Has there ever been a documented perfect NCAA tournament bracket? What are the odds?

[brickbacon]

Ok, so I am relatively sure that there has never been anyone who has filled out a perfect bracket, but how probable is it in the real world?

I think the theoretical probably is 1/(2^63), but it would seem that the real world likelihood is far greater. Is there a way to ballpark it based on relatively good assumptions (#1 beats #16 100% if the time, #2 beats #15 98% of the time, etc.)?

Also, I'd like to pat myself on the back for getting 11 of 16 correct in the Sweet 16.

[Oakminster]

They were talking about this on one of the ESPN radio shows today, and the odds are...really bad. I think the number they gave was something like 1 in a trillion. They said you have a better chance of being hit by lightning and winning the lottery in the same day than you do of submitting a perfect bracket. I'm not a math guy, and have no idea if what they said is accurate. I am comfortable with the notion that a perfect bracket is very unlikely.

[KarlGauss]

If it's truly 1/2⁶³, it's a lot less than one in a trillion. There's something like 20 digits (that is, a one followed by nineteen zeros) in 2⁶³.

[Bijou Drains]

I heard today that ESPN has 5 million entries and only 4 entries got 15 of the sweet 16 teams correct. Nobody got all 16.

[Chronos]

If I were to try to maximize my odds of picking a perfect bracket, I'd want to pick the better seed in every single game. Yes, in the real world, there are always upsets, but there are also always more non-upsets than there are upsets. So the way to go about this would be to start in the first round, and look at the historical data to see how often a 1 seed beats a 16 seed, and how often a 2 seed beats a 15 seed, and so on, and multiply those together, and then see what matchups that makes in the second round (I think it'd be 1 seed vs. 8, 2 vs. 7, and so on), and multiply all those chances together, and so on.

To go any further, we're departing from the realm of mathematics and entering the realm of observation. There's no better way to determine the odds of a 1 seed beating a 16 seed than by just looking at the historical record.

[Bijou Drains]

A 16 seed has never beaten a 1 seed. 15 seeds have beaten #2 seed.

[Freddy the Pig]

Here is a good article that answers this question, to the extent that it can be answered. I checked the math myself, and the author is correct--the inevitable need to correctly forecast upsets moves the odds of a perfect bracket from "it will happen eventually if enough people fill out brackets for enough years" to "unlikely in the lifetime of the universe".

[samclem]

This one is probably better suited to the Game Room, as it's about sports. Moved from GQ.

samclem Moderator, GQ

[anson2995]

Originally Posted by Bijou Drains

A 16 seed has never beaten a 1 seed. 15 seeds have beaten #2 seed.

And the same holds true for playoff brackets in other sports, but clearly, the higher seeds win more often.

What makes the NCAA bracket so interesting from a game theory perspective is that it's not simply about picking the results of 64 games. Since the scoring is cumulative, there's a heavy penalty for missing a pick early. And when there's a big upset early (like the Kansas loss this weekend), that knocks about a third of the bracketologists out of the running.

If the contest was to pick the winner of all 64 games, a lot more people would get perfect scores.

[Chronos]

Here is a good article that answers this question, to the extent that it can be answered. I checked the math myself, and the author is correct--the inevitable need to correctly forecast upsets moves the odds of a perfect bracket from "it will happen eventually if enough people fill out brackets for enough years" to "unlikely in the lifetime of the universe".

To be clear, there are really two different questions here, since the number of filled-out brackets is much, much greater than the number of actual tournaments. If I follow optimum strategy, I'll have a 1 in 3.5 billion chance of getting a perfect bracket. And if I fill out one bracket each for 3.5 billion tournaments, I'll probably get about one exact match. But this does not mean that if 3.5 billion people, all using the optimum strategy, fill out brackets for one tournament, that there will probably be about one exact match. The average number of matches will be 1, but that'll come about from a whole heck of a lot of cases where nobody wins, and 1 chance in 3.5 billion of there being 3.5 billion winners.

[Death of Rats]

Originally Posted by Bijou Drains

I heard today that ESPN has 5 million entries and only 4 entries got 15 of the sweet 16 teams correct. Nobody got all 16.

