Going Conventional: A March Madness Case Study

I was talking with friends the other day about sports. All of my friends like sports either significantly more than I do, or significantly less. Thus I was basically talking to myself and wondering how likely conventional wisdom was to be wise.

I know there are all sorts of bookies who know exactly what seeds mean what, but I was more interested in the exception cases. Specifically, what is the largest sub-tree of an NCAA bracket that has had no upsets.

I was positive that 2 team subtrees had this property: that's simply the higher-seeded team winning a game. I would have bet a lot of money at long odds that 4 teams had done it (that is, 1 beats 4 and 2 beats 3 and then 1 beats 2. Of course, in a 16-team seeding, that really means 1 beats 16 and 8 beats 9 and 1 beats 8). But 8 games... I thought happened. And 16 I thought maybe hadn't.

Turns out, 8 teams has happened. As recently as 2007. #2 Georgetown is triumphant over 7 other, lower-seeded teams.

16 teams has happened too. If my scan is correct (though it's late, so I'm open to other examples), in the 1985 tournament. The East region was won by #1 seed Georgetown, who beat seed 16, seed 8 (who beat seed 9), seed 4 (who beat seed 13 and seed 5 (who beat seed 12)), and seed 2 (who beat seed 15, seed 7 (who beat seed 10), and seed 3 (who beat seed 14 and seed 6 (who beat seed 11))).

But before that, I had found that it has also happened to 12 teams. Back in 1982, with a 48-team field, the West region was won by... Georgetown.

I guess the moral of the story is: if you find yourself seeded in a sub-bracket with Georgetown seeded higher than you, you're in for a not-very-upsetting time.

P.S. As a side note, I checked out Georgetown. In 10 out of 17 tournaments I looked at, they won exactly when they were the higher-seeded team. In 4 they lost as a higher seed, and in 3 they won as a lower seed. Thus, in the future, you should expect Georgetown to win exactly those games as they are expected to. They're rather dependable.