Saturday, March 19, 2011

March Madness: It Didn't Happen Again!

Since 1985, when the NCAA Division I Men's Basketball Tournament expanded to 64 teams, a team seeded (or ranked) 16 (last in each of the four regions) has never beaten a team seeded first. Over the 27 years from 1985 to 2011, (108 pairings) the number 1 seed has won by as much as 58 points (in 1998, Kansas(1) over Prairie View(16) 110-52). But twice over that time, both times in 1989, the number 1 seed narrowly edged out the number 16 seed by only 1 point (Georgetown(1) over Princeton(16) 50-49 and Oklahoma(1) over East Tennessee State(16) 72-71.

The histogram above shows the winning point margins. It closely fits a normal distribution with a mean of about 25 and a standard deviation of about 12. This gives us an estimate of the probability that a 16 seed could beat a number 1 seed, as just the probability that this normal distribution is less than zero. Here, we get a value of about 2%.

Wait 'til next year!

P.S. (3/20/2011)
A colleague observed that since a 16 seed has never won over a 1 seed in 108 trials of men's basketball (although it has happened in women's in 1998, 16 seed Harvard over 1 seed Stanford 71-67) that a 2% probability of an upset is perhaps too high and the probability should be less than 1% (1/108). But this treats a trial as only a success or failure and ignores how close the score was to an upset. A value near 1% is likely too small.