Ridiculous odds for a perfect NCAA bracket

Every year, millions of people fill out a bracket for the NCAA Tournament. If you’re anything like us, you’ll hear that little voice say, “What if I became the first person ever to fill a perfect chip? It might be this year!”

This little voice knows one thing: No one has had a verifiably perfect chip in the history of the NCAA Tournament. But there’s also one thing very wrong: It won’t be this year. It won’t happen next year, or any next millennium.

Brackets: Print the official March Madness bow

Yes, it’s technically possible, and even the ridiculous overwhelming odds don’t mean it can’t theoretically happen this year. But we’re pretty sure to say it won’t.

How small is this chance?

Here’s the TL/DR version of the perfect NCAA slide odds:

• 1 in 9,223,372,036,854,775,808 (if you are guessing or flipping a coin)
• 1 in 120.2 billion (if you know a little about basketball)

Your chances will increase with more knowledge of current teams, tournament history, and an understanding of the sport itself. For example, before UMBC’s historic upset in Virginia last year, it was practically a guarantee that all four seeds would win their games (still 135 to 136 by modern tournament history), giving you four automatically valid games to start with. with. But this kind of knowledge is almost impossible to quantify or factor into the equation precisely.

We’ll get to the advanced calculations trying to take knowledge into account later, but to get a better understanding, let’s first look at the basic calculations.

What are your odds if you had a perfect 50-50 chance of correctly guessing each game? Well, it will depend on the possible total number of bracket permutations for the tournament.

So how do we calculate this? We’ll look at a small sample slide first. Like the NCAA Tournament, our sample bracket will be a single-elimination tournament, but it will feature only four teams.

Let’s fill in all possible outcomes for that tournament segment:

This gives us eight permutations of parentheses.

It’s easy to draw a small field of just four. But even if we double the field to eight teams, the results are horrific.

With eight teams, we go from eight parenthetical permutations to 128:

That’s the cool thing about exponents: they increase exponentially.

(And for those of you who are so bored I wanted to capitalize on each of those 128 parentheses, no, we didn’t take the time to fill in each one correctly. That could take a long time. That’s kind of the point here.)

But instead of just plotting every possible outcome for each game, we can also get the number of possible brackets using those exponents.

All we have to do is take the number of match results (2) and raise it to the power of the number of matches in the tournament. In our first example, that’s 2^3, which gives us 8. For the second example, it’s 2^7, which gives us 128.

MORE: This Is The Longest We Think The March Madness Slide Has Ever Stayed Perfect

Now let’s apply that to the modern NCAA tournament.

Since 2011, the NCAA Tournament has 68 teams competing on its field. Eight of these teams compete in the “First Four” – four matches that take place prior to the first round of the tournament. Almost all bracket groups ignore these games and only have players selected from the first round, when 64 teams remain.

Therefore, there are 63 regular season NCAA tournament games.

As such, the number of possible outcomes for a parenthesis is 2^63, or 9,223,372,036,854,775,808. That’s 9.2 quintillion. In case you were wondering, one quintillion equals one billion billion.

If we treat the odds of each game as the flip of a coin, that makes the odds of choosing 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 history improves your chances of picking games. But it’s one of the easiest ways to quantify, so let’s have fun with it.

How crazy is 1 in 9.2 quintillion odds?

Let’s do another visual experiment.

Here is a picture of one point:

Lost? Don’t worry, we’ll help you. It’s inside the circle.

Well, now let’s look at a million of these points:

Certainly easier to see.

But we still have a long way to go. Now imagine a new picture where each of those dots in the image above contain a million dots themselves. Million million points. Also known as a trillion.

We would need 9.2 million of those new images to get 9.2 quintillion points.

Not affected yet? fine.

A group of researchers at the University of Hawaii estimated that there are 7.5 quintillion grains of sand on Earth. If we were to choose one of these at random, and then give you one chance to guess which of the 7.5 quintillion grains of sand on the entire planet we chose, the odds of getting it right would be 23 percent better than a perfect choice. Coin obverse bracket.

These numbers are too big to fully comprehend, but here are some more stats for your reference, compared to 9.2 quintillion.

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

But we already said that the number 1 in 9.2 quintillion is a bit deceptive. Others have tried to refine the approximation.

Georgia Tech professor Joel Sokol (this is above) has I worked for years on a statistical model to predict college basketball games, and he says the best models we have today are only three-quarters of the time, at best.

“In general, about 75 percent is where you’d get basically any model,” Sokol said. “Any of the best games. And that’s partly why people think about a quarter of tournament games are annoying. It may be a little bit higher or a little bit lower, but it’s closer to 75 percent, where the best performers can pick the best teams out of the others and then it’s just a matter of what If the ball bounces the right way, who plays better that day, or whatever, and whether or not you feel bad that day.”

Sokol said using a model that correctly predicts regular season games 75 percent of the time will give you odds of getting a perfect chip anywhere between 1 in 10 billion to 1 in 40 billion. Much better than 1 in 9.2 quintillion, but still crazy high. So high that Sokol doesn’t think it will ever happen.

“Even the most optimistic number I’ve seen, which is about 1 in 2 billion, that means give or take, if you want a 50-50 chance of seeing it in your life, you have to play in 1 billion NCAA tournaments,” he said. “And you might say, well, there are millions of people filling out these brackets every year, but there really isn’t a lot of difference between the brackets, compared to how many people there might be.”

About that, last year, of the millions of brackets entered in our Bracket Challenge, 94.4 percent were unique. Even with 94.4 percent of the millions of brackets being unique, we’ve only covered 0.0000000000182 percent of all possible bracket permutations. Too close.

Speaking of Bracket Challenge users, we can use this data to get another estimate on the odds of the perfect category. We have the history of choice for millions of players over the past five years.

We looked at average user selection accuracy for all 32 first-round games over the past five years (that’s 160 games per user). We then weighted those percentages based on the frequency of difference seed matching. For example, a 5-for-12 game has a seed difference of 7. There have been 222 games with a 7-seed difference in the modern history of the NCAA tournament.

Then, we combined all the percentages to give us the average player’s accuracy for an average game: 66.7 percent. not bad. Now, for the odds of a perfect slice using that percentage:

667 ^ 63 = 0.00000000000831625.

This equates to odds of 1 in 120.2 billion – 70 million times better than if each game were a coin flip.

How do you achieve odds of 1 in 120.2 billion?

If everyone in the United States filled in a completely unique bracket that was 66.7 percent accurate, we would expect to see a perfect bracket 366 years from now. You know, if March Madness still takes place in the year 2385.

But until All-Americans come together to brilliantly fill out their unique brackets, keep ignoring that little voice in your head, and revel in the fact that you don’t have to be anywhere near perfect to win. In the past eight years of Bracket Challenge, the winners have averaged just 49.8 correct matches in their brackets. Now this is achievable.