Odds of a perfect NCAA bracket
Want to make sure you get 100% on your office betting pool. You’ve just got to fill out 18,446,744,073,709,551,616 brackets. Yes, that’s 18.5 quintillion. Even if every person on earth filled out a different bracket, the odds are still remarkably small that any one bracket would be perfect.
Link from UtterlyBoring.com
That is wrong number the correct number is 9,223,372,036,854,775,808.
Go to http://mathforum.org/library/drmath/view/56223.html
It depends if you’re picking the 65th team as well. The bracket is 64, but there is a play-in team.
i think you guys need to get these things called lives…….available at walmart
I don’t know about coming to a blog and then making fun of people for not having lives. But I may have to use the “get a life, Walmart sells ‘em now” line.
Ronnie is right. There are 63 total games, its not because there are 64 teams. (2^63)
With the Play in game there are 64 games. The Yahoo article that I linked to uses the play in game as part of the number.
But whether it’s 18.5 quintillion or just 9.2 quintillion the odds of a perfect bracket are still really, really slim.
DAMN!!! I know I won’t be getting a perfect bracket anytime soon!
If these games are all perfect toss-ups, then the numbers you guys are dealing with would be accurate. Please someone tell me the odds that all four 16-ranked teams beat the top-seeded teams in each of the regions. Once the odds are weighted more in favor of the higher-ranked teams, the odds of making a perfect bracket are far less than 9.2 or 18.5 quintillion (WSJ online says it is as low as 1 in 150,000,000). I love you numbers guys: you get so stuck in your world of odds and statistics that common sense flies right out the window. And Ryan, there is no “r” in quintillion. Idiot.
Ryan, I’m sorry. The font was entirely too small on my computer. You did not put any “r” in quintillion, but you are still an idiot, just marginally less of an idiot than I thought before.
wow… everyone’s so hostile… i thought he was just trying to point out an interesting fact and was ignoring the strength factor for each team. Seems like Ed normally loses in his office pools… LOSER
Thanks Ed. I really value the opinion of people who come to other’s sites and call them idiots.
What’s great is I spent about 30 seconds a year ago posting a link to a fairly obscure Yahoo article and now I’m getting around 500 visits a day just through this one article.
And Hell Ed, you’re probably right. The article I linked to didn’t take team strength in to account.
I love large numbers.
There is a way to take into account the “weight” associated with teams being “better” than others, but it is highly inaccurate. In fact, any route to a perfect bracket probability number is highly inaccurate. What you would have to do is assign weights to teams in each round and use the weights to calculate instead of the 50:50. The obvious problem is that you can’t go past the first round. So, in filling out the bracket you’d have to basically assume a coin flip for second round and beyond. I didn’t look at WSJ, but what they probably did. Worst case scenario is 9.2 quintillion (by the way the 18 quin takes into account the play-in game). Best case scenario is much better than that, but not nearly what WSJ reports. A very rough guesstimate would be in the upper trillions:1 against. You’d be many thousands of of times more likely to win powerball and several million times more likely to be struck by lightning. In short, I don’t fucking know. good luck, though; you’ll need it.
you have to take into acount that there has never been a 16 over 1 upset so that takes 4 of the games out of the bracket right there so that makes your picks a little easier. and mathimatically makes its substantially easier as well. still hard as shit though
that’s not exactly true. just b/c something hasn’t happened doesn’t mean that it won’t. a 16 beating a 1 is unlikely, not because it has never happened, but because ones are that much better than sixteens. So, you might give a 1 a 98% chance of winning, but it will never be 100%
you can’t just take the 1 over 16 games out. they are not guaranteed. but obviously it should be weighted. you cannot just say there are 59 games instead of 63 because it can and will happen eventually.
Okay, first of all … there will never be a number 16 seeded team that will beat a number 1 seeded team. I’m not going into that any further, the bracket is set up that way for a reason. Second of all, it is completely stupid to believe your chances of getting the complete bracket correct are 1 in 9.2 quintillion. I am in 4 pools. I got all of the first round games right in each, and had all of the elite 8 teams correctly picked as well. Where I ran into trouble was in the second round leading into the sweet 16. My only mistake was having 3 of the 4 brackets the same, which I did not intend to do. My buddy and I, who is also in the same 4 pools, picked random brackets (out of a possible 135) that made up all 4 pools. We only needed to go as far as 9 brackets, take certain picks from those 9 brackets, and were able to make the perfect picks leading up to the final four. I encourage you all to do the same sort of thing, it took us 20 minutes to look at the brackets … we certainly didn’t have to go through 9.2 quintillion. My point is, picking games in the tournament does not have a relevant probability. It’s not like sticking a quarter in a slot machine and hoping your lines match up. There IS predictability in picking games to win. Yes, I agree, it is extremely hard to get all of the games correct, but it does happen more often than you think. Want proof? There are not 9.2 quintillion brackets filled out each year, and with a little research, I was able to come up with 28 confirmed “perfect brackets.” There’s no math involved …
Shoot … what I meant to say was “picking games in the tournament DOES have a relevant probability.”
At the Top where it said something about if everyone in the world filled out a bracket its still a slim chance that someone would get it right…thats rediculous…u think if some 6.6 billion people filled out a different bracket nobody would get at least 1 100% right…if you think this you have NO common sense…the odds of a 1 beating a 16 are so crazy that you wouldnt have to pick that upset…its way less than 1 in 18.5 or 9 quintillion…but if u morons wanna keep fighting about 1s beating 16s and play in games and whatever then go right ahead…ur wasting ur time…and mark my words…i will make a perfect bracket before i die
Your odds are based on the assumption that in every game played, each team has an equal probability of winning. This isn’t the case. The odds of a 16 defeating a 1 are very low, thus the odds of predicting that game are high. Even with that factored in, the odds of a perfect braket are still excessively low.
