Bayesian state-space models for the modelling and prediction of the results of English Premier League football

The attraction of using state-space models (SSMs) is their ability to efficiently and dynamically predict in the presence of change. In this paper, we formulate a Bayesian SSM capable of predicting the outcomes of football matches and the associated states, which are the attacking and defensive strengths of each side and the common home goal advantage. Our filter achieves accuracy and efficiency by exploiting conjugacy in its update step and using exact expressions to describe the evolution of the states. The presence of conjugacy enables us to use a mean-field approximation to update the states given fresh observations. The method is evaluated using the full history of the English Premier League and shown to be competitive, or superior, to weighted likelihood or score-driven time-series-based methods.