The European Physical Journal B

, 87:41

Emergence of self-similarity in football dynamics


  • Akifumi Kijima
    • Graduate School of Education, University of Yamanashi
  • Keiko Yokoyama
    • Division of Applied Physics, Faculty of Engineering, Hokkaido University
    • Japan Society for the Promotion of Science
    • Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and EngineeringUniversity of Yamanashi
  • Yuji Yamamoto
    • Research Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya University
Open AccessRegular Article

DOI: 10.1140/epjb/e2014-40987-5

Cite this article as:
Kijima, A., Yokoyama, K., Shima, H. et al. Eur. Phys. J. B (2014) 87: 41. doi:10.1140/epjb/e2014-40987-5


The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H ~ 0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field.


Statistical and Nonlinear Physics
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© The Author(s) 2014