A bioengineering grad student got tired of filling out his March Madness bracket based on faulty intuition, so he decided to apply some mathematics to the problem. In and of itself, of course, that’s nothing new: sports statistics are probably the most crunched numbers in the world, and Vegas is on top of that game. What’s interesting is his approach, in that he modeled the Division I teams as a network and then applied graph theory to it to find the winners. This has also probably been done before, but the approach is very elegant and therefore worth a second look.

A tournament represented as a directed graph

First, he based his analysis only on the teams’ win-loss records; this is nice because

1. winning is all that matters, and
2. it keeps the analysis from getting out of hand with complexity.

He modeled the teams as nodes in a directed graph (in which the edges between the network’s nodes have directions) and made the edges point in the direction of the win. To each edge, he also assigned a weight, from 0 to 1, based on the magnitude of the defeat — because not all wins are created equal. Then he represented this network as an adjacency matrix, did some math on it to calculate the eigenvector centrality for each team to determine their relative importance in the network, and got a ranking of the Division I teams. Based on that ranking, he filled out a bracket (PDF):

He also has the entire ranked list of Division I teams, and his blog post has a lot more detail on the methodology, if you’re math nerd.

From BioPhysEngr, via Slashdot