
given
as
input
(?).
0
1
3
4
5
6
7
8
9
Table
2:
Table
showing
the
identificatio
0
1
2
3
4
5
6
7
8
9
our
method
on
the
2010-2011
English
Premier
League
socProblem
Formulation
cer
data.
•
Automatically
analyze
an
unseen
match
in
te
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
as
as
a
playbook
of
play-segments,
we
can
characterize
the
Table
2:
Table
showing
the
identification
rate
by
breaking
tics.
addition
to
experiments
which
show
the
suitability
of
these
for
tactical
of the
Table
showing
the
rate
by
breaking
provided
team
trace
and
a D.;
lit040,brary
,t4t•1441Table
,t4Show
t22:2experiments
t2:
tthe
,team
, fully
, ttthe
,,observed
ttidentification
,,ashow
tidentification
11 , trefer
22 , tof
3
4 , team
Problem
Formulation
of
given
as
input
(?).
of
this
approach
on
an
iPad,
46
4proach,
4 addition
444a t4team
4
t0behavior
,We
tas
, each
tto
t55team
,play-segments.
t66of,behaviors,
twhich
3full
7
88were
B,
aswe
short,
observable
seganalyzing
aanalysis
match
over
match.
Given
possession
string
is
,to
,,,ttaTable
,,,that
ttto
tt55a5utilization
,time
tt666plans
,which
t99team’s
and
Algorithms.
In
AAAI.
s,
we
cantactical
characterize
0cer
3playbook
4
77, t88, tallows
99 By
Table
rate
by
breaking
tics.
Avrahami-Zilberbr
Avrahami-Zilberb
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbrand,
Avrahami-Zilberbra
Avrahami-Zilberb
D.;
D.;
Banerjee,
D.;
Banerj
Baner
D.;
D.;
D.;
Ba
Btw
for
tactical
analysis
of
the
suitability
of
these
3
44,,showing
7that
9plans
data.
the
into
different
time
series
and
Table
2:
Table
showing
the
identification
rate
by
breaking
tics.
ows
for
analysis
of
t
,
t
,
t
t
,
t
,
t
,
t
,
t
We
refer
team
behaviors,
B,
as
short,
observable
seg
of
time,
which
we
call
analyzing
a
match
as
a
play-segments,
can
characterize
the
brary
of
full
team
plans
were
given
as
input
(?).
the
plans
into
different
series
and
the
field
into
differEnglish
Premier
League
Ball
Action
Data
We
refer
to
team
behaviors,
B,
as
short,
observable
seg0
1
2
3
4
7
8
cer
shows
viability
used
for
level
use.
athe
team
over
match.
aof
team’s
possession
string
is
plans
into
different
time
series
and
the
field
into
differork
,We
tdata.
,English
trefer
tit’s
,,Premier
tteach
, tbehaviors,
,,team
ttmovement
ttto
, be
t B,
5shows
575of
5 555of5
5English
5full
which
allows
foramateur
tactical
analysis
brary
oflength
team
plans
given
as
input
(?).
2:
showing
the
identification
rate
by
breaking
Premier
League
Ball
Action
Data
23,,ttcoordinated
34,to
5
6behaviors,
78,,describe
8
refer
team
B,
asBall
short,
observable
segLyle,
Lyle,
J.
J.
2010.
2010.
Mul
Mu
Lyle,
Lyle,
Lyle,
J.
Lyle,
2010.
Lyle,
J.
J.
Lyle,
2010.
2010.
J.amateur
Lyle,
J.
Lyle,
Multi-Agent
2010.
J.
2010.
2010.
Lyle,
Multi-Agent
Multi-Agent
2010.
J.
Lyle,
J.
Multi-Agent
2010.
2010.
Multi-Agent
J.
Multi-Agent
Multi-Agent
J.
2010.
Plan
2010.
Multi-Ag
Multi-Ag
Plan
Plan
Multi
Recog
Mu
Pla
Pl
R
RP
refer
behaviors,
B,
as
short,
observable
segtasks
We
our
dataset.
plans
time
series
and
the
field
into
differfficacy
usability
of
T
,tinto
the
resulting
play-segments
for
each
it’s
be
used
for
level
use.
Related
Work
,We
t5t515a2the
,English
trefer
,team
,ato
ttics.
,Table
tmatch.
,areas.
tGiven
,different
ttmovement
,,that
ttto
,that
ttime
t0 ,tas
t0awe
t1playbook
,behavior
tof
,of
t45of
1
Banerjee,
B.;
Kraemer,
L.;
and
Lyl
League
Action
Data
a2Table
over
awere
Given
that
aand
possession
string
is
an
the
ent
quantization
areas.
The
results
are
th
3
45team
6behaviors,
7
8are
9
to
team
as
short,
observable
segments
and
action
executed
team
asteam’s
short,
observable
seg
Work
plans
series
and
the
field
into
differ1We
2mentioned.
6 , tteam
7first
9 9we
over
ateam
Given
aB,
team’s
possession
string
is
team’s
We
show
the
efficacy
and
usability
of
wscharacterize
for and
tactical
tasks
mentioned.
We
first
describe
our
dataset.
• performance.
Show
the
utilization
of
this
approach
on
an
iPad,
,6tments
t06we
,We
,team
tof
tcoordinated
,to
tdifferent
,into
t5viability
,match.
tbehaviors,
,number
quantization
areas.
The
results
the
trace
the
team
a, behavior
of
play-segments,
can
characterize
the
Premier
League
Ball
Action
Data
action
executed
by
1
3 ,T
6into
8
9(T
The
results
are
the
trace
of
the
team
We
B,
as
short,
observable
segRelated
Work
of
,to
the
resulting
number
of
play-segments
for
each
the
efficacy
and analysis
usability of
of as
ork
66ent
6refer
6by
6of
6a
6which
6t60ent
6
6length
each
which
allows
for
tactical
analysis
of
•quantization
Show
the
utilization
of
this
approach
on
an
iPad,
athe
over
a7The
match.
Given
that
aof
team’s
possession
string
10
14team
the
plans
different
time
series
and
the
field
into
differ−T
)+1
ments
of
coordinated
movement
and
action
executed
by
aiPad,
and
and
Algorithms.
Algorithms.
InI
and
and
and
Algorithms.
and
Algorithms.
Algorithms.
and
and
Algorithms.
Algorithms.
Algorithms.
and
and
Algorithms.
In
and
Algorithms.
Algorithms.
and
AAAI.
In
In
Algorithms.
AAAI.
AAAI.
Algorithms.
In
In
In
AAAI.
In
AAAI.
AAAI.
AAAI.
In
In
AAA
AAA
In
ent
quantization
areas.
results
are
the
trace
of
the
team
Related
Work
a
team’s
performance.
We
show
the
efficacy
and
usability
ork
Plan
Recognition:
Formalization
an
We
refer
to
team
behaviors,
B,
as
short,
observable
seg6
ments
of
coordinated
movement
and
action
executed
by
a
recognition.
2
10
14
English
Premier
League
Ball
Action
Data
•
Show
the
utilization
of
this
approach
on
an
which
ent
quantization
areas.
The
results
are
the
trace
of
the
team
length
T
,
the
resulting
number
of
play-segments
for
each
ments
of
coordinated
movement
and
action
executed
by
a
possession
is
therefore:
N
=
.
If
the
possession
Related
Work
h
Premier
League
socof
length
T
,
the
resulting
number
of
play-segments
for
each
We
refer
to
team
behaviors,
B,
as
short,
observable
se
recognition.
1
18
)+1
English
Premier
League
Ball
Action
Data
1 the
ments
coordinated
movement
and
action
executed
by
We
refer
to
team
behaviors,
B,
as
short,
observable
segtactical
analysis
of
rest
of
the
paper
describes
the
method
of
doing
•quantization
Show
the
ofshort,
this
approach
on
an
ourWith
method
on
the
2010-2011
English
Premier
League
socments
ofthe
coordinated
movement
and
action
executed
by
athis,
team
(e.g.
pass
from
agent
Ashow
to
agent
B)
.analysis
A
plan
can
bedede7
7recognition.
7of
7use.
7
7 777 in
7We
7possession
77The
T−T
and
military
domains,
15
refer
to
team
B,
as
observable
seghe
and League
usability
of behavior
of
each
team
which
allows
for
tactical
of
shows
it’s
viability
to
be
used
for
amateur
level
ent
areas.
The
results
are
the
of
the
team
Problem
Formulation
of
Tbehaviors,
,viability
the
resulting
number
of
play-segments
for
ea
rest
of
describes
the
method
of
doing
thiaa
team
(e.g.
pass
from
agent
A(Tto
to
agent
B)
.trace
A
plan
can
be
de
ments
of
coordinated
movement
and
action
executed
by
aan
obvious
applications
to
sport
and
military
domains,
recognition.
rkefficacy
aThe
team’s
performance.
We
the
efficacy
and
usability
of
shows
it’s
be
used
for
amateur
level
use
1paper
islength
therefore:
Nutilization
=
.Banerjee,
If
the
possession
Problem
Formulation
Banerjee,
Banerjee,
B.;
B.;
Krae
Kra
Banerjee,
Banerjee,
Banerjee,
Banerjee,
Banerjee,
B.;
Banerjee,
Banerjee,
Kraemer,
B.;
Banerjee,
Kraemer,
Banerjee,
B.;
Kraemer,
B.;
B.;
Banerjee,
B.;
Kraemer,
Kraemer,
Kraemer,
B.;
L.;
B.;
Kraemer,
L.;
and
Kraemer,
L.;
B.;
Kraemer,
B.;
and
L.;
and
Kraem
Lyle,
L.;
L.;
Kra
and
L.;
Ly
Ly
nglish
Premier
socRelated
Work
(T
−T
)+1
(T
−T
)+1
team
(e.g.
pass
from
agent
A
to
agent
B)
.Premier
A
plan
can
bebe
our
method
on
the
2010-2011
English
League
socBeetz,
M.;
von
Hoyningen-Huene
recognition.
T
port
and
military
domains,
kort
string
is
smaller
in
duration
than
T
we
discard
To
reprePremier
League
Ball
Action
Data
Related
Work
team
(e.g.
pass
from
agent
A
to
agent
B)
.B.;
Ait.
plan
can
be
deProblem
Formulation
With
the
obvious
applications
to
sport
and
military
domains,
ments
of
coordinated
movement
and
action
executed
by
a10
English
Premier
League
Ball
Action
Data
possession
isProblem
therefore:
=
.it.
If
the
possession
10
10
10
10
10
1010
10
10
10
10
10
(T
−T
)+1
ments
of
coordinated
movement
and
action
executed
by
possession
isfrom
therefore:
N
=
.Recognition:
If
the
possession
Formulation
team
(e.g.
pass
from
agent
A
to
agent
B)
.A
A
plan
can
deshows
it’s
viability
to
be
used
for
amateur
level
use.
ort
and
military
domains,
20
recognition.
team
(e.g.
pass
agent
AN
toT,Plan
agent
.Siles,
A
plan
can
be
de
With
the
obvious
applications
to
sport
and
military
domains,
cer
data.
shows
it’s
viability
to
used
for
amateur
leve
acy
and
usability
of soc- English
of
coordinated
movement
and
action
executed
by
a
TB)
Plan
Plan
Recognition:
Recognition
Plan
Plan
Recognition:
Plan
Recognition:
Plan
Recognition:
Plan
Plan
Recognition:
Recognition:
Plan
Recognition:
Plan
Formalization
Recognition:
Recognition:
Plan
Formalization
Formalization
Recognition:
Recognition
Formalizatio
Formalizat
Formaliza
Formaliz
Form
Form
and
F
aaA
aments
team’s
performance.
We
show
thewhich
efficacy
and
usability
of
Tbe
addition
to
experiments
show
the
suitability
of
these
ments
of
coordinated
movement
and
action
executed
by
a
team
(e.g.
pass
from
agent
A
to
agent
B)
.
plan
can
be
defined
as
an
ordered
sequence
of
team
behaviors
describing
string
is
smaller
in
duration
than
,
we
discard
To
reprePartial
Team
Tracing
from
Ball
Action
Data
port
and
military
domains,
grown
quite
substantially
fined
as
an
ordered
sequence
of
team
behaviors
describin
possession
is
therefore:
N
=
.
If
the
possessi
addition
to
experiments
which
show
the
suitability
of
glish
Premier
League
team
(e.g.
pass
from
agent
A
to
agent
B)
.
A
plan
can
be
deresearch
interest
into
MAPR
has
grown
quite
substantially
Partial
Team
Tracing
from
Ball
Action
Data
our
method
on
the
2010-2011
English
Premier
League
socWith
the
obvious
applications
to
sport
and
military
domains,
Gedikli,
S.;
F.;
Durus,
M.;
an
Tthe
each
play-segment
pduration
{p
.of
. .than
,agent
p,Twe
quantized
cer
data.
Formulation
Formulation
15
15
15
1515
15
15
15
15
15
fined
as
an
ordered
of
team
behaviors
describing
09
rest
the
paper
describes
the
of
doing
this,
in
The
rest
the
paper
describes
the
of
doing
string
is
inp
T−1
, },
we
discard
it.
To
repregrown
quite substantially
is
smaller
in
than
Tteam
discard
it.
To
repreas
ordered
team
behaviors
describing
t0fined
,With
tWith
, tresearch
, The
tpass
,obvious
tthe
,from
t52010-2011
,of
tapplications
, sequence
tsequence
,MAPR
t8A
, tto
25
tsent
,fined
tsent
,15
tstring
,step
tpass
,string
t4ordered
,from
tsmaller
,of
tsmaller
, sequence
tsequence
,=
tduration
, duration
tto
interest
into
MAPR
has
grown
quite
substantially
team
(e.g.
pass
from
A,achieve
to
B)
.method
A
plan
can
be
d
team
pass
from
A
to
agent
B)
.method
A(?).
plan
can
be
de015
115
2
3an
5is
6Problem
8A
1
2(e.g.
3
4
6Problem
7agent
9
the
to
sport
and
military
domains,
rt
and
military
domains,
fined
as
an
of
behaviors
describing
as
an
ordered
of
team
describing
research
interest
into
has
grown
quite
substantially
Beetz,
Beetz,
M.;
M.;
von
von
H
Beetz,
Beetz,
Beetz,
M.;
Beetz,
M.;
Beetz,
M.;
von
Beetz,
Beetz,
M.;
von
M.;
von
M.;
Hoyningen-Huene,
Beetz,
M.;
Beetz,
von
Hoyningen-Huen
von
Hoyningen-Huen
M.;
von
M.;
von
Hoyningen-H
M.;
Hoyningenvon
Hoyningen
von
M.;
Hoyninge
von
Hoynin
Hoyni
von
Ho
rown
quite
each
play-segment
=
{p
,tof
.9time
.POGAMO:
.team
,Beetz,
pstep
the
quantized
in
than
T
,A
we
discard
it.
To
repr
our
method
on
English
Premier
League
socAutomated
Sports
Gam
emier
League
soceach
is
then
used
to
populate
ea
team
(e.g.
agent
agent
.},
plan
can
be
de0populate
TB)
−1
each
time
is
then
used
to76agent
populate
each
entry.
the
obvious
applications
to
sport
and
military
domains,
team
(e.g.
agent
agent
B)
.behaviors
A
plan
can
be
dea
recipe
used
by
a
team
to
a
goal
(?).
A
team
pe
and
military
domains,
fined
as
an
ordered
sequence
of
team
behaviors
describing
fined
as
an
ordered
sequence
behaviors
describing
recently.
The
significance
of
considering
group
actions
in
ortasks
we
mentioned.
We
first
describe
our
dataset.
a
recipe
used
by
a
team
to
achieve
a
goal
A
team
pertasks
we
mentioned.
We
first
describe
our
dataset.
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
cer
data.
research
interest
into
MAPR
has
grown
quite
substantially
grown
quitesubstantially
substantially
ering
group
actions
in
orProblem
Formulation
20
20
20
20
20
20
20
20
20
20
20
20
20
0
1
2
3
4
5
7
8
0
1
2
3
4
5
6
7
8
9
ball
position
at
each
time
step
is
then
used
to
populate
each
each
time
step
is
then
used
to
each
entry.
Problem
Formulation
The
rest
of
the
paper
describes
the
method
of
do
The
rest
of
the
paper
describes
the
method
of
doing
this,
in
30
sent
each
play-segment
p
=
{p
,
.
.
.
,
p
},
the
quantized
sent
each
play-segment
p
=
{p
,
.
.
.
,
p
},
the
quantized
each
time
step
is
then
used
to
populate
each
entry.
experiments
which
show
the
suitability
0ternational
T
−1
,afined
taA
, ,trefer
,addition
tused
tteam
,to
,, sequence
tt16
0{p
T
−1
recipe
used
by
team
to
achieve
aGedikli,
goal
(?).
A
team
per,afined
tresearch
, ,trefer
,addition
tused
tteam
,into
,,MAPR
tt16
to
experiments
which
show
the
suitability
oft725
these
recently.
The
of
considering
group
actions
inororaWe
recipe
used
by
ainto
team
to
achieve
aa goal
(?).
AA
team
perWe
behaviors,
B,
as
short,
observable
segGedikli,
Gedikli,
S.;
S.;
Siles,
Siles
F
Gedikli,
Gedikli,
Gedikli,
Gedikli,
S.;
Gedikli,
S.;
Siles,
S.;
Gedikli,
Gedikli,
S.;
Siles,
S.;
Gedikli,
S.;
F.;
Siles,
Gedikli,
S.;
Siles,
Siles,
Durus,
F.;
F.;
S.;
Siles,
S.;
Durus,
Durus,
F.;
Siles,
Siles,
S.;
F.;
F.;
Durus,
S.;
M.;
F.;
Siles,
Durus,
Durus,
F.;
Siles,
Durus
M.;
F.;
M.;
and
Du
Du
M
F.
ao
aL
M
deringgroup
groupactions
actionsininoror- t10
10
11
as
an
ordered
of
team
behaviors
describin
of
Computer
Sc
11
13
14
15
behaviors,
B,
as
observable
research
interest
MAPR
has
grown
quite
substantially
ball
position
time
is
then
used
to
populate
each
3describing
19
sent
each
play-segment
p
=
,goal
.short,
.Figure
.Journal
,Siles,
paentry.
},
the
quantiz
recipe
by
aa15
team
to
achieve
aas
(?).
A
team
per
as
an
sequence
of
team
behaviors
description
of
this
process
is
in
Figure
4.
Given
each
time
step
is
then
used
to
populate
each
entry.
of
this
process
is
given
recently.
The
significance
considering
group
actions
in
rown
quite
substantially
t25
t12
,ball
tposition
,to
t,time
,14
teach
,taof
teach
,step
tprocess
,given
tachieve
tdescription
11
cer
data.
0goal
Tmajor
−1
recipe
by
aFigure
team
to
achieve
goal
(?).
team
perering
trecipe
t12
,to
t,ordered
tteam
,tsignificance
tsequence
, 3:
tto
,rather
tachieve
,considering
tteam
fined
an
ordered
sequence
of
team
behaviors
0as
1description
3at
4
515
6
7used
8A,step
9
25
25
25
25
252525
25
25
25
25
interest
has
grown
quite
substantially
a213
group
these
plans
to
achieve
goal
(e.g
each
step
is
then
to
populate
each
A
description
of
this
is
given
in
4.
