Dynamics of tournaments: the soccer case

TL;DR

This paper models soccer tournaments using a random walk approach, analyzing score distributions and comparing different tournament formats, with findings aligning well with empirical data from major European leagues.

Contribution

Introduces a stochastic model for soccer scores that captures non-Gaussian distributions and compares tournament structures, providing new insights into competitive dynamics.

Findings

Scores exhibit non-Gaussian, asymmetric distributions.

Model aligns well with empirical league data.

Differences in tournament formats affect score dynamics.

Abstract

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.