Applying graphs and complex networks to football metric interpretation

Using machine learning pipeline to predict entry into the attack zone in football

Sports sciences are increasingly data-intensive nowadays since computational tools can extract information from large amounts of data and derive insights from athlete performances during the competition. This paper addresses a performance prediction problem in soccer, a popular collective sport modality played by two teams competing against each other in the same field. In a soccer game, teams score points by placing the ball into the opponent's goal and the winner is the team with the highest count of goals. Retaining possession of the ball is one key to success, but it is not enough since a team needs to score to achieve victory, which requires an offensive toward the opponent's goal. The focus of this work is to determine if analyzing the first five seconds after the control of the ball is taken by one of the teams provides enough information to determine whether the ball will reach the final quarter of the soccer field, therefore creating a goal-scoring chance. By doing so, we can further investigate which conditions increase strategic leverage. Our approach comprises modeling players' interactions as graph structures and extracting metrics from these structures. These metrics, when combined, form time series that we encode in two-dimensional representations of visual rhythms, allowing feature extraction through deep convolutional networks, coupled with a classifier to predict the outcome (whether the final quarter of the field is reached). The results indicate that offensive play near the adversary penalty area can be predicted by looking at the first five seconds. Finally, the explainability of our models reveals the main metrics along with its contributions for the final inference result, which corroborates other studies found in the literature for soccer match analysis.

Analysis of the Football Transfer Market Network

Using publicly available data from the football database transfermarkt.co.uk, it is possible to construct a trade network between football clubs. This work regards the network of the flow of transfer fees between European top league clubs from eight countries between 1992 and 2020 to analyse the network of each year's transfer market. With the transfer fees as weights, the market can be represented as a weighted network in addition to the classic binary network approach. This opens up the possibility to study various topological quantities of the network, such as the degree and disparity distributions, the small-world property and different clustering measures. This article shows that these quantities stayed rather constant during the almost three decades of transfer market activity, even despite massive changes in the overall market volume.

A new model for predicting the winner in tennis based on the eigenvector centrality

The use of statistical tools for predicting the winner in tennis matches has enjoyed an increase in popularity over the last two decades and, currently, a variety of methods are available. In particular, paired comparison approaches make use of latent ability estimates or rating calculations to determine the probability that a player will win a match. In this paper, we extend this latter class of models by using network indicators for the predictions. We propose a measure based on eigenvector centrality. Unlike what happens for the standard paired comparisons class (where the rates or latent abilities only change at time t for those players involved in the matches at time t), the use of a centrality measure allows the ratings of the whole set of players to vary every time there is a new match. The resulting ratings are then used as a covariate in a simple logit model. Evaluating the proposed approach with respect to some popular competing specifications, we find that the centrality-based approach largely and consistently outperforms all the alternative models considered in terms of the prediction accuracy. Finally, the proposed method also achieves positive betting results.

Passing Networks and Tactical Action in Football: A Systematic Review

The aim of this study is to examine the most significant literature on network analyses and factors associated with tactical action in football. A systematic review was conducted on Web of Science, taking into account the PRISMA guidelines using the keyword “network”, associated with “football” or “soccer”. The search yielded 162 articles, 24 of which met the inclusion criteria. Significant results: (a) 50% of the studies ratify the importance of network structures, quantifying and comparing properties to determine the applicability of the results instead of analyzing them separately; (b) 12.5% analyze the process of offensive sequences and communication between teammates by means of goals scored; (c) the studies mainly identify a balance in the processes of passing networks; (d) the variables allowed for the interpretation of analyses of grouping metrics, centralization, density and heterogeneity in connections between players of the same team. Finally, a systematic analysis provides a functional understanding of knowledge that will help improve the performance of players and choose the most appropriate response within the circumstances of the game.

Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior

Pattern analysis is a well-established topic in team sports performance analysis, and is usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of these interactions, this work presents novel entropy mathematical models for Markov chain-based pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition Entropy applied to both passing and reception patterns. To demonstrate their applicability, these mathematical models were used in a case study in football—the 2016/2017 Champions League Final, where both teams were analyzed. The results show that the winning team, Real Madrid, presented greater values for both individual and team transition entropies, which indicate that greater levels of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide information to game analysts, allowing them to provide coaches with accurate and timely information about the key players of the game.

Play-by-Play Network Analysis in Football

This study identifies dominant and intermediary players in football by applying a play-by-play social network analysis (SNA) on 70 professional matches from the 1. and 2. German Bundesliga during the 2017/2018 season. SNA provides a quantification of the complex interaction patterns between players in team sports. So far, the individual contributions and roles of players in football have only been studied at match-level considering the overall passing of a team. In order to consider the real structure of football, a play-by-play network analysis is needed that reflects actual interplay. Moreover, a distinction between plays of certain characteristics is important to qualify different interaction phases. As it is often impossible to calculate well known network metrics such as betweenness on play-level, new adequate metrics are required. Therefore, flow betweenness is introduced as a new playmaker indicator on play-level and computed alongside flow centrality. The data on passing and the position of players was provided by the Deutsche Fußball Liga (DFL) and gathered through a semi-automatic multiple-camera tracking system. Central defenders are identified as dominant and intermediary players, however, mostly in unsuccessful plays. Offensive midfielders are most involved and defensive midfielders are the main intermediary players in successful plays. Forward are frequently involved in successful plays but show negligible playmaker status. Play-by-play network analysis facilitates a better understanding of the role of players in football interaction.