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The Haka Network: Evaluating Rugby Team

Performance with Dynamic Graph Analysis

Paolo Cintia1, Michele Coscia2and Luca Pappalardo1

1KDDLab - ISTI CNR, Via G. Moruzzi 1 - 56124 Pisa, Italy Email: {name.surname}@isti.cnr.it

2Naxys - University of Namur, Rempart de la Vierge 8, 5000 Namur Belgium Email: michele.coscia@unamur.be

Abstract—Real world events are intrinsically dynamic and

analytic techniques have to take into account this dynamism. This

aspect is particularly important on complex network analysis

when relations are channels for interaction events between

actors. Sensing technologies open the possibility of doing so

for sport networks, enabling the analysis of team performance

in a standard environment and rules. Useful applications are

directly related for improving playing quality, but can also shed

light on all forms of team efforts that are relevant for work

teams, large ﬁrms with coordination and collaboration issues

and, as a consequence, economic development. In this paper, we

consider dynamics over networks representing the interaction

between rugby players during a match. We build a pass network

and we introduce the concept of disruption network, building

a multilayer structure. We perform both a global and a micro-

level analysis on game sequences. When deploying our dynamic

graph analysis framework on data from 18 rugby matches, we

discover that structural features that make networks resilient to

disruptions are a good predictor of a team’s performance, both at

the global and at the local level. Using our features, we are able

to predict the outcome of the match with a precision comparable

to state of the art bookmaking.

I. INTRODUCTION

Mining dynamics on graphs is a challenging, complex

and useful problem [4]. Many networks are representation

of evolving phenomena, thus understanding graph dynamics

brings us a step closer for an accurate description of reality.

Sensing technologies open the possibility of performing dy-

namic graph analysis in an ever expanding set of contexts.

One of them is competition events. Sports analysis is par-

ticularly interesting because it involves a setting where both

environment and rules are standardized, thus providing us an

objective measure of players’ contributions.

These possibilities power a number of potentially useful

applications. The direct one is related to the improvement

of a team’s performances. Once the most important factors

contributing or preventing victories are identiﬁed, the team

can work on strategies to regulate their collective effort to-

ward the best practices. However, there are non-sport related

externalities too. A sport team is nothing more than a group of

people with different skills that is trying to achieve a goal in

the most efﬁcient way possible. This description can be applied

to any other form of team [15]: a start-up enterprise, a large

manufacturing ﬁrm, a group of scientists writing a scientiﬁc

IEEE/ACM ASONAM 2016, August 18-21, 2016, San Francisco, CA, USA

978-1-5090-2846-7/16/$31.00 c

2016 IEEE

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Fig. 1: The pass and tackles networks imposed on the same

structure for one match in our dataset: Italy (blue nodes, home

team) versus New Zealand (black nodes, away team). The

number of the node refers to the role of the player. Green

edges are the pass network and red edges are the tackle

network. Node layout is determined by the classical rugby

player positioning on the pitch during a scrum.

paper. If we are able to shed light on how group dynamics

affect sport teams, we can try to universalize collaboration best

practices to enhance productivity in many different scenarios.

It comes as no surprise that analyzing sport events is a fast

growing literature in data science. Previous works involve the

analysis of different sports: from soccer [14] [9] to basketball

[27], from American football [20] to cycling [8]. In this paper

we focus on a sport that was not analyzed before: rugby.

The reason is that rugby has some distinctive features that

makes it an ideal sport to consider. Like American football,

it is a sport where there is a very clear and simple success

measure: the number of meters gained in territory. Again like

American football, it contains a disruption network: tackles.

Unlike American football, performance is also related to how

well a team can weave its own pass structure, involving all

the players in the ﬁeld in the construction of uninterrupted

sequences that can lead to a score.

One of the main contributions of the paper is to use both

the pass and disruption networks at the same time, creating a

multilayer network analysis [13] [3] of dynamics on graphs.

Figure 1 depicts an example of such structure. To the best

of our knowledge, there has not been such attempt elsewhere

in the literature. We also do a multiscale analysis: we ﬁrst

focus on the multilayer network as a whole – as a result of

all interactions during a match like in [9] – and we perform

also a micro-level analysis on each match sequence.

