Complexity emerges in measures of the marking dynamics in football games

Abstract

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.