Football displays fractal dynamics (Vol. 45 No.3)

Players’ and ball’s positions captured on video.

Physicists reveal that the real-time dynamics in a football game are subject to self-similarity characteristics in keeping with the laws of physics, regardless of players’ psychology and training.

Football fascinates millions of fans. Despite their seemingly arbitrary decisions, each player obeys certain rules, as they constantly adjust their positions in relation to their teammates, opponents, the ball and the goal. In this work the authors have now analysed the time-dependent fluctuation of both the ball and all players’ positions throughout an entire match.

The authors considered two previous football matches. Thanks to their analysis of the time-series variation in the ball versus the front-line movements of the players, they were the first to discover that these dynamics have a fractal nature. This finding implies that the movement of the ball/front-line at any given time has a strong influence on subsequent actions. This is due to the so-called memory effect, linked to the game’s fractal nature.

A. Kijima, K. Yokoyama, H.Shima and Y. Yamamoto (2014), “Emergence of self-similarity in football dynamics”, Eur. Phys. J. B, 87, 41 (2014)
[Abstract]