Hypernetworks Reveal Compound Variables That Capture Cooperative and Competitive Interactions in a Soccer Match.

The combination of sports sciences theorization and social networks analysis (SNA) has offered useful new insights for addressing team behavior. However, SNA typically represents the dynamics of team behavior during a match in dyadic interactions and in a single cumulative snapshot. This study aims to overcome these limitations by using hypernetworks to describe illustrative cases of team behavior dynamics at various other levels of analyses. Hypernetworks simultaneously access cooperative and competitive interactions between teammates and opponents across space and time during a match. Moreover, hypernetworks are not limited to dyadic relations, which are typically represented by edges in other types of networks. In a hypernetwork, relations (with > 2) and their properties are represented with hyperedges connecting more than two players simultaneously (the so-called -plural, ). Simplices can capture the interactions of sets of players that may include an arbitrary number of teammates and opponents. In this qualitative study, we first used the mathematical formalisms of hypernetworks to represent a multilevel team behavior dynamics, including micro (interactions between players), meso (dynamics of a given critical event, e.g., an attack interaction), and macro (interactions between sets of players) levels. Second, we investigated different features that could potentially explain the occurrence of critical events, such as, aggregation or disaggregation of simplices relative to goal proximity. Finally, we applied hypernetworks analysis to soccer games from the English premier league (season 2010-2011) by using two-dimensional player displacement coordinates obtained with a multiple-camera match analysis system provided by STATS (formerly Prozone). Our results show that (i) at micro level the most frequently occurring simplices configuration is 1vs.1 (one attacker vs. one defender); (ii) at meso level, the dynamics of simplices transformations near the goal depends on significant changes in the players' speed and direction; (iii) at macro level, simplices are connected to one another, forming "simplices of simplices" including the goalkeeper and the goal. These results validate qualitatively that hypernetworks and related compound variables can capture and be used in the analysis of the cooperative and competitive interactions between players and sets of players in soccer matches.