# The Sweet 16: The Chalkiest Round of March Madness

As we get deeper into the March Madness tournament, it is tough to weight the importance of a team’s seed with its performance in previous tournament games this year. While most people would not initially pick an 11-seed over a 2-seed in the Sweet Sixteen, many more consider it a possibility once the 11-seed has already established itself early on by causing two big upsets. Because of this, I set out to quantify which rounds are most governed by tournament seeding.

My first thought was to just look at the probability that the lower seeded team wins in each round, to try and figure out which rounds have the most upsets. I charted the upset probability of each of the first four rounds since 1985. This doesn’t take into account whether the upset, for example, is a 1-vs-16 or an 8-vs-9 matchup.

 Round of 64 Round of 32 Sweet 16 Elite Eight Upset Probability 0.25 0.296 0.286 0.435

The first thing to notice is that the probability of an upset generally increases as the rounds progress. This is because all upsets are not equal in likelihood. A 15 beating a 2 is significantly more of an upset than a 2 beating a 1. As the rounds progress, the seeds get closer in value and the probability of an upset increases.

The second observation is that despite this general increase, the Sweet 16 does not fit the general trend. In fact, the Sweet 16 has fewer upsets per game than the Round of 32. Still, to come to any conclusive results, we need a metric to determine how likely each upset is based on the seeds, so that we can account for the seeds getting closer throughout the rounds.

Once we have an expectation for how each team will perform based purely off of its seed, we can then back-test this on all of the NCAA games in our sample and project how many upsets we would see based off of each team’s seed. Then we can compare this to the actual number of upsets and look to see if the Sweet 16 actual does have fewer upsets than we would expect.

To determine the relative strength of each seed, I ran a logistic regression on all of the tournament games from 1985 to 2015 that considered three variables: each team’s seed and the round that they played in. Since all of these variables were statistically significant, this indicates that round helps to determine the win probability. This is probably due to selection bias in the later rounds; a seven seed that makes the Sweet 16 is most likely underseeded, thus making an upset more probable.

The next step is to eliminate the bias of the round and control this sample so that it considers the average value of the seed, instead of the average value of the seed given the round it is in. To do this, I reran predictions of every game, this time assuming that the game was played in the first round, where no selection bias has occurred. For example, this means we simulate each game based on the average strength of a seven seed, instead of the average strength of a seven seed that has made the 3rd round. I only ran the first four rounds, as these are the rounds where there is a clear favorite and clear underdog with the seeding (No. 1 seeds playing each other).

Finally, I compared the results to the actual number of upsets in the tournament since 1985.

 Projected Upsets Based on Seed Actual Upsets Difference Round of 64 7.954 8 -0.046 Round of 32 4.880 4.74 0.138 Sweet 16 2.856 2.290 0.566 Elite 8 1.662 1.742 -0.080

As you can see, this model fairly accurately predicts every round except for the Sweet 16. It seems that the Sweet 16 is indeed substantially more chalk than every other round, with only 80% of the predicted number of upsets occurring. To quantify the significance of the result, I ran a one sample t-test using the number of upsets in each year since 1985, and the projected mean of 2.856. One has to adjust the significance level for multiple comparisons, so that the probability of one test being a false positive is still 5%. The adjusted significance level, therefore, is .0127. The test yielded a p-value of 0.0245, which is very close to being significant, but not quite.

I have a few ideas for why the Sweet 16 behaves this way. Besides the Round of 64 (which is essentially the control for this model), the Sweet 16 is the only game each team plays after multiple days off. It is likely that there would be less variance in the results when each team is playing fully healthy and rested. Additionally, these days off give the teams a chance to scout and prepare. The more time that these teams have to prepare for their opponent, the more likely it is that team’s perform at their normal levels. Additionally, stronger teams probably have better scouting and coaching departments to help them in their days off.

Another reason could be that the selection committee is much better at properly seeding the top seeds than it is with lower ones. By the Sweet 16, a low seed that has made it this far is probably facing a 1 or 2 seed. Despite it potentially being underseeded, this team is still more likely to get beat by one of the top talents in the tournament. By the Elite Eight, the bracket is again filled with mostly 1 and 2 seeds which are properly valued by their seed.

Regardless of the reason, when you are filling out those second chance brackets, make sure to temper your upset expectations in the Sweet 16.