Characterizing different team sports using network analysis

Abstract

Team sports are complex dynamic systems based on the frequent interaction of various players. Recently, social network analysis has been introduced to the study of sports dynamics in order to quantify the involvement of individual players in the interplay and to characterize the organizational processes used by teams. Nonetheless, only a limited set of team sports has been assessed to date, and the focus of most studies has been on the application of small sets of network metrics to a single sport. Our study aims at comparing the network patterns of different team sports in order to contribute to the understanding of their underlying nature. It considers three invasion games, namely professional matches from basketball, football and handball. By applying relevant centrality measures and minimum spanning trees a first comparison between the nature of interplay in various team sports is offered as well as a deeper understanding of the role of different tactical positions in each sport. The point guard in basketball, defensive midfielder in football and center in handball are identified as the most central tactical positions. Direct interplay is most balanced in football followed by basketball and handball. A visualization of the basic structure of interplay for each sport is achieved through minimum spanning trees.

Full text

Characterizing dierent team sports using
network analysis
Florian Korte1, 2, * & Martin Lames2
1 Center for Digital Technology and Management, Munich, Germany
2 Department of Sport and Health Sciences, Technical University of Munich, Germany
* Corresponding author: Center for Digital Technology and Management, Marsstraße 20-22, 80335 Munich, Germany,
Tel: +49 (0) 89-28928163, Fax: +49 (0) 89-28928459
Email: korte@cdtm.de
COMMENTARY
Article History:
Submitted 12th October 2017
Accepted 14th March 2018
Published 25th April 2018
Handling Editor:
Ernst-Joachim Hossner
University of Bern, Switzerland
Editor-in-Chief:
Martin Kopp
University of Innsbruck, Austria
Reviewers:
Reviewer 1: Filipe Manuel Clement
Instituto Politecnico de Viana do
Castelo, Portugal
Reviewer 2: Anonymous
ABSTRACT
Team sports are complex dynamic systems based on the frequent interaction of various players.
Recently, social network analysis has been introduced to the study of sports dynamics in order to
quantify the involvement of individual players in the interplay and to characterize the organizational
processes used by teams. Nonetheless, only a limited set of team sports has been assessed to date,
and the focus of most studies has been on the application of small sets of network metrics to a
single sport. Our study aims at comparing the network patterns of dierent team sports in order
to contribute to the understanding of their underlying nature. It considers three invasion games,
namely professional matches from basketball, football and handball. By applying relevant centrality
measures and minimum spanning trees a rst comparison between the nature of interplay in various
team sports is oered as well as a deeper understanding of the role of dierent tactical positions in
each sport. The point guard in basketball, defensive midelder in football and center in handball
are identied as the most central tactical positions. Direct interplay is most balanced in football fol-
lowed by basketball and handball. A visualization of the basic structure of interplay for each sport is
achieved through minimum spanning trees.
Keywords:
social network analysis – team sports – interaction matrices – minimum spanning trees
Citation:
Korte, F., & Lames, M. (2018). Characterizing dierent team sports using network analysis. Current Issues in Sport Science, 3:005. doi: 10.15203/
CISS_2018.005
Current Issues in Sport Science 3 (2018)
2018 I innsbruck university press, Innsbruck
Current Issues in Sport Science I ISSN 2414-6641 I http://www.ciss-journal.org/
Vol. 3 I DOI 10.15203/CISS_2018.005 OPEN ACCESS
Introduction
Matches, or games, in team sports can be seen as complex
dynamic systems (Glazier & Davids, 2009). The frequent inter-
action of various players is an integral part of any team sports
match (Passos, Araújo & Volossovitch, 2016). Hence, a team
must be regarded as more than the sum of its parts, and the
secret to successful performance is believed to lie in the coll-
ective action of team members (Grund, 2012). Understanding
the patterns of play is important to deduce the nature of the
sport. Moreover, the individual contribution of each player to
the organizational process is highly relevant to revealing how
a team functions (Vilar, Araújo, Davids, & Bar-Yam, 2013). The
complexity of matches and team dynamics makes breaking
down such patterns dicult, creating an ongoing challenge
for performance analysis in team sports.
There is an increasing interest in applying Social Network Ana-
lysis (SNA), a method that exploits familiar performance variab-
les such as passes, in order to detect patterns in the interplay of
teams (Clemente & Martins, 2017). Network approaches focus
on breaking down the web of interactions in systems of multip-
le agents also referred to as nodes (Passos et al., 2011). Traditio-
nal application areas of this method can be found in biological
(e.g. spread of diseases) and sociological (e.g. acquaintance net-

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 2
works) contexts. In sports, the frequent interaction between a
limited set of players, e.g. through the passing of a ball qualies
network theory as a powerful performance analysis method.
