Ralph Abbey was a member of the PUP March Mathness ESPN group and completed his bracket in the 91.8 percentile which is a fantastic achievement. However, we’re already looking forward to 2013, so in this post, he shares a few tips for improving your bracket next tournament.
I am a PhD graduate student in mathematics at North Carolina State University. My adviser is Dr. Carl Meyer, coauthor of Who’s #1? While sports ranking isn’t my PhD topic, I do find it very interesting, and it is actually quite a good topic of conversation, even among non-math people.
It was less than 24 hours before the first games and I still hadn’t made a bracket—-to be honest, I had completely forgotten. Somehow the thought came to mind at the last minute, and I realized that I didn’t have enough time to research all the teams in depth to create my own bracket. To put off the stress (and the blame if I got things wrong) I turned to a few ranking algorithms I knew for help. The games data was found on Massey’s website: masseyratings.com
I formed a matrix in which entry i,j was the total number of points team i scored against team j over the entire season. Division 2 teams were included as well. Using this data matrix, I used both the offense defense model, and a pagerank model to rank the teams. I made 2 brackets, compiled by having the higher ranked team always beat the lower ranked team.
Additionally I formed a few other brackets: a “no-upsets” bracket that used the NCAA committee’s rankings. I also created 2 “upset” brackets. The first was a bracket in which if two teams seeded between 4 and 13 (inclusive) played, the worst ranked always won. If one or neither of the teams were in the range, then the better ranked team won. The other upset bracket was formed the same way, except by decreasing the range from 6 to 11.
In the end the winner for me was the offense defense model. It scored 1310 points on the ESPN challenge, placing above 91.8% of all ESPN brackets–absolute rank of 529,254. While it messed up on a lot of the first round upsets, the offense defense model was able to predict 3 of the 4 final four teams, 1 of the 2 championship teams, and it did predict Kentucky to win the whole tournament.
The plans for next year are uncertain, but one thing I do want to try is rank aggregation to see if it can combine the best of multiple models!