The odds of getting a perfect NCAA bracket are way better than 1 in 9,223,372,036,854,775,808
1 in 9,223,372,036,854,775,808
At a first glance and taking the most naive approach to the tournament, the odds are somewhere around 1 in 9.2 quintillion.Before the 2012 tournament, DePaul University math professor Jeff Bergen posted a video on YouTube explaining where this number comes from.
There are 63 total games in a tournament bracket. For each of those games, two teams play, and one team wins. So, filling out a bracket consists of picking 63 winners.So, you have two options for the first game, two options for the second game, two options for the third game, and so on, for all 63 games. To get the total number of possible ways to fill out a bracket, you multiply together all 63 of these twos, giving us 263, or 9,223,372,036,854,775,808 possible brackets.If all of these brackets are equally likely - if each game in the entire tournament is a 50-50 tossup, and picking the winner is basically a coin flip - we then get the odds of a correct bracket at one in 9.2 quintillion.
Actually, it's more like 1 in 576,460,752,303,423,488
Of course, flipping a coin 63 times is probably not a very good strategy for deciding how to fill out your bracket. Most of the games are not 50-50 matchups.
Consider the first round (the round of 64) of the NCAA Tournament. Of the 32 games in the first round, there are four games in which four of the best 64 teams (1st seeds) play four of the worst 64 teams (16th seeds).Since 1985, when the tournament first expanded to 64 teams, no 16th seed has ever beaten a 1st seed in the round of 64.
If we're comfortable assuming that this trend continues, we can safely fill in the four 1st seed vs. 16th seed games on our brackets.
Now we have 59 games to pick, and if we flip coins for all those, we have a one in 259, or one in 576,460,752,303,423,488, chance of winning the tournament. Still pretty terrible odds, but by making this one assumption, we have boosted our chances by a factor of 16.
Or maybe it's more like 1 in 128 billionProfessor Bergen suggests that by taking a more nuanced approach to the tournament along these lines and factoring in ratings and seedings, we can improve our odds to around one in 128 billion.
Watch Bergen's video here:
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