Given
aforming
recipe
used
by
team
to
aPOGAMO:
(?).
Adescribing
team
perder
to, trefer
isolate
plans,
than
abehaviors
sequential
process
of
Figure
3.
fined
asrecently.
of
0
1an
3 ,to
4significance
5team
6behaviors,
7of
8
9
The
of
group
actions
insegorentry.
We
refer
to
team
behaviors,
B,
observable
seg
Related
Work
wn
substantially
aforming
used
by
aof
ashort,
goal
(?).
Adescribing
team
perA
of
this
process
is
given
in
Figure
4.POGAMO:
Given
a2ordered
group
these
plans
to
achieve
amajor
major
goal
(e.g.
ball
at
time
step
is
then
used
to
populate
each
dering
group
actions
in orn a aquite
sequential
process
of
We
team
B,
as
short,
observable
segposition
at
each
time
is
then
used
to
populate
each
k
addition
to
experiments
which
show
the
suitabil
POGAMO:
POGAMO:
Autom
Auto
POGAMO:
POGAMO:
POGAMO:
POGAMO:
POGAMO:
POGAMO:
Automated
POGAMO:
POGAMO:
Automated
Automated
POGAMO:
Automated
Automated
Automated
Automated
Sports
Automated
Automated
Sports
Sports
Automa
Game
Sports
Auto
Sport
Spo
Ga
Spo
Ga
tasks
we
mentioned.
We
first
describe
our
dataset.
addition
to
experiments
which
show
the
suitability
of
these
forming
a
group
of
these
plans
to
achieve
a
major
goal
(e.g.
There
has
been
an
explosion
in
the
interest
in
live-sport
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
the
possession
string
a
=
{a
.to
.the
.time
,achieve
aprocess
}step
shown,
we
first
der
to
isolate
team
plans,
rather
than
a
sequential
process
of
ments
of
coordinated
movement
and
action
executed
by
a
entry.
ball
position
at
each
is
then
used
to
populate
ea
Cohen,
P.,
and
Levesque,
H.
1990.
possession
string
a
=
{a
,
.
.
.
,
a
A
description
of
this
is
given
in
Figure
4.
Given
tasks
we
mentioned.
We
first
describe
our
dataset.
0 ,=
13
a
recipe
used
by
a
team
a
goal
(?).
A
team
pe
forming
a
group
of
these
plans
to
achieve
a
goal
(e.g.
0
1
2
3
4
5
6
7
8
9
Related
Work
There
has
been
an
explosion
in
the
interest
in
live-sport
recently.
The
significance
of
considering
group
actions
in
or0
1
han
sequential
process
of
30
30
30
30
30
30
30
30
30
30
30
30
30
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
,
t
forming
a
group
of
these
plans
to
achieve
a
major
goal
(e.g
ments
of
coordinated
movement
and
action
executed
by
a
der
to
isolate
team
plans,
rather
than
a
sequential
process
of
A
description
of
this
process
is
given
in
Figure
4.
Given
Work
the
possession
string
a
{a
,
.
.
.
,
a
}
shown,
we
first
We
refer
to
team
behaviors,
B,
as
short,
observable
s
a
recipe
used
by
a
team
to
achieve
a
goal
(?).
A
team
per0
1
2
3
4
5
6
7
8
9
ring
group
actions
in
orthe
possession
aprocess
=
{a
, . .0given
.to
, aternational
}and
shown,
we
first
abreak
recipe
used
bypossession
awe
to
achieve
afield
goal
(?).
A
team
perTable
2:
Table
showing
the
identification
rate
bycan
breaking
13
Aments
description
ofstring
this
in
Figure
4.
Given
forming
group
of
these
plans
toagents.
achieve
major
goal
(e.g.
recently.
The
significance
of
considering
group
actions
in
orwinning
aentry.
match),
be
said
be
employing
tactics.
nan
sequential
process
of
0is
13
forming
aof
group
of
these
plans
achieve
a13
major
goal
(e.g.
recognizing
plans
ofplans,
individual
Outside
oftactics.
the
sport
ternational
ternational
Journa
Journ
ternational
ternational
ternational
ternational
ternational
ternational
Journal
ternational
ternational
Journal
Journal
ternational
Journal
Journal
Journal
Journal
Computer
of
of
Journal
Journal
Computer
Computer
ofwe
of4
of
Journal
Comput
of
Compu
Journ
Comp
Scien
Com
of
C
SC
S
entry.
We
to
team
behaviors,
B,and
short,
observable
segder
toarefer
team
rather
than
aas
sequential
process
of
coordinated
movement
executed
by
a recipe
used
by
aplans
to
achieve
afrom
goal
(?).
A
team
perngaagroup
actions
in orforming
aof
group
of
these
plans
to
achieve
aamajor
goal
(e.g.
winning
aisolate
match),
can
be
said
be
employing
Partial
Tracing
Ball
Action
D
sequential
process
of
the
field
up
into
aof
grid
of
4grid
×
and
then
itof
ents.
Outside
of
the
sport
ments
coordinated
movement
action
executed
by
awhich
tasks
mentioned.
We
describe
our
datase
Commitment.
Artificial
Intelligence
break
the
into
aternational
grid
of
×
5of
an
the
string
a5of
=
{a
,and
.,vectorize
.aobservable
.up
,action
aA
shown,
first
Related
Work
Aentry.
description
of
this
process
isreal-time
in
Figure
4.
Given
0first
winning
match),
can
be
said
to
be
employing
tactics.
Partial
Tracing
Ball
Action
Data
We
refer
to
team
behaviors,
B,
as
short,
seghas
created
aTeam
demand
for
statistics
and
virecognizing
of
individual
agents.
Outside
of
the
sport
team
(e.g.
from
A
to
agent
.in
plan
can
be
detasks
we
mentioned.
We
first
describe
our
dataset.
the
possession
string
a
=
{a
,from
.5achieve
.and
}vectorize
shown,
we
first
With
the
applications
sport
and
domains,
break
field
up
into
athis
4.given
×
then
vectorize
itgoal
forming
aAthe
group
these
plans
to
a}Cohen,
major
(e.
der
to
isolate
team
plans,
rather
than
aemploying
sequential
process
break
the
field
up
into
athis
grid
of
×
5
and
then
it
0be
13
Work
the
plans
into
different
time
series
and
the
field
into
differwinning
aapass
match),
can
be
said
to
employing
tactics.
winning
aobvious
match),
can
be
said
to
be
employing
tactics.
recognizing
plans
of
individual
agents.
Outside
of
the
sport
which
has
created
aTeam
demand
for
real-time
statistics
and
vi-of
gents.
Outsideof
ofthe
thesport
sport
We
refer
to
team
behaviors,
B,
as
short,
observable
segthe
possession
string
aagent
=
{a
,4A
.recognize
.grid
,is
aagent
}B)
shown,
we
first
ments
of
coordinated
movement
action
executed
bHt
team
(e.g.
pass
from
agent
A
toto
agent
B)
.military
A
plan
can
be
deA
description
of
process
given
Figure
4.
Given
tnts.
and
military
domains,
forming
ashowing
group
of
these
plans
to
achieve
aball
major
goal
(e.g.
description
of
is.employing
given
in
Figure
4.P.,
Given
0process
13
forming
a
group
of
these
plans
to
a
major
goal
(e.g.
Cohen,
Cohen,
P.,
P.,
and
and
Lev
Le
Cohen,
Cohen,
Cohen,
Cohen,
P.,
Cohen,
and
Cohen,
P.,
P.,
Cohen,
and
Cohen,
and
P.,
Levesque,
P.,
P.,
and
Levesque,
P.,
Levesque,
and
Cohen,
and
P.,
and
P.,
Levesque,
Levesque,
Levesque,
and
and
P.,
H.
Levesque,
and
Levesque
1990.
H.
Levesqu
H.
and
1990
Leve
H.
1990
H.
Le
H.
In
19
der
to
isolate
team
plans,
rather
than
aachieve
sequential
process
of
naussed
a
sequential
process
of
winning
match),
can
be
said
to
be
tactics.
realm,
most
of
this
work
has
focussed
on
dynamic
teams
Ideally,
we
would
like
to
team
tactics
for
soc
to
give
quantized
ball
positions.
At
each
time
step,
the
quanRelated
Work
winning
a
match),
can
be
said
to
be
tactics.
recognizing
plans
of
individual
agents.
Outside
of
the
sport
team
(e.g.
pass
from
agent
to
B)
.
A
plan
can
be
de
Outside
With
the
obvious
applications
to
sport
and
military
domains,
to
give
quantized
positions.
At
each
ments
of
coordinated
movement
and
action
executed
by
a
break
the
field
up
into
a
of
4
×
5
and
then
vectorize
it
Hervieu,
A.,
and
Bouthemy,
P.
201
forming
a
group
of
these
plans
to
achieve
a
major
goal
(e.g.
the
possession
string
a
=
{a
,
.
.
.
,
a
}
shown,
we
first
A
description
of
this
process
is
given
in
Figure
4.
Giv
Table
Table
2:
Table
Table
Table
showing
the
the
identification
identification
rate
rate
by
by
breaking
breaking
Table
Table
Table
Table
2:
Table
2:
Table
Table
2:
Table
Table
2:
Table
Table
2:
Table
Table
Table
2:
showing
Table
Table
2:
showing
Table
2:
showing
Table
2:
showing
2:
Table
2:
showing
Table
showing
Table
the
showing
the
showing
the
identification
showing
showing
the
identification
the
showing
identification
the
identification
the
identification
identification
the
the
identification
the
identification
the
rate
identification
identification
rate
identification
rate
by
rate
by
breaking
rate
by
breaking
rate
by
breaking
by
rate
by
rate
breaking
by
breaking
rate
breaking
by
rate
breaking
by
breaking
by
breaking
by
breaking
breaking
sequential
process
of
winning
a
match),
can
be
said
to
be
employing
tactics.
break
the
field
up
into
a
grid
of
4
×
5
and
then
vectorize
it
ents.
Outside
of
the
sport
0
13
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
socteam
(e.g.
pass
from
agent
A
to
agent
B)
.
A
plan
can
be
deto
give
quantized
ball
positions.
At
each
time
step,
the
quansport and
military
domains,
ent
quantization
areas.
The
results
are
the
trace
of
the
team
to
give
quantized
ball
At
each
time
step,
the
quanments
ofteam
coordinated
movement
and
executed
by
a Intellig
Team
Tracing
Ball
Action
realm,
of
work
has
focussed
onwith
dynamic
Ideally,
we
would
like
to
recognize
team
tactics
for
socfined
as
an
ordered
sequence
of
team
describing
sualizations.
Due
to
the
difficulty
associated
with
tracking
research
interest
into
MAPR
has
grown
quite
substantially
winning
aPartial
match),
can
be
said
to
be
tactics.
tseries
,series
tpossession
,time
tthe
,series
tcan
,apositions.
tdiffer,athe
,into
t{a
recognizing
plans
of
individual
agents.
Outside
of
the
sport
Commitment.
Commitment.
Arti
Ar
Ar
Commitment.
Commitment.
Commitment.
Commitment.
Commitment.
Commitment.
Commitment.
Commitment.
Commitment.
Artificial
Artificial
Artificial
Commitment.
Artificial
Artificial
Artificial
Intelligence
Artificial
Intelligenc
Intelligen
Artificial
Artificial
Artifi
Intell
Inte
Art
Int
4D
break
the
field
up
into
grid
of
4
×
5
and
then
vectorize
it
the
string
=
,action
.differabehaviors
}behaviors
shown,
we
first
realm,
most
of
this
work
has
focussed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
soc
the
possession
string
a
=
{a
,.each
.,from
.employing
shown,
first
10
11
12
13
15
16
tized
ball
position
is
used
to
populate
a.
Using
T
10,
we
(e.g.
pass
from
agent
A
to
agent
B)
.Commitment.
A
plan
can
be
0differ4plans
8different
With
the
obvious
applications
to
sport
and
domains,
of
movement
action
executed
by
ateams
cussed
ondynamic
dynamic
teamsments
Ideally,
we
would
like
to
recognize
team
tactics
for
socTeam
Tracing
from
Ball
Action
Data
sualizations.
Due
to
the
difficulty
associated
tracking
0.differwinning
aball
match),
be
said
to
be
tactics.
tized
ball
position
to
populate
a.
fined
as
ordered
sequence
of
team
behaviors
describing
12
recognizing
plans
of
individual
agents.
Outside
of
the
sport
to
give
quantized
ball
positions.
At
each
time
the
quanown
quite
substantially
16
20
video
trajectories.
tcoordinated
,an
tmatch),
,most
tpass
,individual
tcan
,this
tlike
,Formulation
tto
,and
tA
(i.e.
where
individual
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
istpositions.
low-scoring,
continuous
and
com
winning
aPartial
match),
can
be
said
to
be
employing
tactics.
the
the
plans
plans
into
into
into
different
different
time
time
series
series
and
and
the
the
field
field
into
into
differthe
the
plans
the
the
plans
the
the
plans
into
the
plans
into
the
plans
into
the
different
plans
the
into
the
plans
different
into
plans
into
different
plans
plans
different
into
into
different
time
into
into
different
time
different
time
different
series
time
different
time
different
time
series
time
and
series
time
series
and
time
and
time
series
the
series
and
and
series
field
the
and
series
field
and
the
the
field
the
and
into
and
the
field
into
and
field
into
the
and
the
field
into
the
differinto
field
into
differfield
into
field
differdifferfield
differinto
differdifferinto
differrealm,
most
of
this
work
has
focussed
onmilitary
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
socfined
as
an
ordered
sequence
of
team
describin
nts.
Outside
the
sport
to
give
quantized
ball
At
step,
the
quanresearch
interest
into
MAPR
has
grown
quite
substantially
break
the
field
up
into
a14
grid
of
4into
×
5employing
then
itwe
the
possession
string
a
=
{a
,.13
.,=
.atime
.13
,isplayers
a}vectorize
}step,
shown,
we
fi
Problem
10
11
12
13
14
15
16
recognition.
ssed
on
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
soctized
ball
position
is
used
to
populate
a.
Using
Tused
=
10,
we
tized
position
is
used
to
populate
a.
Using
T
=
10,
we
Figure
3:
Figure
3.
0using
13
team
(e.g.
from
agent
to
agent
B)
.domains,
A
plan
can
be
deport
and
domains,
winning
awhere
be
said
to
be
employing
tactics.
s.
Outside
ofof
the
sport
team
(e.g.
pass
from
agent
A
to
agent
B)
.and
plan
can
be
deWith
the
obvious
applications
sport
and
military
ussed
onmilitary
dynamic
teams
Ideally,
we
would
to
recognize
team
tactics
for
soceave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
comfined
as
an
ordered
sequence
of
team
behaviors
describing
(i.e.
where
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
coma
recipe
used
by
a
team
achieve
a
goal
(?).
A
team
pers
grown
quite
substantially
Partial
Team
Tracing
from
Ball
Actio
break
the
field
up
into
athe
grid
of
4team
×
5A
and
then
vectorize
it
tion
to
give
quantized
ball
positions.
At
each
time
step,
the
quanplayers
and
ball,
data
containing
this
information
is
still
recently.
The
significance
of
considering
group
actions
in
orthen
chunk
athe
into
N
=
(14
−
10
+
1)/10
=
5the
play-segments
Hervieu,
Hervieu,
A.,
A.,
and
and
BP
Hervieu,
Hervieu,
Hervieu,
Hervieu,
Hervieu,
Hervieu,
A.,
Hervieu,
A.,
and
A.,
Hervieu,
Hervieu,
and
A.,
and
Hervieu,
Bouthemy,
A.,
A.,
Hervieu,
A.,
and
Bouthemy,
Bouthemy,
and
and
A.,
A.,
and
Bouthemy,
Bouthemy,
Bouthemy,
and
A.,
and
Bouthemy
P.
A.,
and
Bouthe
Bouth
2010.
P.
P.
and
20
Bo
20
P.
break
the
field
up
into
a
grid
of
4
×
5
and
then
vectorize
it
realm,
most
of
this
work
has
focussed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
so
igure
3.
There
has
been
an
explosion
in
the
interest
in
livethen
chunk
a
into
N
=
(14−
10+
1)/10
(i.e.
individual
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
com
Zhang,
L.;
and
Jones,
G.,
eds.,
Intel
tized
ball
position
is
used
to
populate
a.
Using
T
=
10,
we
ent
ent
quantization
quantization
areas.
areas.
The
The
results
results
are
are
the
the
trace
trace
of
of
the
team
team
ent
ent
quantization
ent
ent
quantization
ent
quantization
ent
quantization
ent
quantization
ent
quantization
ent
quantization
ent
ent
quantization
areas.
quantization
quantization
areas.
quantization
areas.
areas.
The
areas.
areas.
The
The
areas.
results
The
areas.
results
The
areas.
results
The
areas.
areas.
The
results
results
are
The
results
are
The
results
the
The
are
The
results
the
are
results
are
trace
the
are
results
results
trace
the
are
the
trace
the
are
of
are
the
trace
of
the
trace
are
the
of
are
the
trace
the
team
the
the
of
of
trace
the
of
trace
team
team
of
trace
the
trace
of
the
team
of
team
team
the
of
the
team
of
the
team
the
team
team
t
,
t
,
t
,
t
,
t
,
t
,
t
fined
as
an
ordered
sequence
of
team
behaviors
describ
research
interest
into
MAPR
has
grown
quite
substantially
tized
ball
position
is
used
to
populate
a.
Using
T
=
10,
we
10
11
12
13
14
15
16
team
(e.g.
pass
from
agent
A
to
agent
B)
.
A
plan
can
be
derealm,
most
of
this
work
has
focussed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
socleave
and
jointeams
teams
over players
cer.
However,
as
soccer
is
low-scoring,
continuous
and
comdssed
military
domains,
chunk
a into
N
=
(14
− low-scoring,
10
+At
1)/10
=
5a
play-segments
to
give
quantized
ball
positions.
each
time
the
quanbreak
field
into
a.video
grid
of
4continuous
×
5Using
and
then
vectorize
Partial
Team
Tracing
from
Ball
Action
Data
then
chunk
a the
into
N
=up
(14−10+1)/10
=
5step,
play-segments
and
the
data
containing
this
information
is
still
a cer.
recipe
used
by
team
achieve
aquite
goal
(?).
Arecognition.
team
per(i.e.
where
individual
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
and
comathen
recipe
used
aball
team
to
achieve
goal
(?).
A
team
pe
ing
group
actions
inteams
orrecently.
The
significance
of
group
actions
in
orThere
has
been
explosion
in
the
interest
in
live-sport
on
dynamic
we
like
to
recognize
team
tactics
for
socave
and
join
over
However,
as
soccer
is
low-scoring,
continuous
and
comvideo
video
using
using
playe
play
video
video
using
video
video
using
using
video
players
video
using
video
using
using
players
video
using
using
players
using
trajectories.
players
players
players
using
trajectories.
trajectories.
using
players
players
trajectori
trajector
trajecto
players
trajec
play
In
tra
tas
tball,
,would
taby
,like
,an
tagents
,toautomatically
t15
,considering
t16
Figure
3:
3.recognition.
resulting
in
five
play-segments
{p
,team
. (14−10+1)/10
.−
,is
p
}in
shown.
fined
an
ordered
sequence
of
behaviors
describing
toordered
give
quantized
At
each
step,
the
quanfined
as
an
sequence
of
behaviors
describing
grown
quite
substantially
tized
ball
position
isby
used
topositions.
populate
a.
