The striking proliferation of sensing technologies that provide high- delity data streams extracted from every game, induced an amazing evolution of football statistics. Nowadays professional statistical analysis rms like ProZone and Opta provide data to football clubs, coaches and leagues, who are starting to analyze these data to monitor their players and improve team strategies. Standard approaches in evaluating and predicting team performance are based on history-related factors such as past victories or defeats, record in quali cation games and margin of victory in past games. In contrast with traditional models, in this paper we propose a model based on the observation of players' behavior on the pitch. We model a the game of a team as a network and extract simple network measures, showing the value of our approach on predicting the outcomes of a long-running tournament such as Italian major league.
Thanks to the sensing technologies that provide high- delity data streams extracted from every game, in recent years football statistics have evolved in an amazing way. Nowadays professional statistical analysis rms like ProZone and Opta provide data to football clubs, coaches and leagues, who are starting to analyze these data to monitor their players, search for new talented ones, improve team strategies, and ensure themselves competitive advantage versus their peers. These football Big Data, which describe in great detail the behavior of teams during the games, pave the road to understand, model and possibly predict the complex patterns underlying sports success. An intriguing question is whether and how these data can be used to capture the performance of a team during a game: what are the features of the strongest teams? Can we extract from the data reliable measures of the performance of a team that correlate with its success during a competition?
Standard approaches provide a history-based answer to these questions: they assess the strength of a team using information about past victories or defeats, record in quali cation games and other global competitions and margin of victory in past games. In this paper we provide a di erent point of view on the problem: in contrast with history-based prediction techniques, we describe the performance of a team by observing its behavior on the pitch as captured by football data extracted from games. We show that this data-driven approach provides a description of the performance that shows an interesting correlation with the success of that team during the competition.
Starting from the list of frequent events occurred in the game { passes, crosses, assists, goal attempts { we model each football team as a complex system and infer a network whose nodes are players or zones on the pitch, and edges are movements of ball between two nodes, also labeled with weights to represent the amount of interactions among any pair of nodes. We describe the performance of a football team during a game by means of three simple measurements: the mean degree of a network's nodes, a proxy for the volume of play expressed by a team in a game, the variance of the degree of a network's nodes, a proxy for the diversity of play expressed by a team in a game, and a combination of the two. We observe a correlation among these performance indicators and the success of team, and therefore set up a simulation on the games of the FIFA World Cup 2014 and the Italian Serie A 2013/2014. The outcome of each game in the competition was replaced by a synthetic outcome (win, loss or draw) based on the network indicators of the teams in all the past games of the competition. We compare the outcomes of our simulation with the outcomes of two null models: a naive model which just sets the outcome of the game randomly, and a history-based model which assigns the victory to the team with the highest rank in recent o cial rankings. We observe that our approach outperforms the other models for long-running competitions as the Italian Serie A.
Football analytics has only begun to scratch the surface in the quest to understand, measure and predict performance. Our indicators have proven to be a good proxy of the performance of a team. If simple indicators like ours exhibit surprising connections to the success of teams, then a more complete view which includes defense strategy and movements without the ball has the potential of revealing hidden patterns and behavior of superior quality. 2
We have football data about two football competitions: (i) the FIFA World Cup 2014 with 32 teams and 64 football games; (ii) the Italian Serie A 2013/2014 with 20 teams and 380 football games. In our dataset, provided by TIM company3, a football game is described by a sequence of events on the eld { passes, crosses, assists, goal attempts and so on. Each event consists in a timestamp, the player who generates the event, the position of the ball on the eld when the event is generated, the position of the ball on the eld when the event ends, the outcome of the event (completed or failed). Table 2 shows some examples of events as stored in our dataset, while Figure 1 shows the total number of football events in all the games of our datasets. 3 www.tim.it 300,000 250,000 200,000 150,000 100,000 50,000 0
Events in football games passecsrosses foulhcsoerandeerdsdualstacckleleasrgaonaclekesepingcagrdotasaklseaotntisnetmeprctesptions
event time player origin destination outcome pass 17:24 Messi (65.4, 20.2) (67.8, 44.1) completed attempt 18:12 Messi (49.8, 10.5) (115.8, 10.5) failed assist 45:00 Pirlo (65.87, 22.1) (65.9, 30.6) completed cross 78:54 Tevez (110, 31.1) (115.7, 30.2) completed We describe the performance of a team in terms of passing activity using the information about pass events, the most frequent events occurring during a football game (Figure 1). We rst represent the behavior of a team during a game by two kinds of passing networks. In the player passing network nodes are players and edges represent ball displacements between two players. In this type of network the number of nodes is constant across the di erent games and teams, while the density of edges and the networked structure de ne the passing strategy of a team during the game. Figure 2 shows a visualization of a player network extracted from a game by Juventus. We also introduce a zone passing network, a weighted directed network where nodes are zone of the pitch and edges represent ball displacements between the two zones (Figure 3). Formally, the zone passing network of team A is a weighted directed graph GA = (V; E), where V is the set of zones (obtained by splitting the pitch into cells of size 11m 6.5m, 100 cells totally) and E is the set of edges, where an edge (z1; z2) represents all the passes, assists, or crosses started from zone z1 and ended in zone z2. In a zone passing network the number of nodes (zones on the pitch) varies across the teams and the games, allowing to detect signi cant di erences in the passing strategy of the same team across di erent games. The player passing network and the zone passing network are abstractions of the team's behavior that synthesize the passing history during a game in a compact model, and it can be constructed e ciently from the event data. They can be used to determine hot zones of the pitch (zones where a team prefers to play) or at what extent the team uses short distance or long distance passes, to detect preferred positions for players, crosses, assists or shots, and even to understand how much predictable the strategy of a team is.
