J. Sánchez-Flores, J.M. Martín-González, J.M. García-Manso, Y. de Saá, E.J. Arriaza-Ardiles and M.E. Da Silva-Griglotetto. Revista andaluza de medicina del deporte. 2016. 9(2):55–61. ISSN: 1888-7546.
Objective: The aim of this study is to analyze, 2000/01season through 2012/13season, the goal scored distribution by game and team; as its behavior in time. We also analyze the relationship with the league competitiveness degree. Method: We used the Poisson and the Negative Binomial distributions in order to study the goals distribution; and the Normalized Shannon Entropy for calculating the leagues uncertainty.Results: The Spaniard league has lost competitiveness in the seasons evaluated as the entropy and index of dispersion (team-game) display, especially in the last seasons analyzed. From the perspective of teams, it is not Poisson anymore, above all beyond 2008/09 season. From the perspective of games it does not take place the same phenomenon, specially the last seasons studied (a = 0.0099±0.0097; b = 0.9622±0.077;R2 = 0.316; p = 0.045 vs. a=0.0162±0.009; b = 0.9952±0.0715; R2 = 0.588; p = 0.002). Regarding time differences between each goal, the behavior is different from 200 minutes, where the process follows an exponential distribution, and can be considered as a Poissonian process. This modification points out a possible memory effect that can be understood as a Mathew effect, which explains that the less powerful teams are unable to overcome the situation. Conclusions: The superiority of most powerful teams seems to be more clear, perhaps excessive, compared to the rest of participating teams, as well as the probability that a lot of goals take place (> 5 goals) in a single game.
Keywords: Soccer; Goal; Shannon entropy normalized; Poisson distribution; Negative binomial distribution; Mathews Effect