"What are the odds?" Of Picking a Perfect NCAA Bracket

One of my former coworkers is launching a unique concept that lottery-izes March Madness - assigning every entrant in a pool an equal number of possible bracket combinations, and then paying out the winner who happened to be assigned the actual bracket that happened. You can sign up here, PerfectBracketLottery.com, so if you (randomly) win this pool, you could say you picked the first perfect bracket (kind of!).

What are the odds of actually doing this organically? It's so unlikely that Warren Buffet famously offered $1 billion to anyone who did it, and in recent years dropped that to $1m every year for life to anyone who picked the entire Sweet 16 correctly, which is still ridiculously unlikely.

Of course this question has been answered before, with the chances ranging from "anywhere from one in nine quintillion to about one in two billion." The differences lie in how you assign probabilities to each game - for example, a 1 seed obviously is extremely likely to beat a 16 seed, while the 8/9 games are roughly 50/50 (historically declining between these two seeding matchups, except for the 5/12 matchup, which is indeed an outlier).

But I want to calculate my own attempt to answer this question - so I'll take 2 routes.

First, let's just assume every game is 50/50, so every possible bracket outcome is equally likely. Just consider the 64-team bracket (over 63 games), which is what is reflected on the Perfect Bracket Lottery site. So that equals 0.5 ^ 63, or 1 in 9,223,372,036,854,775,808 (Nine quintillion, two hundred and twenty-three quadrillion, three hundred and seventy-two trillion, thirty-six billion, eight hundred and fifty-four million, seven hundred and seventy-five thousand, eight hundred and eight). This reflects the most extreme end cited in the previous USA Today link.

The second method I'll calculate will use Ed Feng's long-term win rate from the Power Rank - 71.4%, which is very good straight up. 0.714 ^ 63 is 1 in 1,648,210,430 (One billion, six hundred and forty-eight million, two hundred and ten thousand, four hundred and thirty). This is (relatively) close to the other extreme calculated by the USA Today. In other words, 5,595,991,791 times more likely (Five billion, five hundred and ninety-five million, nine hundred and ninety-one thousand, seven hundred and ninety-one).

So there you have it - your best bet is to enter Perfect Bracket Lottery and hope the randomly assigned brackets fall your way.