# NCAA Tournament Fun Facts, from Steve Leslie

March 13, 2007 |

The odds of one person's filling out a perfect bracket for the NCAA basketball tournament, i.e., the odds of picking every single game winner correctly is nine quintillion to one.

Another way to view this is that if every person on the planet were to randomly fill out one million sheets the chances would be one in 1000 that a perfect sheet would be found.

The odds of picking the five numbers in the Powerball lottery are one in 3,563,609 but to pick all five numbers and the powerball are one in 146,107,962.

## Alston Mabry writes:

If the tournament were a coin-tossing exercises, there would indeed be 2^63 = nine quadrillion outcomes. But can we improve those odds?

Looking at the NCAA Tournament results for 2005 and 2006, 86 of 126 games were won by the higher-seeded team, a 68.3% win rate for the NCAA seeding committee. If the seeding were random, one would expect a win rate of 50% with a 4-5% standard deviation, so the committee's results are inconsistent with randomness.

If you go further and rank the games by the difference in seeding (low seed minus high seed, so that a one seed playing a 16 seed would be a 15-spread game), and then look at the quartiles, you see that the committee is even more successful. The first column is the average difference in seeding between the teams in the quartile, and the second column is the rate at which higher-seeded teams won in that quartile:

seed diff / win rate
12.29 87%
7.79 75%
4.25 69%
1.27 42%

## Andy Moe remarks:

I would suggest that spreads and seedings should be examined closely in the tournament, as there are statistically significant edges that can be of use both at the sportsbook and in an office pool. For the most part, I believe the edges are present because the tournament selection committee is better at seeding the teams than the general public is. Add plenty of "amateur" money chasing favorite schools and you have the perfect recipe for mispricings.

The memes surrounding the tournament are surprisingly similar to those found in the markets. The length of time since a #16 seed beat a #1, the danger of the #5 vs #12 matchups, past greatness of teams, coaching vs players, upset specials, giant-killers, hot hands, the list goes on and on. Thankfully, almost all of this centers on how to pick winners, not how to beat the spread.

So while the rest of America concentrates on filling in brackets, I'll be packing my bags for Vegas. As in the markets, it pays to know when to break out the cane and hobble down to the sportsbook.

## From John De Palma:

From the New York Times

"When it comes time to pick a champion in an N.C.A.A. bracket, people tend to cluster around a few of the favorites…. At first glance, this focus on the favorites seems to make perfect sense. History suggests that the top-ranked teams really are more likely than other teams to win the tournament. If you cared only about picking the correct national champion, it would be smart to choose a team like Ohio State or Kansas this year. The problem is that you would have a lot of company. To finish at the top of your pool, which is what matters to most people, you would have to do extraordinarily well in the rest of your bracket … The lesson is basic: As long as everyone else is clustering around a couple of favorites, you hurt your chances by joining them … But pools do make a broader point about human behavior. Frequently, people make decisions without fully taking into account the actions of others. Investors, for instance, may buy stock because they believe a company will do well in coming years, but they fail to consider the possibility that the stock price already reflects that information…"