Using
T
=
10,
we
research
interest
into
MAPR
has
substantially
0
4
10 ,used
11
12
14
ed
on
dynamic
teams
Ideally,
we
would
to
recognize
team
tactics
for
socresulting
five
play-segments
{p
.qua
.tra
.Bp
,
give
quantized
positions.
time
step,
the
quanrecognition.
recognition.
recognition.
recognition.
recognition.
recognition.
recognition.
recognition.
recognition.
recognition.
forming
ato
group
of
plans
to
achieve
aarmy
goal
(e.g.
Understanding.
Springer
der
to
isolate
team
plans,
rather
than
ateam
sequential
process
of
eave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
comthen
aused
into
N
=
=
5video
play-segments
aIdeally,
recipe
at13
team
achieve
aFigure
goal
(?).
A
team
perscarce.
Most
of
the
data
collected
via
an
of
human
Inas
this
paper,
we
are
looking
to
answering
the
0 , com
sidering
group
actions
in orthen
chunk
asoccer
into
N
=
(14
+
1)/10
5players
play-segments
(i.e.
where
individual
agents
can
leave
and
join
teams
over
cer.
However,
as
is
low-scoring,
continuous
and
which
has
demand
for
real-time
statistics
an
resulting
in
five
play-segments
{p
,10
.0Zhang,
.,Zhang,
,a.
p
}At
shown.
Using
There
has
been
explosion
in
the
interest
in
liv
resulting
in
five
play-segments
{p
.and
.L.;
,each
pL.;
}=
shown.
Using
aforming
recipe
used
by
a12
team
atime
goal
(?).
A
team
to
give
quantized
ball
positions.
each
time
step,
the
tized
ball
position
is
to
populate
Tmajor
=
10,
we
recently.
The
significance
ofgrown
considering
group
actions
inrecognition.
or0,achieve
4Using
4
tinto
,chunk
tcreated
,these
tto
,ball
ta−
,an
tto
t.ysis
,.At
t{p
(i.e.
where
individual
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
cometically
3:
Figure
3. process
fined
an
ordered
sequence
of
team
behaviors
describing
quite
substantially
10
11
13
14
15
16
a
group
of
these
plans
to
achieve
a
major
goal
(e.g
Zhang,
Zhang,
L.;
L.;
and
and
Jon
Jo
Zhang,
Zhang,
Zhang,
Zhang,
and
L.;
Zhang,
and
Zhang,
L.;
and
Jones,
L.;
L.;
Zhang,
and
L.;
Jones,
Jones,
Zhang,
and
and
L.;
and
L.;
G.,
Jones,
Jones,
Jones,
and
L.;
and
G.,
eds.,
G.,
Jones,
L.;
and
Jones,
eds.,
G.,
Jones,
eds.,
G.,
Intellig
and
G.,
G.,
eds.,
Jone
eds.
Inte
Inte
ed
Jo
G
G
ef
der
to
isolate
team
plans,
rather
than
a
sequential
process
of
thisbehavior
process,
we
can
get
play-segments
from
all
the
possesforming
a
group
of
these
plans
to
achieve
a
major
goal
(e.g.
scarce.
Most
of
the
data
collected
is
via
an
army
of
human
answering
the
adering
sequential
of
tized
ball
position
is
used
to
populate
a.
Using
T
=
10,
we
ave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
comthis
process,
we
can
get
play-segments
then
chunk
a
N
=
(14
10
+
1)/10
=
5
play-segments
which
has
created
a
demand
for
real-time
statistics
and
via
recipe
used
by
a
team
achieve
a
goal
(?).
A
team
perresulting
in
five
play-segments
,
.
.
.
,
p
}
shown.
Using
tized
ball
position
is
used
to
populate
a.
Using
T
=
10,
we
recently.
The
significance
of
considering
group
actions
in
orresulting
in
five
play-segments
{p
,
.
.
.
,
p
}
shown.
Using
can
look
at
the
short-term
of
a
team
from
a
particThere
has
been
an
explosion
in
the
interest
in
live-sport
a
recipe
used
by
a
team
to
achieve
a
goal
(?).
A
team
perHess,
R.,
and
Fern,
A.
2009.
Discr
0
4
group
actions
in orFigure
3:
Figure
3.the
this
process,
we
can
get
play-segments
from
all
the
possest10
, soccer
tquestions
,ofof
t12
, tlow-scoring,
, plans
trather
t15
, achieve
t16
0 for
4a.the
winning
a
match),
can
be
said
to
be
employing
tactics.
recognizing
plans
individual
Outside
of
sport
this
process,
we
can
get
play-segments
from
all
possese
and
join
teams
over
cer.
However,
as
is
continuous
and
comannotators
who
label
all
actions
that
occur
around
the
ball
following
tactical
for
soccer:
11
13
14 ,agents.
forming
a
group
these
to
a
major
goal
(e.g.
tized
ball
position
is
used
to
populate
Using
T
=
10,
w
then
chunk
a
into
N
=
(14−10+1)/10
=
5
play-segments
than
a
sequential
process
of
sualizations.
Due
to
the
difficulty
associated
with
tra
which
has
created
a
demand
real-time
statistics
forming
a
group
of
these
plans
to
achieve
a
major
goal
(
ysis
ysis
and
and
Understan
Understa
ysis
ysis
ysis
and
ysis
and
and
ysis
Understanding.
ysis
and
Understanding.
Understanding.
and
ysis
ysis
and
Understanding.
Understanding.
ysis
Understanding.
and
and
ysis
Understanding.
and
Understanding
Understanding
and
Springer
Understand
Springer
Understa
Springer
Spring
Spri
Ber
Spr
Sp
der
to
isolate
team
plans,
than
a
sequential
process
of
sion winning
strings
to
represent
a team’s
behavior.
We
this
asplay-segments
wethe
There
has
been
an
in
interest
i
used
by
a team
toProblem
achieve
aFormulation
goal
(?).
Aprocess
team
peraof
match),
can
be
said
to
tactics.
then
chunk
atointo
N
(14−10+
=
5from
sion
to4employing
aall
team’s
behavio
group
actions
in
recognizing
plans
ofsaid
individual
agents.
Outside
of
thegoal
sport
ure
3:
Figure
resulting
in
five
play-segments
{s
,behavior.
.,explosion
..1)/10
.be
,Filters
sdo
}represent
shown.
Using
this
process,
we
can
get
play-segments
the
possesular
region.
By
not
chunking
into
play
segments,
this
local
this
process,
can
get
play-segments
from
all
the
possesticle
for
Complex
Multi-Obj
winning
awho
match),
can
be
to
employing
tactics.
then
chunk
awe
into
N
=
(14−10+1)/10
=
5goal
play-segments
ts. Outside
of3.
theorsport ofa recipe
sion
strings
tofive
represent
a=
team’s
behavior.
do
this
as
we
annotators
all
actions
that
occur
around
the
ball
-can
0strings
forming
athey
group
these
plans
to
achieve
major
(e.g.
der
toforming
isolate
team
plans,
rather
abe
sequential
of
sion
strings
represent
ateam
team’s
We
do
this
as
we
sualizations.
Due
to
the
difficulty
with
tracking
which
has
created
athan
demand
for
real-time
statistics
and
vithen
chunk
a
into
N
=
(14−10+1)/10
=
5feed
play-segmen
group
of
these
plans
to
acan
major
(e.g.
realm,
most
of
this
work
has
focussed
onassociated
dynamic
teams
Ideally,
we
would
like
recognize
team
tactics
for
socresulting
in
play-segments
.behavior.
.,R.,
,.aWe
s.R.,
},short-term
shown.
Using
han
a sequential
process
which
call
actions.
The
F24
soccer
data
colcan
look
at
the
behavior
team
from
particThere
has
been
an
inagoal
the
interest
in
live-sport
0a{s
4
can
can
look
look
at
the
at
the
the
short-term
short-term
behavior
aparticteam
ato
from
from
aHess,
particaparticparticcan
can
look
can
look
can
look
can
look
atmaybe
can
at
look
the
can
look
atthe
can
at
look
short-term
the
can
at
look
the
short-term
atlook
the
look
short-term
at
look
the
short-term
atthe
short-term
at
short-term
the
atat
the
short-term
behavior
the
short-term
behavior
short-term
behavior
short-term
short-term
behavior
behavior
behavior
of
behavior
of
athe
behavior
of
team
behavior
astrings
behavior
aball
of
team
of
behavior
team
of
aabehavior
from
of
ateam
from
of
team
afrom
ofteam
arepresent
of
aof
from
from
particteam
of
afrom
team
aaof
afrom
team
particaafrom
ateam
from
particparticparticfrom
particfrom
a{s
particparticaparticsualizations.
Due
to
the
difficulty
with
Hess,
Hess,
R.,
R.,
and
and
Fern
Fer
Hess,
Hess,
Hess,
and
Hess,
R.,
Hess,
and
Fern,
Hess,
R.,
R.,
and
R.,
Hess,
Fern,
and
and
Hess,
R.,
A.
R.,
and
Fern,
Fern,
Fern,
A.
2009.
and
R.,
A.
and
Fern,
R.,
2009.
A.
2009.
and
Fern,
Fern,
A.
A.
and
Discrim
2009.
A.
Fern,
2009.
2009
Disc
A.
Disc
A.
200
Fer
2
players
and
the
ball,
data
containing
this
information
winning
aaoflabel
match),
can
be
said
toexplosion
beaachieve
employing
tactics.
winning
ashort-term
match),
can
be
said
to
be
employing
tactics.
agents.
Outside
the sport
recognizing
plans
of
individual
agents.
Outside
of
the
sport
can
at
the
behavior
of
atriD
resulting
in
five
play-segments
.R.,
saand
}associated
shown.
Using
behavior
lost
as
we
will
see
in
next
subsection.
sion
to
aaof
team’s
We
do
this
as
we
sion
strings
to
represent
aaaalook
team’s
behavior.
We
do
this
as
we
which
has
created
demand
for
real-time
statis
0team
4tactics.
this
process,
we
can
get
play-segments
from
all
the
possescan
look
atresulting
the
short-term
behavior
of
aHess,
from
a.Fern,
particrmulation
realm,
most
of
this
work
has
focussed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
soc
resulting
in
five
play-segments
{s
,
.
.
.
,
s
}
shown.
Using
forming
a
group
these
plans
to
achieve
major
(e.g.
1.
What
type
playing
style
can
we
expect
from
team?
Hess,
R.;
Fern,
A.;
and
Mortensen
quential
processofof
can
look
at
the
short-term
behavior
of
a
team
from
a
partic0
4
winning
a
match),
can
be
said
to
be
employing
Problem
Formulation
recognizing
plans
of
individual
agents.
Outside
of
the
sport
sed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
socin
five
play-segments
{s
,
.
.
,
s
}
shown.
Usi
which(i.e.
they
callmost
ball
actions.
The
F24
soccer
data
feed
colthis
process,
we
can
get
play-segments
from
all
the
possesular
region.
By
not
chunking
into
play
segments,
this
local
ular
ular
region.
region.
By
By
By
not
not
not
chunking
chunking
into
into
play
play
segments,
segments,
this
this
local
local
ular
ular
ular
region.
ular
ular
ular
region.
region.
ular
region.
ular
By
ular
By
ular
region.
ular
not
By
By
not
By
region.
not
chunking
region.
By
not
chunking
By
not
chunking
not
By
chunking
not
By
chunking
not
into
not
chunking
not
into
chunking
into
chunking
chunking
into
chunking
play
into
play
segments,
into
play
play
segments,
into
play
segments,
into
segments,
segments,
into
play
segments,
this
segments,
play
play
segments,
this
segments,
this
local
segments,
local
this
segments,
this
local
this
this
local
local
local
this
this
local
this
local
this
local
local
local
ticle
ticle
Filters
Filters
for
for
Com
CT
ticle
ticle
ticle
Filters
ticle
Filters
ticle
Filters
for
Filters
Filters
ticle
Filters
ticle
for
Complex
Filters
for
ticle
Filters
Complex
for
Filters
Complex
ticle
for
for
Complex
for
Complex
Filters
Complex
Multi-Object
for
for
Complex
Multi-Ob
Multi-Ob
Complex
for
Comple
for
Multi
Com
Mul
Mu
Co
M
0team
4 Filters
where
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
continuous
and
complayers
and
the
ball,
data
containing
this
information
is
still
sualizations.
Due
to
the
difficulty
associated
tracking
winning
aindividual
match),
can
be
said
toautomatically
be
employing
tactics.
ular
region.
By
not
chunking
into
play
s
for
the
Premier
League
(EPL)
by
Opta
(?)
players
and
the
ball,
containing
this
information
gents.
Outside
of
the
sport
aanswering
=region.
{a
,teams
aregion.
aregion.
,region.
a
,By
achunking
,strings
,region.
aplay
,process,
ainto
,English
arepresent
,into
aplay
,play
achunking
,achunking
acan
,low-scoring,
aget
,data
a
}behavior
look
at
the
short-term
behavior
of
aticle
from
alocal
partic10
this
we
can
get
play-segments
from
all
the
posses60with
9lected
9ascarce.
9can
9Most
14
15
15
12
12
12difficulty
can
at
the
short-term
of
afrom
team
from
aand
particof
the
data
collected
is
via
an
army
of
h
which
has
created
a
demand
for
real-time
statistics
15, soc2the
3 , asion
49and
5ular
6vi7
8
9look
10
11
12
13
14
In
this
paper,
we
are
looking
to
By
not
into
play
segments,
this
local
realm,
of
this
work
has
focussed
on
dynamic
Ideally,
we
would
like
to
recognize
team
tactics
for
s
Parts
Pictorial
Structures
for
Object
to
team’s
behavior.
We
used
this
apocussed
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
pect
from
a
team?
this
process,
we
play-segments
all
the
possesular
region.
By
not
into
play
segments,
this
sualizations.
Due
to
the
associated
wi
(i.e.
where
individual
agents
can
leave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
com
afor
match),
can
be of
said
to
be
employing
tactics.
m
Formulation
behavior
behavior
maybe
maybe
maybe
lost
lost
lost
as
as
we
we
will
will
see
see
in
in
the
the
next
next
subsection.
subsection.
behavior
behavior
behavior
behavior
behavior
behavior
maybe
behavior
maybe
behavior
maybe
behavior
maybe
behavior
behavior
maybe
lost
maybe
lost
maybe
lost
as
maybe
lost
as
we
maybe
lost
maybe
as
lost
we
as
will
lost
we
as
lost
will
as
we
we
lost
will
see
as
we
lost
will
as
see
will
we
as
in
see
will
we
as
as
in
we
will
the
see
see
we
in
will
see
the
we
will
next
the
in
see
in
will
in
next
will
see
the
the
next
see
in
the
subsection.
see
in
next
the
see
subsection.
in
next
subsection.
the
in
the
next
in
subsection.
subsection.
the
next
subsection.
the
next
subsection.
next
subsection.
next
subsection.
subsection.
subsection.
behavior
maybe
lost
as
we
will
see
inget
the
next
subsection.
Outside
of theteams
sportover2: winning
this
process,
we
can
play-segments
from
all
the
posse
realm,
most
of
this
work
has
focussed
onthe
dynamic
teams
Ideally,
we
would
like
to
team
tactics
for
socsion
strings
to
represent
arecognize
team’s
behavior.
We
used
this
apHess,
Hess,
R.;
R.;
Fern,
Fern,
A.
Hess,
Hess,
Hess,
R.;
Hess,
Hess,
R.;
Fern,
R.;
Hess,
Fern,
Hess,
R.;
Fern,
Hess,
R.;
R.;
A.;
R.;
Hess,
Fern,
Fern,
Fern,
Hess,
A.;
R.;
A.;
and
R.;
Fern,
A.;
and
Fern,
R.;
and
Fern,
Mortensen,
A.;
A.;
R.;
A.;
and
Fern,
Mortense
Mortense
and
and
A.;
Fern,
A.;
and
Morte
and
A.;
Mo
and
MA
Figure
(From
the
XML
feed,
we
can
infer
behavior
maybe
lost
as
we
will
see
inMort
the
ve
and join
cer.Are
However,
as
soccer
isball,
low-scoring,
continuous
and
comular
region.
By
not
chunking
into
play
segments,
this
local
lected
the
English
Premier
League
(EPL)
by
Opta
(?)
ular
region.
By
not
chunking
into
play
segments,
this
local
maybe
as
we
will
see
in
Problem
Formulation
to
aall
team’s
We
used
this
aptEA
players
and
the
data
containing
information
is
2.
there
any
areas
the
field
which
they
tend
to
utilize
scarce.
Most
of
collected
via
an
army
of
In
In
this
paper,
we
are
looking
to
automatically
answering
is
astill
example
of
data
is
time
coded
scarce.
Most
of
the
data
collected
is
viathis
an
army
of
human
automatically
answering
the
behavior
maybe
we
will
in
next
subsection.
proach
it
allows
to
analyze
behavior
of
on dynamic
teams
Ideally,
we
would
like
to
recognize
team
for
socwho
label
actions
that
occur
around
the
following
tactical
questions
for
soccer:
aa14
We
used
this
ap(i.e.
where
individual
agents
can
leave
and
join
teams
over
as
soccer
low-scoring,
continuous
and
co
=
a{a
=
{a
,14a,,a6annotators
,35a{a
asion
,2a25However,
,a336strings
a
,to
a
a,to
a
a
,the
,The
,ais
,a
,behavior.
,a
a13
,a}Parts
aPictorial
,is
aa
}Structures
}
atactics
a=
a
={a
a=
{a
=
a
a
{a
=
a{a
,=
a
{a
,,a
=
a{a
a,with
a
=
,{a
,aa=
,a=
{a
,31a
=
,1,0{a
a,a{a
,the
,402a
a0,2,10{a
,4a
,good
,a513a
acer.
,10abehavior
,=
a
,1a
,3as
a
,,a
a
,sion
a
,behavior
a
aas
,,84a
a
,sion
,a
a
,a
,9,57a
,a,a7,4a
,10
,8a
a
,3maybe
a
,,lost
a8,a56aa
,7us
a
,10
,a
,6represent
a
,4a
,lost
a
,,7,this.
,represent
a
aa
,5to
,as
a9,8,aa
,represent
,analyze
a11
a,12
aa
,a
,a,10
a,7we
a12
,13
a,data
,a,11
,the
a
,10
a
,team’s
a
}F24
,see
a
,a14
a
,11
a}912
,short-term
,the
a}Parts
,see
a
a
,14
aaICCV.
a
,14
}the
anext
,behavior.
}14
,aParts
,aa
}a
,subsection.
}13
,next
a14
}14
}
sualizations.