Clemente, Martins, Wong, Kalamaras and Mendes (2015b) ana-
lyze professional football matches by applying SNA. On a micro
level, i.e. focusing on the prominence of individual players in a
team, the authors identify the position of the central midel-
der as the most prominent player in their study, as midelders
are responsible for building oensive lines of attack. Pena and
Touchette (2012) detect certain cliques within football teams
that interact more frequently than others. This is in line with
another micro-level study by Gama et al. (2014), who nd that
only a subset of players in football teams is responsible for the
majority of interaction and thus shaping the pattern of play. On
both, micro and macro level, i.e. focusing on the collective or-
ganization of a team, Duch, Waitzman and Amaral (2010) iden-
tify a strong connection between several network measures
and traditional performance indicators whereas Grund (2012)
connects the distribution of individual networks measures to
performance outcomes. In his macro-level analysis, the author
nds that successful teams in football demonstrate a more ba-
lanced interplay.
In basketball, SNA has been applied in professional and ama-
teur settings. Fewell, Armbruster, Ingraham, Petersen and
Waters (2012) and Clemente, Martins, Kalamaras and Mendes
(2015a) identify the Point Guard as the dominant player struc-
turing plays for the team.
However, the set of sports that SNA has been applied to has
been limited so far. Moreover, the focus of most studies has
been on the application of small sets of network metrics to a
single sport. Our study aims at comparing the network patterns
of dierent team sports in order to contribute to the under-
standing of their underlying nature. It considers three invasion
games, namely professional matches from basketball, football
and handball. The overarching task of each team trying to coll-
ectively outperform or -score its opponent unites these popu-
lar team sports. However, as they dier in their environmental
constraints (e.g. areas, rules), dierent interaction patterns are
needed in order to succeed (Araújo & Davids, 2016).
SNA enables us to investigate the resulting complex webs of
interaction between the players in the dierent sports. To en-
sure a thorough analysis, individual and team metrics are ap-
plied alongside the computation of minimum spanning trees,
a network technique that facilitates an intuitive visualization of
the strongest relationships in complex networks revealing the
basic structure of the sports.
In combination with the macro-level analysis, i.e. applying team
metrics, this assesses the overall interaction patterns. The micro-
level analysis, i.e. applying individual metrics, is specically tar-
geted at revealing the dominant tactical positions in terms of
their involvement in the interplay for each sport and who are re-
sponsible for structuring these patterns. The combined analysis
enables us to break down the complex organizational processes
within teams and thus contributing to the understanding of the
underlying nature of basketball, football and handball.
To our knowledge, this is the rst study that attempts a com-
parison of dierent team sports applying SNA. Furthermore, it
is the rst analysis that takes handball into consideration along
with football and basketball and applies minimum spanning
trees in the context of team sports.
Hence, this study breaks down the underlying complexity of
team sports by characterizing and quantifying individual and
team performance through SNA.
Methods
Samples
For each sport, eight knockout round matches in the men´s
competition at major professional tournaments are conside-
red for analysis, minimizing the home/away bias (Courneya &
Carron, 1992). For basketball and handball the knockout sta-
ges at the Rio 2016 Summer Games Olympics tournaments are
recorded and analyzed. For football, the authors consider the
last eight matches from the knockout stage of the FIFA World
Cup 2014 tournament. A total of 16 adjacency matrices for each
sport are generated, capturing the interaction between players
of each team. A total of 4059 passes are analyzed in basketball,
6934 in football and 8054 in handball.
Procedure
In order to apply SNA, adjacency matrices capture the passing
distribution seen in every analyzed match. The matrices are
constructed from a set of nodes and edges for every team res-
pectively. Players represent nodes such that the number of pas-
ses between them denes the edge weight. The overall match-
based interaction matrix per team is a result of an aggregation
of the units of attack dened as the moment from ball recovery
until possession is lost (Passos et al., 2011).
The tracking process for basketball and handball games was
executed through video analysis applying the software Dart-
sh®. The passing distribution at the FIFA World Cup 2014
tournament was provided in the ocial FIFA match reports on
their website (www.fa.com/worldcup/archive/brazil2014). In
a thorough post-match analysis players were assigned to their
respective tactical position to ensure the comparability bet-
ween teams and focus on the tactical aspects of each sport. In
line with O`Donoghue (2009), we acknowledge the increasing
complexity of tactical roles in team sports, i.e. forwards taking
on defending tasks in football. Players might temporarily occu-
py dierent areas on the pitch and fulll dierent tasks which
can be acknowledged as part of the role repertoire of the dif-
ferent tactical positions, especially in football. Eventually, this is
part of why we see complex webs of interaction in team sports
and why we expect that this nds its expression in the results of
our analysis. The denition of tactical roles for the three sports
is displayed in Table 1.

