Posted by Laura McLay on March 17, 2010
A few articles about the NCAA tournament using math were in the news.
Depaul math professor Jeffrey Bergen illustrates how hard it is to fill out a correct bracket using straight up combinatorics. You are less likely to randomly choose winners in a bracket (ignoring seeds) than to win the lottery. This is because there are 63 games in the tournament (with two potential winners in the first round and 65 potential winners in the final round), whereas there are only 6 numbers in the lottery (with about 40 numbers to choose from, with replacement). Of course, you increase your odds of correctly predicting all the tournament games by taking the seeds into account, but it’s still tough. The winning brackets in online contests from a field of millions of entries typically do not predict all games correctly.
An article in the business section of CBS News summarizes some hints that rely on mathematical tools (rather than listening to the talking heads). They suggest using online tools, including the OR model LRMC (developed by Joel Sokol and others). The article also suggests playing the odds in the first round and choosing all #1 seeds to advance. They also suggest to play some mind games if you are filling out an office pool, since you can increase your odds of winning by make different–but not unlikely–choices. They recommend choosing the third or fourth overall pick as the champion rather than the first or second overall pick that most of your rivals are choosing. It also advises to guard against the bias of availability by not favoring teams that have played against the home town favorite.
ESPN maintains a list of Giant Killers for predicting upsets, which is mainly useful in the early rounds of the tournament. A giant killer is a “team that beats a tournament opponent seeded at least five spots higher in any round”. ESPN has a methodology behind their approach–they have
zeroed in on team stats that correlate strongly with upset wins and losses in past tournaments. We’ve conducted multiple regression analyses, which essentially is a way to tell how strongly each member of a group of inputs (those stats) affects an output (giant-killing success or failure). Statistically, [Giant Killers] have:
• Low turnover rates and high rates of generating opponent turnovers.
• High offensive-rebound percentages.
• High 3-point scoring as a proportion of all points scored.