Modeling the winning seed distribution of the NCAA Division I men׳s basketball tournament |
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| Institution: | 1. Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL 61801, United States;2. Department of Computer Science, University of Illinois, Urbana, IL 61801, United States;1. Houston Methodist Orthopedic and Sports Medicine, Houston, Texas;2. Vanderbilt University Medical Center Orthopaedic Surgery and Rehabilitation, Nashville, Tennessee, U.S.A;1. Management Department, Bentley University, Waltham, MA 02452, USA;2. School of Information, Renmin University of China, Beijing 100872, China;3. Department of Systems Science and Industrial Engineering, SUNY at Binghamton, Binghamton, NY 13902, USA;1. Harvard Extension School, 51 Brattle Street, Cambridge, MA 02138, USA;2. Princess Margaret Cancer Centre, 101 College Street, Toronto, Ontario M5G 1L7, Canada;3. Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada;4. Laboratory Medicine Program, University Health Network, 200 Elizabeth Street, Toronto, Ontario M5G 2C4, Canada;5. Department of Laboratory Medicine and Pathobiology, University of Toronto, Toronto, Ontario M5S 1A8, Canada;6. Department of Medical Biophysics, University of Toronto, Toronto, Ontario, Canada;1. Amsterdam Collaboration on Health and Safety in Sports, Department of Public and Occupational Health, Amsterdam Public Health Research Institute, VU University Medical Center, Van der Boechorststraat 7, Amsterdam 1081 BT, The Netherlands;2. Department of Sport, Exercise and Health, University of Basel, Birsstrasse 320 B, Basel 4052, Switzerland;3. Division of Exercise Science and Sports Medicine, University of Cape Town, Anzio Road, Observatory, Cape Town 7925, South Africa;1. Division of Orthopaedic Surgery, Sunnybrook Health Sciences Centre, University of Toronto, MG323 – 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada;2. Division of Orthopaedic Surgery, University of Toronto, MG323 – 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada |
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| 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. |
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| Keywords: | Exponential distribution Markov model NCAA basketball tournament |
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