We describe the performance of a team T during a football game i by three network measures extracted from its player (zone) passing network: (i) the mean of nodes' degree iT , a measure of the passing volume expressed by the team during the game; (ii) the standard deviation of nodes' degree iT , a measure of the passing heterogeneity expressed by the team during the game; (iii) and a combination of the two measures by their harmonic mean HT = 2=(1= iT + i 1= iT ). We compute the three network measures of teams for every game and observe a correlation among the proposed network measures and the success of a team during the competition (see Figure 4), and therefore set up a simulation experiment to validate our approach. In the simulation the outcome of each game of a competition (World Cup or Italian league) is predicted according to the value of the network measures of the two teams in all the past games of the competition. We simulate the outcome of game i of a football team T with the following two steps procedure: 1. for each of the two teams, we compute the three exponentially smoothed means of previous performances of the team iT 1, iT 1, HiT 1; 2. we compare the predicted measures of the two teams setting the team with the highest measure as winning.
At game i the performance history of team T is described as a list L = P1; : : : ; Pi 1 where Pi 1 = ( i 1; i 1; Hi 1). We build a prediction for the performance of a team at game i by computing the exponentially smoothed means of previous performances of each team i 1, i 1, Hi 1. The exponential smooth is used to weight the recent past and take into account the recent shape of the team. We validate our model against two null models: the 48-26-26 model and the ranking model. In the 48-26-26 model the outcome is extracted randomly from a probability distribution computed on our data: 48% is the probability of a win for the home team, then 26% is the probability of a draw, 26% is the probability that the away team wins. The ranking model is a history-based model where the winner of a game is the team who ended the previous tournament in the highest standing. We take the FIFA o cial rankings updated to may 2014 for World Cup and the nal rankings of Italian league 2012/2013 for Serie A 2013/2014. Table 2 provides the result of our experiments, where the values for null models are the means over 100 experiments. We observe that H is the measure that produces the best results for our model. The 48-26-26 model is the worst one predicting the outcome of games only in about the 30% of times. Our model outperforms both 48-26-26 model (30%) and ranking model (48%) for Serie A, reaching the best performance (0.53%) when using the player passing network. In contrast, for FIFA World Cup 2014 we have performance lower than the ranking model. Our results suggest that the proposed network measures are able to describe the performance of teams, adding predictive power with respect to the outcomes of games especially for long running competitions.
Italian league
Juventus 14 12 10 r o t ca 8 i d inσ 6 , μ H 4 2 0 5 10 15
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Fig. 4. Evolution of H indicator in player passing networks of Italian league. We
highlight the three teams which achieved the quali cation to Champions League. We
observe that the strongest teams show the highest values of H measure.
Model
H ;
In the last decade data science have entered the world of sports increasing its
pervasiveness as the technological limits were pushed up. Many works exploit
data mining or network science techniques to understand the complex patterns
of success in both individual and team sports. Cintia et al. developed a rst large
scale data-driven study on cyclists' performance by analyzing data about
workout habits of 30,000 amateur cyclists downloaded from popular tness social
network application [
In the context of football, the possibility of observing strategies and
decisions of teams by means of football data is attracting the interest of scientists
and football teams [
In this paper we describe the performance of a team during a football game by means of network indicators. We observe that these indicators correlate with the success of teams and them to predict the outcomes of the games in FIFA World Cup 2014 and Italian Serie A 2013/2014. We compare our results with the outcomes of two null models observing that our model performs better on longer and complex competitions like the Italian major league. As future work, we plan to include information about defensive events { tackles, goalkeeping actions, recoveries of ball and so on { and information about the movements of players without the ball. Defensive actions are crucial in the strategy of a team and they can make the description of a team's game more realistic. Moreover, studying the behavior of players without ball is crucial since it is known that most of the time (around 80% of the time) players move without the ball. Second, we plan to build other network features on the football networks to build models and classify the outcome of a game: which features are the most predictive of the outcome of a football game?
The authors wish to thank TIM company and Mariano Tredicini for providing the football data. We also thank Marco Malvaldi, Fabrizio Lillo, Dino Pedreschi, Fosca Giannotti, Daniele Tantari, Adriano Bacconi and Maurizio Mangione for their insightful discussions. We also must thank Max Pezzali and Edoardo Galeano for the useful suggestions about the nature of football.