Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective.

Johann H. Martínez,José L Herrera-Diestra,Javier Busquets,Javier M. Buldú,Ricardo Sevilla-Escoboza,David Garrido

doi:10.3390/e22020172

Abstract

We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player’s average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.

Highlights

In the recent years, the analysis of organization and performance of both football teams and their players underwent a revolution [1,2,3,4,5]
Datasets were provided by Opta [27] and consist of all passes completed in a football match by each team of the first division of the Spanish national league (“La Liga”) during the season 2017/2018
Summarizing, we have investigated the spatial and temporal entropies of football teams, focusing on the locations of the passes made during a match and the evolution of the organization of each corresponding passing network

Summary

Introduction

The analysis of organization and performance of both football teams and their players underwent a revolution [1,2,3,4,5]. The application of network science [12] to football datasets is giving a completely new perspective about football analysis, since it allows one to understand the roles of players as a whole, not as isolated components without interactions between them. In this way, it is possible to construct football passing networks, composed of nodes (players) and links (passes between players), whose organization is far from being random. The analysis of football passing networks has shown that their properties continuously evolve during a match and that key events, such as goals, may affect the network organization [13]

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Results

Conclusion