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 3
Basketball Football Handball
Center (C) Defensive Midelder (DM) Oensive Midelder (OM) Center (C)
Point Guard (PG) Goalkeeper (GK) Right Central Defender (RCD) Left Back (LB)
Power Forward (PF) Left Central Defender (LCD) Right Defender (RD) Left Wing (LW)
Shooting Guard (SG) Left Defender (LD) Right Forward (RF) Pivot (P)
Small Forward (SF) Left Forward (LF) Right Midelder (RM) Right Back (RB)
Left Midelder (LM) Right Wing (RW )
Following the codication for each tactical position ensured
that frequent substitutions of players lead to a reassignment
of the given tactical positions. Predominantly, substitutions
lead to a direct replacement for the corresponding tactical po-
sition, meaning the player who was codied to a specic po-
sition was replaced by his substitute. However, substitutions
occasionally implied the reassignment on multiple positions,
mostly in basketball and handball. To detect these changes,
each unit of attack was considered separately. Tracking and
codication processes were executed by researchers with
more than ten years of experience in the sports described. In
order to ensure the reliability of the study, Cohen´s kappa and
Gwet’s AC1 inter-rater statistic were computed in a two-stage
process (Gwet, 2001). In a rst step, the agreement on the oc-
currence of passes was analyzed using Gwet`s statistics. In a
second step, the agreement on passer and pass receiver was
tested applying Cohen’s Kappa. 12.5% of the overall data were
tested for reliability purposes. The Kappa (Gwet, 2001) values
were above 0.94 (0.85) respectively for each sport, ensuring
the reliability of the data.
Network Metrics
For the 16 adjacency matrices in each sport a set of individu-
al- and team-related centrality network metrics are computed.
The analysis was carried out using the software Matlab® and
the visualization of networks was generated by applying Cytos-
cape®.
Centrality calculations allow a quantication of the inuence
of tactical positions on their team´s interplay as well as the ba-
lance of inuence between players overall. To account for the
nature of the sports, metrics that consider weighted directed
graphs were applied. This allows for a breakdown of the con-
nection between any two players in both passing directions.
For individual (or micro-level) analysis weighted in-/out-de-
gree, weighted betweenness and weighted closeness were
computed. For team (or macro-level) analysis, the correspon-
ding centralization values were calculated. These metrics are
explained in detail in the following.
Individual Metrics Weighted in-degree (CWID), also referred to as
Prestige, is the sum of the incoming weighted edge values of a
node. Hence, these metrics capture the number of successfully
received passes of a player and a high value is often taken as
a rst indicator for the prominence of a particular player (Cle-
mente et al., 2015b). Team members appear to trust this player,
when in possession, to positively contribute to the team´s per-
formance and therefore target him more frequently than others.
Weighted out-degree (CWOD), also referred to as Centrality, is
the sum of outgoing weighted edges of a node. In the context
of sports, (CWOD) is the number of completed passes of a player
and a high value is often associated with a high contribution to
ball circulation (Clemente et al., 2015b).
We also calculate the ratio CWID /CWOD to assess a potential de-
viation between the share in pass reception and execution. A
player with a higher reception than execution share, i.e. a va-
lue above 1, could indicate a player who rather nishes attacks.
He frequently receives the ball from team members to execute
shots on target rather than passing on. The opposite, i.e. a value
below 1, might be a player who initiates attacks.
Weighted betweenness (CWB) assesses how often a node is on
the shortest path between two other nodes (Wassermann &
Faust, 1994). A modied version of the standard computation
of CWB according to Newman (2001) is applied, which is more
suitable for team sports since it favors strong connections
rather than penalizing them. It measures how often a player
is in between the most frequent passing connections of any
other two players, thus functioning as a bridging unit (Pena &
Touchette, 2012). As this implies a certain level of dependency
on that particular player to ensure ball circulation it can be con-
sidered as a playmaker indicator.
Weighted closeness (CWC) addresses how well connected a
node is to all other nodes, directly or indirectly, within a net-
work following Freeman (1978) and Opsahl, Agneessens and
Skvoretz (2010). In a nearly complete network, i.e. in which al-
most every node is connected to each other, the metric can be
seen as a more sophisticated approach to the weighted degree
computations as the distribution of weights between other
nodes is taken into account. In team sports, CWC describes the
Table 1: List of tactical roles in basketball, football and handball

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 4
As MSTs are only applicable to undirected graphs, the total
passing intensity between pairs of players is considered in their
construction. Reducing the amount of edges and thus comple-
xity of the otherwise nearly complete networks, oers an alter-
native perspective on the pattern of interplay of the dierent
team sports and hierarchical structure of weighted graphs (Go-
wer & Ross, 1969).
