Analysis of a double Poisson model for predicting football results in Euro 2020

Abstract

First developed in 1982, the double Poisson model, where goals scored by each team are assumed to be Poisson distributed with a mean depending on attacking and defensive strengths, remains a popular choice for predicting football scores, despite the multitude of newer methods that have been developed. This paper examines the pre-tournament predictions made using this model for the Euro 2020 football tournament. These predictions won the Royal Statistical Society’s prediction competition, demonstrating that even this simple model can produce high-quality results. Moreover, the paper also presents a range of novel analytic results which exactly quantify the conditions for the existence and uniqueness of the solution to the equations for the model parameters. After deriving these results, it provides a novel examination of a potential problem with the model—the over-weighting of the results of weaker teams—and illustrates the effectiveness of ignoring results against the weakest opposition. It also compares the predictions with the actual results of Euro 2020, showing that they were extremely accurate in predicting the number of goals scored. Finally, it considers the choice of start date for the dataset, and illustrates that the choice made by the authors (which was to start the dataset just after the previous major international tournament) was close to optimal, at least in this case. The findings of this study give a better understanding of the mathematical behaviour of the double Poisson model and provide evidence for its effectiveness as a match prediction tool.