More Probability Models for the NCAA Regional Basketball TournamentsNeil C. Schwertman; Kathryn L. Schenk; Brett C. HolbrookThe American Statistician, Vol. 50, No. 1. (Feb., 1996), pp. 34-38.Stable URL:http://links.jstor.org/sici?sici=0003-1305%28199602%2950%3A1%3C34%3AMPMFTN%3E2.0.CO%3B2-2The American Statistician is currently published by American Statistical Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/astata.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact [email protected]://www.jstor.orgWed Jan 2 12:50:54 2008More Probability Models for the NCAA Regional Basketball Tournaments Neil C. SCHWERTMAN, and Brett C. HOLBROOKKathryn L. SCHENK, teams to the regional tournament to achieve parity in the Sports events and tournament competitions provide ex- cellent opportunities for model building and using basic statistical methodology in an interesting way. In this ar-ticle, National Collegiate Athletic Association (NCAA) re- gional basketball tournament data are used to develop sim- ple linear regression and logistic regression models using seed position for predicting the probability of each of the 16 seeds winning the regional tournament. The accuracy of these models is assessed by comparing the empirical prob- abilities not only to the predicted probabilities of winning the regional tournament but also the predicted probabilities of each seed winning each contest. KEY WORDS: Basketball; Logistic regression; Regres- sion. 1. INTRODUCTION Enthusiasm for the study of probability is enhanced when the concepts are illustrated by real examples of interest to students. Athletic competitions afford many such opportu- nities to demonstrate the concepts of probability and have been extensively studied in the literature; see, for example, Mosteller (1952), Searls (1963), Moser (1982), Monahan and Berger (1977), David (1959), Glenn (1960), Schwert- man, McCready, and Howard (1991), and Ladwig and Schwertman (1992). One excellent probability analysis op- portunity for use in the classroom occurs each spring when "March Madness," as the media calls it, occurs. "March Madness" is the National Collegiate Athletic Association (NCAA) regional and Final Four basketball tournaments that culminate in a National Collegiate Championship game. The NCAA selects (actually, certain conference champi- ons or tournament winners are included automatically) 64 teams, 16 for each of 4 regions, to compete for the national championship. The NCAA committee of experts not only selects the 64 teams from 292 teams in Division 1-A, but as- signs a seed position to each team in the four regions based on their consensus of team strengths. The format for each regional tournament is predetermined following the pattern in Figure 1, where the number one seed (strongest team) plays the sixteenth seed (weakest team), the number two seed (next strongest team) plays the fifteenth seed (second weakest), etc. The experts attempt to evenly distribute the Neil C. Schwertman is Chairman and Professor of Statistics, Depart- ment of Mathematics and Statistics, California State University, Chico, CA 95929-0525. Kathryn L. Schenk is Instructional Support Coordina- tor, Computer Center, California State University, Chico, CA 95929-0525. Brett C. Holbrook is Student, Department of Experimental Statistics, New Mexico State University, Las Cruces, NM 88003-0003. The American Statistician, February 1996, Vol. 50, No. I quality of each region. Schwertman et al. (1991) suggested three rather ad hoc probability models that predicted remarkably well the em- pirical probability of each seed winning its regional tour- nament and advancing to the "final four." The validity of the three models was measured only by each seed's prob- ability of winning its regional tournament. In this article we use the NCAA regional basketball tournament data as an example to illustrate ordinary least squares and logistic regression in developing prediction models. The parame- ter estimates for the simple models considered are based on the 600 games played (1985-1994) during the first ten years using the 64-team format. Validity of the eight new empirical and the three previous models in Schwertman et al. (1991) are assessed by comparing the empirical proba- bilities not only to the predicted probabilities for each seed winning the regional tournament but also to the predicted probabilities of each seed winning each contest. 2. TOURNAMENT ANALYSIS Predicting the probability of each seed winning the re- gional tournament (and advancing to the final four) requires the consideration of all possible paths and opponents. Even though there are 16 teams in each region, the single elimina- tion format (only the winning team survives in the tourna- ment, i.e., one loss and the team is eliminated) is relatively easy to analyze compared to a double-elimination format. [See, for example, the analysis of the college baseball world series by Ladwig and Schwertman (1992).] In the first game each seed has only one possible opponent, but in the sec- ond game there are two possible opponents, four possible in the third game and eight possible in the regional finals. Hence there are 1 . 2 . 4 . 8 = 64 potential sets of oppo-