What Are The Odds Of A Perfect NCAA Basketball Bracket?

Good luck with your picks!

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[MindYourDecisions]

Small correction: around 0:52, I mixed up counting "games" with "teams advancing." The second round has 16 games for 32 teams; the third round has 8 games for 16 teams, etc. By the way, I always use game theory for my NCAA bracket. Bloomberg has tips from experts, including one from me, in this nice article:

[jaylambert]

Some of you appear confused.

He is not saying that the games all have 50/50 odds. Obviously the higher rated teams are more likely to win, and the greater the distance in ranking the more likely one can predict the outcome accurately. Or in other words, not all possible iterations are equally likely.

What he is saying is that if you were selecting by “luck” (ie, at random) the chances you will perfectly predict the outcome of all the games is 1/2^63.

There is a difference between (a) the likelihood of guessing the right outcome by pure luck vs (b) the likelihood of each bracket iteration being correct.

Or, simply put - all coin flips are created equal, but not all NCAA teams are created equal.

[toddbiesel]

So, if every person on Earth can submit about 1.5 billion distinct brackets, and no two of them match, then you just might find one perfect bracket somewhere in the bunch.

[cpsof]

You can generalize it even more: in a single elimination tournament of n teams with any number of byes, there are n - 1 games.

[d-litesinsight]

So you are saying there's a chance?

[technodrome]

A Math student picked March Madness brackets. Here is what happened to his grades.

[jumbo]

I've always just imagined each game being represented by a binary digit 1 for team 1 winning and digit 0 for team 2 winning. Strung together, you have a 63 long binary number (ex. 01010001010...) which is the code for a perfect bracket and everyone is just guessing that code.

Not that it's better, different, or more straightforward... I just find visualizing possibilities with a binary number easier to wrap your mind around.

[derickocrusher]

The odds are less than 9.2 quintillion. Not all teams are created equal. Some teams's chance of winning each match is significantly higher than 50% which reduces the 9.2. then again upsets also impact the odds.
By no means am I saying that it's possible to have a perfect bracket.
The only way to have a perfect bracket is to travel back in time.

[jazznik]

Except that there are actually 68 teams in the mens NCAA tournament (dont know about the womens' tournament) w 4 "play-in" games (against the #16 seeds in each region). There would be a 1 in 16 chance of guessing the champions of these play-in games by luck. So the answer would be 1 over the above stated denominator times 16, or about 1 in 147.6 quintillion.

[aidanmartin]

That’s if you randomly pick every single game, your chances are much higher if you put thought into it

[kabirmalik]

Great video Presh!! I’m a big basketball fan and I really like how you take math and apply it to something I find cool and exciting

[somerandom]

from my understanding, this answer is only correct if you get to make a choice after each round/ before each match. Is that right?
If so, how would you go about working out the odds of picking a perfect bracket if you only had one chance to pick the outcome of every match right from the start?

[Noneblue]

what if each game has its own probability so it wasnt 50/50 each time?

[martinfloyd]

Actually, there are 68 teams (8 of them play each other prior to the "Final 64, " reducing the number to 64. But if you take into account the original total of 68 teams, at 50/50 odds per game the initial odds would be 1/2 to the power of 67, which is 1 chance out of 147, 573, 952, 589, 676, 000, 000(147 quintillion, 573 quadrillion, 952 trillion, 589 billion, 676 million).

[Xelianow]

The Problem here is that your chances of guessing right are always more than 50%, because teams are usually different in strength. As soon as you have some insight into the game you get better chances than 50% ... and if you consider maybe 70% to be your average hit rate, than your chances of getting all 63 right is already 1 : 5.7billion - which is an increase in chance by a factor of 1.6 billion.

[tcenko]

I think the odds of Michigan State taking the title are 100% tho

[beegdigit]

Zion and Barret basically round up the chances for duke to win 95% so Presh is wrong this time :(

[jakeremmert]

The first puzzle he’s posted that I actually got right, purely because I applied the rules for probability with genetics. Proud of myself even though I shouldn’t be

[mskiles]

Need a followup i have always wondered about. What is the REAL probability of picking a perfect 64 team bracket considering that the games arent 50/50 chances? 1 vs 16 is a 99÷% lock, etc.

[matthewgraham]

While this is a "pure luck" scenario, what would be the chances given a reasonable likelihood of predicting several early round games? For instance only one 16 seed has ever won, as well as only a few 15 seeds. Also include high probability of teams playing close to home having a better chance (60% ?) than those traveling great distances. How low could the odds reasonably be?