(mods – this is more a pure math question rather than a sports question, but I could see this in Game Room)
Every year there are news pieces on the astronomical odds of a perfect NCAA men’s basketball bracket. This is mainly due to the number of games played (63 not including the 4 play in games) If each game was a 50/50 chance the odds would be 1/(2^63).
But each game ISN"T a 50/50 chance. WITHOUT even knowing the specific teams involved, if you choose a #1 seed to win vs. a #16 seed, you are guessing correctly 99+% of the time. (on the other hand a #12 seems to beat at least one #5 95% of the time, but which one(s)?)
Do any odds calculations take this into account? Surely there exists the historic % of time a #4 has beaten a #13. Of course just picking the higher seeded team won’t work either, but the odds are definitely better than always picking the lower seeded team…
In the 2018 tournament, I see these results, favorite wins to non-favorite wins:
Round of 64: 23-9
Round of 32: 10-6
Round of 16: 4-4
Round of 8: 3-1
Treating the originally lower-seeded team as the favorite, the favorite won 40 out of 60 games. (This ignores that a good handicapper may often know the “non-favorite” is actually favored.)
If the geometric mean chance that your individual guesses are correct is p, p^63 gives the chance that all 63 guesses are correct. This yields:
50% --> 1 chance in 10 quintillion
55% --> 1 chance in 23 quadrillion
60% --> 1 chance in 95 trillion
65% --> 1 chance in 611 billion
70% --> 1 chance in 5.7 billion
75% --> 1 chance in 74 million
80% --> 1 chance in 1.3 million
Just for fun, I checked to see what p would be necessary for it to be a 1 in 2 chance of getting it right. Seems each game would have to have a team favored to win 98.9% of the time for it to be even money to guess all of them correctly by picking the favored team.
Some years ago I looked up the history of #8 v #9 games and found that #9s had actually won more games. It was only one or two more, but still. That probably hasn’t held up since then, but it’s still probably close to a coin flip on those games.
That’s the type of thing I was looking for. By the way, I watched a lot more of the live win % on 538 than actual names (and used a lot less bandwidth)
Sure, a no-upsets bracket is fantastically unlikely, but if you want a perfect bracket, it’s still the way to bet, because any other bracket is even more fantastically unlikely.
On the other hand, it won’t win you much money in any pool, because there are guaranteed to be many people who pick the no-upsets bracket, so in the unlikely event that it does go through, the pot will be split many ways.
Are you basing “no upsets” on the seedings or the Vegas odds? Is a 9 seed over an 8 seed really an upset? Historically it’s probably pretty close to 50/50.
Every year the two afternoon drive guys talk about their brackets and every year their newsreader’s bracket lasts longer than theirs. She uses analysis like, “My uncle went to Baylor so I’ll pick them over Syracuse.” It drives them crazy.
Ideally, I’d be basing it on the a priori probabilities of winning, which aren’t actually addressed by either the Vegas odds nor by the seeding. And yeah, in cases like 8 seed vs. 9 seed, it probably is very close to 50-50, and so it would make very little difference to make the “wrong” choice there. But it wouldn’t be no difference: If you can, in some way, assess that one team has a 51% chance of winning and the other team has a 49% chance, and you wanted to maximize your odds of a perfect bracket, then you’d pick the 51% team.
On the other hand, if you’re worried about the problem of splitting the pot, then picking the “underdog” in a few of those very close contests would be a cheap way of distinguishing yourself from the large set of people who pick the bracket with no underdogs at all.
And on the gripping hand, you might place some value on being able to frustrate the knowledgeable folks by beating them with meaningless picks, like DesertDog’s newsreader. In that case, you’d want to pick lots of upsets, just so it looks more impressive when you do get a few of them right.