Abstract Predictive football modelling has become progressively popular over the last two decades. Due to this, numerous studies have proposed different types of statistical models to predict the outcome of a football match. This study provides a review of three different models published in the academic literature and then implements these on recent match data from the top football leagues in Europe. These models are then compared utilising the rank probability score to assess their predictive capability. Additionally, a modification is proposed which includes the travel distance of the away team. When tested on football leagues from both Australia and Russia, it is shown to improve predictive capability according to the rank probability score.

中文翻译：

---

足球预测模型的探索

摘要在过去的二十年中，预测性足球建模已逐渐流行。因此，许多研究提出了不同类型的统计模型来预测足球比赛的结果。这项研究回顾了学术文献中发表的三种不同模型，然后将这些模型应用于欧洲顶级足球联赛的最新比赛数据。然后利用排名概率得分对这些模型进行比较，以评估其预测能力。另外，提出了包括客队的旅行距离的修改。在来自澳大利亚和俄罗斯的足球联赛中进行测试时，根据排名概率得分，可以提高预测能力。