Evaluating probabilistic forecasts of football matches: The case against the Ranked Probability Score

Abstract

A scoring rule is a function of a probabilistic forecast and a corresponding outcome that is used to evaluate forecast performance. A wide range of scoring rules have been defined over time and there is some debate as to which are the most appropriate for evaluating the performance of forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is `sensitive to distance', that is it takes into account the ordering in the outcomes (a home win is `closer' to a draw than it is to an away win, for example). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the actual aims of using scoring rules. A related property of scoring rules is locality. A scoring rule is local if it only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out in the context of football matches to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the ignorance score, which is local and insensitive to distance. The ignorance score is found to outperform both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.