Our data comes from the 2012 Tri-Nations championship,

2012 New Zealand Europe tour, 2012 Irish tour to New

Zealand and 2011 Churchill Cup (only USA matches), for

a total of 18 matches. The data was collected by Opta1, using

ﬁeld positioning and semi-automatically annotated events.

We ﬁnd that there are some features of the pass networks

that make teams more successful in their quest for territorial

gain. In particular, the connectivity of the network seems to

play an important role. Being able avoid structurally crucial

players, that would make part of the team isolated if they were

removed from the network by a tackle, is associated with the

highest amounts of meters made. This is also conﬁrmed if

we do not analyze only the global network as the result of

the entire match, but also mining the patterns of each single

sequence of the game. In the latter case, the signal is harder

to disentangle from noise, and most analyzed features did not

yield any signiﬁcant result. This highlights how much rugby

is a game dependent on a grand match strategy, rather than on

just a sequence-by-sequence short term tactical one.

When applied to a real world prediction task, our framework

fares well in comparison with state of the art attempts. The

power in predicting the winner of a match is comparable with

the one of bookmakers, who have access to the full history

of teams and of the players actually performing on the pitch.

In particular, our framework is less susceptible to reputation

bias: the algorithm is not afraid to design New Zealand as a

loser in what bookmakers saw as a great upset result – its loss

to England in the December 1st, 2012 Twickenham clash.

II. RE LATE D WOR K

In the last decade, sports analytics has increased its per-

vasiveness as large-scale performance data became available

[23]. Researchers from different disciplines started to analyze

massive datasets of players’ and teams’ performance collected

from monitoring devices. The enormous potential of sports

data is affecting both individual and team sports, providing

a valid tool to verify existing sports theories and develop

new ones. As an example in individual sports, Cintia et

al. [8], [6] develop a ﬁrst large scale data-driven study on

cyclists’ performance by analyzing the workouts of 30,000

amateur cyclists. The analysis reveals that cyclists’ perfor-

mances follow precise patterns, thus discovering an efﬁcient

training program learned from data. In tennis, Yucesoy and

1http://www.optasports.com/

Barab´

asi develop a predictive model that relies on a tennis

player’s performance in tournaments to predict her popularity

[28]. In NBA basketball league the performance efﬁciency

rating introduced by Hollinger [12] is a stable and widely

used measure to assess players’ performance by combining

the manifold type of data gathered during every game (pass

completed, shots achieved, etc.). Vaz de Melo et al. [27]

introduced network analysis to the mix. In baseball, Rosales

and Spratt propose a new methodology to quantify the credit

for whether a pitch is called a ball or strike among the catcher,

the pitcher, the batter, and the umpire involved [21]. Smith et

al. propose a Bayesian classiﬁer to predict baseball awards

in the US Major League Baseball, reaching an accuracy of

80% in the predictions [25]. In soccer, networks are a widely

used tool to determine the interactions between players on

the ﬁeld, where soccer players are nodes of a network and

a pass between two players represents a link between the

respective nodes. For example, Cintia et al. [9], [7] exploit

passing networks to detect the winner of a game based on the

passing behavior of the teams. [14] shared the aim, without

using networks. They discovered that, while the strategy of

the majority of successful teams is based on maximizing

ball possession, another successful strategy is to maximize a

defense/attack efﬁciency score. Dynamic graph analysis has

also been applied for ranking purposes [24], [20], [18]. Other

examples of wider applicability of team-based success research

comes from analysis of citation [22] and social [15] networks.

Methodologically, our paper is indebted with the vast ﬁeld

of dynamics on networks analysis [4]. This ﬁeld is usually ap-

proached both from a statistical [26] and a mining perspective

[5]. We adopt the latter approach. In mining network dynam-

ics, the aim is to ﬁnd regularities in the evolution of networks

[2]. There are many applications for these techniques, beyond

sports analytics: epidemiology [17], mobility [10] and genetics

[16]. In this work, we focus on a narrower part of this ﬁeld,

since our networks are multilayer: nodes can be connected

with edges belonging to multiple types. A good survey on

multilayer networks, both modeling and analysis, can be found

in [13]. The speciﬁc multilayer model we adopt is the one of

multidimensional networks ﬁrstly presented in [3].

