has anyone done the naive math on the odds of a single bracket being perfect if you assume the betting line odds are accurate in a typical year? (I.e. since that’s substantially easier than the case where it’s 50/50).

(The much harder math is how much coverage you get from millions of different people submitting brackets with tons of overlap, but I assume other bracket sites have that number internally)

@Ziddletwix iirc the naive math is pretty straightforward since it's a sequential odds question. I'm no statistics expert, so someone else chime in if I make a fundamental mistake. if we assume every game has accurate 80% odds and you bet down the line, and each individual game could break your streak, you'd have 0.8^63 chances of being right, which I believe is 1 in 1.274M. every gimme (bye, DQ, etc.) improves this, and every 50/50 game drops it a bunch. that's assuming you bet "with the odds" (or you have 80% accuracy rate, regardless of the odds), and ofc the real odds are both not as clean and probably not perfectly accurate

if you're asking "will anybody at all get it right?" then I guess it's a function of how many people deviate from the favored positions, aka number of unique brackets. the 50/50 scenario gives us an insight: in that case if there are 9.2 quintillion possibilities and 1 million unique entries then there's a 1 in 9.2 trillion chance of anybody getting it

since Kalshi suggests the people who predict best have a 2/3s chance of being right for any given game, we can generalize that: 1 in 124B for any one (they say 1 in 120B, but using their 67% gives 1 in 90.6B... so it's somewhere in there), but that's IFF only experts select brackets. Still, it's probably much worse because there is a smaller "valid" prediction space when you must be correct 2/3s of the time, even though the actual possibility space remains much wider (9.2 quintillion).

I suspect they're doing this as a gimmick to show how prediction market odds can provide greater accuracy. they'd love it if someone won to use as an anecdote to show their system works, and maybe it's even better if they don't have to pay out but their calibration is provably superior.

@Stralor with Kalshi's numbers, and assuming my math isn't garbage: 1 million expert entries could mean the chances of anybody getting it right could be as low as 1 in 124,000. that's a massive negative EV for them if true

@Stralor actually calculating the chances by hand based on real odds would be... extensive... even if I had them in front of me, unless you only counted "favored" wins

@Stralor They have almost certainly bought prize insurance for this, so they know the odds. The insurance cost is greater than the odds so the insurer makes money, but the odds are so long that this is a very cheap contest to offer.

@SteveSokolowski yeah they even mention who's backing the contest. fairly routine!

@Ziddletwix Here's what I got for the betting odds optimal bracket:

2026: 1 in 116,161,939

2025: 1 in 944,534,668

2024: 1 in 5,969,220,394

I just took the product of the probabilities of reaching X round for each of the 32 picks. The average reach probability went from 52% to 54% to 58% this year. I think that's real, but it might be an artifact of how I calculated the betting probabilities.