Statistical Procedures
The authors of this paper utilized multiple one-way ANOVA to
test for statistical dierences between the centrality levels of the
tactical positions within each sport, and between the analyzed
sports. The assumption of normality for dependent variables
was tested using Kolmogorov-Smirnov tests (p-value < .05). The
assumption of homogeneity for groups’ variances was exami-
ned by using Levene’s test. There were no violations of either
normality or homogeneity. Pairwise comparisons were establis-
hed by running Bonferroni post-hoc tests. The statistical analy-
ses were all conducted at a signicance level of p < .05 using
Matlab®. Following Ferguson (2009) and Clemente and Martins
(2017), η2 is reported to interpret the eect size according to the
following criteria: no eect (η2 < .04); small eect (.04 ≤ η2 < .25);
moderate eect (.25 ≤ η2 < .64); strong eect (η2 ≥ .64).
Results
The tests found statistical dierences in the dependent variab-
les for all centrality measures applied for the three team sports
considered in this study. The η2 values reported in Table 2 al-
most all demonstrate moderate to strong eects sizes for the
multiple one-way ANOVA in this study.
Individual Parameters
Table 3 shows the descriptive statistics and post-hoc results
for tactical positions in basketball. The PG position is assigned
the highest values for all centrality metrics and is signicantly
more central than every other tactical position. For weighted
betweenness, the normalized value of the PG is 0.87 and thus
more than ten times higher than the next ranked tactical posi-
tion. There is no value assigned here for the forward positions
implying that no strongest connection between any two play-
ers on the team runs via those tactical positions. In general, the
other four tactical positions demonstrate similar values and no
statistical dierences are found between them for the other
metrics applied in this study.
The CWID /CWOD ratios are shown in Figure 1. Notable in the ra-
tio revealed is the relatively low value for the center position.
Here, the share in pass completion rate outweighs the share in
pass reception.
how well a player directly or indirectly interacts with all other
team members on the eld. Hence, a player with high weigh-
ted degree values but comparatively low weighted closeness
value might only interact strongly with a subset of his team
members.
Team Metrics Centralization measures are concerned with the
distribution of the individual metrics in a network. Following
Freeman (1978) and Wasserman and Faust (1994), weighted in-
degree centralization (CWIDC) captures the deviations from all in-
degree values to the highest value in the network adjusted by
the number of passes and the number of players. This adjust-
ment in the computation allows a comparison between die-
rent sports. Weighted out-degree centralization (CWODC), weigh-
ted betweenness centralization (CWBC) and weighted closeness
centralization (CWCC) is calculated accordingly.
By construction, all centralization values are bounded between
0 and 1. A network is regarded as highly centralized, i.e. a va-
lue close to 1, when the score of a particular node clearly out-
weighs the scores of all others and rather decentralized, i.e. a
value close to 0, when the scores are similar among all nodes
(Grund, 2012). In a sports context, CWIDC and CWODC scores can
be seen as indicators for the balance of direct interplay in a
team. CWBC and CWCC scores signal how balanced the inuence
on the overall interplay is within the team, considering direct
and indirect connections. In general, high values could imply
that interplay depends on only a subset of players.
For reasons of comparability between dierent matches, we
normalized all centrality values by the total scores of the res-
pective metrics following Leydesdor (2007). The values them-
selves have no direct relevance. Relative comparisons between
the dierent values of a respective metric for the tactical posi-
tions were highly crucial.
Visualization
A more intuitive visualization of the underlying structure of the
networks was allowed for by computing minimum spanning
trees (MSTs) for each sport. MSTs are meant to provide a revelati-
on of the strongest relationships in complex networks (Manteg-
na, 1999). As a visualization method, they reduce the complexity
of connected graphs of n nodes with up to n(n-1) connections
to the strongest n-1 edges under the side condition that each
node is still contained. According to Araújo and Davids (2016),
sport teams demonstrate a task-specic organization to reach
a common goal under certain constraints. In past studies, MSTs
have been applied to visualize how sets of team members orga-
nize themselves to form an eective collective organization for
a specic task (Lappas, Liu, & Terzi, 2009; Li & Shan, 2010). Hence,
we apply MSTs to trace how teams consisting of a limited set of
players organize their interplay in order to achieve group suc-
cess. The method reduces the complex network of passes to the
most basic structure presenting the most intensive connections
under the consideration of all players.

