What Are The Odds: A Perfect Bracket

While compiling the list of NCAA tournament pools, I've noticed a trend. Every large betting site has a contest in which you can win an extremely large amount of money- $11 million, in Sportsbook's- by picking all 63 games correctly.

This is obviously difficult. But so many people fill out brackets, somebody has to get them all correct, right?

In a word: no.

To do this, let's make the simplifying assumption that you pick all favorites. Clearly, these are the teams that are most likely to win- thus the "favorites" thing. So the numbers I come up with will actually overestimate the chance of going 63/63, since very few people actually do this.

By favorites I do not mean the higher seed- I mean the team that is favored in the game. From the lines at Pinnacle Sports, we can figure out the percentage chance each team has of winning their first round game. The favorites range from UCLA (-32 vs. Mississippi Valley St.), to Miami FL (-1 vs. St. Mary's). Picking all favorites, you have a 0.0052% chance of getting the entire first round right- 1 in 19,323.

Considering the number of people that fill out brackets, it's pretty likely that somebody will do this. However, we're only halfway home.

We don't have the lines to the other 32 games, but we can make some reasonable estimates. In round 1, the average favorite had a 75.3% chance of winning. Let's assume that this number decreases uniformly each round, until the favorite in the title game (read: Kansas) has a 55% chance of winning. So for every second round game it's 71.2%, third round it's 67.2%, etc., etc.

The table below shows the chance of the favorites staying undefeated through each round.

Now, one in three billion, four hundred seventy-five million, one hundred fifty-five thousand, one hundred eighty-two odds might not seem good, but this is actually higher than I expected. If you did this 300 million times- one for each person in the country- there's an 8.27% chance one or more would be perfect.

This is not acceptable. The favorites assumption is the cause of this. Let's say you throw in a few first round upsets- Siena over Vanderbilt, George Mason over Notre Dame, and San Diego over UConn. This is more realistic, although we're still being quite optimistic. We've gone from a a 0.0052% chance of going 32/32 (1 in 19,323) to 0.00011% (1 in 952,302). So that was dumb.

I'm going to be nice and say in the later rounds, the teams picked each have a 60% chance of advancing. This is still generous- I can't imagine the average person filling out a bracket is even close to this knowledgeable- and it's going to give us a more realistic answer. Here is the new table:
Notice that the width of the table has increased.

We've gone from one in about 3.5 billion to one in around 7.2 trillion. Ouch.

If you did this 300 million times, there's a 1 in 23,924 chance that you'd go 63/63 in one. If you did it 6 billion times, it's 1 in 1,197.

As usual, the books are smart. Sportsbook can run a promotion and put "$11 million" in the title, without having to worry about actually losing that much money. I do wonder if they take out insurance on this anyway- however unlikely, it is possible.

So, if you enter the free contests at these sportsbooks, here's my advice. Pick all the favorites in the first round. After that, pick the team you think will be favored in each game after that. This won't increase your chances to 1 in 3+ billion, but it's a huge improvement over arbitrarily picking upsets, just because it seems unlikely that all the favorites will win. Of course it's unlikely- that's the point.

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