Soccer matches as experiments: how often does the ‘best’ team win?

Abstract

Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is superior and examine the probability that the outcome of the experiment (match) truly represents the relative abilities of the two teams. Given a final score, it is possible by using a Bayesian approach to quantify the probability that it was or was not the case that ‘the best team won’. For typical scores, the probability of a misleading result is significant. Modifying the rules of the game to increase the typical number of goals scored would improve the situation, but a level of confidence that would normally be regarded as satisfactory could not be obtained unless the character of the game was radically changed.

Keywords:

• football
• soccer
• experiment design
• Poisson statistics
• Bayesian

Acknowledgements

We are grateful to an anonymous referee for pointing out the link between crowd size and uncertainty.

Notes

We note that in a tournament w may not be constant, but may increase in later stages as teams become more equally matched. For simplicity, we adopt a mean value.