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 5
Table 2: Eect size values η2 for multiple one-way ANOVA
Basketball Football Handball All
CWID .59 (moderate) .23 (small) .92 (strong) CWIDC .89 (strong)
CWOD .46 (moderate) .27 (moderate) .92 (strong) CWODC .81 (strong)
CWB .87 (strong) .32 (moderate) .91 (strong) CWBC .89 (strong)
CWC .72 (strong) .44 (moderate) .93 (strong) CWCC .83 (strong)
No eect (η2 < .04); small eect (0.04 ≤ η2 < .25); moderate eect (.25 ≤ η2 <.64); strong eect (η2 ≥ .64)
Table 3: Descriptive statistics and post-hoc results for basketball
PG SG SF PF C
CWID 0.30 (0.04)all 0.20 (0.03)PG 0.16 (0.03)PG 0.16 (0.02)PG 0.17 (0.02)PG
CWOD 0.28 (0.04)all 0.18 (0.04)PG 0.17 (0.03)PG 0.16 (0.03)PG 0.21 (0.03)PG
CWB 0.87 (0.20)all 0.07 (0.19)PG - - 0.05 (0.10)PG
CWC 0.27 (0.02)all 0.19 (0.03)PG 0.17 (0.02)PG 0.17 (0.02)PG 0.19 (0.02)PG
Subscripts indicate to which tactical positions given value is statistically dierent for p < .05, e.g. PG: given value is statistically dierent to the value of the
point guard; All: value is statistically dierent to all other tactical positions.
Figure 1: WID/WOD ratios for basketball, football and handball

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 6
For handball, C is signicantly more central than all other tacti-
cal positions based on CWID, CWOD and especially CWB . The CWB
values indicate that C frequently functions as the bridging
unit between other tactical positions. Table 5 shows that the
remaining back positions (LB and RB) have similar values for
each metric and are signicantly dierent to all other tactical
positions for CWID, CWOD and CWB . The same applies for the wing
positions (LW and RW). However, their values fall into the same
category with the pivot position. The GK values are neglecting
low and ranked last for the considered metrics.
The CWID /CWOD ratios in Figure 1 reveal a high value above 1 for
the point. Its share in pass reception outweighs share in pass
completion.
The corresponding results for football matches under inves-
tigation can be seen in Table 4. The DM position scores the
highest CWID and CWOD values, meaning that this position had
on-average the highest number of successfully received and
executed passes. Statistically signicant dierences can only be
shown in comparison with the GK position for CWID and certain
attacking positions for CWOD additionally. DM is also leading the
CWB scores followed by the RD and central defender positions.
Their respective values are signicantly dierent to the values
of the other tactical positions; whereas the CWC values are simi-
lar between all tactical roles apart from the GK.
The CWID/CWOD ratios in Figure 1 show values below 1 for de-
fensive positions and above 1 for oensive positions, especially
strikers.
Table 4: Descriptive statistics and post-hoc results for football
GK LD LCD RCD RD DM LM RM OM LF RF
CWID
0.03
(0.01)all
0.08
(0.02)GK
0.09
(0.02)GK
0.09
(0.02)GK
0.10
(0.02)GK
0.12
(0.03)GK
0.10
(0.02)GK
0.11
(0.02)GK
0.11
(0.02)GK
0.09
(0.04)GK
0.09
(0.02)GK
CWOD
0.06
(0.02)mult
0.10
(0.02)mult
0.10
(0.02)mult
0.11
(0.02)mult.
0.12
(0.02)mult
0.13
(0.02)GK,LM,Fs
0.08
(0.02)mult
0.09
(0.02)mult
0.10
(0.02)mult
0.06
(0.03)mult
0.06
(0.02)mult
CWB
0.00
(0.01)mult
0.08
(0.09)mult
0.12
(0.06)mult
0.13
(0.07)mult
0.18
(0.14)mult
0.18
(0.10)all-CDs,OM,RD
0.05
(0.05)mult
0.07
(0.07)mult
0.11
(0.09)mult
0.05
(0.08)mult
0.03
(0.06)mult
CWC
0.06
(0.01)all
0.09
(0.01)mult
0.09
(0.01)mult
0.10
(0.01)mult
0.10
(0.01)mult
0.11
(0.01)GK,Fs,LD,LF,LM
0.09
(0.01)mult
0.10
(0.01)mult
0.10
(0.01)mult
0.08
(0.02)mult
0.08
(0.01)mult
Subscripts indicate to which tactical positions given value is statistically different for p < .05, e.g. GK: given value is statistically different to the
value of the goalkeeper; All: value is statistically different to all other tactical positions; All-“tactical position(s)”: value is statistically different to all
other tactical positions except the listed ones; Mult: value is statistically different to various tactical positions that are not part of further analysis in
this study; Fs includes LF and RF; CDs includes LCD and RCD.
