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.

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.

If it’s truly 1/2[sup]63[/sup], 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 2[sup]63[/sup].

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.

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”.

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.

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.

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.

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.

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.