Regular Article

The European Physical Journal B

, 87:41

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Emergence of self-similarity in football dynamics

  • Akifumi KijimaAffiliated withGraduate School of Education, University of Yamanashi
  • , Keiko YokoyamaAffiliated withDivision of Applied Physics, Faculty of Engineering, Hokkaido UniversityJapan Society for the Promotion of Science
  • , Hiroyuki ShimaAffiliated withDepartment of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi Email author 
  • , Yuji YamamotoAffiliated withResearch Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya University


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