Table 5: Descriptive statistics and post-hoc results for handball
GK LW LB C RB RW P
CWID - 0.04 (0.02)C,Bs 0.23 (0.02)all-RB 0.36 (0.03)all 0.26 (0.02)all -LB 0.05 (0.02)C,Bs 0.05 (0.02)C,Bs
CWOD 0.01 (0.00)all-LW,P 0.04 (0.02)C,Bs 0.23 (0.02)all-RB 0.38 (0.03)all 0.26 (0.02)all-LB 0.05 (0.02)C,Bs,GK 0.03 (0.01)C,Bs
CWB - 0.03 (0.04)C,Bs 0.23 (0.05)all-RB 0.45 (0.05)all 0.25 (0.10)all-LB 0.02 (0.02)C,Bs 0.02 (0.02)C,Bs
CWC 0.04 (0.01)all 0.14 (0.02)all-P,RW 0.18 (0.01)all-RB 0.18 (0.01)all-Bs 0.18 (0.01)all-C,LB 0.15 (0.01)all-LW 0.13 (0.02)all-LW
Subscripts indicate to which tactical positions given value is statistically different for p < .05, e.g. C: given value is statistically different to the value
of the center; All: value is statistically different to all other tactical positions; All-“tactical position(s)”: value is statistically different to all other tactical
positions except the listed ones, e.g. All-C: given value is statistically different to all other values but the one of the center; Bs includes LB and RB.

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 7
calculation, we were able to follow Freeman’s denition in our
between each sport. As the highest values were unique in eve-
ry computations. The average CWIDC and CWODC values are highest
for handball, followed by basketball in second place. This order
for rst and second rank switches between these two sports
for CWBC and CWCC. Football has the lowest average values for all
team metrics employed in this study.
Visualization
Figure 2 displays the aggregated passing distribution of all
matches in each sport and the corresponding MSTs next to that
on the right-hand side. As edge weights were unique in each
network, the resulting MSTs are unique as well (Li, Hou & Sha,
2005). The tree representing the passing network in basketball
shows a typical star network topology with the PG as the cen-
tral node to which all other tactical positions are connected.
The topology of the handball MST has a strong resemblance
with the tactical formation of the sport. The C position emer-
ges as the centrally located node connected to the pivot and
back positions who themselves are adjoined to the wings. No
Team Parameters
The descriptive statistics and post-hoc results for the team
metrics in Table 6 show that the considered sports have signi-
cantly dierent values for almost all centralization measures
Table 6: Descriptive statistics and post-hoc results for team
metrics
Basketball Football Handball
CWIDC 0.13 (0.05)FB,HB 0.05 (0.02)BB,HB 0.24 (0.04)BB,FB
CWODC 0.10 (0.04)FB,HB 0.05 (0.01)BB,HB 0.25 (0.03)BB,FB
CWBC 0.89 (0.15)FB,HB 0.22 (0.09)BB,HB 0.35 (0.06)BB,FB
CWCC 0.13 (0.03)FB,HB 0.05 (0.01)BB 0.05 (0.01)BB
Subscripts indicate to which team sport given value is statistically
different for p < .05, e.g. FB: given value is statistically different to the
value in football.
Figure 2: Visualization of aggregated passing distribution and MSTs for basketball, football and handball

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 8
In basketball the central role of the PG becomes obvious loo-
king at the CWB scores. A majority of the strongest connec-
tions between positions run via the PG, identifying him as the
bridging player between tactical positions in basketball. The
star network topology of the MST with the PG situated in the
center visualizes these ndings. The dominant role of this tacti-
cal position is also in line with several previous studies (Cle-
mente et al., 2015a; Fewell et al., 2012).
In handball, the CWB results suggest a central role of the C po-
sition in facilitating the ball and structuring the interplay in
that sport. The CWC metric evaluates how closely a player is con-
nected with all other players. The fact that the corresponding
CWC share is less than half as high (0.18 to 0.45) suggests that
C predominantly interacts with a subset of players i.e. the back
positions. The CWID and CWOD scores support the argument that
the back positions are the dominating players here.
A deeper role division can be taken from the reported CWID/
CWOD ratios. In football, the ratios indicate a subdivision bet-
ween attacking and defensive roles. The defensive roles show
higher CWOD than CWID values, thus ratios below 1, as they initiate
plays while attacking roles rather nish them. This observation
is not made in the other two sports. Solely in the case of hand-
ball, the P has a relatively high CWID /CWOD ratio as that player is
mostly targeted to nish attacks rather than initiating them.