III. DATA

The data has been collected by Opta and made available in

2013 as part of the AIG Rugby Innovation Challenge2. Opta

performs a semi-automatic data collection that happens as the

game unfolds. Sensors feed a team composed by two or more

humans, who annotate the various actions of the match. Once

the event ended, the data is double-checked for consistency

and then serialized as an XML ﬁle.

A pass pis deﬁned by an action that was coded as successful

pass in the data. This means we drop forward, intercepted or

otherwise erroneous passes, that directly result in the team

losing possession. A pass is composed by a pair of players:

2http://optasports.com/news-area/aig-rugby-

innovation-challenge-competition-launched.aspx

10

100

1000

Score

Meters Made

Fig. 2: The relationship between meters made on a carry and

ﬁnal score in our dataset. We exclude outliers for teams who

did not score in a match (two occurrences in our data).

the pass originator and the pass receiver. Both players have to

be part of the same team. We refer to Pt,g as the set of passes

made by team tin game g– i.e. what we call “Pass network”.

|Pt,g|is the number of total passes made, which is equivalent

to the sum of the edge weights of the pass network.

A disruption d, also called tackle, is deﬁned by an action

that was coded as successful tackle in the data. This means we

keep all different tackle types recorded by the data provider

(chases, line, guard, etc), but we drop the ones whose result

was not a clean tackle, meaning that the defender conceded

a penalty or allowed the attackers to continue the offense. A

disruption is composed by a pair of players: the tackler and the

tackled. Players have to belong to different teams, making this

a bipartite network. Similarly to the pass notation, Dt,g and

|Dt,g|denote the set and number of tackles made, respectively.

For convenience, we deﬁne an aggregate of the disruption

action: du,t,g is the number of all disruptions targeted at player

uby team tin in game gover all disruptions made by tin g.

A sequence sis a list of passes and disruptions. Roughly,

we deﬁne a sequence as a phase of the game going from the

starting of a possession to its end. In rugby terminology, this

means deﬁning a sequence as a phase of game going from

an interruption of the game to another. Interruptions are tries,

penalties, drop goals, scrums and lineouts. Note that clean

changes in possession (intercepts, ruck steals and others) are

considered interruptions too. The union of the pass and tackle

networks result in a structure of the type depicted in Figure 1.

In Section V, the quality measure used to distinguish

between successful and unsuccessful teams is the number of

meters made with a carry. Rugby is a very territory oriented

game, and it can be won basically by gaining more meters ball

in hand. There is a very high correlation between meters made

and score/victory, and Figure 2 depicts this relationship (in the

ﬁgure, the Pearson correlation is ∼.58). As a consequence,

we use the information recorded in the metres attribute of

each actionrow element in the data as our success measure.

Symbol Meaning

uPlayer

tTeam

gSingle game (match)

pPass

dDisruption (tackle)

du,t,g Relative number of disruptions targeted to uby tin g

sSequence, a set of passes and tackles

Pt,g Passes made in game gby team t

Dt,g Disruptions made in game gby team t

ms,t Meters made in sequence sby team t

Mg,t Meters made in game gby team t

TABLE I: The notation used in the paper.

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Fig. 3: A toy model of a directed graph.

We refer to meters gained in a sequence sby team tas ms,t,

and we use it in the sequence analysis (Section V-B). In the

case of the structural analysis (Section V-A), we consider the

game gas a whole, and we deﬁne the overall success as all

the meters made, i.e. Mg,t =P

∀s∈g

ms,t.

Table I sums up the notation used in the paper.

IV. FEATURES

In this section we consider the multilayer network of passes

and disruptions as a whole, as it results from all interactions

between and within the two teams over the entire length of the

match. We deﬁne a set of features characterizing the network.

We aim at predicting the number of meters made on a carry

by the team over the match. The features are team-dependent,

thus for each match we have two observations: the feature for

the home team and for the away team. Each team has two set

of features: the pass features and the disruption features.

A. Pass Features

The pass features are features calculated over the team’s

pass network Pt,g. We consider the topology of Pt,g in

isolation, as a directed graph that is not interacting with

other external events. The features we deﬁne are purely

topological ones and they are: connectivity (γt,g(Pt,g )), assor-

tativity (ρt,g(Pt,g )), number of strongly connected components

(σt,g(Pt,g )), and clustering (∆t,g (Pt,g )).

