Bracket Odds

Now that March Madness is nearly over, people all across the country are either hopeful about their brackets or have already thrown in the towel. For those of you (like myself) whose brackets are completely rubbish after the multitude of upsets this year, fear not. You're not alone. To make you feel better, here are some stats on how unlikely it is you will get a perfect bracket.

First you have to figure out how to find out what the odds are of getting a perfect bracket. The way you have to look at it is if you have a 4 team bracket (Team A vs. Team B, Team C vs. Team D), then you will have two winners and two losers. That means that on each side, you have two possible outcomes: Team A could win or Team B could win, and Team C could win or Team D could win. So, two possibilities on the left, and two possibilities on the right, which you multiply together for a total of 4 possible ways the final matchup could be. Then when you have the winner of both sides, you again have a possibility of two scenarios: the winner of the left will win, or the winner of the right will win. So you multiply the 4 possibilities from the left and right brackets by the 2 possibilities in the final matchup, which leaves you with 8. What does that mean? It means that if you have a 4 team bracket, you have a 1 in 8 chance of picking the winner. The shorter way of figuring it out if that of the 4 teams, 3 will fail. Each failure has 2 possibilities of who will win, so you multiply 2 three times, or 2 x 2 x 2, which still equals 8.

So how does this work with a bracket containing 64 teams? In the same way. Out of 64 teams, 63 will lose. Each matchup has 2 possibilities, so you mutiply 2 times itself 63 times, one time for each loser. Do you have any idea how big of a number 2 times itself 63 times is? 9,223,372,036,854,775,808, or what mathematicians call 9.2 quin-trillion. So, essentially, you have a 1 in 9.2 quin-trillion chance of filling out a perfect bracket. That's just the sheer math of it. If you know some about basketball, you have shave off a bit of that, but your odds still aren't that good. So, knowing how unlikely it is to fill out a perfect bracket, are you curious about the sheer facts about this huge number?

1. If everyone on the planet each randomly filled out a bracket, the odds would be 1,000,000,000 (1 billion) to 1 of anyone having a perfect bracket.
2. If 1 bracket per second were filled out, it would take 292,000,000,000,000 (292 trillion) years to fill out all possible brackets.
3. If everyone on the planet filled out a bracket per second, it would take 43 years to fill out every possible bracket.
4. If all possible brackets were stacked on top of each other on regular paper, it would reach from the earth to the moon and back 1.1 million times.
5. If you weighed all possible brackets that are on regular paper, they would weigh approximately 90,000 times heavier than every person on earth combined. 

Also, keep in mind that if you had a 90% chance of picking the correct games, your odds of filling the rest out correct would be 763 to 1. 

So if you're feeling low because your brackets have failed, don't worry. You're definitely in good company with the other 9.2 quin-trillion of chances!