Apart from these indications, a clear division into distinct ro-
les is not visible in either basketball or handball. Although
we analyzed matches from tournaments at the highest pro-
fessional level, dierences in CWID and CWOD values might also
be ascribed to limited technical abilities to a certain extent.
Whereas in basketball (13.5 turnovers against 253.7 passes for
a 94.9% passing success rate on average per match for each
team ) and handball (10.8 turnovers against 503.4 passes for
a 97.9% passing success rate) this aspect might be considered
rather negligible, the passing success rate in football for the
considered matches is only at 76.5%. Therefore, technical limi-
tations might add to the high ratios of CWID to CWOD in football
for some players.
The results of the team metrics show that general interplay is
most balanced between players in football based on the dis-
tribution of all individual metrics among tactical positions. As
the DM and RD have relatively high CWB scores in comparison
to the other tactical positions, the corresponding CWBC value is
slightly higher than for the other team metrics in football. This
could mean, that although interplay is quite balanced, there is
a tendency towards a few players having a stronger inuence
on the structuring of the interplay.
The interplay in basketball was demonstrated to be more un-
balanced than in football. Although pass reception and execu-
tion were equally distributed between most tactical positions,
the PG leads both categories signicantly also resulting in high-
er CWIC and CWOC values than in the case of football. The bridging
player characteristic of the PG also explains the high CWBC score
of 0.89. In fact, in 9 of the 16 networks in basketball the CWBC
score takes on the maximum value of 1. This implies that every
strongest connection between any two players in these mat-
distinct shape can be taken from the football MST. However,
defensive positions are centrally located, and the tree displays
three clusters in the longitudinal direction. Apart from the di-
rect connection between the RD and LF, tactical positions are
subdivided into left, central and right areas of the pitch and
were shown as directly connected.
Discussion
The aim of this study was to characterize and compare the com-
plex interactions visible in team sports. Network properties aid
in breaking down this complexity and assessing the overall co-
operation or collective organization of players and their indi-
vidual contribution to a team’s interaction. This is known to be
vital in the analysis of team sports (Vilar et al., 2013).
This research study was conducted using passing data from se-
veral matches of major professional tournaments in basketball,
football and handball. Of course, team interactions might also
take other forms than passing events to express the relation-
ship between players, e.g. the communication between the
players on the eld. Although there is no doubt on the impor-
tance of these forms of interaction, we assess direct passes bet-
ween players as the most relevant form of interaction to cha-
racterize collective organization in team sports (Grund, 2012).
The resulting analysis of our study reveals statistical dierences
in the pattern of play between dierent sports and the tactical
positions therein with moderate to strong eect sizes.
The results of the individual metrics identied the DM as the
most prominent player in football. He and the central defen-
ders who act as the bridging players, as revealed by their lea-
ding CWB scores, secure the ball circulation. The MST topology
supports this line of argument, as these positions are centrally
located within the tree, implying a strong contribution to the
interaction in the sport. A centrally located player in the MST
indicates a close connection or interaction with team members
supporting the argument that he is a vital part in forming the
collective organization of his team. There are several reasons
why the RD position is also ascribed a central role to in this stu-
dy according to the network metrics. First, 50% of all attacks
on average were built via the right wing in comparison to 31%
via the left wing. Second, the RD was among the top 3 pass
executers in 10 out of 16 networks conrming the involvement
of that position in building attacks via the right wing. Third, re-
nowned players such as Philipp Lahm took on the RD position
during the tournament. He alone produced 10-20 deliveries or
solo runs into the attacking third per game in comparison to
2-5 for his counterpart on the LD position. This supports the
dominant role of the RD and strong connection to forward po-
sitions visualized trough the connection in the MST. However,
the similar CWC scores suggest that all players in general are
equally strongly connected with each other, directly or indi-
rectly, implying that a quick ball circulation from any player to
another is given in football, in line with previous studies (Pena
& Touchette, 2010).

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 9
Moreover, it is important to make two remarks regarding the
application of weighted closeness in this study. First, one could
argue that the nearly completeness of the present networks in
this study, in which almost all players are directly connected
with each other, mostly account for the similar CWC scores in
football. However, in basketball, for example, we nd statisti-
cal dierences especially with regard to the PG while having
complete networks in every analyzed match exclusively. We
claim that in weighted networks, in comparison to unweighted
networks, strong indirect connections might dominate weak
direct connections and thus weaken the inuence of the level
of completeness in a network to a certain degree.
Second, only 13 of the 16 analyzed networks could be conside-
red in the one-way ANOVA of the CWC scores in handball, as the
GK was not involved in any interplay in some matches. Howe-
ver, as the metric analyzes the connection with all players in the
network and cannot consider disconnected components by
denition, we had to drop three networks (Opsahl et al., 2010).
