Abstract

Every year, people across the United States predict how the field of 65 teams will play in the Division I NCAA Men's Basketball Tournament by filling out a tournament bracket for the postseason play. This article discusses two popular rating methods that are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. The article also discusses how both methods can be adapted to take late season momentum into account. All the methods were used to produce brackets in 2009 and their results are given, including a mathematically-produced bracket that was better than 97% of the nearly 4.5 million brackets submitted to ESPN's Tournament Challenge.

Introduction

Every year around the beginning of March, students and faculty at 65 schools along with a large portion of the United States get excited about the prospects of March Madness, the Division I NCAA Men's Basketball Tournament. At the start of the tournament each of the 65 teams has a chance of ending the season crowned the champion. With the excitement of watching basketball comes the adventure of attempting to predict the outcome of the tournament by filling out a bracket. The NCAA estimates that 10% of the nation will fill out a bracket [4].