Due
to
the
difficulty
associated
tracking
a
,a6a9,a5,astrings
,a
,a13
a
a
,a
aPictorial
}Structures
ncussed
leave
and
join
teams
over
cer.
However,
as
soccer
is
low-scoring,
continuous
and
com0
2
2
3
3
44strings
4
6
6
712
89
9
9
10
11
11
12
12
13
0 ,Maps
0
1
0a
01
2
01a
0
1
2a
02
3
2
13a
3,a
24a
3
21
5
2
4
2
4
6
7
3
5
4,6a
3
5
4
7
6
5,1
7,a
6
4a
5
8
7
6a
8,2
5
55
8
6
79
6
9
7
810
11
9
7
8
7
8
10
11
9
11
10
8
9
8
10
11
12
11
10
9a
11
10
12
13
12
11
10
12
13
11
13
13
12
13
12
14
13
12
13
13
14
14
14
and
the
ball,
data
containing
this
informa
a,a14
team’s
behavior.
We
used
this
aO
0
6
8
10
11
12
13
14
Parts
Parts
Pictorial
Str
Parts
Parts
Pictorial
Parts
Pictorial
Pictorial
Parts
Pictorial
Pictorial
Parts
Structures
Pictorial
Parts
Pictorial
Parts
Pictorial
Structures
Pictorial
Structures
for
Pictorial
for
Objects
Structure
for
Objec
for
Struc
Objec
for
for
Ob
fo
w
proach
as
itplayers
allows
us
the
short-term
behavior
Entropy
(i.e.possession
where
individual
agents
can
leave
and
join
teams
over
cer.
However,
soccer
is
low-scoring,
continuous
and
comlost
as
will
in
the
subsection.
on
dynamic
teams
Ideally,
we
would
like
to
recognize
team
tactics
for
soca
=
{a
,see
a
,14
a,that
,a
a11
,,Structures
a
,Structures
,Structures
aof
aof
,Stru
aStr
a
=
{a
,
a
,
a
,
a
,
a
,
a
,
a
,
,
a
,
a
,
a
,
a
,
a
,
}
behavior
maybe
lost
as
we
will
in
subsection.
0
1
2the
3next
4,2012.
5
6a,14
7a
8},e
ball
position
and
at
every
time
step
(solid
proach
as
it
allows
us
to
analyze
the
short-term
behavior
0
1
2
3
4
5
6
7
8
9
10
12
13
a
=
{a
,
a
,
a
,
a
,
a
,
a
,
a
,
a
,
a
,
a
a
,
a
a
,
a
,
m
Formulation
IBM
SlamTracker.
www.aus
annotators
who
label
all
actions
occur
around
th
h
they
tend
to
utilize
following
tactical
questions
for
soccer:
�
a
team
over
a
particular
region,
which
maybe
lost
otherwise.
more
than
others?
is
a
good
example
of
this.
The
F24
data
is
a
time
coded
0 player
2 ball
3 us
4 actions.
5events
6Inanalyze
7In
8
9F24
10
11game
12
13 feed
14
scarce.
Most
ofthe
the
data
collected
is via this
an
army
ofcomhuman
proach
as1call
it,asaallows
to
analyze
the
short-term
behavior
ofa
feed -Tthe
that
lists
all
action
the
with
ng
to automatically
answering
=
10
annotators
who
label
all
actions
that automatically
occur
around
the
ball
soccer:
which
they
The
soccer
In
ICCV.
ICCV.
ICCV.
ICCV.
In
In
ICCV.
In
ICCV.
In
In
ICCV.
ICCV.
leave
and
joinover
teams
overcer. the
cer.
However,
asof
soccer
isball,
low-scoring,
continuous
and
proach
short-term
behavior
team
region,
maybe
otherwise.
=aa particular
{a
,aaallows
, a (1)
,awhich
a
,data
aen_AU/ibmrealtime/index.
awithin
,a
a7ICCV.
,aalost
, ICCV.
aICCV.
aICCV.
adata
a13
scarce.
Most
via
army
players
and
data
containing
information
isaMaps
still
In
this
paper,
we
are
looking
answering
Tto
1it
4the
8the
11
T
=Tover
10
=
,particular
,,region,
aa3us
,region,
awhich
,,In
awhich
,In
,ICCV.
,InIn
a,is
, a,otherwise.
,an
a, 12
, a, 13
a{6,
team
a0{a
particular
maybe
otherwise.
H(X)
=
p(x)
log
p(x)
12, a23of
45,=
5610
67collected
89, alost
910
10
1112
r1
nd
join
teams
However,
as all
soccer
iswho
low-scoring,
continuous
and
com1.lists
What
type
playing
style
can
we
expect
from
aEntropy
team?
Entropy
Maps
Maps
Entropy
Entropy
Entropy
Entropy
Entropy
Maps
Entropy
Entropy
Maps
Maps
Entropy
Entropy
Entropy
Maps
Maps
Maps
Maps
Maps
Maps
=a.over
10
lines and dots
are
annotated,
dotted
lines
are
in-to
s�
p
=
5,
.team
.�
,�
15}
awhich
team
over
a0type,
maybe
lost
they
call
ball
actions.
The
F24
soccer
data
fe
0
aMaps
player,
team,
event
minute
and
second
for
each
acannotators
label
all
actions
that
occur
around
the
ball
-�
s for
soccer:
IBM
IBM
SlamTracker.
SlamTracke
IBM
IBM
IBM
SlamTracker.
IBM
SlamTracker.
IBM
SlamTracker.
IBM
SlamTracker.
IBM
SlamTracker.
SlamTracker.
IBM
SlamTracker.
IBM
SlamTracker.
2012.
IBM
SlamTracker.
2012.
SlamTracker.
2012.
SlamTracker
www.austr
2012.
2012.
2012.
www.au
www.au
2012.
www.
2012
2012
www
ww
w2
aannotators
over
a particular
region,
which
maybe
lost
otherwis
feed
thatscoring
player
action
events
within
the
game
with
�
�
�
�
�
�
�
T
=
10
lected
for
the
English
Premier
League
(EPL)
by
Op
sp�
which
they
call
ball
actions.
The
F24
soccer
data
feed
col=
{6,
5,
.
.
.
,
15}
00�
T
=
10
1.
What
type
of
playing
style
can
we
expect
from
a
team?
who
label
all
actions
that
occur
aroun
following
tactical
questions
for
soccer:
x∈X
s
3.
In
situations
where
are
their
strengths
and
weakscarce.
Most
of
the
data
collected
is
via
an
army
of
human
king
to
automatically
answering
the
p
=
{6,
5,
.
.
.
,
15}
00
Intille,
S.,
and
Bobick,
A.
1999.
A
p
=H(X)
{5,
9,
.
.
.
,
12}
s
ferred).
s
H(X)
H(X)
=
=
p(x)
p(x)
log
log
p(x)
p(x)
(1)
(1)
H(X)
H(X)
H(X)
H(X)
=
H(X)
H(X)
=
H(X)
=
H(X)
=
H(X)
=
p(x)
=
H(X)
p(x)
=
p(x)
log
=
p(x)
=
p(x)
log
=
p(x)
log
=
p(x)
p(x)
log
log
p(x)
p(x)
log
p(x)
p(x)
log
p(x)
p(x)
p(x)
log
log
log
p(x)
log
p(x)
p(x)
(1)
p(x)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
n we expect from
a team? a player,2.team,
1
en_AU/ibmreal
en_AU/ibmrea
en_AU/ibmrealtime/index.ht
en_AU/ibmrealtime/index
en_AU/ibmrealtime/index
en_AU/ibmrealtime/ind
en_AU/ibmrealtime/i
en_AU/ibmrealtime/in
en_AU/ibmrealtime/
en_AU/ibmrealtim
en_AU/ibmrealtim
en_AU/ibmrealt
en_AU/ibmrea
0
lected
for
the
English
Premier
League
(EPL)
by
O
p0 9,
.5,
. . ., .15}
s=0has
sp11 as=
{5,
. {6,
.=
. ,.{6,
12}
tion.
Each
event
a5,
ofEntropy
qualifiers
describing
it.a Evwhich
they
call
ball
actions.
The
F24
soccer
data
feed
colMaps
. ,of
15}
Are
there
areas
ofPremier
the and
fieldsecond
which
they
tend
to
utilize
is
good
example
this.
The
F24
data
issoccer
timeda
event
type,
minute
for
eachby
acp
9,
.they
. ,series
12}
nizing
Multi-Agent
Action
from
Vic
lected
for
theany
English
League
(EPL)
Opta
(?)
1x∈X
which
ball
actions.
F24
p
=
{9,
.1x∈X
.{5,
.p
,012}
19,
2ball
sx∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
s=
annotators
who
label
actions
that
occur
around
the
-is
ons
for we
soccer:
yle
can
expect
from a team? nesses?
2
pa
=
{5,
9,
.9,
. . ., call
strengths
and
weakIntille,
Intille,
S.,
S.,
and
Bob
Bo
Intille,
Intille,
Intille,
Intille,
S.,
Intille,
S.,
and
Intille,
S.,The
Intille,
and
Intille,
S.,
and
Bobick,
S.,
S.,
Intille,
and
S.,
Bobick,
Bobick,
and
Intille,
and
S.,
and
S.,
Bobick,
Bobick,
A.
Bobick,
and
S.,
and
Bobick,
A.
S.,
1999.
A.
and
Bobick,
Bobick,
and
1999.
A.
1999.
A.
Bobi
A.
A
A.
199
Bo
19
F1A
Analysis
Using
Maps
2.1.than
Are
there
anyofareas
ofallthe
field
they tend
toOpta
utilize
1 x∈X
example
ofaction
this.
The
F24
data
is
aand
time
=
{9,
9,
. x∈X
.=
. ,.{5,
12}
sgood
spx∈X
What
type
playing
style
canwhich
we
expect
from
aEntropy
team?
11lists
p
.12}
.for
, 12}a
�
22{9,
ery
event
collected
by
Opta
given
match
is
listed
within
s
p
=
{9,
9,
.
.
,
12}
more
others?
lected
for
the
English
Premier
League
(EPL)
by
(?)
feed
that
all
player
events
within
the
game
p
=
9,
.
.
.
,
12}
2
2
Kim,
K.;
Grundmann,
M.;
Shamir,
3
tion.
Each
event
has
a
series
of
qualifiers
describing
it.
Evtype
of
data
is
currently
used
for
the
real-time
online
visuallected
for
the
English
Premier
League
(EPL)
bf
s3 colsp22 9,
ld which they tend to utilize
nizing
nizing
Multi-Agen
Multi-Age
nizing
nizing
nizing
Multi-Agent
nizing
nizing
Multi-Agent
Multi-Agent
nizing
nizing
Multi-Agent
nizing
Multi-Agent
Multi-Agent
nizing
Multi-Agent
nizing
Action
Multi-Agent
Multi-Agent
Action
Action
Multi-Agent
Multi-Age
Action
from
Action
Action
Action
from
from
Visua
Acti
Act
from
frp
V
V
{9,
9, .9,
. .all
isdefine
a good
example
ofofball
this.
The
F24
data
isAnalysis
aAnalysis
time
coded
=
{9,
. Maps
.Maps
,.lists
12}
H(X)
=
p(x)
log
s=
which
they
call
actions.
The
F24
soccer
data
feed
spMaps
more
than
others?
feed
that
action
events
within
the
gam
p
=.of
{9,
., .12}
. ,player
12}
Determining
Parameters
22Maps
33{9,
Analysis
Using
Using
Using
Entropy
Entropy
Maps
Analysis
Analysis
Analysis
Analysis
Using
Analysis
Analysis
Using
Analysis
Using
Analysis
Analysis
Using
Using
Entropy
Using
Entropy
Using
Entropy
Using
Entropy
Using
Entropy
Using
Entropy
Maps
Entropy
Entropy
Maps
Entropy
Entropy
Maps
Entropy
Maps
Maps
Maps
Maps
Maps
p
=
{9,
9,
.
.
,
12}
s
We
a
team
as
a
set
agents
having
a
shared
obp
=
9,
.
.
.
,
10}
gins,
J.;
and
Essa,
I.
2010.
Motio
3
3
this
feed.
The
type
events
listed
are:
goals,
shots,
passes
4
he
field
they tend
toautilize
a
player,
team,
event
type,
minute
and
second
for
eac
is
a
good
example
of
this.
The
F24
data
is
a
time
coded
p
=
{9,
9,
.
.
.
,
12}
style
canwhich
we expect
from
team?
s
Kim,
Kim,
K.;
K.;
Grundma
Grundm
Kim,
Kim,
Kim,
K.;
Kim,
Kim,
K.;
K.;
Grundmann,
Kim,
Grundmann,
K.;
Kim,
Grundmann,
Kim,
K.;
K.;
K.;
Grundmann,
Kim,
Grundmann,
Grundmann,
Kim,
K.;
K.;
Grundmann,
M.;
K.;
Grundmann,
Grundmann,
K.;
M.;
M.;
Grundman
Shamir,
Grundm
M.;
Shami
Shami
M.;
M.;
M.;
Sh
S
A
M
S
3
izations
of events,
well
as
post-analysis
for
prominent
telep
=
{9,
9,
.
.
.
,
10}
2.
Are
there
any
areas
of
the
field
which
they
tend
to
utilize
3
is
a
good
example
of
this.
The
F24
data
is
a
ery as
event
collected
by
Opta
for
a
given
match
is
listed
within
4
x∈X
s33 9,
p
= .{9,
.is,
.event
. ,do
12} type,
feed
listsmental
all the
player
action
events
within
the
game
with
3.andInthat
situations
where
are
their
strengths
and
weakteam,
minute
and
second
for
ea
How
discriminative
are
our
representations?
paMaps
=
{9,
.That
.tackles,
,.9,
10}
Evolution
in
Dynamic
Sports
Scene
lected
for
English
Premier
League
(EPL)
by
Opta
(?)
Determining
Parameters
Parameters
Determining
Determining
Determining
Determining
Determining
Determining
Determining
Determining
Determining
Determining
Parameters
Determining
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
4 player,
jectiveentities
ascoring
shared
state
(?).
As
we
are their
dealing
with
pMaps
= {9,
9,
. .has
, 10}
Entropy
gins,
gins,
J.;
J.;
and
and
Essa,
gins,
gins,
gins,
gins,
gins,
J.;
and
J.;gins,
and
and
J.;
Essa,
gins,
J.;
gins,
and
Essa,
J.;
Essa,
and
gins,
and
J.;
I.
gins,
and
J.;
Essa,
Essa,
Essa,
2010.
and
I.and
I.
J.;
Essa,
J.;
2010.
2010.
and
I.Essa,
Essa,
I.I.
and
2010.
Motion
I.2010.
Essa,
2010.
Moti
2010
I.Essa
Moti
I.Essa
20
2M
(with
start/end
clearances,
cards,
free
kicks,
3.(e.g.
Inmore
scoring
situations
where
are
strengths
and
weak4point),
tion.
Each
event
a series
ofJ.;
qualifiers
describing
iI
feed
that
lists
all
player
action
events
within
the
game
with
Entropy
vision
and newspaper
ESPN,
The
Guardian).
p
=
{9,
9,
.
.
.
,
10}
than
others?
feed
that
lists
all
player
action
events
within
the
s
having
a
shared
obteams
have
unique
styles
of
play?
And
if
so,
can
we
detect
4
Entropy
Maps
Entropy
Maps
4
this
feed.
The
type
of
events
listed
are:
goals,
shots,
passes
nesses?
tion.
Each
event
has
a
series
of
qualifiers
describing
Laviers,
K.;Dynamic
G.;
Molin
a each
player,
event
type,fixed
and
second
for
each
acHow
How
discriminative
are
are
our
our
representations?
representations?
That
That
is,
is,
do
do
How
How
How
How
discriminative
How
discriminative
How
discriminative
How
discriminative
How
discriminative
How
discriminative
How
How
discriminative
discriminative
discriminative
are
discriminative
are
are
our
are
our
are
our
are
representations?
our
are
representations?
our
are
representations?
our
are
our
representations?
are
representations?
are
our
representations?
our
representations?
our
our
representations?
representations?
representations?
representations?
That
That
That
is,That
That
That
is,
do
is,That
is,
That
do
is,
That
is,
do
That
is,
do
do
That
is,
is,
do
is,
do
do
is,
do
do
Evolution
Evolution
in
in
Dynam
Dyn
Evolution
Evolution
Evolution
Evolution
Evolution
in
Evolution
Evolution
in
Evolution
inSukthankar,
Dynamic
Dynamic
Evolution
in
in
in
Evolution
Dynamic
in
Dynamic
Dynamic
Sports
Dynamic
in
in
Sports
Sports
Dynamic
Dynamic
in
Scenes.
Sports
in
Dynam
Sports
Sport
Dyn
Scen
Spor
Scen
SS
Entropy
Maps
Entropy
Maps
fieldstrengths
which
they
tend
to
utilize
is ateam,
good
example
ofminute
this.
The
F24
data
is
adiscriminative
time
coded
soccer,
agent
isteam,
permanently
to no
one
team.
Unless
Analysis
Using
Entropy
Maps
nesses?
corners,
offsides,
substitutions
and
stoppages.
An
example
The
information
content
of
ado
random
discrete
variable,
X
�
rethe
their
and
weakwhen
they
deviate
from
this
style
and
quantify
it?
ery
event
collected
by
Opta
for
aEvolution
given
match
is
w
Entropy
Maps
player,
eventclearances,
type,
minute
and
second
for
each
acEven
though
this
data
hasa been
widely
used,
there
are
The
information
content
of
aby
random
discrete
variable,
X
2009.
Improving
Offensive
Perform
aofevent
player,
team,
event
type,
minute
and
second
fM
�
teams
teams
have
unique
unique
unique
styles
styles
of
of
play?
play?
And
And
if
if
so,
so,
can
can
we
we
detect
detect
teams
teams
teams
teams
have
teams
have
teams
have
teams
have
unique
teams
have
unique
teams
teams
have
teams
unique
have
unique
have
unique
styles
unique
have
styles
have
have
unique
styles
unique
styles
of
unique
styles
unique
styles
of
play?
of
styles
play?
styles
of
play?
of
styles
of
And
styles
play?
play?
styles
of
play?
And
of
And
play?
if
play?
And
of
And
so,
if
play?
of
And
if
play?
so,
And
can
play?
so,
if
ifAnd
can
if
And
so,
can
we
if
so,
And
And
we
if
so,
can
detect
we
if
can
so,
if
detect
so,
can
we
we
detect
ifwe
so,
can
can
so,
we
detect
detect
detect
can
we
can
we
we
detect
detect
we
detect
detect
The
information
content
of
adetect
random
variable,
X
Entropy
Maps
we
are their
dealing
with
ery
collected
Opta
for
adiscrete
given
match
islisted
listed
(with
start/end
point),
tackles,
cards,
free
kicks,
Laviers,
Laviers,
K.;
K.;
Sukth
Suk
Laviers,
Laviers,
Laviers,
Laviers,
Laviers,
K.;
Laviers,
K.;
K.;
Sukthankar,
Laviers,
Laviers,
K.;
Sukthankar,
Sukthankar,
Laviers,
K.;
K.;
Laviers,
K.;
Sukthankar,
Sukthankar,
Sukthankar,
K.;
K.;
Sukthankar,
G.;
K.;
Sukthanka
Sukthanka
K.;
G.;
G.;
Molinea
Suktha
G.;
Sukt
Mol
Mol
G.;
GG
H(X)
=
p(x)
log
p(x)
(1)
here
are
strengths
and weaktion.
