Analysis of paired comparison data using Bradley-Terry models with applications to football data

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This dissertation focusses mainly on the Bradley-Terry model and its extensions to in- vestigate three aspects of English Premier League football. Firstly, a comparison of the estimated model rankings with the actual league table will be discussed and how well the model serves as a predictor of the final standings at the end of the season after sev- eral games have been played. Secondly, a home advantage analysis of the teams will be conducted. Thirdly, an estimation of player rankings based on team performances will be attempted. All analyses were conducted in R using the glm() framework, with the exception of the third model, which was specifically coded and solved using an optimi- sation function in R. While the first two analyses generally showed a good fit and clear results, the third one was not as straightforward. The failure to find stationary points in the optimisation problem suggests more work needs to be done to refine the model.

University of Warwick