Local network structures of passing networks in football: Detecting styles of play through triadic analysis

Lucio Palazzo, Riccardo Ievoli, Giancarlo Ragozini

Contact: riccardoievoli@gmail.com

Summary statistics of football matches such as final score, ball possession and percentage of completed passes are not satisfyingly informative about style of play seen on the pitch. In order to evaluate connections and closeness within a team, it is crucial to highlight the dynamical interactions among players. In this context, the passes are most representative events, in terms of magnitude, with respect to scored goals, shots, corner kicks, free kicks, penalties and cards among others. Undoubtedly, technical individual skills and tactical level of the whole team may have an impact on the number of passes and on the quality of these relationships, but they are also deemed in relation to the social attitudes of players. Networks and related graphs can be useful tools to visualize and quantify how teams are different from each other. In this work, structural features of weighted and directed networks are discussed in order to evaluate team strategies in terms of passing behavior, and intelligible graphic visualizations are provided to compare teams and their own level of connection. Our main goal is twofold: firstly we study if network properties, here expressed in terms of triadic census, are able to distinguish among different styles of play. The analysis could provide useful tool for football staff and trainers in comparing team strategies, helping to identify the presence of partnerships, conflicts, outvoting effects of individuals towards other network members. We formally test their own properties against random graph inferential and probabilistic properties. The main aim is to find how observed triads deviate from a random scenario, identifying the intrinsic football features of this relationship. The second goal is to use triadic census in order to classify teams by their passing behavior. With this purpose, Correspondence Analysis on triad census matrices is applied to detect competitive football strategies and to classify teams through their styles of play in terms of passes. This kind of classification is made using the so-called ``tandem approach'', combining CA with a non-parametric cluster analysis method (k-means). Robustness of our results is checked through a more appropriate algorithm, named CA-clust, which simultaneously combines CA and clustering. Usefulness of this approach is checked through a real dataset regarding the Group Stage of UEFA Champions League, involving the best European football teams.

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