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We propose a novel algorithm that outputs the final standings of a soccerleague, based on a simple dynamics that mimics a soccer tournament. In ourmodel, a team is created with a defined potential(ability) which is updatedduring the tournament according to the results of previous games. The updatedpotential modifies a teams' future winning/losing probabilities. We show thatthis evolutionary game is able to reproduce the statistical properties of finalstandings of actual editions of the Brazilian tournament (Brasileir\~{a}o).However, other leagues such as the Italian and the Spanish tournaments havenotoriously non-Gaussian traces and cannot be straightforwardly reproduced bythis evolutionary non-Markovian model. A complete understanding of thesephenomena deserves much more attention, but we suggest a simple explanationbased on data collected in Brazil: Here several teams were crowned champion inprevious editions corroborating that the champion typically emerges from randomfluctuations that partly preserves the gaussian traces during the tournament.On the other hand, in the Italian and Spanish leagues only a few teams inrecent history have won their league tournaments. These leagues are based onmore robust and hierarchical structures established even before the beginningof the tournament. For the sake of completeness, we also elaborate a totallyGaussian model (which equalizes the winning, drawing, and losing probabilities)and we show that the scores of the "Brasileir\~{a}o" cannot be reproduced. Suchaspects stress that evolutionary aspects are not superfluous in our modeling.Finally, we analyse the distortions of our model in situations where a largenumber of teams is considered, showing the existence of a transition from asingle to a double peaked histogram of the final classification scores. Aninteresting scaling is presented for different sized tournaments.

A Simple Non-Markovian Computational Model of the Statistics of Soccer Leagues: Emergence and Scaling effects