A Blog by Jonathan Low

 

Mar 15, 2017

The Statistical Probability That Your NCAA Basketball Tournament Bracket Will Be Perfect

March Madness, aka the NCAA collegiate basketball tournament, starts tomorrow. Which means that until then, your bracket - the process by which millions of Americans bet on which teams will win - is as good as anyone else's.

You will probably be able to maintain that exalted status until midway through the first day's games, at which point, in the 2016 tournament, approximately 99.9% of those predicting were proved wrong. Other than that, you're still in it. JL

Neil Paine and Jay Boice report in 538:

Making it through six rounds’ worth of picks without a miscue is all but impossible. The oft-quoted number — 1 in 9.2 quintillion — is derived from treating all 63 games like coin flips. Even if you use a more sophisticated picking method the chances of perfection are still 1 in 2 billion, depending on the year. No wonder Warren Buffett discontinued his $1 billion perfect-bracket contest back in 2015.
Right now, at this very moment, your bracket is unblemished, and it seems so clear how it will stay that way: This upset is so obvious, and that top seed is definitely making it to the Final Four. You’ve done your research, and 2017 is the year it will all pay off. Forget winning the office pool — you’re destined for a perfect run of picks.
If you’re really lucky, that feeling will last about halfway through the first day of games of the men’s tournament, on Thursday.
Even one full day of perfection would be a big accomplishment. When we looked at actual results from ESPN’s Tournament Challenge back in 2015,1Excluding the play-in games, which take place before the contest’s picks are finalized. only 273 of the 11.6 million brackets that were filled out for the contest escaped the tourney’s first day unscathed. Making it through six rounds’ worth of picks without a miscue is all but impossible.
Putting an exact number on the odds of a perfect bracket, though, is a fun exercise. The oft-quoted number — 1 in 9.2 quintillion — is derived from treating all 63 games like coin flips, which doesn’t make a lot of sense, because that’s not how most people make their selections. But even if you use a more sophisticated picking method — like, say, FiveThirtyEight’s March Madness predictions — the chances of perfection are still in the neighborhood of 1 in 2 billion, depending on the year.
No wonder Warren Buffett discontinued his $1 billion perfect-bracket contest back in 2015.
Buffett did make things a bit easier in his follow-up contest, which pays $1 million a year for life to any Berkshire Hathaway employee who correctly picks the entire Sweet 16. According to the FiveThirtyEight model, the odds of doing that this year are only about 1 in 1.9 million. (Two years ago, they were about 1 in 3.4 million.) Buffett also promised a cool million to any worker who picked all 32 first-round games correctly. Our model sets the odds for that at about 1 in 3,500 this year, which is surprisingly reasonable. (For comparison’s sake, the odds were 1 in 10,000 two years ago.)
So the odds against a perfect first round — or even a flawless Sweet 16 — aren’t astronomical, as far as these kinds of things go. Still, a perfect bracket, the crown jewel of March Madness picking, will probably remain out of reach for another year, doomed behind a wall of probabilities that multiply themselves into oblivion.
For those curious, here’s what our model says the cumulative odds are of making it through each round of the 2017 NCAA men’s tournament with a perfect bracket intact:
ROUNDCUMULATIVE GAMESCUMULATIVE ODDS (1 IN …)
1323,426
2481,943,573
35647,043,011
460328,660,947
5621,245,078,766
6632,150,573,838

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