Statistical modelling and Bayesian inference for match outcomes and team behaviour in association football
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This thesis presents advances in modelling and inference for match outcomes in the association football English Premier League. We firstly extend earlier models by introducing a behavioural aspect which can be used to investigate how teams react to the state of play in a match. We show that the model, in its simplest form, outperforms existing models and is able to select a portfolio of pro table bets against a bookmaker. Secondly, we introduce a dynamic component to the model by allowing team ability parameters to vary stochastically in time. We employ particle filtering methods to cope with a mixture of static and dynamic parameters and find that the updating of posterior distributions is particularly fast, a necessary attribute should we wish to update parameter estimates while matches are in-play. Furthermore, it is shown that the methods are able to recover model parameters based on simulated league data. Finally, we propose an extension to the model so that we are able to investigate how a team modifies its behaviour based on their league situation. We consider league positions that are closely attainable and suggest that since teams modify their behaviour based on their current league position, outcomes of different matches are not necessarily independent.