Connectivity is deﬁned as follows. Given two nodes, con-

nectivity is the number of nodes that must be removed to

break all paths from the two nodes in Pt,g [1]. For instance,

in Figure 3, to separate nodes 2 and 4 you need only to remove

one node (3). With γt,g(Pt,g )we refer to the average of local

node connectivity over all pairs of nodes of Pt,g.

Assortativity (ρt,g(Pt,g )) is the Pearson correlation coefﬁ-

cient of the degrees of all pairs of nodes connected by an

edge [19]. A positive assortativity means that in the network

nodes with high degree tends to connect with other nodes with

high degree and vice versa. Figure 3 represents an assortative

network, as the degree correlation coefﬁcients is ∼0.15.

A strongly connected component in a network is a set of

nodes for which there is a path from any node of the compo-

nent to any other node in the component following the directed

edges of the graph. Given a directed network, there might

be zero, one or more strongly connected components. Our

σt,g(Pt,g )detects and counts the number of strongly connected

components in Pt,g . Figure 3 depicts a directed graph with

three strongly connected components: one composed by nodes

1, 2 and 3; and two other components composed by the single

nodes 4 and 5, since they are connected by a single directed

edge which does not allow to reach node 4 from 5.

The clustering of a node uis the fraction of possible

triangles through that node that exist:

cu=2Tu

ku(ku−1),

where Tuis the number of triangles through node u, and

ku>1is its degree (for ku≤1the convention is to ﬁx

cu= 0). The ∆t,g(Pt,g )feature is the mean clustering, or:

∆t,g(Pt,g ) = 1

nX

u∈t

cu,

where nis the number of nodes in Pt,g (for rugby usually

n= 15, because there are 15 players in a rugby team, although

in some cases a player might never receive a pass, setting

n= 14). Note that clustering is deﬁned for undirected graphs.

Thus, in this case, Pt,g is projected in a derived structure in

which we ignore edge direction. This is the only one of the

four measures for which we have to perform this projection.

The graph in Figure 3 has a high clustering coefﬁcient (∼

0.87), because nodes 1, 2, 4 and 5 all have cu= 1 – they are

all part of the only triangle they could be part of – while node

3 is part of only two of its six possible triangles.

B. Disruption Features

The disruption features exploit the multilayer nature of the

conjunction between Pt,g and Dt,g . We consider how different

the features of Pt,g become when one of its nodes gets disabled

by a tackle. We compare these features with the version of Pt,g

where no node gets removed and we weight this difference by

the relative number of times that the disruption has been made.

For each disruption feature we use the same notation as the

pass feature, with an overline. We deﬁne P∼u

t,g as the pass

network Pt,g when deprived of node u.

For connectivity, our deﬁnition is as follows:

γt1,g(Pt1,g ) = X

u∈t1

du,t2,g ×(γt1,g(P∼u

t1,g)−γt1,g (Pt1,g )).

In practice, the γt1,g (P∼u

t1,g)−γt1,g (Pt1,g )term calculates

what happens to the connectivity of Pt1,g when removing u.

A negative number means that the connectivity decreases, or

γt1,g(P∼u

t1,g)< γt1,g (Pt1,g ): you need to remove fewer nodes

to disconnect pairs of nodes in the network. A positive value

means that the connectivity increases. The du,t2,g term weighs

this connectivity change with the relative number of times t2

was able to disable player uwith a successful disruption. The

sum term aggregates the measure over all players representing

team t1, the team receiving the tackles.

To have an intuition of this operation, consider the tackle

features as an expression of the resilience level of the pass

network: they estimate how much the network is resistant to

disruptions. The higher the value, the more resilient the pass

network is.

The other disruption features are deﬁned following the same

template:

ρt1,g(Pt1,g ) = X

u∈t1

du,t2,g ×(ρt1,g(P∼u

t1,g)−ρt1,g (Pt1,g )),

σt1,g(Pt1,g ) = X

u∈t1

du,t2,g ×(σt1,g(P∼u

t1,g)−σt1,g (Pt1,g )),

∆t1,g(Pt1,g ) = X

u∈t1

du,t2,g ×(∆t1,g(P∼u

t1,g)−∆t1,g (Pt1,g )),

for assortativity, number of strongly connected components,

and clustering, respectively.

