  A random walk-like model is considered to discuss statistical aspects of
tournaments. The model is applied to soccer leagues with emphasis on the
scores. This competitive system was computationally simulated and the results
are compared with empirical data from the English, the German and the Spanish
leagues and showed a good agreement with them. The present approach enabled us
to characterize a diffusion where the scores are not normally distributed,
having a short and asymmetric tail extending towards more positive values. We
argue that this non-Gaussian behavior is related with the difference between
the teams and with the asymmetry of the scores system. In addition, we compared
two tournament systems: the all-play-all and the elimination tournaments.
