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

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 distribu- tions 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 empiri- cal 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).