I am betting none of those four were die-hard UNI Panthers fans.

[JohnT]

Originally Posted by brickbacon

Ok, so I am relatively sure that there has never been anyone who has filled out a perfect bracket, but how probable is it in the real world?

I think the theoretical probably is 1/(2^63), but it would seem that the real world likelihood is far greater. Is there a way to ballpark it based on relatively good assumptions (#1 beats #16 100% if the time, #2 beats #15 98% of the time, etc.)?

Also, I'd like to pat myself on the back for getting 11 of 16 correct in the Sweet 16.

One year my dad was 31 of 32, 15 of 16, 8 of 8, 4 of 4, 2 of 2, and picked the winner. It was one of the damndest things I've ever seen.

[fusoya]

Originally Posted by Bijou Drains

A 16 seed has never beaten a 1 seed. 15 seeds have beaten #2 seed.

Fairfield University, back in the 90s, came extremely close to being the first team to do this, against North Carolina. They finally lost by something like 5 points.

Some of my friends and high school teachers (many of which attended Fairfield) still talk about that moment whenever the tournament subject comes up.

[ElvisL1ves]

Princeton almost pulled it off against Georgetown in 1989 - 50-49, on a Mourning block at the buzzer.

[Mahaloth]

Originally Posted by JohnT

One year my dad was 31 of 32, 15 of 16, 8 of 8, 4 of 4, 2 of 2, and picked the winner. It was one of the damndest things I've ever seen.

Wow. I mean...wow.

[ultrafilter]

Originally Posted by Chronos

If I were to try to maximize my odds of picking a perfect bracket, I'd want to pick the better seed in every single game.

That's not necessarily as good a strategy as you might think it is.

[Chronos]

I know it's not a great strategy. It's just better than the alternative (or at least, no worse).

[Rysto]

Originally Posted by ultrafilter

That's not necessarily as good a strategy as you might think it is.

From that article:

“Eights and nines play ones in the second round, when their ranking still has value,” he said. “Fours and fives potentially could play a one in the third round, when one still has value. So if you want to go far in the tournament, I would rather be a 10-seed than an eight or a nine, as paradoxical as that may sound.”

I've never liked bracket tournaments and this sums up exactly why.

[Chronos]

I would imagine that the reason that ones still have value in the second and third round, but not so much the fourth, is precisely the fact that the ones are playing nines, eights, fours, and fives in those early rounds, while in the later rounds, they're mostly playing twos and other ones. Clearly there's less difference between a one-seed and a two-seed than there is between a one-seed and an eight-seed.

[Bootis]

Originally Posted by Mahaloth

Wow. I mean...wow.

I'll say. That handily beats any winner in the history of Espn's Tournament Challenge, which has gone for years, drawing millions of brackets every year. It quite probably stands alone as the most accurate NCAA bracket predicted by anyone on this planet, ever.

[Cyberhwk]

Yeah, but couldn't there be some fluke postseason where an unusual number of higher seeds win? Everybody's brackets are balls this year because who would have predicted 8 10+ seeds winning the first round, but that's not always going to be the case.

Maybe we have a season where there's definitely Haves and Have-Nots. Very few first round upsets, and the Final Four ends up with a 1, 1, 1, & a 2. Out of millions of brackets submitted nobody randomly got there?

[Bootis]

1st round stats, since tournament expanded to 64 in '85:

1 seeds win 100%
2 seeds win 96%
3 seeds win 84%
4 seeds win 79%
5 seeds win 68%
6 seeds win 69%
7 seeds win 63%
8 seeds win 42%

If you pick the favorites, in every game, (which statistically give you the best chance to be perfect), based on these numbers, if my math is right, you have around a 1 in 25,000 chance for a perfect first round.
So, if you get that far, there's still 32 games to go, likely half of them coin flips. calling 16 straight coinflips is about a 1 in 50,000 shot. combined with your 1 in 25,000 perfect first round, you're already at over 1 in a billion, and you still got 16 more game you need to call. Easier games to guess, but even if you had an 80% chance of calling each of the other 16 games, your overall chance of a perfect bracket would still grow to around 1 in 50 billion.

