Upset dreams

What's the probability that a sixteen will upset a one seed in the first round of the NCAA Men's Basketball Tournament? I've finally got my hands on the data so I can take a look. Thank you HoopsTournament.net.

It's hard to know how often something will happen if you've never seen it before. Such is our plight. But take a look at this:


The histogram shows wins, counted by seed, for all first round games between 1985 (when the field was expanded to sixty-four) and 2005. When I saw this graph, I was astonished at how nearly linear it is. The only strangeness is that twelves do better than elevens (27 wins vs. 25), and nines have beaten up on eights (46 to 38 head-to-head).


The best fit line suggests that the ones will win in the first round 99.1% of the time. If that's so, then we may not have to wait too much longer. But it also isn't at all clear that we should expect a line to fit this data. Still, none of the observations are significantly (in the statistical sense) different from their projected probabilities. The eight-nine anomaly has a p-value of just over 0.15.

Stay tuned for further analysis, looking past the first round.