Spain retains its title and sets a new record – generalized linear mixed models on European football championships

Abstract

AbstractNowadays many approaches that analyze and predict the results of football matches are based on bookmakers’ ratings. It is commonly accepted that the models used by the bookmakers contain a lot of expertise as the bookmakers’ profits and losses depend on the performance of their models. One objective of this article is to analyze the role of bookmakers’ odds together with many additional, potentially influental covariates with respect to a national team’s success at European football championships and especially to detect covariates, which are able to explain parts of the information covered by the odds. Therefore a pairwise Poisson model for the number of goals scored by national teams competing in European football championship matches is used. Moreover, the generalized linear mixed model (GLMM) approach, which is a widely used tool for modeling cluster data, allows to incorporate team-specific random effects. Two different approaches to the fitting of GLMMs incorporating variable selection are used, subset selection as well as a Lasso-type technique, including an L1-penalty term that enforces variable selection and shrinkage simultaneously. Based on the two preceeding European football championships a sparse model is obtained that is used to predict all matches of the current tournament resulting in a possible course of the European football championship (EURO) 2012.