In the case of disruptions, we have an additional feature.

For each player uin a t, g pair we can calculate a centrality

value, answering the question: how central was player ufor

team tin game g? Thus, βu,t,g is deﬁned as u’s closeness

centrality [11] in Pt,g . The tackle centrality disruption is then

deﬁned as:

βt1,g(Pt1,g ) = X

u∈t1

(du,t2,g ×βu,t1,g).

It represent the weighted average closeness centrality of the

players tackled in t1by t2.

V. ANALYSIS

In this section, we perform the network analysis to estimate

the meters gain by rugby team using their network features.

We start by looking at the global pass and disruption features,

calculated over the entire aggregated match (Section V-A). We

then focus on an analysis considering each match sequence as

a single observation (Section V-B).

A. Structural Analysis

In this section we calculate the network features presented in

the previous section over the pass and disruption networks. We

use these features as independent variables of a simple OLS

model. The dependent variable of the model is the number of

meters made carrying the ball, as described in Section III. We

log transform the dependent variable.

Dependent variable:

Mg,t

(1) (2) (3) (4)

h0.058 0.160∗0.081 0.077

(0.096) (0.084) (0.096) (0.084)

log |Pt,g|0.366∗−0.218 0.379∗∗ 0.159

(0.201) (0.217) (0.158) (0.165)

∆t,g 0.451

(0.758)

γt,g 0.285∗∗∗

(0.075)

ρt,g 0.471

(0.360)

σt,g −0.073∗∗∗

(0.024)

Constant 5.118∗∗∗ 7.547∗∗∗ 5.451∗∗∗ 6.609∗∗∗

(0.724) (0.891) (0.764) (0.816)

Observations 36 36 36 36

R20.247 0.474 0.277 0.409

Adjusted R20.176 0.424 0.210 0.353

Residual Std. Error 0.273 0.229 0.268 0.242

F Statistic 3.500∗∗ 9.602∗∗∗ 4.096∗∗ 7.375∗∗∗

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

TABLE II: The regression results predicting meters made

using pass network features.

Note that in the regression we control for the home factor

with a binary variable h. This is done because home advantage

is very strong in rugby3, and we want to make sure it does not

affect our results. A second control we impose is the number

of passes made. There is an expected correlation between

how many meters a team will advance and the time it has

possession of the ball. The number of passes made is a good

proxy for this information.

We ﬁrst check the correlations between the pass features

and the number of meters made. Table II reports the results

of our models. We check one feature at a time, always

including our controlling factors. Two of the four features

do not exhibit a signiﬁcant correlation with the number of

meters made: clustering (∆t,g ) and assortativity (ρt,g). This

means that, when crafting their own pass network, teams are

not required to encourage or discourage triadic closure – a

receiver of a pass passing to the passer that originated the

action – and assortativity – passing the ball to a player with

a team connectivity similar to their own.

More interesting are the signiﬁcant associations with con-

nectivity (γt,g) and number of strongly connected components

(σt,g). These two measures are related and it is no surprise they

have opposite signs: the higher the connectivity of a network

the fewer components it has. We interpret these coefﬁcients

as follows: a rugby team’s pass network should ensure a

strong connectivity, likely establishing that there are multiple

and reciprocal pathways for the ball to reach all players.

Redundancy and structural strength are important in a rugby

team.

These two factors are able to explain away the simple con-

trol on quantity of possession, represented by the number of

passes made. Note that it is remarkable to obtain a signiﬁcance

3As of 2016, a weak team like Italy won only 12 out of 85 matches in the

Six Nations, and 11 of them were in Italy.

