Odds of a Perfect Bracket
Let me start by wishing you a happy Saint Patrick’s Day!
It used to be that this time of year you could find me pulling the hair out of my head and you still sometimes do. A question that you often hear asked in the media is “What are the odds of filling out a perfect March Madness bracket?” The number you usually hear is 1 in 9,223,372,036,854,775,808, or 1 in 9.2 quintillion. This number is exactly 2^63. The 63 comes from the 63 games in the tournament, not counting the “First Four.”
Image source: NCAA.com
This probability is assuming the picker is picking randomly, which nobody does. However, it used to be that this qualifier was never made. The number was just thrown out there cold. Things are better now, and I hope I may have had something to do with that by showing for years how the probability improves significantly by simply picking the higher seeded team in each game. Here is an example of a much better answer to the question, which you can find at ESPN.com.
“Here's the TL/DR version of the odds of a perfect NCAA bracket:
- 1 in 9,223,372,036,854,775,808 (if you just guess or flip a coin)
- 1 in 120.2 billion (if you know a little something about basketball)”
Source: NCAA.com.
That website doesn’t say this, but I find they get that second number by assuming the picker has a 2/3 chance of picking all 63 games successfully. That’s certainly better than the coin-flip estimate, but still mathematically lazy. For one thing, the chances of picking a 1 seed vs 16 seed game are not the same as picking an 8 seed vs 9 seed.
Image source: NCAA.com
My web site, at the time of this writing, puts the probability of a perfect bracket at 1 in 55,380,246,81. However, I am going to update that soon. The reason is that estimate comes from looking at the exact historical averages for the probability of winning any given matchup. For example, at the time I wrote that, the probability of a 1 seed beating a 2 seed was 53.73%. I now find in looking at every single game every played in the tournament and smoothing out the data, the probability of a 1 seed beating a 2 seed is closer to 56.89%.
I won’t bore you with all the math, but my updated probability is now 1 in 17.5 billion. I’ll explain in more detail when I update my perfect bracket page in the next week. I plan to create a page on March Madness proposition bets too, which I’ve been working hard on this week.
Until next week, may the odds be ever in your favor.