Each
event
has
a
series
of
qualifiers
describing
it.
Ev3.
In
scoring
situations
where
are
their
strengths
and
weak�
The
information
content
of
a
random
discrete
variable,
X
Entropy
Maps
with
a
probability
distribution
p(x)was
defined
by
Shannon
an
agent
has
been
dismissed
from
the
match,
each
team
alfeed
that
lists
all
player
action
events
within
the
game
with
of
the
data
feed
is
given
in
Figure
5(a).
This
type
of
data
We
define
a
team
as
a
set
of
agents
having
a
shared
obEntropy
Maps
H(X)
=
p(x)
log
p(x)
(1)
�
Modeling.
In
AAAI
Conference
on
with
afrom
probability
distribution
p(x)was
defined
by
Shannon
this
feed.
The
type
of
events
listed
are:
goals,
shots,
pO
when
when
they
deviate
deviate
deviate
from
from
this
this
style
style
and
and
quantify
quantify
it?
it?a2009.
when
when
when
when
they
when
they
when
they
when
deviate
they
when
deviate
they
when
they
deviate
when
when
deviate
they
deviate
they
from
deviate
they
from
they
deviate
they
from
deviate
this
from
deviate
from
deviate
this
from
this
style
from
this
style
from
this
style
this
from
and
style
this
from
style
and
this
style
and
quantify
this
style
this
and
quantify
and
style
this
quantify
and
style
style
and
quantify
quantify
style
quantify
and
it?
and
quantify
it?
and
it?
quantify
and
quantify
it?
quantify
it?
quantify
it?
it?
it?
it?
it?
Determining
Parameters
systems
which
use
this
data
or
data
like
this
for
automatic
with
a
probability
distribution
p(x)was
defined
by
Shannon
tion.
Each
event
has
a
series
of
qualifiers
describing
it.
Ev2009.
2009.
Improving
Improving
2009.
2009.
Improving
2009.
2009.
Improving
Improving
2009.
2009.
Improving
2009.
Improving
Improving
2009.
Improving
Offensive
2009.
Improving
Improving
Offensive
Offensive
Improving
Offensive
Offensive
Improving
Offensive
Performan
Offensive
Perfor
Offens
Perfor
Offen
Pe
O
P
tion.
Each
event
has
series
of
qualifiers
descri
We
define
a
team
as
a
set
of
agents
having
a
shared
obthis
feed.
The
type
of
events
listed
are:
goals,
shots,
x∈X
�
H(X)
=
p(x)
log
p(x)
(1)
Mutual
Information
to one team. Unless
corners,
offsides,
substitutions
and
stoppages.
An
example
with
a
probability
distribution
p(x)was
defined
by
Shannon
H(X)
=
p(x)
log
p(x)
(1)
Figure
3:
Given
a
possession
string,
we
break
it
up
(?)
nesses?
Interactive
Digital
Entertainment.
ery
event
collected
by
Opta
for
a
given
match
is
listed
within
�
x∈X
ways has
the asame
of by
agents
(11).
refer
to
team
(?)(with
iswith
currently
used
for
the
real-time
online
visualizations
of
jective
and
anumber
shared
mental
state
(?).
As
weAs
are
dealing
with
player,
event
type,
minute
and
second
for
each
acModeling.
Modeling.
In
In
AAA
AA
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
In
Modeling.
AAAI
Modeling.
In
AAAI
Modeling.
AAAI
In
Modeling.
In
Conference
In
AAAI
In
AAAI
AAAI
Conference
Conference
AAAI
In
Inrepresenta
Conference
AAAI
AAAI
Conferen
In
Confere
Confere
In
AAAI
on
Con
AAA
Con
Art
on
on
(?) (with
start/end
point),
tackles,
cards,
free
H(X)
=tackles,
p(x)
log
p(x)
(1)
The
information
content
of
aclearances,
random
discrete
variable,
tactical
analysis.
How
discriminative
are
our
ery
event
collected
Opta
for
aWe
given
match
is
listed
within
jective
andteam,
a shared
mental
state
(?).
we
dealing
ery
event
by
Opta
for
aIn
given
match
is
lik
x∈X
start/end
point),
clearances,
cards,
free
H(X)
=Information
−
p(x)
log
p(x)
(2)
x∈X
Mutual
Information
Information
Information
Mutual
Mutual
Mutual
Mutual
Mutual
Mutual
Information
Mutual
Information
Mutual
Information
Mutual
Information
Mutual
Mutual
Information
Information
Information
Information
Information
(?)
where
are
their
strengths
and
weakcan
be
into
N
equal
chunks
and
use
thecollected
quantized
ball
pomatch,
each
team
alLaviers,
K.;
Sukthankar,
G.;
Molin
the
data
feed
isThe
given
in
Figure
5(a).
This
type
ofare
data
Interactive
Interactive
Digital
Digita
Interactive
Interactive
Interactive
Interactive
Interactive
Interactive
Interactive
Digital
Interactive
Interactive
Digital
Digital
Interactive
Digital
Entertainment.
Interactive
Digital
Digital
Digital
Entertainment.
Entertainment.
Digital
Digital
Entertainme
Entertainm
Entertain
Digital
Entertai
Digita
Ente
EnteE
can
be
�
�
�
�
�
�
�
�
�
�
�
�
�
agents
having
a shared
ob-ofwe
Analysis
Using
Entropy
Maps
behaviors,
B,
as
short,
observable
segments
of
coordinated
can
be
this
feed.
type
of
events
listed
are:
goals,
shots,
passes
events,
as
well
as
post-analysis
for
prominent
television
and
with
a
probability
distribution
p(x)was
defined
by
Shann
x∈X
soccer,
each
agent
is
permanently
fixed
to
one
team.
Unless
teams
have
unique
styles
of
play?
And
i
corners,
offsides,
substitutions
and
stoppages.
An
exa
tion.
Each
event
has
a
series
of
qualifiers
describing
it.
EvFor
this
work
used
the
2010-2011
EPL
season
F24
Opta
Analysis
Using
Entropy
Maps
We
define
a
team
as
a
set
of
agents
having
a
shared
obset
of agents
having
a shared
obsoccer,
each
agent
is
permanently
fixed
to
one
team.
Unless
x∈X
this
feed.
The
type
of
events
listed
are:
goals,
sh
this feed. The type of events listed are:sition
goals,values
shots,
passes
corners,
offsides,
substitutions
and
stoppages.
An
ex
can
be
The
information
content,
namely
(Shannons)
entropy
of
H(X)
H(X)
=
=
−
−
p(x)
p(x)
log
log
p(x)
p(x)
(2)
(2)
H(X)
H(X)
H(X)
H(X)
=
H(X)
H(X)
=
−H(X)
=−
H(X)
=
−
H(X)
=H(X)
=
−
p(x)
−
=
−H(X)
p(x)
=
−
p(x)
=
log
−
=
p(x)
p(x)
−
=
log
p(x)
−
log
−
p(x)
p(x)
log
log
p(x)
p(x)
log
p(x)
p(x)
log
p(x)
p(x)
log
log
log
p(x)
log
p(x)
p(x)
(2)
p(x)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)Laviers,
(2)
(2)
2011.
Improving
Offensive
Perform
The
information
content,
namely
(Shannons)
entropy
of
as
our
play-segment
representation,
s.
Laviers,
Laviers,
K.;
K.;
Sukth
Suk
Laviers,
Laviers,
Laviers,
Laviers,
K.;
Laviers,
K.;
K.;
Sukthankar,
Laviers,
Laviers,
K.;
Sukthankar,
Sukthankar,
Laviers,
K.;
K.;
Laviers,
K.;
Sukthankar,
Sukthankar,
Sukthankar,
K.;
K.;
Sukthankar,
G.;
K.;
Sukthanka
Sukthanka
K.;
G.;
G.;
Molinea
Suktha
G.;
Sukt
Mol
Mol
G.;
G
G
M
The
information
content,
namely
(Shannons)
entropy
of
Analysis
Using
Entropy
Maps
1). We
refer to
team
when
they
deviate
from
this
style
and
qu
�of
(?)
Analysis
Using
Entropy
Maps
iswith
currently
used
for
the
real-time
visualizations
ofdealing
movement
and
action
executed
by
aonline
team
(e.g.
pass
from
Determining
Parameters
with
newspaper
entities
(e.g.
ESPN,
The
Guardian).
Even
though
start/end
point),
tackles,
clearances,
cards,
free
kicks,
an (with
agent
has
been
dismissed
from
the
match,
each
team
althe
data
feed
is
given
in
Figure
5(a).
This
type
of
feed,
consists
of(with
380
games
and
more
than
760,000
Modeling.
In
International
Joint
anjective
agent
has
dismissed
from
the
match,
each
team
alThe
information
content,
namely
(Shannons)
entropy
of
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
x∈X
and
abeen
shared
mental
state
As
we
are
with
a
discrete
random
variable
X
that
has
a
probabilitydistribuery
event
collected
by
Opta
for
a(?).
given
match
isH(Y
listed
within
l (?).
stateAs
(?).weAsare
wedealing
arewhich
dealing
of
the
data
feed
is
given
in
Figure
5(a).
This
type
Determining
Parameters
(with
start/end
point),
tackles,
clearances,
cards,
start/end
point),
tackles,
clearances,
cards,
free
kicks,
2011.
2011.
Improving
Improving
O
2011.
2011.
2011.
Improving
2011.
2011.
Improving
Improving
2011.
2011.
Improving
2011.
Improving
Improving
2011.
Improving
Offensive
2011.
Improving
Improving
Offensive
Offensive
Improving
Offensive
Offensive
Improving
Offensive
Performan
Offensive
Perfor
Offens
Perfor
Offen
Pe
O
P
Analysis
Using
Entropy
Maps
a�
discrete
random
variable
X that
hashas
a probabilitydistribu) = −�
p(y)
log
p(y)
(3)
aDetermining
discrete
random
variable
X that
a probabilitydistribucan
be
�
�
�
�
�
�
�
�
�
�
Parameters
ments
coordinated
agent
Aways
to
agent
B).
These
behaviors
are
observed
from
parHow
discriminative
are
our
representations?
That
is,
do
Intelligence
Conference.
Determining
Parameters
events,
as
well
as
post-analysis
for
prominent
television
and
this
data
has
been
widely
used,
there
are
no
systems
which
fixed
to
oneto
team.
Unless
has
the
same
number
of
agents
(11).
We
refer
to
team
a�
discrete
random
variable
X(3)
that
has
aonline
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
events.
Each
team
plays
38corners,
games
each,
which
corresponds
Modeling.
Modeling.
In
Inte
In
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
Modeling.
In
Modeling.
Modeling.
International
In
InModeling.
International
International
In
Modeling.
In
In
International
In
International
International
In
Internationa
In Internati
Joint
Internati
InInIn
Joint
Inter
Joint
Co
In
Jo
is
currently
used
for
the
real-time
visualizatio
corners,
offsides,
substitutions
and
stoppages.
An
example
ways
has
the
same
number
of
agents
(11).
refer
toH(Y
team
currently
used
for
the
real-time
online
visualizat
soccer,
each
agent
isof
permanently
fixed
toWe
one
team.
Unless
aly
set
ofoffixed
agents
having
a shared
oby∈Y
tionpX
=(p1,...,pn)isthendefinedas:
How
discriminative
are
our
representations?
That
is,
do
anently
one team.
Unless
corners,
offsides,
substitutions
and
stoppages.
A
this
feed.
The
type
events
listed
are:
goals,
shots,
passes
tionpX
=(p1,...,pn)isthendefinedas:
H(Y
H(Y
H(Y
)−
)=
=
)p(y)
=
−
−
p(y)
log
log
p(y)
p(y)
(3)
(3)
H(Y
H(Y
)H(Y
=
H(Y
) H(Y
=
)teams
−=
H(Y
)−
)H(Y
=
−
)=
H(Y
H(Y
=
−
)have
p(y)
−
=
)−
p(y)
)=
p(y)
−
)is
=
log
p(y)
p(y)
log
−
=
log
−
−
p(y)
p(y)
log
log
p(y)
p(y)
log
p(y)
p(y)
log
p(y)
p(y)
p(y)
log
log
p(y)
log
p(y)
log
p(y)
p(y)
(3)
p(y)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
offsides,
substitutions
and
stoppages.
An
example
Mutual
Information
Determining
Parameters
The
information
content,
namely
(Shannons)
entropy
unique
styles
of
play?
And
if
so,
can
we
detect
Intelligence
Intelligence
Confer
Conf
Intelligence
Intelligence
Intelligence
Intelligence
Intelligence
Intelligence
Intelligence
Conference.
Intelligence
Intelligence
Conference.
Conference.
Intelligence
Intelligence
Conference.
Conference.
Conference.
Conference.
Conference
Confere
Conf
Li,
R.,
and
Chellappa,
R.Conference
2010.
Gro
�
�
tionpX
=(p1,...,pn)isthendefinedas:
tial
spatio-temporal
tracings,
which
in
this
case
refers
to
ball
How
discriminative
are
our
representations?
That
is,
do
number
of
play-segments
for
a
possession,
and
M
is
the
toIn
[85],
Shannon
uses
probability
theory
to
model
inforHow
discriminative
are
our
representations?
That
is,
do
eam
(e.g.
pass
from
use
this
data
or
data
like
this
for
automatic
tactical
analysis.
behaviors,
B,
as
short,
observable
segments
of
coordinated
teams
have
unique
styles
of
play?
And
if
so,
can
we
detect
newspaper
entities
(e.g.
ESPN,
The
Guardian).
Even
though
with
each
team
playing
each
other
team
twice
(once
home
behaviors,
B,
as
short,
observable
segments
of
coordinated
events,
as
well
as
post-analysis
for
prominent
televisio
om
the
match,
each
team
al�
In
[85],
Shannon
uses
probability
theory
to
model
infory∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
y∈Y
events,
as
well
as
post-analysis
for
prominent
televisi
In
[85],
Shannon
uses
probability
theory
to
model
inforof
the
data
feed
is
given
in
Figure
5(a).
This
type
of
data
an
agent
has
been
dismissed
from
the
match,
each
team
alof
the
data
feed
is
given
in
Figure
5(a).
This
ty
tal from
state (?).
As we are
with of the
ed
the match,
eachdealing
team ala
discrete
random
variable
X
that
has
a
probabilitydistrib
when
they
deviate
from
this
style
and
quantify
it?
(with
start/end
point),
tackles,
clearances,
cards,
kicks,
data
feed
is
given
in
Figure
5(a).
This
type
H(X,
Y ) of
=free
−data
p(x,
y)
log
p(x,
y)
(4)
Using
a
Spatio-Temporal
Driving
F
How
discriminative
are
our
representations?
That
is,
do
teams
have
unique
styles
ofproduced
And
ifaby
so,
can
we
detect
teams
have
unique
styles
of
play?
And
if
so,
can
we
detect
Li,
Li,
R.,
R.,
and
and
Chellap
Chella
Li,
Li,
R.,
Li,
R.,
and
Li,
R.,
and
R.,
and
Li,
Chellappa,
R.,
Li,
and
Chellappa,
R.,
Li,
Chellappa,
and
and
R.,
Li,
and
R.,
Chellappa,
Chellappa,
Li,
Chellappa,
and
R.,
and
Chellappa,
R.
R.,
and
Chellappa,
2010.
Chellappa,
R.
R.
and
2010.
Chellapp
2010.
R.
R.
Chella
Group
R.
2010.
R.
2010
201
Gro
Gr
20
R
RT
In
[85],
Shannon
uses
probability
theory
to
model
infor�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
H(X)
=
−
p(x)
log
mation
sources,
i.e.,
the
data
produced
by
aLi,
source
is
treated
when
they
deviate
from
this
style
and
quantify
it?
movement
infer
from
hand-annotated
ball-action
(see
tal
number
of play-segments
for
a
team
over
aplay?
match.
Given
mation
sources,
i.e.,
the
data
by
source
is
treated
For
our
work
we
used
the
2010-2011
EPL
season
F24
and
action
executed
byof
a agents
team
(e.g.
pass
from
mation
sources,
i.e.,
the
data
produced
aGuardian).
source
is
treated
movement
and
action
executed
by
a data
team
(e.g.
pass
from
once
The
team
names
and
rankings
for
the
2010observed
from
parentities
(e.g.
ESPN,
The
Even
th
newspaper
entities
(e.g.
ESPN,
The
Guardian).
Even
data
has
been
widely
used,
there
are
no
systems
which
tionpX
=(p1,...,pn)isthendefinedas:
gents
(11).fixed
Weand
refer
toaway).
team
ways
has
the
same
number
(11).
We
refer
to
team
ismovement
currently
used
for
the
real-time
online
visualizations
of
x∈X
y∈Y
is
currently
used
for
the
real-time
visua
H(X,
H(X,
H(X,
YY−
))−
Y
=
=
)p(x,
=
−
−p(x,
p(x,
p(x,
y)
y)
log
log
p(x,
p(x,
y)
y)
(4)
(4)
H(X,
H(X,
H(X,
H(X,
YH(X,
)Y
H(X,
=
Y
)H(X,
Y
=
)H(X,
−Y=
)H(X,
−
Y
H(X,
)=
−
)Y
=of
=
−
Y)a−Y
=
)−
Ynewspaper
)=
)p(x,
=
=p(x,
−
−
y)
−
p(x,
y)
p(x,
log
y)
log
p(x,
p(x,
log
y)
y)
p(x,
y)
p(x,
p(x,
log
p(x,
y)
y)
log
p(x,
p(x,
y)
p(x,
log
y)
y)
y)
log
y)
log
p(x,
y)
y)
y)
log
(4)
p(x,
p(x,
log
y)
(4)
p(x,
(4)
y)
p(x,
y)
(4)
(4)
(4)
y)
y)
(4)
(4)
(4)
(4)
(4)
teams
have
unique
styles
of
play?
And
can
we
detect
remanently
of
agents
(11).
refer
to this
team
Using
Spatio-Tem
aSpatio-Te
Spatio-T
Using
Using
Using
aUsing
Spatio-Temporal
Using
aManya,
aUsing
Spatio-Temporal
Spatio-Temporal
Using
aUsing
aif
Spatio-Temporal
Spatio-Temporal
Using
aso,
Spatio-Temporal
Using
aUsing
aonline
Spatio-Tempora
Spatio-Tempora
aaDriving
Spatio-Tem
ais
Driving
Driving
Drivi
Forc
Driv
Dr
D
toWe
one
team.
Unless
when
they
deviate
from
this
style
and
quantify
it?
when
they
deviate
from
this
style
and
quantify
it?
Li,
C.;
F.;
Mohamedou,
N
is
currently
used
for
the
real-time
online
visualizations
corners,
offsides,
substitutions
and
stoppages.
An
example
mation
sources,
i.e.,
the
data
produced
by
aSpatio-Temporal
source
treated
x∈X
as
random
variable.
