# Bracket Odds for March Madness: A tool for picking a winning bracket

Will a one seed win the tournament?  How many 4-16 seeds will be in the Final Four?  Bracket Odds, a probabilistic analysis tool by Sheldon Jacobson at the University of Illinois provides the answers.  It is one of a series of tools that can be used by the more quantitative sports fans for picking better brackets.

Rather than making a prediction for a specific matchup (e.g., Duke vs. VCU), Bracket Odds makes seed-based predictions that are probabilistic, not absolute.  The recommendations are based on analyzing patterns from the past tournaments and prior seed matchups in each round of the tournament using a truncated geometric distribution.

Sheldon Jacobson recommends picking Final Four teams with seeds that are a combination of 1, 2, 3, since they result in the most likely outcomes.  Here is his reasoning:

[T]he probability of the Final Four comprising the four top-seeded teams is 0.026, or once every 39 years. Meanwhile, the probability of a Final Four of all No. 16 seeds – the lowest-seeded teams in the tournament – is so small that it has a frequency of happening once every eight hundred trillion years.

Sheldon Jacobson also writes about March Madness Math in the latest OR/MS article (for INFORMS members).  He gives a few hints about how to fill out a winning bracket:

In its most basic form, the game of basketball can be described as a sequence of dependent (Bernoulli) trials with well-defined outcomes. The sum of the resulting outcomes produces a final score. A superbly talented team will consistently defeat a much weaker opponent, even if the talented team plays very poorly and their weaker adversary plays well. This is why a No. 16 seed has never (so far) beaten a No. 1 seed in the first round of the tournament.

Everyone loves upsets, which occur with great regularity and predictability every year, in the first two rounds of the tournament. On average, more than four teams seeded No. 11 to 15 win a first round game; five such upsets occurred in 2010, the same number seen in both 2008 and 2009. On average, more than three teams seeded No. 7 to 14 reach the Sweet Sixteen; four such teams were so fortunate in 2010. In fact, it is rare not to see a team seeded No. 11 or lower in the Sweet Sixteen; this has only happened four times since 1985.

Joel Sokol provides team rankings using the LRMC method, which I have found to be useful for predicting the outcome of a game based on the teams rather than the seeds.  It has performed well in the past, and I’ve found that it does well with predicting upsets in the early rounds.