A Bayesian approach for predicting match outcomes: The 2006 (Association) Football World Cup

Abstract

In this paper we propose a Bayesian methodology for predicting match outcomes. The methodology is illustrated on the 2006 Soccer World Cup. As prior information, we make use of the specialists’ opinions and the FIFA ratings. The method is applied to calculate the win, draw and loss probabilities at each match and also to simulate the whole competition in order to estimate classification probabilities in group stage and winning tournament chances for each team. The prediction capability of the proposed methodology is determined by the DeFinetti measure and by the percentage of correct forecasts.

Appendices

Appendix A: Useful results

Result 1

• If X|λ∼ Poisson (λ c),c>0, and λ follows a Jeffreys prior given by π(λ)∝λ ^−½, then λ|X=x∼ Gamma (x+½,c).

Proof

• The result follows immediately from

  

Result 2

• If X|λ∼ Poisson (λ c),c>0, and λ∼ Gamma (α,β), then the marginal distribution of X is a negative binomial distribution with parameters α and .

Proof

• From the hypothesis above we have

  

  Hence, the marginal distribution of X is given by

  

Appendix B: FIFA ratings

See Table B1.

Table 11 FIFA ratings prior to 2006 World Cup