Regression to the Chalk: March Madness

Did you fill out a bracket this year for the NCAA tournament, dear reader?

I did. I'll report the following three points about the experience: I wasn't even close to winning the billion dollars; I didn't try to predict any of the "first round" games; and I've decided that tournament results exhibit a definite pattern, which I have come to think of as "regression to the chalk."

The first of those three points needs no particular explanation.

As to the first round, I'll offer this. I am still sentimentally attached to the idea of a 64-team field. Nowadays, though, the Powers that Be have mandated that 68 teams be involved. So they have four "first round" games on Tuesday and Wednesday of the first week of the tournament to eliminate four of those 68. By Thursday morning, we're back to a 64 team field, and that is the best time to fill out the form, IMHO. The "second round" is exactly what the first round was in days of yore, 32 games over two exciting days, setting up the continued whittling down by halves until we get to the final four and the terminal two.

In the third of the above three points I have created a portmanteau of the phrases "regression to the mean" and "playing the chalk."

Playing the chalk means predicting the victory of the favored team. Regression to the mean is a more complicated concept: if a variable in at an extreme end of its range at the time of a first measurement, it will be likely to be closer to the center at the second. Galton -- the charming fellow portrayed above --noticed back in the 19th century that tall parents tended to have more average-sized children. Not midgets, by the way. The reversion is not toward the opposite extreme but toward the mean.

This brings us back to the NCAA tournament. In one sense, the idea of "regression" doesn't apply here, because the concept implies a continuum of possible outcomes, with a mean and two distinct extremes. As with height. In the NCAA tourney there are only two different outcomes of a game. Its a simple W/L equation. A winning team can win by more or less, but what counts in determining whether it continues on in the tournament is simply its place on that two-branch decision tree. It won or it lost.
Still, since we're all just having fun here, let's understand the "mean" as being represented by any game in which the higher-seeded team wins. An "extreme" is a game in which the lower seeded team wins (in sports terms, an upset.)
The regression to the chalk theory is this: upsets tend to cluster in the early round, in the later rounds the mean re-asserts itself.
Thus, in this year's tournament there were as usual lots of upsets in the "second round" (the one I think of as the first round, in accord with my old school sympathies explained above). Dayton (11th seeded) defeated Ohio St (6th seeded, and with a decades-long reputation as a powerhouse). Meanwhile in New York, Harvard (12th) was defeating Cincinnati (5). Harvard! The team that has always consoled itself for its losses with the famous cheer, "That's all right, that's okay, you're gonna work for us some day." Most surprising of all, Mercer (14th seed) ended the season of the Duke Blue Devils. (3d).
Oh! you say, a chalk player's nightmare!
Except that it wasn't. All the 1st seeded teams survived that round. so did all the #2s and three of the #3s. And the upsets will taper off as we move forward. The "Cinderellas" like Mercer almost never seem to make it to the final four, much less do they wed the King's charming boy. A typical Final Four will consist of two #1 seeds, one #2 seed, and a#3 seed.
This year, Harvard lost its second round game, so its time at 'the ball,' though no doubt precious, was brief. It headed home long before midnight. Likewise, Mercer shocked everybody by overcoming Duke, and then succumbed to Tennessee in the second round. That is how regression to the chalk works.
By the time we got to the "elite eight" with Friday night's results, there were two #1 teams still in it (Florida and Arizona). There were also two #2 teams, Wisconsin and Michigan. Since Wisconsin and Arizona will play each other today, they obviously won't both get into the final four.
Nonetheless, it seems a good guess at this point that the final four will consist of one #1, two #2s, and a #4. I don't think that would surprise Dalton.
The Final Four itself will like much like the chalk players expected.

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