The Mathematics of the Perfect Bracket

Calculating the odds of filling out a perfect NCAA Tournament bracket

Typically the stated odds of picking all 64 teams correctly for the perfect NCAA Tournament bracket are one in 9.2 quintillion. However, Duke mathematician Jonathan Mattingly says the formula to reach that number is not ideal because it's based on the calculations that the chance of winning each game is 50-50.

Professor of mathematics and statistical science, Mattingly developed his own formula that ranks teams based on their seed, resulting in perhaps a more realistic view on the odds of getting a perfect bracket, which he says is one in 2.4 trillion. "This one in 9.2 quintillion prediction is based on the idea that you just are flipping a coin for each game, that you don’t know anything else. But we know that’s wrong," Mattingly said. "For instance, if you look at historical information, since we’ve had the modern NCAA tournament, a one seed has never lost to a 16 seed. So why would you ever pick the 16 seed to beat the one seed?

"And it doesn’t happen that often that a two seed loses to a 15 seed, so I try to take into account that effect. So I get a more realistic number, which is not perfect but it’s probably better than just assuming every one happens with one-half probability.

"I don’t expect to see a perfect bracket in my life very often. It happens every once in a while, but it’s pretty rare."