June 15, 2014
June 15, 2014
June 18, 2014
24.930.1 - 24.930.11
NCAA Basketball Tournament Analysis for High School Mathematics Commonly referred to as “March Madness”, the NCAA men’s basketball tournament fuelsthree weeks of excitement – and anguish – nationwide as fans root for their favorite collegiateteams to advance through each stage of the competition. Following a committee selectionprocess and set of initial play-in games, sixty four teams – ranked 1 through 16 in four separateregions – participate in a single elimination tournament format to determine who will be crownedchampion. The structure of such a competition, coupled with the immense national interest,makes it an ideal event for the creation of so-called “office pools”, where people try to predictwhich teams will advance in the elimination bracket prior to the start of the tournament. Ratherthan basing these decisions on favorite teams or mascots, one can gain a better understanding ofthe likelihood of certain seeded teams advancing in each round based on the statistics associatedwith prior historical results. This work applies introductory level probability methods towards the analysis of the NCAAmen’s basketball tournament in an exciting week long instructional session for high schoolprobability and statistics classes. During the week prior to Selection Sunday – the day teams areselected and seeded for the tournament – students learn how the truncated geometric distributioncan be used to model the likelihood of seeds advancing in each round. The results from the pasttwenty nine tournaments are used to validate the model through a chi-squared goodness of fittest. Students learn how mathematics can be used to model uncertainty, and gain a betterunderstanding of the outcome of random events through a real world scenario. A combination oflecture slides and computational analysis using Microsoft Excel allows the students to learnabout the underlying probability concepts, and then apply them through programming exercises.In-class and homework assignments provide indications of how well the students understand theunderlying concepts. In addition to the week long course, high school students not enrolled in the math class areinvited to participate in a school wide tournament challenge, where each student is invited tosubmit a bracket in the hopes of winning token prizes, such as basketballs, school apparel, orcollegiate accessories. This event helps promote the probability and statistics class in the hopesof motivating students to enroll in this elective course in the future. The number of submittedbrackets along with the year-to-year class enrollment helps indicate the effectiveness ofpromoting the class through the tournament challenge. The analysis of the NCAA basketballtournament offers a unique and interesting opportunity to learn how probability distributions canbe used to model and predict real life events. The application of this work represents two years ofin-class instruction, and the theoretical material is derived from published academic research.
Lee, A. J., & Jacobson, S. H., & Cragoe, W. A. (2014, June), NCAA Basketball Tournament Analysis for High School Mathematics Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--22863
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