It's tournament time again and if you're filling out your bracket at the last minute there are four games you probably aren't agonizing over: Louisville vs. Morehead St., UConn vs. Chatanooga, Pittsburgh vs. Eastern Tennessee St., and North Carolina vs. Radford. I don't know you and I don't know your bracket, but I'm fairly certain that you have the #1 seeds winning those games.
Since the inception of the 64-team tournament in 1985, there have been 96 #1 vs. #16 games, and 96 times the #1 seed has won. There have been close calls, but no victories yet for the underdogs.
The fact that the #1 seeds are poised to go 100-0 this year has a lot of people wondering - will a #16 seed ever win? As I said earlier, there have been several close games - on back to back days in 1989 Georgetown and Oklahoma both escaped embarassement by winning by just one point.
The frequency of these close games can clue us in to whether the #16 seed win will ever occur - and how soon? The following chart shows the margin of victory for each of the games since 1985 (pulled from the indispensible bbstate website).
The average margin of victory was 25 points and the standard deviation of this margin was 12 points. As you can see from the chart above, the data are roughly normal, with the distribution about the same on either side of 25 points.
Taking advantage of this normal distribution, we can use the data to calculate the chance that a #1 team will actually beat a #16 - that the margin of victory for the #1 seed will actually be negative.
So what's the probability that a #1 loses to #16? A mere 1.75% - a small but not impossible chance. So far that probability hasn't come true, but it doesn't mean it won't. In fact, each year there is approximately a 7% chance that one of the #1 seeds will lose. So if it happens this year, you can be surprised, but not shocked, that a top seed has finally fallen.