Math bracketologyology

Jordan Ellenberg wrote a piece for Sunday’s New York Times on The Math of March Madness. It’s centered around a paper by Michael J. Lopez and Gregory J. Matthews which claims that a model combining point spreads and “possession based team efficiency metrics” (i. e. average numbers of points scored or given up per possession) did quite well in Kaggle’s 2014 March Madness competition. (For legal reasons, Kaggle had to call it “March Machine Learning Mania”.)

Sadly, this article doesn’t include Jordan’s own contribution to bracketology, the “Math Bracket”, in which the school with the better math department is picked to win each game: here are the 2015, 2014,”>2013, and 2010 (the original). If there are 2011 or 2012 math brackets, they don’t appear on his blog. In 2010 the math bracket picked Berkeley (excuse me, “Cal”, since we’re talking athletics) to win; in 2013 through 2015, Harvard.

I don’t know how well a totally random bracket (i. e. picked by coin flips) would do, but the math bracket at least starts out better than this. The math bracket usually picks the higher-seeded team in the first round – 19 of 32 in 2015, 22 of 32 in 2014, 23 of 32 in 2013, and 23 of 32 in 2010. This is because bigger schools (up to a point) tend to have better math departments and are better at basketball. (Quality of a department is judged by how many people an anonymous group of number theorists and geometric group theorists can name so is correlated with department size, which in turn is correlated with undergraduate enrollment, etc.)

The math brackets seem to break down in the later rounds, though. The 2010 bracket has a final four featuring teams seeded 2, 4, 8, and 11; 2013 is 2, 6, 12, and 14; 2014 is 2, 2, 10, and 12; 2015 is 7, 11, 11, and 13. The average final four team in the math brackets is therefore an 8 seed (the average of those numbers is 127/16 = 7.9375); the average team in the tournament is of course an 8.5 seed. The very best basketball teams just aren’t at schools with the best math departments.

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