The
information
content,
namely
as
a
random
variable.
The
information
content,
namely
as
a
random
variable.
The
information
content,
namely
that
a
team’s
possession
string
is
of
length
T
,
the
resultnext
subsection).
Mutual
Information
1
agent
A
to
agent
B).
These
behaviors
are
observed
from
parOpta
feed,
which
consists
of
380
games
and
more
than
agent
A
to
agent
B).
These
behaviors
are
observed
from
par2011
EPL
data
is
given
in
Table
1.
In
our
approach,
to
this
data
has
been
widely
used,
there
are
no
systems
In
[85],
Shannon
uses
probability
theory
to
model
info
this
data
has
been
widely
used,
there
are
no
systems
w
when
they
deviate
from
this
style
and
quantify
it?
x∈X
x∈X
x∈X
y∈Y
y∈Y
y∈Y
x∈X
x∈X
x∈X
y∈Y
x∈X
y∈Y
x∈X
x∈X
y∈Y
x∈X
y∈Y
y∈Y
x∈X
y∈Y
x∈X
y∈Y
x∈X
x∈X
y∈Y
y∈Y
y∈Y
y∈Y
his
refers
tocoordinated
ball
behaviors,
B, post-analysis
as is
short,
observable
segments
of coordinated
Cycle
Structures
inMoh
M
use this
dataevents,
orofas
data
like
this
for
automatic
tactical
analysis.
Mutual
Information
ble
segments
ofmatch,
well
as The
post-analysis
for
prominent
tel
�
Li,
Li,
C.;
C.;
Manya,
Manya,
F.;
Li,Exploiting
Li,
C.;
Li, C.;
Li,
C.;
Manya,
Li,
Li,
Manya,
C.;
Manya,
C.;
Li,
Li,
C.;
Manya,
F.;
Manya,
Manya,
Li,
C.;
C.;
Manya,
Li,
F.;
Mohamedou,
F.;
C.;
Manya,
Manya,
Mohamedou,
C.;
F.;
Mohamedou,
F.;
Manya,
F.;
Mohamedo
F.;
Manya,
Mohamed
Mohame
F.;
F.;
Moham
N.;
Moh
F.;
FF
N
as
aevents,
random
variable.
information
content,
namely
events,
well
as
post-analysis
for
prominent
television
and
servable
segments
of coordinated
(Shannons)
entropy
ofas
ay)
discrete
random
variable
X
that
has
as
well
as
for
prominent
television
and
ssedcase
from
theanalyze
each
team
al�
the
data
feed
given
in
Figure
5(a).
This
type
of
data
(Shannons)
entropy
of
a
discrete
random
variable
X
that
has
(Shannons)
entropy
of
a
discrete
random
variable
X
that
has
�
�
�
ing
number
of
play-segments
for
each
possession
is
therefore:
p(x,
mation
sources,
i.e.,
the
data
produced
by
a
source
is
treat
tial
tracings,
which
incase
this
case
refers
to
ball
A
plan
can
bespatio-temporal
defined
as
anaction
ordered
sequence
ofteam
team
Mutual
Information
tional
Conference
on
Theory
and
H(X)
=
−
p(x)
log
p(x)
(2)
Mutual
Information
use
this
data
or
data
like
this
for
automatic
tactical
an
760,000
events.
Each
team
plays
38
games
each,
which
the
tactics
of
a
team
we
are
required
to
know
the
tial
spatio-temporal
tracings,
which
in
this
refers
to
ball
Exploiting
Exploiting
Cycle
Cycle
Exploiting
Exploiting
Exploiting
Exploiting
Exploiting
Exploiting
Exploiting
Cycle
Exploiting
Exploiting
Cycle
Cycle
Exploiting
Structures
Cycle
Exploiting
Cycle
Cycle
Structures
Cycle
Structures
Cycle
Cycle
Structures
Structures
Structure
Cycle
Structur
in
Cycle
Struc
Struc
MAX
in
in
S
M
i
use
this
data
or
data
like
this
for
automatic
tactical
ana
movement
and
executed
by
a
(e.g.
pass
from
H(Y
)
=
−
p(y)
log
pM
(Shannons)
entropy
of
a
discrete
random
variable
X
that
has
ball-action
data
(see
I(X;
Y
)
=
−
p(x,
y)
log
(5)
newspaper
entities
(e.g.
ESPN,
The
Guardian).
E
a
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
H(X)
=
−
p(x)
log
p(x)
(2)
�
For
our
work
we
used
the
2010-2011
EPL
season
F24
by
a
team
(e.g.
pass
from
�
cuted
by
a
team
(e.g.
pass
from
a
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
a
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
newspaper
entities
(e.g.
ESPN,
The
Guardian).
Even
though
newspaper
entities
(e.g.
ESPN,
The
Guardian).
Even
though
ber of agents (11).
We ofrefer
team
p(x,
p(x,
y)
y)
p(x,
p(x,
p(x,
y)
p(x,
p(x,
y)
p(x,
y)variable.
p(x,
y)
y)
p(x,
y)
p(x,
y)
p(x,
y)
p(x,
y)
y)
y)
bility
Testing.
Mutual
Information
as
a each
random
The
information
content,
name
ismovement
currently
used
forThese
the
online
visualizations
of
p(x)p(y)
tional
tional
Conference
Conferenc
tional
tional
tional
Conference
tional
tional
Conference
Conference
tional
tional
Conference
tional
Conference
Conference
tional
Conference
on
tional
Conference
Conference
on
Theory
on
Conference
Theory
on
Theory
Conference
on
on
Theory
on
and
Theory
Theor
on
Theo
on
and
and
Ap
TTo
x∈X
=I(X;
(T
TY)data
))I(X;
1.
If
possession
string
is
smaller
in
durainfer
from
hand-annotated
1I(X;
behaviors
describing
atofrom
recipe
used
byitareal-time
team
toNball-action
achieve
For
our
work
we
used
the
2010-2011
EPL
seaso
position
the to
ball
and movement
which
team
has
possession
of
at
corresponds
with
team
playing
each
other
team
twice
infer
hand-annotated
ball-action
data
(see
H(X)
=
−
p(x)
log
p(x)
(2)
y∈Y
a=p(x,
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
H(X)
=log
−
p(x)
log
p(x)
(2)
YY−
)−
)Ywhere
)p(x,
=
=
−
−
p(x,
p(x,
y)
y)
log
log
I(X;
I(X;
Y−
I(X;
Y
)I(X;
I(X;
Y
=
Y+
=
)Y
I(X;
)=
I(X;
−
I(X;
)(see
Y=−
Y
=
)I(X;
−
=
Y
)Ywhere
−
)=
)the
=
=−
=
−
p(x,
−
−
y)
−
p(x,
y)
p(x,
log
p(x,
y)
log
p(x,
log
y)
y)
p(x,
y)
p(x,
log
y)
log
p(x,
p(x,
y)
log
y)
log
y)
log
y)
log
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
x∈X
y∈Y
For
our
work
we
used
the
2010-2011
EPL
season
�
x∈X
0
log
=
0
and
the
base
of
the
logarithm
determines
agent
A
agent
B).
behaviors
are
observed
from
parwhere
0
log
=
0
and
the
base
of
the
logarithm
determines
this
data
has
been
widely
used,
there
are
no
sys
0
log
=
0
and
the
base
of
the
logarithm
determines
�
feed,
which
ofas
380
games
and
more
thanTtelevision
bility
bility
Testing.
Testing.
bility
bility
bility
Testing.
bility
bility
Testing.
Testing.
bility
Testing.
bility
bility
Testing.
Testing.
Testing.
bility
Testing.
bility
Testing.
Testing.
viors
are observed
from
par-Opta
behaviors
are
observed
par(Shannons)
entropy
of
a−
discrete
random
variable
X
that
h
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
p(x)p(y)
this
data
hasconsists
been
widely
there
areare
nonosystems
which
this
data
has
been
widely
used,
there
systems
which
Li,
R.;
Chellappa,
R.;Testing.
and
Zhou,
observable
segments
of from
coordinated
next
subsection).
tion
than
, =we
discard
it.
To
represent
each
play-segment
x∈X
H(X)
=
p(x)
log
p(x)
(2)S.
asdo
well
post-analysis
for
prominent
and
�
x∈X
x∈X
x∈X
y∈Y
y∈Y
x∈X
x∈X
x∈X
y∈Y
x∈X
y∈Y
x∈X
x∈X
y∈Y
x∈X
y∈Y
y∈Y
x∈X
y∈Y
x∈X
y∈Y
x∈X
x∈X
y∈Y
y∈Y
y∈Y
y∈Y
Opta
feed,
which
consists
of
380
games
and
mor
a goal
(?).
Aevents,
team
performing
a used,
group
ofwhich
these
plans
to
where
0if
log
=2measure
0the
and
the
base
of
the
logarithm
determines
x∈X
every time
step (i.e.
every
second).
To
this,
we
infer
the
(once
home
once
away).
The
team
names
and
ranking
next
subsection).
the
unit,
e.g.
base
2base
is
inLi,
bits,
if
its
the
natural
H(X)
+
H(Y
)and
−
H(X,
Y
)the
�
�
H(Y
)y∈Y
=
−
p(y)
log
p(y)
(3)
Opta
feed,
which
consists
of
380
games
and
more
the
unit,
e.g.
measure
is
in
bits,
if
its
the
natural
the
unit,
e.g.
if
base
2data
the
measure
is
in
bits,
if
its
the
natural
tial
spatio-temporal
tracings,
in
thistactical
case
refers
to
ball
this
or
data
like
this
for
automatic
tactic
Modal
Densities
on
Discriminativ
aifuse
probabilitydistributionpX
=(p1,...,pn)isthendefinedas:
Li,
Li,
R.;
Chellappa,
Chellappa
Li,
R.;
Li,
R.;
Li,
Chellappa,
R.;
Li,
Chellappa,
R.;
Li,
Chellappa,
R.;
Li,
Li,
R.;
Chellappa,
Chellappa,
Chellappa,
R.;
Li,
R.;
Chellappa,
R.;
Li,
Chellappa,
R.;
Chellappa,
R.;
and
R.;
R.;
Chellappa,
and
R.;
and
Zhou,
Chellappa
R.;
R.;
R.;
and
Zhou,
Zhou,
and
and
R.;
R.;
and
S.
Zho
Zh
an
Z
a2R
SS
H(Y
))Y
=
−
p(y)
log
p(y)
(3)
�
dichsequence
team
gs,
which
incase
this
case
refers
to
ball
760,000
events.
Each
team
plays
38
games
each,
which
in this
refers
to
ball
�
use
this
data
or
data
like
this
for
automatic
analysis.
x∈X
use
this
data
or
data
like
this
for
automatic
tactical
analysis.
H(X,
Y
)
=
−
p(x,
y)
s
=
{s
,
.
.
.
,
s
},
the
quantized
ball
position
is
tabulated
the
unit,
e.g.
if
base
2
the
measure
is
in
bits,
if
its
the
natural
A
plan
can
be
defined
as
an
ordered
sequence
of
team
=
=
=
H(X)
H(X)
+
+
H(Y
H(Y
)
−
)
−
H(X,
H(X,
Y
)
Y
)
=
=
=
H(X)
=
H(X)
=
H(X)
=
H(X)
=
+
H(X)
=
H(X)
+
H(Y
=
H(X)
+
=
H(Y
H(X)
+
H(Y
+
H(X)
)
+
H(X)
H(Y
−
H(Y
H(X)
)
+
H(Y
)
−
H(X,
+
−
H(Y
+
H(X,
)
)
H(Y
H(X,
+
−
)
−
H(Y
+
−
Y
H(Y
)
H(X,
H(Y
−
)
H(X,
)
Y
−
H(X,
)
−
)
H(X,
Y
)
−
H(X,
Y
−
)
H(X,
)
Y
H(X,
)
Y
Y
)
)
Y
Y
)
)
xecuted
by
aof
team
(e.g.
pass
from
760,000
events.
Each
team
plays
38
games
each,
0
T
−1
e then
its
in in
nats,
The
term
log
1/pi
indicates
aAmajor
goal
(e.g.
winning
ahand-annotated
match),
can
beball-action
saidof team
ball location fromachieve
the data
feed.
We be
describe
our
y∈Y
number
ewhere
then
in
nats,
etc.
The
term
log
1/pi
indicates
newspaper
entities
(e.g.
ESPN,
Guardian).
Even
though
fornumber
the
2010-2011
EPL
data
is
given
in
Table
1.
number
e then
its
nats,
The
term
log
1/pi
indicates
plan
can
defined
as method
an
orderedThe
sequence
Manifold
for
Group
Activity
Recog
Modal
Modal
Densities
Densities
o
Modal
Modal
Modal
Modal
Densities
Modal
Modal
Densities
Densities
Modal
Modal
Densities
Densities
Densities
Modal
on
Densities
Modal
Densities
on
Densities
Discriminative
on
Densities
Discriminati
on
Discriminat
on
Densities
on
on
Discrimi
Discrim
Discri
on
on
Discr
D
o
Dw
760,000
events.
Each
team
plays
38
games
each,
H(Y
)−
=and
−
p(y)
log
p(y)
(3)
movement
infer
from
data
(see
0its
log
=etc.
0etc.
the
base
of
the
logarithm
determin
y∈Y
H(Y
)
=
p(y)
log
p(y)
(3)
For
our
work
we
used
the
2010-2011
EPL
�
x∈X
y∈Y
d-annotated
ball-action
data
(see
number
e
then
its
in
nats,
etc.
The
term
log
1/pi
indicates
yse
abehaviors
team
to are
achieve
corresponds
each
team
playing
each
other
team
twice
otated
ball-action
data 2.
(see
For
our
work
we
used
the
EPL
season
F24
behaviors
describing
athe
recipe
aeach
team
tosystems
achieve
the
amount
of
uncertainty
with
the
atEPL
time
step.
An
example
of
description
is
given
in
the
amount
of the
uncertainty
associated
with
the
corresponding
corresponds
each
team
playing
each
other
team
Manifold
Manifold
for
for
Grou
Gro
Manifold
Manifold
Manifold
Manifold
Manifold
Manifold
for
Manifold
for
Group
Manifold
for
Manifold
Group
for
Manifold
Group
for
for
Manifold
Activity
Group
for
Group
Group
Activity
for
Group
Activity
Group
for
Activity
Group
Activity
Recognit
for
Activity
Activit
Group
Reco
Reco
Gro
Act
AcR
Forwith
our
work
we
used
2010-2011
season
F24
the
amount
ofunit,
uncertainty
associated
with
the
corresponding
via observed
Figure
At
t0partheemploying
ball
is
passed
to
the
at
t2010-2011
to
be
tactics.
However,
as
soccer
is low-scoring,
from
y∈Y
1 .used
Molineaux,
M.
2008.
Working
Spe
To
analyze
the
tactics
of
a
team,
we
require
to
know
where
this
data
has
been
widely
used,
there
are
no
which
behaviors
describing
alocation
recipe
used
by
a by
team
to
achieve
H(Y
)y∈Y
=the
−
p(y)
log
p(y)
(3)
the
e.g.with
ifassociated
base
2team
measure
iscorresponding
in
bits,
iffor
its
the
natur
corresponds
with
each
playing
each
other
team
next
subsection).
Opta
feed,
which
consists
of
380
games
and
the
amount
ofalso
uncertainty
associated
with
the
corresponding
Summary
and
Future
Work
outcome.
It
can
also
be
viewed
asas
the
amount
of
information
outcome.
It
can
beits
viewed
asy∈Y
the
amount
of
information
goal
(?).
Aconsists
team
performing
agames
group
of
these
plans
to
outcome.
It
can
also
be
viewed
the
amount
of
information
3.
Molineaux,
Molineaux,
M.
M.
200
2W
Molineaux,
Molineaux,
Molineaux,
Molineaux,
Molineaux,
Molineaux,
Molineaux,
M.
Molineaux,
Molineaux,
M.
2008.
M.
Molineaux,
2008.
M.
Molineaux,
2008.
M.
M.
Working
M.
2008.
2008.
2008.
M.
Working
Working
M.
2008.
Working
2008.
M.
2008.
Workin
Specifi
Work
M.
Work
200
Sp
Sp
20
W
up
theseinplans
to refers
(once
home
and
once
away).
The
team
names
and
r
Interface.
Technical
report,
Knexus
Opta
feed,
which
consists
of
380
games
and
more
than
(once
home
and
once
away).
The
team
names
and
ranking
The
action
labeled
at
ta4(?).
where
a player
takes
an
number
eWork
then
in
nats,
etc.
The
term
log
1/pi
indicat
continuous
and
complex
due
to
the
various
multi-agent
inOpta
feed,
ofonthis
and
more
than
the
ball
is
and
who
has
possession
of
it
at
every
time
step
(i.e.
ngs,ofwhich
this next
case
to
ball
aisgoal
Aplan
team
a380
group
ofFigure
these
plans
toSummary
(once
home
and
once
away).
The
team
names
and
ra
use
this
data
orperforming
data
like
for
automatic
tactical
analysis.
Summary
Summary
Summary
and
and
Future
Future
Work
Summary
Summary
Summary
Summary
Summary
Summary
Summary
and
Summary
Summary
and
and
Future
and
and
Future
and
Future
and
Future
and
Future
Future
and
Work
and
Future
and
Work
Future
Work
Future
Future
Work
Future
Work
Work
Work
Work
Work
Awhich
can
be
defined
as
an
ordered
of
team
outcome.
It
can
also
beWork
viewed
as
the
amount
of
760,000
events.
Each
team
plays
38
games
e
gained
by
observing
that
outcome.
Thus,
entropy
isinformation
merely
gained
by
observing
that
outcome.
Thus,
entropy
is
merely
Interface.
Interface.
Technica
Techni
Interface.
Interface.
Interface.
Interface.
Interface.
Interface.
Technical
Interface.
Interface.
Technical
Technical
Interface.
Interface.
Technical
Technical
Technical
Interface.
report,
Technical
report,
Technical
report,
Technical
report,
Knexus
Technical
report,
report,
Technic
Knexu
report,
Knexu
rep
rep
Kn
R
K
To
Do sequence
gained
by
observing
that
outcome.
Thus,
entropy
is
merely
achieve
a
major
goal
(e.g.
winning
a
match),
can
be
said
Opta.
2012.
www.optasports.
for
the
2010-2011
EPL
data
is
given
in
Table
1.
From
our
set
of
play-segments
for
a
given
team,
S
or
S
,
the
amount
of
uncertainty
associated
with
the
correspondi
as
an
ordered
sequence
of
team
A
B
760,000
events.
Each
team
plays
38
games
each,
which
match),
can
be
said
opposition
player.
As
nothing
occurred
between
the
time
t
forteractions,
the
EPL
is(e.g.
given
Table
1.
labeling
and
segmenting
the
game
into
series
1 a38
ordered sequence
of team
every
Tobyaverage
do
this,
we
the
ball
location
from
760,000
events.
Each
team
plays
games
each,
which
achieve
aFor
major
goal
match),
can
be
said
for
theaverage
2010-2011
data
isOpta.
given
in
Table
1.
and-annotated
ball-action
data
(see2010-2011
gained
observing
thatinfer
outcome.