Dependent variable:

Mg,t

(1) (2) (3) (4) (5)

h0.162∗0.195∗0.183∗∗ 0.225∗∗ 0.128

(0.091) (0.103) (0.085) (0.109) (0.092)

log |Dt,g| −0.203 −0.263∗−0.175 −0.190 −0.082

(0.129) (0.149) (0.121) (0.152) (0.131)

βt,g 1.601∗∗∗

(0.372)

∆t,g 1.379∗∗

(0.508)

γt,g 0.243∗∗∗

(0.048)

ρt,g 0.805∗∗

(0.378)

σt,g −0.082∗∗∗

(0.019)

Constant 7.206∗∗∗ 7.360∗∗∗ 7.401∗∗∗ 8.077∗∗∗ 7.747∗∗∗

(0.564) (0.642) (0.519) (0.646) (0.544)

Observations 36 36 36 36 36

R20.415 0.250 0.483 0.191 0.414

Adjusted R20.360 0.179 0.434 0.115 0.359

Residual Std. Error 0.241 0.273 0.227 0.283 0.241

F Statistic 7.563∗∗∗ 3.548∗∗ 9.956∗∗∗ 2.517∗7.537∗∗∗

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

TABLE III: The regression results predicting meters made

using tackling network features.

of p<.01 with a very small sample size (N= 36). We do

not show a model containing all features at once, because

the collinearity between γt,g and σt,g makes them both not

signiﬁcant.

We now turn our attention to the disruption features. In

this case, instead of controlling for the number of passes, we

control for the number of disruptions. The control whether a

team played home or away is still in place. Table III reports

the results of these models.

Differently from the pass features, all disruption features are

signiﬁcantly correlated with the number of meters made. The

result of the average tackle centrality βt,g seems surprising:

the highest the centrality of the most targeted players the more

meters the team will make. However, this is only an apparent

surprise: the most central players are the scrum half and ﬂy

half (number 9 and 10 in Figure 1) which are players that do

not usually cover a lot of ground. On the other hand, the wings

(number 11 and 14 in Figure 1) are very peripheral but also

expected to cover most of the ground. This result is indeed

expected and not very interesting.

More interesting is that the more a team can maintain a

high value of clustering, connectivity and assortativity after

being disrupted by the average opponent tackle, the more it

can advance on the pitch. As expected, the number of strong

components is still negative: if after disruption the team still

does not have many isolated components it is expected to be

able to advance. The advice for a team would be to target

their tackles to the players who are the most responsible to

keep their pass network connected, but not the most central.

The signiﬁcance levels of γt,g and σt,g are higher also in this

case.

Note that connectivity is the single most important feature

discovered. Both in Table II and Table III the associated R2is

the highest. Together with our controls, γt,g and γt,g are able

to explain 47-48% of the variance in number of meters made.

Is it true that connectivity is the most important feature to

Lo w Lo w Very Low

Lo wHi g h

Hi g h

2008+/-160 1236+/-296 965+/-151

Tackle Connectivity

Tackle Strong Comps

1622+/-286

Ta ckle Connec tivity

Fig. 4: The decision tree for predicting the number of meters

made in a match using the pass/disruption features. The tree

node’s font size is proportional to the number of observations

with the given characteristics. Leaves report the expected

number of meters made for the branch. Edge labels the value

of the node’s feature.

predict a rugby team’s performance? We conclude this section

by showing how we can use these features in a data mining

framework to predict the number of meters a team will cover

ball in hand. We apply a simple decision tree technique4,

where the target variable is the number of meters made and

the predictors are all the features we discussed so far.

Figure 4 depicts the result. The most important split variable

the algorithm found was indeed a connectivity measure, the

one resulting from tackles. It is such an important feature

that it has been selected twice at two different tree levels –

note that we pruned the tree to avoid overﬁtting. A very low

tackle connectivity means that the team, as result from the

opponent’s disruptions, lost most of its original connectivity.

This is associated with the poorest performances in meters

gained: a very low tackle connectivity resulted in less than

1,000 expected meters made. This is as little as half the

expectation for a team with a high connectivity retention,

plus the ability of not having its own strongly connected

components broken apart. In this case, the team is expected

to advance 2,000 meters.

B. Sequence Analysis

A deeper evaluation of a team performance can be obtained

by the analysis of how team networks are built, action after ac-

tion. To do that, we split each game in sequence of possession

phases, i.e. time intervals where a team is controlling the ball.

The split into possession phases is made by selecting all the

events between two events that identify a start of possession. In

particular, we sort all the events according to their timestamps,

then we select all the sequences between possession events of

the two teams playing. The possession of a team lasts until

4Implementation obtained from http://www.borgelt.net/.

