Interactions between soccer teams reveal both design and emergence: Cooperation, competition and Zipf-Mandelbrot regularity

João Paulo Ramos,Duarte Araújo,Rui J. Lopes

doi:10.1016/j.chaos.2020.109872

João Paulo Ramos, Duarte Araújo + Show 1 more

Open Access

https://doi.org/10.1016/j.chaos.2020.109872

Copy DOI

Abstract

Abstract Considering soccer matches as complex systems facilitates the identification of properties that emerge from the interactions between players. Such properties include the regularities and statistical patterns that characterize couplings and sets between players established during matches. Empirical studies on the statistical distributions of number of items (e.g., words in texts) have shown that these distributions follow scaling properties according to empirical laws known as Zipf-Mandelbrot. Here we investigate whether the (re)occurrence of pitch location of sets of players in a soccer match also obeys these empirical laws. Data collected from 10 soccer matches shows that, for most sets of players, this seems to be the case. Exceptions were found in particular types of sets, such as goalkeeper and goal, and left defender and right attacker from opposite teams. Rather than challenging the hypothesis that a Zipf-Mandelbrot law defines this system, these exceptions may be explained by the players configuration design, which is a trait of human interaction within complex systems. This design expresses match strategy, before the team enters in such dynamical processes (the game).

Highlights

Several approaches have been used to study complex systems, including the identification of well-known complexity features Bar-Yam (2002); Kobayashi, Kuninaka, Wakita and Matsushita (2011); Juarrero (2000); Silva, Vilar, Davids, Araújo and Garganta (2016b)
Rather than challenging the hypothesis that a Zipf-Mandelbrot law defines this system, these exceptions may be explained by the players configuration design, which is a trait of human interaction within complex systems
The red and blue lines in sub-figures 3a, 4a and 5a correspond to the values obtained from the ZM model, for = 1 and = 3, with parameters, and estimated via Maximum Likelihood Estimation (MLE) Izsák (2006)

Summary

Introduction

Several approaches have been used to study complex systems, including the identification of well-known complexity features Bar-Yam (2002); Kobayashi, Kuninaka, Wakita and Matsushita (2011); Juarrero (2000); Silva, Vilar, Davids, Araújo and Garganta (2016b). An interesting and extensively investigated aspect of self-organization is the emerging exchange of information (e.g. verbal and non-verbal communication and their statistical properties) between people interacting in a given system Riley, Richardson, Shockley and Ramenzoni (2011). These communication processes are based on cooperative interactions such as synergistic relations, and on confrontation, which is a non-cooperative type of interaction. The communication processes between players in soccer matches are often visually based and reflected in the players’ moves and interpersonal spatial relationships Schmidt and Richardson (2008); Riley et al (2011); Schmidt and Fitzpatrick (2016); Ramos, Lopes, Marques and Araújo (2017b); Silva, Chung, Carvalho, Cardoso, Davids, Araújo and Garganta (2016a).

Methods

Results

Conclusion