This stresses the low involvement of the GK in building attacks
in handball.
Nevertheless, this study contributes to the understanding of
the nature of team sports and the respective involvement of
the dierent tactical positions within each sport. This identies
SNA as a powerful tool not only to break down the performance
of a single sport but also to allow a profound comparison bet-
ween the styles of interaction in team sports.
Conclusion
The aim of this study was to characterize the nature of team
sports and the role of their respective tactical positions.
By applying methods from social network analysis it was pos-
sible to break down the complexity of a handful of popular
sports, by quantifying and intuitively visualizing roles of play-
ers and overall team interaction. Thus, this is the rst study
that compares the network patterns of dierent team sports.
Moreover, MSTs are applied for the rst time in a team sports
context which in particular turn out to be eective in breaking
down the complexity of almost complete networks.
Ultimately, the analysis revealed signicant ndings, on the
prominent tactical positions for building attacks in the three
sports discussed: in basketball, this dominant tactical position
tended to be the PG, in football the DM and C in handball. The
general pattern of play appears to be signicantly more unba-
lanced in handball than in basketball and football. As a nal
takeaway, the study indicated strong ndings that the level
of xedness in the basic order of the tactical positions in the
sports inuences the prominence levels of players.
We chose three popular invasion games in this study to oer
a rst comparison between the network properties of team
sports. However, as we assess the outlook of this method as
fruitful, more team sports should be incorporated in future stu-
dies to further examine and characterize the dierent dynamic
ches involved the PG conrming the dominant role of this play-
er in facilitating the interplay.
The most unbalanced interplay between tactical positions in
this study can be seen in handball according to the distributi-
on of the direct interplay captured in the CWIC and CWOC scores.
However, the low CWCC score suggest that, similar to football, all
players in handball, are quite equally strongly connected, di-
rectly or indirectly, with each other. The low direct involvement
of the GK in the interplay is partly oset by the consideration of
indirect connections in this metric.
The topology of the MSTs, which reduces the complexity to the
most intense connections between players, oers a richer in-
sight into certain patterns of play. For handball, the patterns
in question perfectly resemble the basic order of the tactical
line-up. This suggests that interplay is quite structured and pre-
dened and therefore that the central role of the three back
positions is primarily a result of their tactical position in a quite
static basic order. They are crucial for the ball circulation and
structure the collective organization of the team in order to
score. In football, we have similar ndings, however, less strong.
Here a longitudinal clustering, meaning a subdivision into atta-
cking wings, is visible. The basic order of the tactical positions
appears to foster a stronger interplay of certain dyads e.g. bet-
ween wing defenders and wing midelders.
In basketball, the central role of the PG in structuring the of-
fensive plays outweighs any other potential cluster formation
of tactical positions, resulting in the star network topology of
the MST. According to Bonanno, Caldarelli, Lillo and Mantegna
(2003) this kind of topology is an argument for a clear hierarchi-
cal structure, i.e. that the PG has a strong impact on structuring
the interplay of his team. Teammates continuously bring the PG
into possession to initiate and structure plays (Bourbousson,
Poizat, Saury & Seve, 2010).
The main limitation seen in this research study was related pri-
marily to the sample size of the data utilized. Moreover, mat-
ches from only one major tournament are considered in each
sport. In order to generalize the results for each sport, a larger
sample across dierent occasions would be needed. Besides,
denitions of tactical positions in football are approximations
in some instances by combining data on tactical lineups and
positional data provided by FIFA (www.fa.com/worldcup/ar-
chive/brazil2014). There is an overall consensus on the deni-
tion of tactical roles in previous studies focusing on basketball
and especially handball induced by its quite static formation
(Cardinale, Whiteley, Hosny, & Popovic, 2017; Fewell et al., 2012;
Karcher & Buchheit, 2014). However, in football, we acknow-
ledge that tactical roles are a more complex factor. Here, we
believe that temporarily occupying dierent areas on the pitch
and fullling dierent tasks, i.e. a striker who takes on defen-
ding tasks, can be acknowledged as part of the role repertoire
of players in football. Eventually, this is why we are faced with
such complex webs of interaction in which dierent tactical
positions interact with each other and that network analysis is
able to capture for the purpose of our study.

F. Korte & M. Lames Characterizing dierent team sports using network analysis
CISS 3 (2018) April 2018 I Article 005 I 10
systems present in team sports. Moreover, individual modica-
tions of traditional network metrics may lead to an even more
accurate quantication of performance in each sport.
Funding
The authors have no funding or support to report.
Competing Interests
The authors have declared that no competing interests exist.
Data Availability Statement
All relevant data are within the paper.
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