(a) Duration in minutes of se-

quences.

(b) Number of events per sequence.

(c) Number of passes per sequence. (d) Number of tackles per se-

quence.

Fig. 5: The distribution of sequence statistics across all the

observed matches.

the opposite team performs a possession event. The possession

events we consider to split a game into possession phases are

the following: 50m Restart, 22m Restart, Free Kick, Turnover

Won, Lineout, Lineout Steal, Scrum, Scrum Steal, Ruck Won,

Maul Won, Penalty, Pass intercepted.

Figure 5 depicts the distribution of various features across

game sequences. The overall trend suggests that these are all

broad distributions: the number of observations does not allow

us to test for a power-law hypothesis, but we can conclude

that there are heavy tails. In particular, Figure 5(a) shows

that usually game sequences are very brief, but some can

last for multiple minutes, when a team performs prolonged

phases of possession – for instance attempting to score a try.

This in turn implies that the number of events per action also

distributes broadly (Figure 5(b)) even when broken down in

passes (Figure 5(c)) and tackles (Figure 5(d)).

The goal of such an analysis is to understand the dynamics

of a game relying on the network features already described

in the previous sections. Here we are not exactly interested on

predicting the result of a game: the focus is on the analysis of

the single features in a dynamic context, in order to evaluate

the additional knowledge provided by the network features we

consider.

Once a game is subdivided into possession phases, we can

observe how the pass network – i.e. the passing interactions be-

tween players – grow across time. As a performance measure,

we use the quantity of meters gained by a team from which

we subtract the meters gained by its opposition. We analyze

the average value of each feature during time and we compare

it to the performance of the team, for each of the 18 games we

have in our dataset. Among the features we are interested in

(Connectivity, Assortativity, Strongly connected components,

Clustering), we observe a signiﬁcant negative correlation be-

Fig. 6: The correlation between strongly connected compo-

nents and meters gained w.r.t. the opposition.

tween the average number of strongly connected components,

and the meters gained (minus the opposition gains). In Figure

6 such a correlation (ρ= 0.49)) is highlighted.

This conﬁrms the global analysis: if a team breaks down its

effort in many isolated components it is unlikely to be able to

gain additional meters. The fact that this is the only relevant

feature – and that no tackle feature was found signiﬁcant –

suggests two additional insights. First, that rugby is a game

fundamentally different than soccer: in the literature it has

been shown that single sequence features were more relevant

than here to evaluate team success [9]. Second, since these

features were relevant when calculated over the entire match

pass network (as Section V-A shows), it suggests that rugby

has a peculiar dynamics. Our evidence points that, in rugby,

each action might matter not in isolation, but as the part

of a grand match strategy, that can be only appreciated by

analyzing the whole pass network.

VI. PREDICTIVE MO DE L

In this section, we test if our model based on pass and

disruption network features is able to accurately predict the

result of the game. We build a cross validation framework

where we train our model on 17 matches, leaving one out,

and then we predict the result of the match left out using

the model trained on the other 17 matches. We repeat this

procedure for all matches in the dataset. Since Section V-B

showed that sequence features are not signiﬁcant, we build

our model using exclusively global pass network features.

We perform two prediction tasks. The two tasks differ in the

target variable of interest. In the ﬁrst task, we aim at predicting

which one between the two teams will gain more meters during

the match. With our model, we are able to obtain the correct

answer for 15 out of 18 matches, i.e. with an accuracy ∼83%.

Since in rugby the number of meters gained is highly

correlated with both score and odds of winning, we can use

our model to predict also who is going to win the match. We

say that the team predicted to gain more meters is going to

win. In this case, we make the correct prediction for 14 out

of 18 matches, i.e. with an accuracy ∼77%. Note that the

reduced accuracy is due to the fact that one of the matches in

the dataset ended up in a draw. This is a very rare occurrence

in rugby, and it was not encoded in the model5.

How good is our prediction? A random predictor would ﬂip

a coin and get the right answer 50% of the times. However,

rugby matches tend to be predictable, given enough infor-

mation about past performances of teams and players. These

performances are recorded by the World Rugby organization,

which publishes weekly updated national rankings of teams.

