Eur. Phys. J. B (2014) 87: 41
https://doi.org/10.1140/epjb/e2014-40987-5

Regular Article

Emergence of self-similarity in football dynamics

¹ Graduate School of Education, University of Yamanashi, 4-4-37, Takeda, Kofu, 400-8510 Yamanashi, Japan
² Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628 Hokkaido, Japan
³ Japan Society for the Promotion of Science, 5-3-1, Koujimachi, Chiyoda-ku, 102-0083 Tokyo, Japan
⁴ Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-4-37, Takeda, Kofu, 400-8510 Yamanashi, Japan
⁵ Research Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya University, Chikusa, 464-8601 Nagoya, Japan

^a e-mail: hshima@yamanashi.ac.jp

Received: 25 April 2013
Received in final form: 7 November 2013
Published online: 19 February 2014

Abstract

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.