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Mission Impossible: A Perfect March Madness® Bracket

Posted 03/04/2022 by Curtis Brown (@cbmathguy)

Your mission, should you choose to accept it: Picking the perfect bracket!

Each year, millions of people across the world gather to watch an incredible display of basketball skill and passion. During this annual tradition, many will attempt to predict the outcome of each game in the tournament. But what are the odds of picking every game correctly? Spoiler alert: To date, no one in the history of the NCAA tournament has ever made a verifiably perfect bracket.

A hand holds a pen to a sheet of paper with a bracket chart printed on it
Approximately 70 million people compete in basketball brackets during March Madness® every year, making them almost as popular as the basketball tournament itself.

Beginning with the first round, through the championship, there are 63 games (64 teams) in a standard NCAA tournament bracket. And, there are many different ways to do the math. First, let’s talk blind luck, assuming that the odds of picking each game correctly are an even 50/50, like a coin flip. The probability of correctly selecting the winners of the first round would be 1/4294967296.

Just to make it out of the first round of the tournament in a blind guess is a long shot. But, it has been done.

In 2019, a remarkably high 15 of the 25 million “official” brackets made it through the first round unscathed, according to the NCAA site. But that’s just round one. If we continue with this blind luck idea, the probability of making it through the first two rounds is 1/(2.814 x 10^14).

And that’s only happened once in the history of recording brackets. As mentioned on the NCAA’s site in 2019, a neuropsychologist’s bracket was correct through the first 49 games of the tournament.

So, if the bracket maker chose completely at random, that would be a probability of, roughly, 1/(5.6295 x 10^14. That’s one in 563 trillion. You’re billions of times more likely to be eaten by a shark than making it through the second round of your bracket without a miss. Talk about a lucky guy!

But we’re not finished yet. If we jump all the way to guessing all 63 games correctly, assuming each team has an equal chance in every game, the probability of a perfect bracket is 1/(9.22337 x 10^18). That’s 1 in 9.22 quintillion. As a reminder, one quintillion is one billion billions.

Let’s put this into perspective. There are roughly 7.53 quintillion grains of sand on earth according to a study conducted by students at the University of Hawaii. If you pick up every grain of sand on the Earth, colored one purple, and then mixed them up and picked one, you would be more likely to pick the purple grain of sand than you would a perfect NCAA tournament bracket (if choosing at random).

Of course, we know that’s not how it really works. There are many things that factor into filling out a bracket: from the seed, to their road/home records, to how well they performed when playing on the east versus west coast, to injury reports. There are also conflicting opinions on how much this information can help increase your odds of scoring the perfect bracket. But it’s safe to say, while predicting the future is hard, predicting a perfect bracket is nearly impossible.

March Madness is a registered trademark of the NCAA.

About the author: Curtis Brown currently works as the Math Segment manager at Texas Instruments, Inc. He taught mathematics and AP® Statistics for several years. Since starting at TI in 2015, he has led many content development projects including the Math in Motion series. He has always found joy in exploring the patterns and logic of mathematics. In his spare time, he enjoys kayaking and fishing with his sons and spending time with his family.

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