[JohnT]

Originally Posted by Bootis

I'll say. That handily beats any winner in the history of Espn's Tournament Challenge, which has gone for years, drawing millions of brackets every year. It quite probably stands alone as the most accurate NCAA bracket predicted by anyone on this planet, ever.

My dad was bizarrely good at picking these things - he won the office pool every year except one.

But even then he realized he had a fluke bracket. Had the thing framed (it was done on a newspaper sheet), but it was lost after his death a few years ago.

[notfrommensa]

Harvard (a #16 seed) beat Stanford (a #1 Seed) in the 1998 NCAA Basketball tournament. Check that, Make it the 1998 NCAA Womens Basketball Tournament.

[garygnu]

Come, now, silly. Wimmin don't play basketball.

[brickbacon]

How much do you think "correct" ranking would factor in. According to the stats provided, #9 seeds beat #8s most of the time. If prognostication on the part of the ranking committee were better, how much would that matter?

[vinniepaz]

http://www.nbcchicago.com/news/sport...-88916437.html

Article about autistic teenager from Chicago who has a perfect bracket through round 2

[SCSimmons]

Originally Posted by ultrafilter

That's not necessarily as good a strategy as you might think it is.

Crap! I did that same analysis years ago, and came to the same conclusion: from the regional semifinals on, seedings are irrelevant. It kind of made sense, in retrospect--a team that gets that far in the tourney can't do it on luck, they've really proved something. Eg. UNI maybe got lucky & caught Kansas on an off night and played the game of their lives, in which case you can expect MSU to crush them like a grape. Or, they're really that good, in which case the Spartans are in trouble*. And if that happens, and the Panthers advance to the Elite Eight, you can't really think of them as an underdog in any of the subsequent games.

Who knew I could have gotten interviewed by a magazine for that (fairly simple) bit of math?

*Not happening, of course. Go Spartans!

[3:20:59 or bust]

Originally Posted by vinniepaz

http://www.nbcchicago.com/news/sport...-88916437.html

Article about autistic teenager from Chicago who has a perfect bracket through round 2

Nice story, and as much as I'd like to buy it...I just can't.

I've been filling out brackets for a long, long time, and I've never seen anyone do this. Ever. And with the upsets this year?

Rainman angle or not, I just can't buy it.

[FoieGrasIsEvil]

Originally Posted by 3:20:59 or bust

Nice story, and as much as I'd like to buy it...I just can't.

I've been filling out brackets for a long, long time, and I've never seen anyone do this. Ever. And with the upsets this year?

Rainman angle or not, I just can't buy it.

I can buy that he got all the picks right so far. What I'm not buying is him having Purdue to win it all!

[Mahaloth]

Originally Posted by vinniepaz

http://www.nbcchicago.com/news/sport...-88916437.html

Article about autistic teenager from Chicago who has a perfect bracket through round 2

I heard his father on the radio this morning. He said it was a combination of being a fan of basketball and luck.

[Robot Arm]

Couldn't someone write a computer program to figure out every possible bracket and save them to disks, and then after the tournament claim that one of them must be perfect?


I have not done the math on how much processing time or disk space this would require. Probably a lot.

[sachertorte]

Originally Posted by ultrafilter

That's not necessarily as good a strategy as you might think it is.

Am I missing the point of that article? It doesn't make sense to me. The NCAA tournament has 4 1-seeds, 4 2-seeds. At elite eight all teams either are a 1-seed, 2-seed or beat a high seed to get there (or beat someone who beat someone).

Essentially, isn't he saying that all the 1-seeds and 2-seeds are about equal?
How is this shocking?

[Contrapuntal]

Originally Posted by Robot Arm

Couldn't someone write a computer program to figure out every possible bracket and save them to disks, and then after the tournament claim that one of them must be perfect?


I have not done the math on how much processing time or disk space this would require. Probably a lot.

According to an ESPN story, there are 9 quintillion possibilities, and filling out one bracket a second would take 3 billion years.

