Ranking World Class Chess Players Using Only Results From Head-To-Head Games

This honors thesis explores a method of ranking the world’s top ten chess grand- masters using only the outcomes of games containing only players in that very set. This method allows for players in a single era to be quickly ranked via algorithmic and numerical means, including very specific information, from a statistical stand- point. Furthermore, unlike the rating systems that are commonly used, the Elo and the Glicko systems, this method is Classicist in its statistical approach, rather than Bayesian. Finally, this ranking method also differs from others as it limits the infor- mation to games between the individuals being ranked. Some of the main topics utilized in this thesis are mathematical statistics through the use of the likelihood approach, statitical inference in the use of the logit disti- bution, and algorithmic design through the formulation of the solution to our given problem. The statistical package “R” was used in order to code all of the programs used during this research endeavor. This area of research used all of these tools in order to find an adequate mechanism for ranking a given set of players in a game with a win, draw, and loss as possible outcomes. Many of the techniques used in this research are extremely valuable in terms of further research. For instance, the likelihood approach that is used is a common statistical method that is often utilized in order to estimate parameters of a given model. Furthermore, algorithmic design and mathematical modelling are common- place in statistical research and are used to statistically infer estimates and to verify the validity of models. Initially assuming a logistical model as the distribution governing the outcomes of players games, an algorithm was constructed in order to rank a set of players based on outcomes of games. This function was then tested in single-simulation tests that followed the logistical model. Finally, after the algorithm was tested, it was applied to the outcomes of games between the world’s top ten chess grandmasters in order to rank-order them