Out of 6.5 million entries, the participants in the March Mathness group of the ESPN Tournament Challenge are doing very well. One third of our group is in the top 20%. Following are summaries from some of those in our group. They describe how they designed their brackets and how they are embracing the excitement of the tournament. The methods mentioned are described in the recently published Who’s #1? By Amy Langville and Carl Meyer.
Additional student reports here: http://blog.press.princeton.edu/2012/03/22/how-are-we-doing-checking-in-with-our-march-mathness-teams/
Bryan Kelley is a sophomore Math major at Davidson College. He is from Rockland, Massachusetts. In the following, he describes how he selected his bracket using the PageRank method from Who’s #1? by Amy Langville and Carl Meyer. You can find more on PageRank in Google’s PageRank and Beyond, also by Langville and Meyer.
The experience of filling out a March Madness bracket is completely new to me this year. I have always resisted it in the past because as a die hard competitor and a passionate sports fan, I cannot enjoy the tournament if I have picked a team that I think will win over a team that I want to win. It is a conundrum I’m sure many other Americans also find themselves in this time of year.
This year, however, I put my internal conflict aside, and in the name of math filled out my first March Madness bracket. To create the bracket, Tim Chartier and I referenced Amy Langville and Carl Meyer’s new book, Who’s #1?. Using that book, I coded an algorithm in MatLab that solves for the stationary eigenvector of a stochastic matrix and used that vector to rank the teams. For the matrix entries, Tim and I decided to use the point differential in teams’ wins/losses.
Considering many of the experts had Kentucky winning this year (which is not surprising considering the season the Wildcats have had) Tim and I did not expect to see the algorithm give us Michigan State as this year’s champion. However, that is what it gave us, and to avoid my internal conflict, that is how I filled out the bracket. In fact, I filled out every spot in the bracket precisely how the algorithm dictated me to fill out the bracket.
This turned out to be a good thing because in my heart I thought Missouri was going to win the tournament this year, but instead, as we saw on the first weekend, they were taken down by the formidable 15 seed Norfolk St. In addition, as a college student, I don’t have time to follow every Division 1 Men’s basketball team in the country so there were also many picks that I had no idea about. Thus, it was nice to have an algorithm to tell me what to do. By the end of the first night of the tournament, I was in the 98.6 percentile, only missing the VCU upset, and by the end of the first round, I fell a little to the 90.1 percentile. The first time I logged on and saw that I was in the top 98.6% of all brackets was a nice jolt. I probably checked my ranking ten more times that night to make sure there was not a mistake.
What has been most exciting to me this during this experience was finally finding a way to combine my academic passions and my love for sports. I think using math to predict a typically unpredictable tournament is about as cool as it gets because it is exciting to math people and non-math people alike. Even at Davidson alone, it has created a lot of conversation between my math friends and my non-math friends because everyone wants to be able to predict who is going to win. The one downfall of this experience is that I have had the pleasure of watching my Davidson Wildcats all season long and was so excited to see them make it back to the tournament this year that it killed me to pick Louisville over them…and then have it come true.
The first night of March Madness 2012 was pretty standard, and thus my bracket did pretty well. And then came the second day. With two 15 over 2 seed upsets this tournament, my bracket was brought back down to life a little bit. However, I suspect most of the rest of the country also did not see that happening so I expect to move on from those losses and perform well in the Sweet 16. As long as Michigan St. keeps winning, I’ll be happy.
I should also mention that in addition to competing in the PUP group, I have several other brackets in a different group that is part of ongoing research. In that group, I developed several variations of the PageRank algorithm, and many of those are also doing well. Tim and I are anxious to see how those results turn out in addition to the standard PageRank algorithm.
David Heilbron is a junior Math major at Davidson College . In selecting his bracket he has used the probability of given seeds to advance and then picked a random number to decide if they do. He is doing very well. Here he describes how he filled in his bracket.
So here are the nuts and bolts of my bracket. Basically I went through each bracket from 1985-2011 and saw how many of each seed number made it to each specific round (Sweet Sixteen, Elite Eight, etc). So say over that time period, eight #5 seeds have made it to the Elite Eight. I took this number and then divided it by the total possible #5 seeds that could have been in the Elite Eight over all those years. There were 4 each year, times 27 years, or 108. I did this for each seed and each round to get all these probabilities of a certain seed making it to each round.
From there, it is a simulation that runs each head-to-head match-up moving through the games. To find the winner of a certain game, we take each seed number’s probability and scale it to make a standard probability that the teams can be judged from. Finally, we get a random number which, if less than or equal to the probability, one team goes on, and if not then the other team goes on.
Long story short, we find each seeds chance of getting to a certain round and then use those in the head to head match-ups to print out the winners of each game and then just put them into a bracket.
In terms of which is more exciting, I really do love the basketball. I grew up watching a lot of ACC basketball so watching the games is so much fun. I actually have been finding the math more interesting though. It is cool to see how everyone thinks up different weightings and strategies.
The Murray State loss may come back to haunt my bracket as the tournament continues and Syracuse really has not looked that good, but I have a good feeling going forward. One game that concerns me though is Louisville vs. Michigan State. I’d love to see Louisville win and keep my bracket going but I do have to be a homer for Davidson and keep licking my wounds after the first round loss.