It’s not that hard…I know a kid in my neighberhood who did it last year…chaa
how can any body even count that high…i know that numbers reapeat them self but thats alot of repeating….
i am very interested in this argument and started to try and do a little research… can someone post a link to any confirmed perfect brackets? I haven’t searched a whole lot yet, but so far i am not even gettting close.
what about odds of getting all picks incorrect? we are thinking 2^32 power, since you only need to get all games in the first round wrong…much easier!
i love bowling!!!!
ill be in the press for making all conference bowling thanks you..!!! h
and for this bracket… calm down brothers and sisters… its just a bracket:)
Peace and Love
i got a perfect bracket before.
not really, but it would be cool if i did
There has never been a perfect bracket and there never will be. The odds are astronomical. Even if you asssign weights to each game like a 1 seed has a 98% chance of winning the first game. The 1 seed is a 85% chance of winning thr first game. The odds of picking a perfect bracket is way out there I canot fathom it occurring.
I have had 5 perfect brackets in the past 5 years. I fill out 18.5 quintillion each year. My hand is tired…. From winning.
well actually the correct number by the mathematical equation:
B = (2A*9) k_i/64^2
where A = the locations of the final four
where K = number of rounds ever played in this NCAA tournament
where i = the imaginary number which is equivalent to a/-1
where _ = the exact odds of getting a perfect bracket
(the star is where you insert your middle name)
The answer therefore is q^-5^10
which equals 1:4096
Actually, the 18 quintillion number doesn’t take in to account that half of the field gets eliminated every round…so your calc really should be.
2^32 + 2^16 + 2^8 + 2^4 + 2^1= 4,295,033,106….still a large number but 4 billion is better than 18 quintillion.
In the championship game, there can be one of two winners, team a or team b. so you get 2^1. in the round before, there are 4 possible out comes. Team a beats team d, team d beats team a, team b beats team c, or team c beats team b. So we get 2^2. double this to move back a bracket for 2^4, then 2^8, 2^16, then 2^32. Add the sum of these squares and you get 4,295,033,110.
well the 1’s always win and the 2’s and 3’s almost always win so you can just pick those and change all the other ones. then the odd go way up. they still aren’t good but they improve significantly.
has anyone ever gotten it all right
in response to clay, I do not think that the calculation you proposed is valid. Even though half the field gets eliminated every round, that does not change the fact that you have still have a 1 in 2 chance of picking every game, and you must do it 63 times in a row. I have no clue why you would add every round the way you did, that makes absolutely no sense to me.
I believe it will be a very long time before anyone gets a perfect bracket. Not only are the odds astronomical, you have to take into account the fact that out of the millions of brackets, most people take fairly obvious picks, which are likely to be the same as other peoples lowering the chances of hitting. Also, the people crazy enough to try and call the cinderellas (Davidson or George Mason) often are crazy enough to pick other huge upsets that don’t happen. It may happen eventually, but i haven’t found any legitimate cases of a perfect bracket.
For normal people who only fill out one or two brackets, I would doubt any of them even fill out a perfect bracket for the first round. I mean, I am a huge Dayton fan. This year (2009) Dayton beat West Virginia in the first round. So what you say? Well according to ESPN, only about 15% of people thought they would win that game. So of those 15%, how many of them picked Cleveland State? Maybe about 25%, and of those, how many picked Michigan to beat Clemson? Maybe 45%, of those how many picked Wisconsin to beat Florida State? 40% tops. You see where I am going with this? I don’t think I have any of those Dayton pickers left, and I still have a bunch of other first round games. My name is Dr. Morty McNutt and you have just read the truth.
You can’t say a 16 will never beat a 1. By comparison, how many of you thought Michigan would lose to Appalachian State in football a few years ago? Or, how many people thought the USA would beat Russia in 1980 at Lake Placid. Other than the people playing on the underdog teams, nobody.
I am just waiting for some MIT computer-wiz to write a script that will generate every possible bracket, enter them all, and win the grand prize. Of course that many entries would probably would make any computer explode.
Well okay odds are sliner beacuse u know that number 1 and mumber 2 are going to win. That slims it alittle but then u know that 4,3’s will usally win so that slims it then really get a life.
morty, check out facebook, the guy who is winning the facebook pool after round 2 is perfect so far, he has picked all of the 16s. just thought id let you know…
yeah the odds might be 9.2 quintillion or whatever but your forgetting that a lot of teams have much better odds, so that number would go down a lot. someones prolly done it before it doesnt have to be recorded..
I tried the Yahoo NCAA bracket challenge this year (2009). There were a couple of million brackets. Anyone could see the highest scoring brackets. None of them were close to perfect. Once again… of the millions of brackets in Yahoo’s competition, NONE were perfect. Not even close. The best one got 57 of 63 picks right.
Sure, the real odds are not quite 1 in 9 quintillion because the games aren’t true 50:50 toss-ups. But, the odds are still astronomically high.
The proof? As someone mentioned in an earlier post, some online sites (such as Yahoo) are willing to offer 1 million dollars if someone gets a perfect bracket. Considering it is free to participate in the game, those sites must be incredibly confident that no one will be perfect. If the odds weren’t so high against the player, no one would make such an offer.
I don’t know why there is so much debate over the “true odds”. All this blog was trying to convey that there are 9.2 quintillion different combinations where only one has every winner chosen correctly. The number comes down when you start adding weights to the match-ups but probably not enough to make the number any less nearly impossible.
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In response to Dave, 1 million isn’t a lot for these companies in the first place. It isn’t really much of a risk for them