Anomalous diffusion in the evolution of soccer championship scores : real data, mean-field analysis, and an agent-based model

Abstract

Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva et al., Comput. Phys. Commun. 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.