Tag Archives: ncaa

Applying Graph Theory To March Madness

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

The Justice Dept Is Investigating College Football

The Associated Press is reporting that the Justice Department antitrust chief has sent a letter to the president of the NCAA asking him to explain why they don’t use a playoff system in college football, adding that the BCS system “may not be conducted consistent with the competition principles expressed in the federal antitrust laws”. Utah’s attorney general is apparently also preparing for a lawsuit against the BCS, on similar grounds. In related history, the NCAA has been saying for a while that they would move to a playoff system if the major schools wanted one, and bin Laden-killing President Obama made an early promise to try to do something about the lack of playoffs in college football. Hopefully the Justice Department will be as successful as the Navy SEALs.

From NPR