Analysis of goals (score) studied in thirteen seasons (2000/01 to 2012/13) for a league of professional spanish football League

Abstract

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.