Modeling the winning seed distribution of the NCAA Division I men׳s basketball tournament

Abstract

The National Collegiate Athletic Association׳s (NCAA) men׳s Division I college basketball tournament is an annual competition that draws widespread attention in the United States. Predicting the winner of each game is a popular activity undertaken by numerous websites, fans, and more recently, academic researchers. This paper analyzes the 29 tournaments from 1985 to 2013, and presents two models to capture the winning seed distribution (i.e., a probability distribution modeling the winners of each round). The Exponential Model uses the exponential random variable to model the waiting time between a seed׳s successive winnings in a round. The Markov Model uses Markov chains to estimate the winning seed distributions by considering a seed׳s total number of winnings in previous tournaments. The proposed models allow one to estimate the likelihoods of different seed combinations by applying the estimated winning seed distributions, which accurately summarize aggregate performance of the seeds. Moreover, the proposed models show that the winning rate of seeds is not a monotonically decreasing function of the seed number. Results of the proposed models are validated using a chi-squared goodness of fit test and compared to the frequency of observed events.