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Daniel Wilco | NCAA.com | November 19, 2018

The absurd odds of a perfect NCAA tournament bracket put into perspective

2019 NCAA tournament bracket The 2019 NCAA tournament bracket, a blank slate that everyone believes they will turn into the first perfect bracket ever. Hint: they're all wrong.

Every year, millions of people fill out a bracket for the NCAA tournament. If you're like us, you might hear that little voice saying, “What if I became the first person ever to fill out a perfect bracket? This could be the year.”

That little voice knows one thing: No one has gotten a verifiably perfect bracket in the history of the NCAA tournament. But it also has one thing very wrong: This will not be the year. And neither will next year, or any in the next millennium.

RELATED: March Madness bracket history | The ultimate guide

Yes, it is technically possible, and even absurdly overwhelming odds don’t mean it couldn’t theoretically happen this year. But we’re pretty confident in saying that it won’t. How crazy small is the chance?

It’s pretty hard to calculate the exact odds of filling out a perfect bracket. Your chances will increase with more knowledge of the current teams, the tournament’s history, and an understanding of the sport itself. For instance, before UMBC’s historic upset of Virginia last year, it was practically a guarantee that all four 1 seeds would win their matchups (they’re still 135 for 136 through the modern tournament’s history), giving you four automatically correct games to start off with. But that type of knowledge is near impossible to quantify or accurately factor into an equation.

We'll get to advanced calculations that attempt to take knowledge into account later on, but to get a better understanding, let’s first look at the most basic calculation.

MORE: This is the longest we believe a March Madness bracket has ever stayed perfect

What are your odds if you had a perfect 50-50 chance of guessing every game correctly?

To determine this, we need to take a quick look at the brackets themselves. Since 2011, the NCAA tournament has had 68 teams competing in its field. Eight of those teams compete in the “First Four” — four games that take place before the first round of the tournament. Virtually all bracket pools disregard these games and only have players pick from the first round, when 64 teams remain.

Therefore, there are 63 games in a normal NCAA tournament bracket. 

2019 NCAA tournament bracket

Obviously, the odds for picking a game correctly get steeper and steeper as the tournament progresses. In the first round, every matchup is set. When you pick a game, you know for certain the two teams playing in the game, and that only one of them can win it. But the possible winners for each game increases every round. In a 64-team tournament, there are 1,024 possible combinations for the championship matchup. Even if you were only picking the championship game matchup, you’d have just a 0.09 percent chance of getting the two teams correct, much less picking the correct winner.

But we’re not just talking about one game here. Since there are 63 games, the number of possible outcomes for a bracket is 2^63, or 9,223,372,036,854,775,808. That’s 9.2 quintillion. In case you were wondering, one quintillion is one billion billions.

If we treated the odds for each game as a coin flip, that makes the odds of picking all 63 games correctly 1 in 9.2 quintillion. Again, this is not a completely accurate representation of the odds, as any knowledge of the sport or tournament’s history improves your chances of picking games, but it’s one of the easiest to quantify, so let’s have some fun with it.

How crazy are 1 in 9.2 quintillion odds?

A group of researchers at the University of Hawaii estimated that there are 7.5 quintillion grains of sand on Earth (fun aside, there are about five sextillion atoms in just one drop of water). If we were to pick one of those at random, and then give you one chance to guess which of the 7.5 quintillion grains of sand on the entire planet we had chosen, your odds of getting it correct would be 23 percent better than picking a perfect bracket by coin flip.

These numbers are way too large to fully wrap your head around, but here are a handful of other statistics for reference, compared to 9.2 quintillion.

  • There are 31.6 million seconds in a year, so 9.2 quintillion seconds is a quick 292 billion years.
  • There have been 5 trillion days since the Big Bang, so repeat the entire history of our universe 1.8 million times.
  • The Earth’s circumference is approximately 1.58 billion inches, so you’d have to walk around the planet 5.8 billion times.
  • As of 2015, the best estimates for the number of trees on the planet was three trillion. Imagine that there was one single acorn hidden in one of those three trillion trees, and you were tasked with finding it on the first guess. Your odds of success are approximately three million times greater than picking a perfect bracket.

But we’ve already said that the 1 in 9.2 quintillion figure is a bit disingenuous. Others have tried to refine the rough estimate.

In 2012, the late DePaul professor Jeff Bergen theorized odds of 1 in 128 billion for someone with basketball knowledge.

In 2014, with Warren Buffett’s $1 billion perfect bracket challenge on the line, FiveThirtyEight tried its hand. The website used its previously calculated probabilities for every NCAA tournament matchup that year to derive refined odds of 1 in 7.4 billion. Of course, even this is an optimistic guesstimate, as it assumes FiveThirtyEight’s algorithms to determine a team’s win probability are perfect.

If we take it at face value, that’s more than a billion times better than the 1 in 9.2 quintillion odds, but still absurdly small. The odds of winning the Powerball are 1 in 292 million, so 25 times better than FiveThirtyEight’s hopeful odds in 2014. The estimate for the world’s population in 2014 was 7.3 billion, so if every single person on the planet filled out a bracket exactly how FiveThirtyEight suggested, and those suggestions were 100 percent accurate, there’s a good chance that we’d get the first ever perfect bracket.

But until that happens, keep ignoring that little voice in your head, and take solace in the fact that you don’t have to be anywhere near perfect to win. In the past eight years of our Bracket Challenge Game, winners have averaged just 49.8 correct games in their brackets. Now that is achievable.