Thus,
entropy
iswww.opta
merely
To
To
Do
Doa statistical
Toa
ToDo
To
To
Do
To
Do
To
Do
To
Do
ToDo
To
To
Do
To
Do
Do
Do
a statistical
ofEPL
uncertainty
information.
describing
ain
recipe
used
by
aDo
team
to
achieve
ourdata
work
we winning
used
the
2010-2011
EPL
F24
ofItof
uncertainty
or
information.
corresponds
with
team
playing
each
other
Opta.
Opta.
2012.
2012.
www.
www
Opta.
Opta.
2012.
Opta.
Opta.
2012.
2012.
Opta.
www.optasports.co
Opta.
2012.
Opta.
2012.
2012.
www.optasports.
www.optasports
2012.
Opta.
Opta.
2012.
www.optaspor
2012.
www.optaspo
www.optasp
www.optasp
2012.
2012.
www.opt
www.o
www
asecond).
statistical
average
uncertainty
orRiley,
information.
outcome.
can
also
beeach
viewed
as
the
amount
of
informati
tobehaviors
be employing
tactics.
However,
aseach
soccer
is
low-scoring,
P.,
and
Veloso,
M.
To
analyze
the
tactics
of
aor
team,
we
require
to2002.
know
we
can
build
aseason
distribution
to
characterize
the
expected
becipe used
a team
toinfer
achieve
and
t4 , achieve
we
the
ball
dribbled
inwith
aeach
straight
line
and
each
team
playing
other
team
twice
of plans
iscorresponds
difficult.
Hence
recognizing
team
tacoccer
is low-scoring,
a statistical
average
of
uncertainty
or
information.
the
data
feed.
The
method
of
doing
this
is
best
described
in
To
analyze
the
tactics
of
a
team,
we
require
to
know
where
towas
beextremely
employing
tactics.
However,
as
soccer
is
low-scoring,
used
by
a by
team
to
To
analyze
the
tactics
of
a
team,
we
require
to
know
corresponds
with
team
playing
each
other
team
twice
�
Riley,
Riley,
P.,
P.,
and
and
Velo
Ve
Riley,
Riley,
Riley,
P.,
Riley,
Riley,
P.,
and
P.,
Riley,
and
Riley,
and
P.,
Riley,
Veloso,
P.,
P.,
and
Riley,
P.,
Veloso,
Veloso,
and
and
Riley,
P.,
and
P.,
Veloso,
M.
Veloso,
Veloso,
and
and
P.,
Veloso,
M.
P.,
M.
2002.
and
Veloso,
Veloso,
and
M.
2002.
M.
2002.
Velos
M.
M.
Ve
200
Re
20
M
M
2
�
a
goal
(?).
A
team
performing
a
group
of
these
plans
to
tic
Opponent
Movement
Models.
�
(once
home
and
once
away).
The
team
names
aw
gained
by
observing
that
outcome.
Thus,
entropy
is
mere
Opta
feed,
which
consists
of
380
games
and
more
than
continuous
and
complex
due
to
the
various
multi-agent
inthe
ball
is
and
who
has
possession
of
it
at
every
time
st
havior
in
each
location.
We
do
this
as
follows:
Given
the
a inuniform
velocity
between
these
two
locations.
We
dovarious
rming
a group
of
these
to
(once
home
and
once
away).
The
team
names
and
ranking
H(X)
= p(x)
p(x)
log
p(x)
(1)Move
thewho
MAPR
framework
we
described
previously
isand
tic
tic
Opponent
Opponent
Mov
Mo
tic
tic
Opponent
tic
Opponent
Opponent
tic
ticTadorokoro,
Opponent
tic
Opponent
Opponent
tic
Movement
Opponent
tic
Opponent
Movement
tic
Opponent
Movement
tic
Opponent
Movement
Movement
Opponent
Movement
Movement
Models.
Movemen
Movemen
Models.
Models.
Mode
Mod
Mo
In
Mo
M
�
H(X)
=
log
p(x)
(1)
Figure
5(b).
rious
multi-agent
S.;
and
S.,
eds.,
RoboC
H(X)
=has
p(x)
log
p(x)
(1)
and
complex
due
to
the
multi-agent
inthetics
ballusing
iscontinuous
and
has
possession
of
it
at
every
time
step
(i.e.
the
ball
is
and
who
possession
of
it
at
every
time
ste
of at
these
plansplans
to
a
statistical
average
of
uncertainty
or
information.
(once
home
and
once
away).
The
team
names
ranking
achieve
a
major
goal
(e.g.
winning
a
match),
can
be
said
for
the
2010-2011
EPL
data
is
given
in
Table
1.
d. awinning
asgroup
an
ordered
sequence
of
team
teractions,
labeling
and
segmenting
the
game
into
a
series
760,000
events.
Each
team
plays
38 games
each,
whichwe
every
second).H(X)
To
do
this,
infer
the
ball
locatio
observations
of a team,
determine
the
of
playS.;
S.;
and
and
Tadorokoro
Tadoroko
S.;World
S.;
and
S.;we
and
S.;
and
Tadorokoro,
S.;
and
S.;
Tadorokoro,
Tadorokoro,
and
S.;
and
S.;
Tadorokoro,
Tadorokoro,
Tadorokoro,
and
S.;
and
Tadorokoro,
S.;
S.,
and
Tadorokoro,
Tadorokoro,
and
S.,
eds.,
S.,
Tadorokoro,
eds.,
Tadoroko
S.,
eds.,
S.,
RoboCu
S.,
eds.,
S.,
eds.,
Robo
Robo
eds.
S.,
eds
S.,R
=subset
p(x)
log
p(x)
(1)
the
samecan
thing
between
t5 for
and
t ,2010-2011
before
the
ball
is passed
Cup
V.
Springer
Verlag.
a match),
be said
x∈X
impossible
without
these
labelled
plans.
the
data
is given
in
Table
1.is
x∈Xx∈X
teractions,
labeling
and
segmenting
theinlocation
game
into
a series
ening
game
into
aby
series
every
ToThe
do
this,
we
infer
the
ball
location
second).
To
do
this,
weEPL
infer
ball
to6plans
be
employing
tactics.
However,
as
soccer
low-scoring,
�
a used
match),
can
belocation
said
the
2010-2011
EPL
data
isthe
given
Table
1.from
Toinfeed.
analyze
the
tactics
of
aCup
team,
we
require
to
of
issame
extremely
difficult.
Hence
recognizing
team
tac- twice
World
World
Cup
Cup
V.
Sprin
Spk
World
World
World
Cup
World
World
Cup
World
V.World
Cup
Springer
World
V.
Cup
V.
Cup
World
Springer
Cup
Springer
V.
World
V.
Cup
V.
Cup
Springer
V.
Springer
Springer
Verlag.
Cup
Springer
V.
V.
Cup
Verlag.
Verlag.
Springer
Springer
V.V.
Verlag.
V.
Verlag
Sprin
Verla
Ver
Spr
V
thesecond).
data
method
of
doing
this
is
best
descr
recipe
a isthe
team
to every
achieve
corresponds
with
each
team
playing
each
other
team
x∈X
segments
S
,
which
originated
quantized
area
d.
From
d
from
atTo
t6 for
to
t
.
Using
the
procedure,
we
7
owever,
as
soccer
low-scoring,
overcome
issue,
we
quantize
aismatch
into
equal
To
analyze
theand
tactics
ofthis
aHence
team,
we
require
to
know
where
H(X)
=via
p(x) log
(
ofToplans
isthis
extremely
difficult.
team
tacthe
data
feed.
The
method
ofpossession
doing
thisp(x)
isMaps
best
describ
Measuring
Team
Tactics
Entropy
Analysis
Using
Entropy
Maps
ecognizing
team
taccontinuous
complex
due
torecognizing
thedescribed
various
multi-agent
intics
using
the
MAPR
framework
we
previously
is
the
data
feed.
The
method
of
doing
best
described
in
the
ball
is
and
who
has
of
it
at
every
tim
Analysis
Using
Entropy
Maps
er, as soccer
is
low-scoring,
Analysis
Using
Entropy
Maps
Figure
5(b).
analyze
the
tactics
of
a
team,
we
require
to
know
where
the
play-segment
vectors
within
S
,
we
keep
a
count
of
the
forming
a
group
of
these
plans
to
d
(once
home
and
once
away).
The
team
names
and
ranking
can estimate
the inball position
andthe
possession
for we
thedescribed
x∈X
due
to the
various
multi-agent
temporal
chunks
which
we
use
describe
team
behavior.
ball
isteam
and
who
hasto
possession
ofplans.
it at
every
time
step
(i.e. Figure
Analysis
Using
Entropy
Maps
ticsthe
using
MAPR
framework
previously
isa series
5(b).
labeling
and
segmenting
the
game
into
impossible
without
these
labelled
Determining
Parameters
scribed
previously
is can
every
second).
To do
this, these
we infer the ball loc
Figure
5(b).
thewinning
various
inDetermining
Parameters
Determining
Parameters
locations
of
where
the
ball travels
or occupies
during
the
ball
isteractions,
and
who
has
possession
of
itgiven
at
every
time
step
(i.e.
Play-Segment
Representation
remaining
times
asthese
the
stoppages
are
tagged
in
the
data
.g.
amulti-agent
match),
be-As
said
for
the
2010-2011
EPL
data
is
in
Table
1.
segments
do
not
describe
a
method
of
achieving
a
egmenting
the
game
into
a
series
impossible
without
these
labelled
plans.
every
second).
To
do
this,
we
infer
the
ball
location
from
Determining
Parameters
of
plans
is
extremely
difficult.
Hence
recognizing
team
tacTo
overcome
this
issue,
we
quantize
a
match
into
equal
How
discriminative
are
our
representations?
the
data
feed.
The
method
of
doing
this
is do
bestMd
Analysis
Using
Entropy
Maps
.
Measuring
Team
Tactics
via
Entropy
play-segments.
As
this
representation
will
yield
a
very
highHow
discriminative
are
our
representations?
ThatThat
do
How
discriminative
are
our
representations?
That
is, is,
do
nting
the game
intoItis
aisseries
every
second).
this,
weof
infer
the
ball
location
fromin
feed.
worth
noting
here
all
data
isdo
normalized
onto
However,
as
soccer
low-scoring,
To
analyze
tactics
of
a team,
we
to
know
where
specific
goal,
we
dofeed.
notTo
call
them
plans,
but
play-segments.
Given
partial
spatio-temporal
tracings
of
the
team
(i.e.
cult.
Hence
recognizing
team tacTo
overcome
this
issue,
we
quantize
athis
match
intodescribed
equal
thethat
data
The
method
doing
isrequire
best
teams
have
unique
styles
of Tactics
play?
And
if
so,
can
detect
2
How
discriminative
are
our
representations?
That
is,Ma
do
temporal
chunks
which
we
use
to we
describe
team
behavior.
tics
using
thethe
MAPR
framework
described
previously
isthe
Measuring
Team
via
Figure
5(b).
teams
have
unique
styles
ofplay?
play?
And
ifdimenso,
canEntropy
we we
detect
teams
have
unique
styles
of
And
if
so,
can
we
detect
dimensional
feature
vector
(D
),
we
would
prefer
the
eework
a
match
into
equal
Determining
Parameters
a
field
of
size
100
×
100,
with
all
positions
given
for
teams
Hence
recognizing
team
tacthe
data
feed.
method
of
doing
this
isteam
best
described
in
Play-Segment
Representation
Measuring
Team
Tactics
via
Entropy
Maps
due towethedescribed
various previously
multi-agent
when
they
deviate
from
this
style
and
it?can wesegWe
use
these
play-segments
to form
a possession
library
or
playbook
of
ballwhen
movement),
we
chunk
this
signal
upquantify
into
discrete
the
ball
issegments
and
who
has
of
it
at
every
time
step
(i.e.
teams
have
unique
styles
ofand
play?
And
ifit?so,
detect
isintemporal
chunks
which
we
use
to
describe
behavior.
Figure
5(b).The
As
these
do
not
describe
aplans.
method
of
achieving
a
when
they
deviate
from
this
style
quantify
they
deviate
from
this
style
and
quantify
it?
impossible
without
these
labelled
sionality to be D for visualization
purposes.
To
achieve
this, it? That is,
attacking
left is
to
right.
team
behavior.
Representation
kcribe
we described
previously
How
discriminative
are
ourrepresent
representations?
Figure
5(b).
when
they
deviate
from
this
and quantify
play-segments,
Psegments
{p1 , do
pwe
pdo
.not
. issue,
. ,call
pm },
where
m but
isaachieving
the
-Play-Segment
called
play-segments.
Westyle
theseofplaysegmenting
the
game into
a series
abelled
plans.
As these
awe
method
aments
specific
goal,
them
plans,
Given
the
partial
spatio-temporal
tracings
the tea
2 ,not
3 , describe
every
To
do
this,
infer
the
ball
from
To=second).
overcome
this
we
quantize
match
into
equal
Play-Segment
Representation
weof
canplay-segments.
use location
either
the
mean,
median,
mode,
total
count
or ifvia
Mutual
Information
Measuring
Team
Tactics
Entropy
teams
have
unique
styles
of
play?
And
so, can
we dete
ethod
of
achieving
a
�
Mutual
Information
Mutual
Information
d
plans.
number
of unique
play-segments
within
the
playbook.
Using
segments
as
an
occupancy
map
which
describes
which
areas
We
use
these
play-segments
to
form
a
library
or
playbook
of
ball
movement),
we
chunk
this
signal
up
into
discre
goal,
we
do
not
call
them
plans,
but
play-segments.
Given
the
partial
spatio-temporal
tracings
of
the
�
ficult.
Hence recognizing
tac- specific
�
we quantize
a match intoteam
equal
the
data
feed.
The
method
of
doing
this
is
best
described
in
temporal chunks
which
we usevia
to describe
behavior.
Measuring
Team
Tactics
Entropy
Maps
even
an team
entropy
measure Mutual
to when
describe
each
),p(x)
which
will
they
deviate
fromd�
this
style
and
quantify it? (2)team
Information
H(X)
= p(S
−
log
p(x)
H(X)
=
−
p(x)
log
p(x)
(2)
H(X)
=
−
p(x)
log
p(x)
(2)
s,mework
but
play-segments.
Given
the
partial
spatio-temporal
tracings
of
the
team
(i.e.
Play-Segment
Representation
this
playbook
we
can:
of
the
field
the
ball
was
during
that
play-segment.
play-segments,
P
=
{p
,
p
,
p
,
.
.
.
,
p
},
where
m
is
the
ments
called
play-segments.
We
represent
these
quantize
a
match
into
equal
use
these
play-segments
a3 library
or playbook
of
we
chunk
this
signal
up
into
discrete
1form
2describe
m
4. team
OCCUPANCY
MAPS
described
previously
e use to we
describe
behavior. is We
Measuring
Team Tactics
via
Entropy
As these
segments
dotonot
ayield
method
ofMaps
achieving
Figure
5(b).
an occupancy
oraball
teammovement),
behavioralH(X)
map.
Vectorizing
the
x∈X
=−
p(x) log p(x)
(2)
x∈X
x∈X
Play-Segment
Representation
�
number
of
unique
play-segments
within
the
playbook.
Using
segments
as
an
occupancy
map
which
describes
whic
brary
or
playbook
of
ball
movement),
we
chunk
this
signal
up
into
discrete
segplay-segments,
P
=
{p
,
p
,
p
,
.
.
.
,
p
},
where
m
is
the
ments
called
play-segments.
We
represent
these
Mutual
Information
to
describe
team
behavior.
3call them
m plans,
method
of achieving
a tracking specific
�
goal,possession
we 1do 2not inforbut play-segments.
the partial
spatio-temporal
tracings(3)
of th
edescribe
labelledaplans.
�
occupancy
map, gives us ourGiven
D-dimensional
spatiotemporal
Given
we have ball
and team
x∈X
H(Y
)
=
−
p(y)
log
p(y)
�
Play-Segment
Representation
this
playbook
we
can:
of
the
field
the
ball
was
during
that
play-segment.
�
H(Y
)occupancy
=
−
p(y)
logp(y)
p(y)
(3)
of
unique
play-segments
within
thethese
playbook.
H(Y
)=
−H(X)
p(y)
(3)which
as
an
map
which
describes
mmation,
isaachieving
the
called
play-segments.
We
ibe
a where
method
of
aments
m },
We
use
these
play-segments
to form
a library
orUsing
playbook
ofsegments
movement),
we
chunk
thislog
signal
into(3)d(
all
them
plans,
but
play-segments.
Given
the
partial
spatio-temporal
tracings
ofplaythe
team
(i.e.
feature
vector
x.Maps
The
mean ball
occupancy
maps
entropy
we into
can
partition
the ball
tracking
data
intorepresent
pos=using
−log
p(x)
p(x) up
ue,
we
quantize
match
equal- number
H(Y
)y∈Y
=y∈Y
−
p(y)
log
p(y)
Measuring
Team
Tactics
via
Entropy
y∈Y
this
playbook
we can:
of
the
field
the
ball
was
during
that
play-segment.
the
playbook.
Using
segments
as
an
occupancy
map
which
describes
which
areas
x∈X
play-segments,
P
=
{p
,
p
,
p
,
.
.
.
,
p
},
where
m
is
the
ments
called
play-segments.
We
represent
session
strings
(i.e.
continuous
movement
of
the
ball
for
to
describe
each
area
is
shown
in
Figure
4
and
can
give
a
ints
to
form
a
library
or
playbook
of
ball
movement),
we
chunk
this
signal
up
into
discrete
segm
plans,
but
play-segments.
Given
the
partial
spatio-temporal
tracings
of
the
team
(i.e.
1 2 3
m
we use to describe team behavior.
y∈Y
Play-Segment
Representation
number
of
unique
play-segments
the discrete
playbook.
Using patterns.
segments
as an
occupancy
which describes w
aor
team
without
turnover
or- was
stoppage),
where
OAsignal
= Wewithin
dication
of
redundant
The top
ranked
teamsmap
have
ofthe
the field
the
ball
during
that
play-segment.
p2describe
, pa3 ,library
. . . ,apm
},single
where
mof
is
ments
called
play-segments.
represent
these
playorm
playbook
movement),
we
chunk
this
up
into
segot
method
of
achieving
aBball
A
A
B
B
{o
,
.
.
.
,
o
}
and
O
=
{o
,
.
.
.
,
o
}
refer
to
the
poshigher
entropy
over
most
of
the
field
compared
to
the
lower
this
playbook
we
can:
of
the
field
the
ball
was
during
that
ments
within
the
playbook.
Using
segments
as
an
occupancy
map
which
describes
which
areas
0
0
I−1
J−1
,
.
.
.
,
p
},
where
m
is
the
ments
called
play-segments.
We
represent
these
play3call them
m plans, but play-segments.
Given
the partial
spatio-temporal
tracings
of the- this
teamgives
(i.e.an indication that these teams uti- play-segmen
session strings
associated
with
each
team
and
Iwas
−1 and
Jwhich
−1
ranked teams
of
the
field
the
ball
during
that
play-segment.
sents
within
the
playbook.
