Professional tennis : quantitative models and ranking algorithms

Professional singles tennis is a popular global sport that attracts spectators and speculators alike. In recent years, financial trading related to sport outcomes has become a reality, thanks to the rise of online betting exchanges and the everincreasing development and deployment of quantitative models for sports. This thesis investigates the extent to which the outcome of a match between two professional tennis players can be forecast using quantitative models parameterised by historical data. Three different approaches are explored, each having its own advantages and disadvantages. Firstly, the problem is approached using a Markov chain to model a tennis point, estimating the probability of a player winning a point while serving. Such a probability can be used as a parameter to existing hierarchical models to estimate the probability of a player winning the match. We demonstrate how this probability can be estimated using varying subsets of historical player data and investigate their effect on results. Averaged historical data over varying opponents with different skill sets, does not necessarily provide a fair basis of comparison when evaluating the performance of players. The second approach presented is a technique that uses data, which includes only matches played against common opponents, to find the difference between the modelled players’ probability of winning a point on their serve against each common opponent. This difference in probability for each common opponent is a “transitive contribution” towards victory for the match being modelled. By combining these “contributions” the “Common-Opponent” model overcomes the problems of using average historical statistics at the cost of a shrinking data set. Finally, the thesis ventures into the field of player rankings. Rankings provide a fast and simple method for predicting match winners and comparing players. We present a variety of methods to generate such player rankings, either by making use of network analysis or hierarchical models. The generated rankings are then evaluated using their ability to correctly represent the subset of matches that were used to generate them as well as their ability to forecast future matches.