NCAA Basketball Tournament Analysis for High School Mathematics

Adrian J. Lee; Sheldon H. Jacobson; William A. Cragoe

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Conference: 2014 ASEE Annual Conference & Exposition
Location: Indianapolis, Indiana
Publication Date: June 15, 2014
Start Date: June 15, 2014
End Date: June 18, 2014
ISSN: 2153-5965
Conference Session: The Use of Games and Unique Textbooks in Mathematics Education
Tagged Division: Mathematics
Page Count: 11
Page Numbers: 24.930.1 - 24.930.11
DOI: 10.18260/1-2--22863
Permanent URL: https://peer.asee.org/22863
Download Count: 580

Paper Authors

biography

Adrian J. Lee Central Illinois Technology and Education Research Institute

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Dr. Adrian Lee received his Ph.D. in mechanical engineering from the University of Illinois at Urbana-Champaign in 2009, specializing in probability and risk analysis of aviation security systems. Dr. Lee served as a post-doctoral research engineer at Vishwamitra Research Institute, Center for Uncertain Systems: Tools for Optimization and Management, and is currently President of Central Illinois Technology and Education Research Institute. Dr. Lee also holds an adjunct academic position in the Department of Bioengineering at the University of Illinois at Chicago, and is a member of the Institute for Operations Research and Management Science (INFORMS), the Institute of Electrical and Electronics Engineers (IEEE), the Society for Industrial and Applied Mathematics (SIAM), and the American Society for Engineering Education (ASEE). His research interests include STEM education, probability and statistics, and stochastic optimization.

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Sheldon H. Jacobson University of Illinois, Urbana-Champaign

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Sheldon H. Jacobson is a Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign. He has a B.Sc. and M.Sc. in Mathematics from McGill University and a Ph.D. in Operations Research from Cornell University. His research interests span theory and practice, covering decision-making under uncertainty and discrete optimization modeling and analysis, with applications in aviation security, health care, and sports. From 2012-2014, he was on leave from the University of Illinois, serving as the Program Director for Operations Research in the Division of Civil, Mechanical and Manufacturing Innovation at the National Science Foundation.

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William A. Cragoe Sacred Heart-Griffin High School

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I am currently (as of 3/7/14) in my 8th year as a high school mathematics teacher. I recently started teaching a Statistics course and this will be the second year of using "Bracketodds" as a class project.

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Abstract

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.

Citation
Format

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

TY  - CPAPER
AB  -      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.
AU  - Adrian J. Lee
AU  - Sheldon H. Jacobson
AU  - William A. Cragoe
CY  - Indianapolis, Indiana
DA  - 2014/06/15
PB  - ASEE Conferences
TI  - NCAA Basketball Tournament Analysis for High School Mathematics
UR  - https://peer.asee.org/22863
DO  - 10.18260/1-2--22863
ER  -