Luis C. Malacarne e Renio S. Mendes

Capítulo do livro: Christophe Clanet. (Org.). Sports Physics. 1ed. Paris: Éditions de l École polytechnique, 2013, p. 1-633.

Football has been attracting large number of spectators, becoming the most popular sports world-wide, specially by its unpredictable characteristic.

Efforts have been made to understand its stochastic behavior in different aspects. Besides complexities concerning football, some regularities can be identified. For instance, regularities in goal distribution per match in championships are well described by negative binomial distribution (Malacarne et al. 2000, Bittner et al. 2009). In addition, in a microscopic analysis, the statistics of the time elapsed between successive ball touches can be described by q-gamma distributions. This behavior was modeled providing information on the characteristics of football dynamics (R. S. Mendes et al. 2007). Another example of investigation on football can be related to statistical aspects of tournaments. A model based on random walks was proposed to this competitive system (Ribeiro et al. 2010). Computational simulations were performed and compared with empirical data from the English, the German and the Spanish leagues showing to be in good agreement. This approach enabled us to characterize a diffusion process where the punctuation are not normally distributed, having a short and asymmetric tail extending towards more positive values. This non-Gaussian behavior has been related with the difference between the teams and asymmetry of the punctuation system. In addition, a comparison between all-play-all and elimination tournaments was performed.