Expected number of goals depending on intrinsic and extrinsic factors of a football player. An application to professional Spanish football league

Abstract

A Bayesian regression model for the number of goals scored by players in the Spanish football league during nine seasons is fitted. The model handles overdispersion in such a way that individual footballers ability for scoring may be estimated regardless of the number of minutes played, the position in the field and the team in which they play. Additionally, the posterior predictive distributions of the fitted model allow to obtain an estimation of the performance of any player in each season with reference to the number of goals scored, locating that number as a quantile in the expected distribution of the goals scored by this player in this season. The results show how the model awards the fact that defenders and midfielders score goals because it does not expect that they score many goals and evaluates a forward more strictly in relation to the expected number of goals.

Keywords:

• Goal scoring ability
• goal scoring performance
• Bayesian analysis
• count data
• Poisson regression
• negative binomial regression
• overdispersion