Every year, as winter comes to an end and spring is right around the corner, sports followers everywhere get ready for March Madness. This is the time of year where the NCAA Division I Men's Basketball tournament begins; a 68 team, single elimination competition to determine who will be the national champion. This month is filled with statistics and analysis of teams and players to try and create the most accurate bracket. What if there is a mathematical approach to predicting who will be the Division I NCAA Men’s Basketball Champion? Is a perfect bracket even possible using math? Most likely not, but we can often improve our bracket using a combination of statistics and linear algebra.
In this lecture we will be looking at two methods, the Colley Method and the Massey Method, to compute rankings of teams by solving linear equations using data from games played during the season. We will explore the mathematics and motivation behind each method. When applied to March Madness brackets, these methods have proven to have very high success rates, especially compared to the data collected by the ESPN bracket submissions over the past few years.