Using
segments
as
an
occupancy
map
describes
which
areas
to form a are
library
playbook
of
ballWemovement),
we the
chunk
up into
discrete
lize more
options
(i.e.segless predictable) which is intuitive
the or
number
of possessions.
then quantize
fieldthis signal
field
the- ball
wasplay-segments.
during
that play-segment.
pm },D where
m isDthe=ofl the
called
We
represent
play-have more skilled players. As the
1 , p2 , p3 , . . . ,into
as these
teamsthese
normally
bins where
× wments
equal size
areas and
vectorize
egments within
playbook.
as an strings
occupancy
describes
which
areas
frequency
counts
incorporate
temporal information (more
thethe
field
via the Using
columns. As segments
the possession
vary map
in which
means the ball is moving quicker), we used the tolength, we apply a sliding window
of field
length
to quantize
or thatcounts,
of the
theT ball
was during
play-segment.
1
1
1
chunk each possession string, o, into a set of play-segments
S = {s0 , . . . , sN −1 } of equal length, where N is the total
1
1
tal count of entires as the entropy measure normalizes this
information.
7
66
(1) Manchester United
(2) Chelsea
(3) Manchester City
(4) Arsenal
(5) Tottenham
55
44
(6) Liverpool
(7) Everton
(8) Fulham
(9) Aston Villa
(10) Sunderland
33
22
(11) West Bromwich Albion
(12) Newcastle
(13) Stoke City
(14) Bolton
(15) Blackburn
11
0
0
(16) Wigan
(17) Wolverhamption
(18) Birmingham City
(19) Blackpool
(20) West Ham United
Figure 4: The mean entropy maps for each of the twenty English Premier League teams characterizing their
ball movement patterns. The maps have been normalized for teams attacking from left to right. The bright
red refers to high entropy scores (i.e. high variability) and the blue areas refer to low entropy scores (i.e very
predictable behavior).
5.
5.1
STRATEGY ANALYSIS
Discriminating Team Behavior
Evaluating team strategy is a very difficult task. The major hurdle to overcome is the absence of strategy labels. But
given we know the team identity, and assuming that teams
exhibit similar behaviors over time, we can treat the task
as an identification problem. We can do this by answering
the question: using only ball movement information, can we
accurately identify the most likely team?
We model team behavior using a codebook of past performances. If a team’s behavior is consistent, then previous
matches will be a good predictor of future performances. For
the experiments, we used 380 games of the season and used a
leave-one-out cross validation strategy to maximize training
and testing data. Before we investigate the difference between home and away performances, we first need to obtain
the best possible representation. To evaluate this, we wanted
to see how effective event-labeled data was in discriminating
between different teams, and if having knowledge of where
teams operate could boost the discriminating power.
To conduct the experiments, we compared our occupancy
representation, to twenty-three match statistics currently
used in analysis (e.g. passes, shots, tackles, fouls, aerials,
possession, time- in-play etc.). We also combined the two
50
40
30
20
10
0
% Teams Correctly Identified
Statistics
Occ Maps
Combined
Figure 5: The identification rate for correctly identifying home performances using event-labeled data
(i.e. no location information), occupancy maps (i.e.
no event information, just location), and a combination of the two.
inputs by concatenating the feature vectors. For classification, we used a k-Nearest Neighbor approach (with k = 30)
and all experiments were conducted using D = 10 × 8
spatial areas (heuristically, we found those values of k and
D gave the best performance). To reduce the dimensionality
but maintain class separability for the spatiotemporal representation and the combined representation, we used linear
discriminant analysis (LDA). We used the number of teams
1
Actual Team Ranking
20
0
1
Predicted Team Ranking
(a) Home vs Home
20
Figure 6: Confusion matrices of the team identification experiments using the combined representation.
as classes (C = 20), which resulted in a C − 1 = 19 dimensional input feature, y = WT x, where W can be found via
solving
WΣb W
)
(1)
WΣw W
where Σb and Σw are the between-scatter and within-scatter
matrices respectively. To test the various representations,
only identity experiments on home performances were tested
(home and away comparisons will be presented next). Results for these experiments are shown in Figure 5. This figure
illustrates how spatiotemporal data greatly improves the discriminability between different teams (19.26% vs 38.79%),
and fusing traditional and spatiotemporal statistics boosts
performances again (46.70%). The confusion matrix of the
combined representation shows that teams who play a similar style often get confused with each other (e.g. the top 5
teams and teams 13-15) and from viewing the entropy maps
in Figure 4, we can see that these teams have similar characteristics.
arg max Tr(
W
5.2
Exp
HvH
HvA
AvA
AvH
18
Comparing Home vs Away Behavior
If a team plays in the same manner at home as they do
away, the home model should be able to yield similar performance in identifying away matches as they do to the home
matches. To test this theory, we used our home models to
identify away performances and our away models to identify
home performances. From the results (see Table 2), we can
see that there is a drop in the hit-rate of the occupancy map
representation – 8.69% for the home model tested on the
away matches and 6.07% on the reverse case. Even though
not excessive, this drop in performance suggests there is a
change in the spatial behavior between home and away performances.
To explore this aspect further, we visualized the difference
in occupancy between the home and away performances. To
do this, we simply subtracted the home occupancy maps
from the away maps and divided by the away occupancy to
obtain a relative measure. The difference maps for all twenty
Event-Labeled
19.26
16.09
13.98
16.36
Occupancy Maps
38.79
30.08
36.41
30.34
Table 2: The hit rate accuracy of experiments which
tested home (H) and away (A) models against home
and away matches (e.g. HvH refers to home model
tested on home matches and HvA refers to the home
model being tested on away matches).
teams is given in Figure 7. To make it easier to quantify the
difference in occupancy, we calculated the difference with respect to certain areas of the field. Specifically we calculated
the difference: for the whole field (W), the attacking half
(H), and the attacking-third (T) - these values are listed below each difference map. As can be seen from the difference
maps, nearly all the teams (18 out of 20) had more possession in the attacking half. More telling is that 19 out of the
20 teams had more possession in the attacking third. Seeing
that the shooting proficiency is essentially the same (10%
vs 9%), we can point to the observation that the more possession in the attacking third leads to more chances, which
in-turn leads to more goals. A potential statistic to back this
observation up is that Chelsea - who were the only team to
have less occupancy in the attacking third - had the smallest discrepancy between home and away shots (only 12, the
next was Arsenal with 45).
With the absence of labels to compare against it is impossible to say whether this was actually this case as other
factors may have contributed to the home advantage (i.e.
referee’s [22], shooting chance quality, game context (winning, losing, red-cards, key injury, derby matches etc.)) –
essentially our analysis provides correlation and not causation. However, this analysis does provide a effective method
of automatically flagging behavioral differences which can
quickly alert an expert (such as a coach or commentator)
into further or deeper analysis which can aid in the decision
making process. In the next section we show some methods
which can do this.
6.
PRE/POST GAME ANALYSIS
Given a coach or analyst is preparing for an upcoming
match, having a measure of how variable a team’s performance is would be quite beneficial. For example, the coach
or analyst may have viewed a previous match and formed a
qualitative model based on their expert observation. However, this model is only formed by a single observation and
may be subject to over-fitting. Having a measure which
could indicate how variable a team’s performance is would
be quite useful. Given they have a feature representation of
each of the previous performances of a team, our approach
could be a method of determining the performance variance.
To do this, the distance in feature space between each of the
past performances, y, and the
PMmean, ŷ, can be calculated
1
where the mean is ŷ = M
i=1 yi , and where M is the
number of previous performances. A distance measure such
as the L2 norm could be used given that the input space
has been scaled appropriately, which generates the distance
measure via
distm = kym − ŷk2
(2)
where m refers to the game of interest. Returning to our
home and away performance example, one way to quantify
100
(1) Man United
W=3.8%, H=7.6%, T=10.7%
(4) Arsenal
W=3.9, H=4.2%, T=9.5%
(5) Tottenham
W=0.1%, H=3.0%, T=8.9%
50
(6) Liverpool
(7) Everton
(8) Fulham
W=1.8%, H=3.5%, T=9.5% W=-2.9%, H=-0.3%, T=5.6% W=-0.2%, H=1.6%, T=4.5%
(9) Aston Villa
W=0.1%, H=0.6%, T=0.2%
(10) Sunderland
W=2.6%, H=7.1%, T=8.4%
0
(11) West Bromwich Albion
(12) Newcastle
W=0.6%, H=3.1%, T=9.0% W=5.2%, H=6.7%, T=0.5%
(13) Stoke City
W=-3.7%, H=2.1%, T=1.9%
(14) Bolton
W=6.2%, H=5.4%, T=8.0%
(15) Blackburn
W=8.1%, H=3.6%, T=7.3%
(16) Wigan
(17) Wolverhamption
W=8.1%, H=12.4%, T=8.1% W=-4.3%, H=0.4%, T=4.1%
(18) Birmingham City
(19) Blackpool
(20) West Ham United
W=5.0%, H=8.3%, T=13.8% W=-1.0, H=3.4%, T=11.9% W=-2.2%, H=-0.7%, T=3.6%
(2) Chelsea
W=1.1%, H=2.5%, T=-0.5%
(3) Man City
W=1.5%, H=3.1%, T=8.7%
-50
-100
Figure 7: The normalized difference maps between home and away performances for all the 20 EPL teams. In
all maps, teams are attacking from left-to-right and a positive value refers to a team having more occupancy
in home games, while a negative value refers to more occupancy in away games. Percentages underneath
each team give a value on this difference (Key: W is whole field, H refers to forward half and T refers to the
attacking third.)
Distortion Variance
120
80
40
0
0
5
10
15
20
15
20
(a) Home Performances
120
80
40
0
0
5
10
(b) Away Performances
Figure 8: Variance in distortion for (a) home and
(b) away performances.
the variation in performance for each team in the EPL is
through calculating the “feature variance” or “variance in
distortion” using Equation 2 (see Figure 9).
As can be seen in Figure 9(a), the variation in playing
style of most home team’s is small - with the exception of
teams 10 and 11 (Sunderland and West Brom). Conversely,
the majority of team’s away performances were highly variable, with only teams 10 and 14 (Sunderland and Bolton)
having low variance. These results suggest that predicting
the playing style of home teams is quite feasible while predicting performances of away teams would be unreliable.
In terms of post-match analysis, a similar approach could
be used to see if a team’s performance was within the expectation range (i.e. ±σ). A good example was Fulham’s away
performance against Manchester United. In this match, they
lost 2-0 and conceded both goals in the first half (12th and
32nd minute). The comparison between this game and their
typical performance can be visualized through their occupancy maps which are given in Figure 10. In this match,
Fulham occupied a lot more possession in the middle of the
field than they normally do. This example highlights the
importance of the match context, as after scoring two early
goals, based on the data it appeared that Manchester United
sat back and allowed Fulham to have the majority of possession(52% of overall possession) [6], but this possession
was in non-threatening positions (i.e. possession outside of
the attacking third). To account for this behavior, analysis
would have to normalize for variations in behavior caused by
changes in match context (i.e. score, strength of opposition
etc.). However, this is a major problem as we would limit
the amount of data we would have to train our model. Future work will be focussed on clustering styles unsupervised
to maximize the amount of context dependent data.
Distance from Mean
60
40
20
(a)
0
0
5
10
Opponent Number
15
20
Figure 9: Example of the distortion for each away
performance of Fulham in the 2010-2011 season. In
match 16 they played Manchester United, and the
performance on the day was far different from their
other away performances (they lost 2-0 on this occasion).
7.
SUMMARY AND FUTURE WORK
Most sports analytics approaches only use event-based
statistics to drive analysis and decision-making despite the
influx of ball and player tracking data becoming available.
The reason why this new and rich source of information
is being neglected stems from the fact that it is continuous, high-dimensional and difficult to segment into semantic
groups. The emerging field of sports spatiotemporal analytics uses spatiotemporal data such as ball and player tracking data to drive automatic team behavior/strategy analysis
which would be extremely useful in all facets of the sports
industry (e.g. coaching, broadcasting, fantasy-games, video
games, betting etc.). In this paper, we gave an overview
of the types of sports analytics work being done both in
industry as well as academia. Additionally, we gave a casestudy which investigated possible reasons for why the home
advantage exists in continuous sports like soccer. Using spatiotemporal data, we were able to show that teams at home
play have more possession in the attacking third. Coupled
with the fact that the shooting and passing proficiencies are
not significantly different, this observation can partially explain why home teams have more shots and score more, and
in-turn win more at home compared to away matches. Using
our feature representation, we also showed examples where
pre and post game analysis can be performed. Specifically,
we were able to show the variation in home and away performances for each team, as well as the ability to flag anomalous
performances.
Our work also highlighted the importance of match context and the limiting factor it could have on training examples. In future work, we will look at unsupervised methods
to cluster playing similar playing styles, which can enrich
our training data set, without effecting its discriminating
power. Additionally, we will explore how player tracking
information can be used to discover team formations and
plays. Predicting team interactions and subsequent performances and outcomes, especially when they have not played
each other, is another application of our research. As reliable
high-level labels are almost impossible to obtain, predicting
match outcomes may be the best indicator of of successful
analytical modeling.
(b)
Figure 10: Occupancy maps of the: (a) mean away
performance for Fulham, and (b) their performance
against Manchester United - in this match they lost
2-0 and conceded early in the match.
8.
REFERENCES
[1] S. Ali and M. Shah. Floor Fields for Tracking in High
Density Crowd Scenes. In ECCV, 2008.
[2] N. Allen, J. Templon, P. McNally, L. Birnbaum, and
K. Hammond. StatsMonkey: A Data-Driven Sports
Narrative Writer. In AAAI Fall Symposium Series,
2010.
[3] BBC-Sports. Footballers may trial wearing microchips
to monitor health.
www.bbc.co.uk/sport/0/football/21460038, 14 Feb
2013.
[4] M. Beetz, N. von Hoyningen-Huene, B. Kirchlechner,
S. Gedikli, F. Siles, M. Durus, and M. Lames.
ASPOGAMO: Automated Sports Game Analysis
Models. International Journal of Computer Science in
Sport, 8(1), 2009.
[5] P. Carr, Y. Sheikh, and I. Matthews. Monocular
Object Detection using 3D Geometric Primitives. In
ECCV, 2012.
[6] ESPNFC. http://espnfc.com/us/en/report/
292849/report.html?soccernet=true&cc=5901.
[7] K. Goldsberry. CourtVision: New Visual and Spatial
Analytics for the NBA. In MIT Sloan Sports Analytics
Conference, 2012.
[8] A. Gupta, P. Srinivasan, J. Shi, and L. Davis.
Understanding Videos, Constructing Plots: Learning a
Visually Grounded Storyline Model from Annotated
Videos. In CVPR, 2009.
[9] Hawk-Eye. www.hawkeyeinnovations.co.uk.
[10] D. Henschen. IBM Serves New Tennis Analytics At
Wimbledon. www.informationweek.com/software/
business-intelligence/
ibm-serves-new-tennis-analytics-at-wimbl/
240002528, 23 June 2012.
[11] A. Hervieu and P. Bouthemy. Understanding sports
video using players trajectories. In J. Zhang, L. Shao,
L. Zhang, and G. Jones, editors, Intelligent Video
Event Analysis and Understanding. Springer Berlin /
Heidelberg, 2010.
[12] S. Intille and A. Bobick. A Framework for Recognizing
Multi-Agent Action from Visual Evidence. In AAAI,
1999.
[13] K. Kim, M. Grundmann, A. Shamir, I. Matthews,
J. Hodgins, and I. Essa. Motion Fields to Predict Play
Evolution in Dynamic Sports Scenes. In CVPR, 2010.
[14] M. Lewis. Moneyball: The Art of Winning an Unfair
Game. Norton, 2003.
[15] R. Li and R. Chellappa. Group Motion Segmentation
Using a Spatio-Temporal Driving Force Model. In
CVPR, 2010.
[16] R. Li, R. Chellappa, and S. Zhou. Learning
Multi-Modal Densities on Discriminative Temporal
Interaction Manifold for Group Activity Recognition.
In CVPR, 2009.
[17] W. Lu, J. Ting, K. Murphy, and J. Little. Identifying
Players in Broadcast Sports Videos using Conditional
Random Fields. In CVPR, 2011.
[18] P. Lucey, A. Bialkowski, P. Carr, E. Foote, and
I. Matthews. Characterizing Multi-Agent Team
Behavior from Partial Team Tracings: Evidence from
the English Premier League. In AAAI, 2012.
[19] L. Madden. NFL to Follow Army’s Lead on Helmet
Sensors in Attempt to Prevent Head Injury.
www.forbes.com/sites/lancemadden/2012/07/16/
nfl-to-follow-armys-lead-on-helmet-sensors-in/
-attempt-to-prevent-head-injury/, 16 July 2012.
[20] R. Masheswaran, Y. Chang, A. Henehan, and
S. Danesis. Destructing the Rebound with Optical
Tracking Data. In MIT Sloan Sports Analytics
Conference, 2012.
[21] V. Morariu and L. Davis. Multi-Agent Event
Recognition in Structured Scenarios. In CVPR, 2011.
[22] T. Moskowitz and L. Wertheim. Scorecasting: The
Hidden Influences Behind How Sports Are Played and
Games Are Won. Crown Publishing Group, 2011.
[23] NBA Shot Charts. www.nba.com/hotspots.
[24] D. Oliver. Basketball on Paper: Rules and Tools for
Performance Analysis. Brassey’s, Incorporated, 2004.
[25] D. Oliver. Guide to the Total Quarterback Rating.
espn.go.com/nfl/story/_/id/6833215/
explaining-statistics-total-quarterback-rating,
4 August 2011.
[26] Opta Sports. www.optasports.com.
[27] S. Pellegrini, A. Ess, K. Schindler, and L. van Gool.
You’ll Never Walk Alone: Modeling Social Behavior
for Multi-Target Tracking. In CVPR, 2009.
[28] M. Perse, M. Kristan, S. Kovacic, and J. Pers. A
Trajectory-Based Analysis of Coordinated Team
Activity in Basketball Game. Computer Vision and
Image Understanding, 2008.
[29] Prozone. www.prozonesports.com.
[30] B. Siddiquie, Y. Yacoob, and L. Davis. Recognizing
Plays in American Football Videos. Technical report,
University of Maryland, 2009.
[31] SportsVision. www.sportsvision.com.
[32] STATS SportsVU. www.sportvu.com.
[33] Statsheet. www.statsheet.com.
[34] D. Stracuzzi, A. Fern, K. Ali, R. Hess, J. Pinto, N. Li,
T. Konik, and D. Shapiro. An Application of Transfer
to American Football: From Observation of Raw
Video to Control in a Simulated Environment. AI
Magazine, 32(2), 2011.
[35] X. Wei, P. Lucey, S. Morgan, and S. Sridharan.
Sweet-Spot: Using Spatiotemporal Data to Discover
and Predict Shots in Tennis. In MIT Sloan Sports
Analytics Conference, 2013.
[36] C. Xu, Y. Zhang, G. Zhu, Y. Rui, H. Lu, and
Q. Huang. Using Webcast Text for Semantic Event
Detection in Broadcast. T. Multimedia, 10(7), 2008.
[37] Zonalmarking. www.zonalmarking.net.