A simple Bayesian procedure for forecasting the outcomes of the UEFA Champions League matches

Foulley, Jean-Louis

Journal de la société française de statistique, Tome 156 (2015) no. 2, pp. 38-50.

Cet article présente la mise en œuvre bayésienne d’un modèle de probit cumulatif en vue de la prédiction des résultats de matches de la ligue des champions UEFA. L’argument de la fonction de répartition normale fait intervenir un seuil, un effet de match joué à domicile et la différence entre les valeurs des équipes en compétition. On suppose que la valeur d’une équipe est distribuée normalement avec une espérance qui s’exprime comme la régression sur une évaluation externe de l’équipe provenant du classement UEFA des clubs ou du système de classement mondial des clubs (FCWR). Les a priori sur ces paramètres sont mis à jour au début de chaque saison à partir des a posteriori obtenus en fin de saison précédente. Cela permet de prédire les résultats des matches de chacune des phases de la compétition  : minichampionnat de groupe et tournoi par élimination. On présente une application de cette méthode à la saison 2013-14. L’ajustement par le système FCWR est meilleur que celui obtenu par le coefficient UEFA. L’utilisation du premier conduit à un gain net de 24% sur la précision et de 23% sur le score de Brier par rapport à la situation témoin de non ajustement a priori pour la valeur d’équipe. On discute également d’un classement des équipes sur leurs performances lors de ce championnat et des possibilités d’inclure d’autres sources d’information dans le modèle.

This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and the difference in strength of the two competing teams. Team strength is assumed to follow a Gaussian distribution the expectation of which is expressed as a linear regression on an external rating of the team from eg. the UEFA Club Ranking (UEFACR) or the Football Club World Ranking (FCWR). Priors on these parameters are updated at the beginning of each season from their posterior distributions obtained at the end of the previous one. This allows making predictions of match results for each phase of the competition: group stage and knock-out. An application is presented for the 2013-2014 season. Adjustment based on the FCWR performs better than on UEFACR. Overall, using the former provides a net improvement of 24% and 23% in accuracy and Brier’s score over the control (zero prior expected difference between teams). A rating and ranking list of teams on their performance at this tournament and possibilities to include extra sources of information (expertise) into the model are also discussed.

Keywords: Football, UEFA Champions League, cumulative probit, Bayesian forecasting
Mot clés : Football, ligue des champions UEFA, probit cumulé, prévision bayésienne

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