Statistical Modelling of Football Results

Abstract

The structure of this thesis is summarised below:

1. In Chapter 2 we will introduce some commonly used football result prediction models. The majority of these models will be used in the analysis described in subsequent Chapters. 2. We will discuss some of the basic principles of gambling theory in Chapter 3, along with definitions relating to the measurement of betting success. We will also introduce the Kelly criterion, a commonly used method for determining the size of bets in an optimal manner. 3. In Chapter 4 we review goodness of fit testing for football prediction models. Key issues include correlation between home and away goals and over (or under) inflation of draws. We will then propose an alternative approach based on the distribution of goal differences. 4. In Chapter 5 we present the results of three simulation studies. The first study illustrates the application of statistical models to a betting application based on the Kelly criterion using simulated data with the aim of comparing different betting strategies. In the second study we use data from past seasons of the English Premier League to determine the profitability of betting using the Kelly Criterion. In the third study we compare two equivalent models using Bayesian and maximum likelihood methods of inference (for the remainder of this thesis, we will often use the term “Bayesian model” to refer to a model where inference is performed using the Bayesian methodology and “Maximum likelihood Model” to refer to a model where inference is performed using maximum likelihood). 5. Finally, in Chapter 6 we introduce a state-space model that seeks to model change over time in team-specific attacking and defensive abilities.