Probabilistic Modelling in Multi-Competitor Games

Previous studies in to predictive modelling of sports have largely concentrated on those which belong to the group of sports and games which can be termed as one-on-one: those where teams or players face each other in pairs e.g. football, basketball and tennis. Here the case of multi-competitor games or sports such golf, horse racing and motor sport, which are defined as ones in which three or more players or teams compete against each other at the same time are considered. Models, which given data in the form of previous performance of players, can make probabilistic predictions on the outcome of future tournaments are investigated. The generalised Bradley-Terry model for repeated multiple rankings of individuals known as the Plackett-Luce model is reviewed. A two-way anova model which uses scores rather than rankings is proposed as an alternative more suited for specific application to sports data. A dynamic extension and Kalman filter approach to fitting data to the two-way anova model is described. The models are firstly developed and tested on artificially generated 'toy' data then are applied to real world data in the form of seven years worth of US PGA tour records. Findings from this study are presented in the form of a comparison of the static models with the Official Golf World Rankings and a case study of the dynamic analysis of two players. A quantitative evaluation of the predictive performance of the models is presented in the form of results from their application in a gambling scenario. The dynamic two-way anova model is found to be competitive in its predictions when compared to those of a human expert.