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

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  • Khatibi, Arash
  • King, Douglas M.
  • Jacobson, Sheldon H.

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.

Suggested Citation

  • Khatibi, Arash & King, Douglas M. & Jacobson, Sheldon H., 2015. "Modeling the winning seed distribution of the NCAA Division I men׳s basketball tournament," Omega, Elsevier, vol. 50(C), pages 141-148.
    • Handle: RePEc:eee:jomega:v:50:y:2015:i:c:p:141-148
    DOI: 10.1016/j.omega.2014.08.004
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    References listed on IDEAS

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    1. Shishebor, Z. & Towhidi, M., 2004. "On the generalization of negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 127-133, January.
    2. Baumann Robert & Matheson Victor A. & Howe Cara A., 2010. "Anomalies in Tournament Design: The Madness of March Madness," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-11, April.
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    5. Jacobson, Sheldon H. & Nikolaev, Alexander G. & King, Douglas M. & Lee, Adrian J., 2011. "Seed distributions for the NCAA men's basketball tournament," Omega, Elsevier, vol. 39(6), pages 719-724, December.
    6. Metrick, Andrew, 1996. "March madness? Strategic behavior in NCAA basketball tournament betting pools," Journal of Economic Behavior & Organization, Elsevier, vol. 30(2), pages 159-172, August.
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    Cited by:

    1. Karpov, Alexander, 2015. "A theory of knockout tournament seedings," Working Papers 0600, University of Heidelberg, Department of Economics.
    2. Ilan Adler & Yang Cao & Richard Karp & Erol A. Peköz & Sheldon M. Ross, 2017. "Random Knockout Tournaments," Operations Research, INFORMS, vol. 65(6), pages 1589-1596, December.
    3. Ira Horowitz, 2018. "Competitive Balance in the NBA Playoffs," The American Economist, Sage Publications, vol. 63(2), pages 215-227, October.
    4. Karlsson, Niklas & Lunander, Anders, 2020. "Choosing Opponents in Skiing Sprint Elimination Tournaments," Working Papers 2020:6, Örebro University, School of Business, revised 01 Sep 2020.

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