[Robot Arm]

Originally Posted by Contrapuntal

According to an ESPN story, there are 9 quintillion possibilities, and filling out one bracket a second would take 3 billion years.

A computer could do it faster than one per second, though. Once you decide on a format, the whole bracket can be represented by 63 bits. And it's independent of the teams, so we could start work on our 3,000,002,011 bracket today.

[Contrapuntal]

Originally Posted by Robot Arm

A computer could do it faster than one per second, though. Once you decide on a format, the whole bracket can be represented by 63 bits. And it's independent of the teams, so we could start work on our 3,000,002,011 bracket today.

Knock yourself out.

I have no idea how fast a computer could do it, or if in fact the information I gave is even correct. It was just something I saw on one of those ESPN March Madness specials.

[Baracus]

Originally Posted by anson2995

What makes the NCAA bracket so interesting from a game theory perspective is that it's not simply about picking the results of 64 games. Since the scoring is cumulative, there's a heavy penalty for missing a pick early. And when there's a big upset early (like the Kansas loss this weekend), that knocks about a third of the bracketologists out of the running.

If the contest was to pick the winner of all 64 games, a lot more people would get perfect scores.

No, they wouldn't. Scores in general would be higher because the penalty for missing in the earlier rounds would be less, but the rate of perfect scores would remain the same. It doesn't matter whether I chose Kansas to win it all in a bracket format or merely to win that individual game, either way in terms of being "perfect", I have lost.

[Spoke]

Originally Posted by vinniepaz

http://www.nbcchicago.com/news/sport...-88916437.html

Article about autistic teenager from Chicago who has a perfect bracket through round 2

It won't hold. He has Duke losing to Purdue!

[ultrafilter]

Originally Posted by Robot Arm

A computer could do it faster than one per second, though. Once you decide on a format, the whole bracket can be represented by 63 bits. And it's independent of the teams, so we could start work on our 3,000,002,011 bracket today.

Doesn't matter, you'd still need about a billion terabyte drives to store them all (I did that in my head, so I'm not 100% sure on the order of magnitudes, but my basic point is correct).

[Chronos]

But, see, the trick is that you store them in a compressed format. Then, after the tournament is over, you just uncompress the appropriate part of the file, and show it off.

[ultrafilter]

Originally Posted by Chronos

But, see, the trick is that you store them in a compressed format. Then, after the tournament is over, you just uncompress the appropriate part of the file, and show it off.

I know, I did that assuming that you're using 63 bits per bracket. 2⁶³ is a large number.

[ultrafilter]

Originally Posted by ultrafilter

I know, I did that assuming that you're using 63 bits per bracket. 2⁶³ is a large number.

[SCSimmons]

Originally Posted by sachertorte

Essentially, isn't he saying that all the 1-seeds and 2-seeds are about equal?
How is this shocking?

It's not, particularly. But it does sometimes fly against common wisdom. Take the example I was discussing in my last post: if UNI beats MSU on Friday (fat chance!), then their next game might be an Elite Eight matchup as a 9 seed against 2 seed Ohio State. Every commentator would talk about them being an underdog in that game--but the statistical analysis of the history of the tournament shows that this is an error--UNI shouldn't be considered much of an underdog against anyone in this situation (my alum homerism above not withstanding). And the Vegas line (correctly, IMO) reflects this--I see the Spartans favored by only one point, in spite of them being a 4 seed facing a 9. The biggest line I see for this round is Purdue getting 8 1/2 against Duke; I'd be inclined to bet on Purdue with that line, and starting with the next round, any underdog is probably the right bet. Even, say, 12 seed Cornell vs. 2 seed West Virginia. If Cornell gets to that game, it's because they beat Kentucky this round after beating Wisconsin last round. At that point, they'll have proved their seeding wrong, and you have to think that they're capable of beating anybody.

[ElvisL1ves]

Both lines may reflect key injuries to MSU and Purdue stars, though.

[ZenBeam]

Aren't the lines based on what's being bet, i.e. the perception of the people making the bets, even if that perception doesn't match reality?