{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99366"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99366","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Modeling and analyzing the NCAA Men’s Division I Basketball Tournament","abstract":"The National Collegiate Athletic Association (NCAA) Men's Division I Basketball Tournament is an annually held basketball tournament between top universities throughout the United States. Along with attracting tens of millions of viewers, the event has become increasingly ingrained in popular culture, with millions attempting to predict the results of the tournament. Naturally, this interest among the general public has sparked similar interest among researchers attempting to statistically model the tournament. This thesis continues these efforts by proposing several methods of estimating the probability distributions of matches. Statistical analysis is conducted to verify these models and various properties of the tournament itself. There are many challenges to face when developing probabilistic models for this tournament. In particular, the relative scarcity of past data (33 years of past tournaments) combined with the sheer number of possible outcomes (2^63 possible brackets) can make formulating accurate models a daunting task. This thesis proposes the following novel methods of estimating winning probabilities of each match of the tournament. The Position Model estimates winning probability distributions using maximum likelihood estimations based on the position of seeds in the bracket. The Upset Model estimates winning probability distributions using maximum likelihood estimations based on the probability of an upset in any given match. In addition to these two models, this thesis puts forth methods of combining the Position and Upset Model with the Geometric Model proposed by Jacobson et al. The models proposed in this thesis are verified through the use of various numerical experiments and statistical analysis. In particular, tens of millions of brackets are generated independently at random according to the proposed models. Assessed using a fairly ubiquitous scoring standard, these generated brackets are compared to those submitted by human participants in popular competitions. Further statistical analysis is performed to investigate and support various aspects of these models.","abstract_html":"The National Collegiate Athletic Association (NCAA) Men's Division I Basketball Tournament is an annually held basketball tournament between top universities throughout the United States. Along with attracting tens of millions of viewers, the event has become increasingly ingrained in popular culture, with millions attempting to predict the results of the tournament. Naturally, this interest among the general public has sparked similar interest among researchers attempting to statistically model the tournament. This thesis continues these efforts by proposing several methods of estimating the probability distributions of matches. Statistical analysis is conducted to verify these models and various properties of the tournament itself. There are many challenges to face when developing probabilistic models for this tournament. In particular, the relative scarcity of past data (33 years of past tournaments) combined with the sheer number of possible outcomes (2^63 possible brackets) can make formulating accurate models a daunting task. This thesis proposes the following novel methods of estimating winning probabilities of each match of the tournament. The Position Model estimates winning probability distributions using maximum likelihood estimations based on the position of seeds in the bracket. The Upset Model estimates winning probability distributions using maximum likelihood estimations based on the probability of an upset in any given match. In addition to these two models, this thesis puts forth methods of combining the Position and Upset Model with the Geometric Model proposed by Jacobson et al. The models proposed in this thesis are verified through the use of various numerical experiments and statistical analysis. In particular, tens of millions of brackets are generated independently at random according to the proposed models. Assessed using a fairly ubiquitous scoring standard, these generated brackets are compared to those submitted by human participants in popular competitions. Further statistical analysis is performed to investigate and support various aspects of these models.","abstract_has_math":false,"creators":["Li, Kevin Yu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Jacobson, Sheldon H."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:48:54Z","date_published":"2018-03-13T15:48:54Z","updated_at":"2026-07-22T22:24:37Z","subjects":["March Madness","National Collegiate Athletic Association (NCAA)","Basketball"],"languages":["en"],"rights":["Copyright 2017 Kevin Li"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99366","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jacobson, Sheldon H."]},{"key":"dc:creator","label":"Author","values":["Li, Kevin Yu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:48:54Z","2017-12-06","2017-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["March Madness","National Collegiate Athletic Association (NCAA)","Basketball"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Kevin Li"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99366"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The National Collegiate Athletic Association (NCAA) Men's Division I Basketball Tournament is an annually held basketball tournament between top universities throughout the United States. Along with attracting tens of millions of viewers, the event has become increasingly ingrained in popular culture, with millions attempting to predict the results of the tournament. Naturally, this interest among the general public has sparked similar interest among researchers attempting to statistically model the tournament. This thesis continues these efforts by proposing several methods of estimating the probability distributions of matches. Statistical analysis is conducted to verify these models and various properties of the tournament itself. There are many challenges to face when developing probabilistic models for this tournament. In particular, the relative scarcity of past data (33 years of past tournaments) combined with the sheer number of possible outcomes (2^63 possible brackets) can make formulating accurate models a daunting task. This thesis proposes the following novel methods of estimating winning probabilities of each match of the tournament. The Position Model estimates winning probability distributions using maximum likelihood estimations based on the position of seeds in the bracket. The Upset Model estimates winning probability distributions using maximum likelihood estimations based on the probability of an upset in any given match. In addition to these two models, this thesis puts forth methods of combining the Position and Upset Model with the Geometric Model proposed by Jacobson et al. The models proposed in this thesis are verified through the use of various numerical experiments and statistical analysis. In particular, tens of millions of brackets are generated independently at random according to the proposed models. Assessed using a fairly ubiquitous scoring standard, these generated brackets are compared to those submitted by human participants in popular competitions. Further statistical analysis is performed to investigate and support various aspects of these models.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Kevin Li, accepted the attached license on 2017-12-05 at 10:16.","The student, Kevin Li, submitted this Thesis for approval on 2017-12-05 at 10:22.","This Thesis was approved for publication on 2017-12-06 at 11:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11842 on 2018-03-13 at 10:10:32","Made available in DSpace on 2018-03-13T15:48:54Z (GMT). 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Naturally, this interest among the general public has sparked similar interest among researchers attempting to statistically model the tournament. This thesis continues these efforts by proposing several methods of estimating the probability distributions of matches. Statistical analysis is conducted to verify these models and various properties of the tournament itself. There are many challenges to face when developing probabilistic models for this tournament. In particular, the relative scarcity of past data (33 years of past tournaments) combined with the sheer number of possible outcomes (2^63 possible brackets) can make formulating accurate models a daunting task. This thesis proposes the following novel methods of estimating winning probabilities of each match of the tournament. The Position Model estimates winning probability distributions using maximum likelihood estimations based on the position of seeds in the bracket. The Upset Model estimates winning probability distributions using maximum likelihood estimations based on the probability of an upset in any given match. In addition to these two models, this thesis puts forth methods of combining the Position and Upset Model with the Geometric Model proposed by Jacobson et al. The models proposed in this thesis are verified through the use of various numerical experiments and statistical analysis. In particular, tens of millions of brackets are generated independently at random according to the proposed models. Assessed using a fairly ubiquitous scoring standard, these generated brackets are compared to those submitted by human participants in popular competitions. Further statistical analysis is performed to investigate and support various aspects of these models.","Submission original under an indefinite embargo labeled 'Open Access'. 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