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

Roberto da Silva, Mendeli H. Vainstein, Sebastián Gonçalves, and Felipe S. F. Paula
Phys. Rev. E 88, 022136 – Published 21 August 2013

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.

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  • Received 31 March 2013

DOI:https://doi.org/10.1103/PhysRevE.88.022136

©2013 American Physical Society

Authors & Affiliations

Roberto da Silva*, Mendeli H. Vainstein, and Sebastián Gonçalves

  • Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil

Felipe S. F. Paula§

  • Instituto de Informática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil

  • *rdasilva@if.ufgrs.br
  • vainstein@if.ufrgs.br
  • sgonc@if.ufrgs.br
  • §felipesfpaula@inf.ufrgs.br

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Vol. 88, Iss. 2 — August 2013

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