Robust fitting of football prediction models

Abstract

Existing methods for the prediction of the final scores in football games focus on modelling the numbers of goals scored by the two competitors with parameter estimation of the assumed model usually based on the maximum likelihood approach. Although this approach allows for sufficiently accurate prediction of the final score, it does not account for large or surprising final scores than may deteriorate parameter estimates. This is especially the case in competitions with insufficient number of games compared to the participating teams (e.g. World Cup or Champions League). In this paper, we propose a weighted likelihood approach which allows the modeller to underweight a specific football score if it is felt that the result was not typical and falsifies (in any way) the parameter estimates. The imposed game weights can be defined subjectively or by assuming a model-based structure where the parameters can be estimated by iterative algorithms. The weight structure usually reflects deviations from the assumed model. Hence, scores that have low probability under the assumed model will be underweighted. This procedure may provide robust estimates even if surprising (under the assumed model) scores are observed. Champions League data are used to demonstrate the potential of the proposed approach.