Breakfast banter this morning was about March Madness, of course, and one topic was when (and whether) a #16 would beat a #1. My colleague's answer was "never", and I countered with the idea that can't happen usually happens anyway. Given enough time, big upsets will occur. He was unconvinced.
So trying to harness the power of mathematical reasoning to bolster my claim, I took some data from previous tournaments, and calculated the average margin of victory for the #1 vs. #16 games each four years from 1985 to 2009. (They ranged from 9 to 34, btw.) Using a handy online linear regression calculator, I was surprised to see that the slope was actually positive (0.480), meaning that my colleague was right -- at this rate, it is unlikely that a 16 will ever beat a 1.
Never one to take no for an answer, I deliberately skewed the data, using every 8th year. (This avoided the anomalous year of 1989 (early in the data), when two #16 teams were beaten by only one point -- the closest margin of defeat yet, and the only two times it's been done.) But again to my surprise, the trend was actually stronger, the slope of the regression line being 0.509
Perhaps my colleague is right. Will it never be done? I hate being wrong.