It is reasonable to assume that the higher ranked team of the

two playing is expected to win. If we use the World Rugby

rankings to predict the outcomes of the matches, we obtain a

very similar accuracy: ∼76%6.

We can do slightly better by looking at historical odds

data7. Bookmakers are more invested in getting right a speciﬁc

match prediction than World Rugby. In fact, their accuracy

was higher, both of World Rugby rankings and of our model:

∼86%. However, we could ﬁnd data only for 14 matches,

the ones involving New Zealand, because there is no historic

record for the USA rugby matches. This makes the prediction

task easier: lower ranked teams are more unpredictable when

playing each other, and the bookmakers always picked New

Zealand for all the matches it played, being New Zealand such

a dominant rugby team.

To conclude this section, it is worthwhile noting two things.

First, our model was able to successfully predict the biggest

upset of the 18 played matches: the victory of England over

New Zealand. Neither World Rugby nor bookmakers predicted

that. Second, our model is a purely structural system, that

has no information about which team and which players are

performing. As such, its information pool is more restricted

than the one available to both World Rugby and bookmakers.

The fact that the model’s performance are on par with theirs

is rather encouraging. It is true that we then feed the model

perfect information recorded during the match, but we detail

in the conclusions how we plan to create a truly predictive

model.

VII. CONCLUSION AND FUTURE WOR KS

In this paper we build a multilayer network analysis frame-

work to describe the performance of rugby teams during a

match. We build two layers: a pass network and a tackle

network. We extract features from these layers and we use

them at two analytical levels. First, we extract features from

the network as a whole, representing the entire match. Then,

we divide the match in sequences of a single match action

and we extract sequence features. We use these features as

correlates of match performance, estimated by the number

of meters a team advanced on the ﬁeld. We discover that,

5The match was Australia v New Zealand, played on October 20th, 2012.

Our model predicted a win for New Zealand.

6Note that this is calculated over 17 matches, not 18, because one match

involved the reserve English national team, the England Saxons, which is not

ranked by World Rugby.

7From http://www.oddsportal.com

using the global features, connectivity is very important for

a team to successfully advance. Second, we perform single

sequence mining and we ﬁnd that, when considering actions

in isolation, most features have no signiﬁcant relation with

a team’s performance. This shows how much rugby is a

different game than soccer, where this analysis yielded the

opposite result [9]. Our interpretation is that soccer is a game

of tactics, where each sequence yields results that are mostly

independent from the other sequences; while rugby is a game

of strategy, where sequences build on each other to obtain the

intended result. This is not to say that sequence analysis is not

useful: by looking at the dynamic graph one might be able

to understand key moments of games – i.e. moments where

the prospective winner change. Finally, we show how our

predictive framework is on par with state of the art bookmaker

estimates, and better suited to predict upset results.

There are a number of directions that we can explore for

future works. First we can work on a network comparison

of different sports, mainly soccer. This would build on top

of the differences between the two sports we highlighted

here. Second, we can investigate other reasons of the poor

predictive performance of sequences. Sequences of sequences

might give more insight to appreciate the dominance of a

team not during the whole game or just one sequence, but

during an intermediate period of time. Third, we are planning

to use our framework to discuss how it is able to shed light on

large performance shocks. In our data, we have several New

Zealand versus Ireland matches, with very different outcomes:

one ended 22-19 and another 60-0. The question would be:

what changed in Ireland’s performances across these two

matches, played only a week apart? Another interesting case

study would be the England versus New Zealand upset:

what made the English team the only one able to beat New

Zealand in the 14 matches in our data? Finally, we could test

our predictive model on an actual prediction. We could build

a predicted match network before the match starts and use it

to pick the winner before the match happens, not after as we

did here. To do so, we would need more data, as 18 matches

are not enough for reliably training our system.

Acknowledgments. We thank Opta for having made avail-

able the data on which this paper is based. We thank Vittorio

Romano for helping us with his knowledge of rugby rules and

game dynamics. Michele Coscia has been partly supported

by FNRS, grant 24927961. This work has been partially

funded by the following European projects: Cimplex (Grant

Agreement 641191) and SoBigData RI (Grant Agreement

654024).

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