Modeling and analyzing the NCAA Men’s Division I Basketball Tournament

The National Collegiate Athletic Association (NCAA) Men's Division I Basketball Tournament is an annually held basketball tournament between top universities throughout the United States. Along with attracting tens of millions of viewers, the event has become increasingly ingrained in popular culture, with millions attempting to predict the results of the tournament. Naturally, this interest among the general public has sparked similar interest among researchers attempting to statistically model the tournament. This thesis continues these efforts by proposing several methods of estimating the probability distributions of matches. Statistical analysis is conducted to verify these models and various properties of the tournament itself. \n \nThere are many challenges to face when developing probabilistic models for this tournament. In particular, the relative scarcity of past data (33 years of past tournaments) combined with the sheer number of possible outcomes (2^63 possible brackets) can make formulating accurate models a daunting task. This thesis proposes the following novel methods of estimating winning probabilities of each match of the tournament. The Position Model estimates winning probability distributions using maximum likelihood estimations based on the position of seeds in the bracket. The Upset Model estimates winning probability distributions using maximum likelihood estimations based on the probability of an upset in any given match. In addition to these two models, this thesis puts forth methods of combining the Position and Upset Model with the Geometric Model proposed by Jacobson et al. \n \nThe models proposed in this thesis are verified through the use of various numerical experiments and statistical analysis. In particular, tens of millions of brackets are generated independently at random according to the proposed models. Assessed using a fairly ubiquitous scoring standard, these generated brackets are compared to those submitted by human participants in popular competitions. Further statistical analysis is performed to investigate and support various aspects of these models.