A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating 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). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out 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 outperforms 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.

中文翻译：

---

评估足球比赛的概率预测：以排名概率得分为例

评分规则是概率预测和用于评估预测性能的相应结果的函数。关于哪些计分规则最适合评估体育赛事的预测存在一些争论。本文重点关注足球比赛结果的预测。排名概率分数 (RPS) 通常被推荐，因为它“对距离敏感”，即它考虑了结果的顺序（主场胜利比客场胜利“更接近”平局）。在本文中，这种推理是有争议的，因为它没有增加使用评分规则的通常目标。本地评分规则是一种仅考虑结果概率的规则。进行了两个仿真实验来比较 RPS 的性能，非局部且对距离敏感的分数，Brier 分数，非本地且对距离不敏感的分数，以及 Ignorance 分数，即局部且对距离不敏感的分数。Ignorance 得分优于 RPS 和 Brier 得分，这让人怀疑在这种情况下作为评分规则属性的非局部性和距离敏感性的价值。