Football scores, the Poisson distribution and 30 years of final year projects in Mathematics, Statistics and Operational Research

Phil Scarf


The development of the Poisson match as a model used in the prediction of the outcome of football matches is described. In this context, many interesting modelling projects arise that are suitable for undergraduate, final year students. In a narrative that discusses the author’s engagement with this model and other related models, the paper presents a number of these projects, their attractions and their pitfalls, and poses a number of questions that are suitable for investigation. The answers to some of these questions would be worthy of the attention of the administrators of their respective sports.


Poisson distribution; sport; competitive balance; tournament design

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