A recent blog entry by Brian Hayes, one of my favorite science writers, discusses the age-old ritual of dividing a group of kids into two teams:
The simplest algorithm has two captains, A and B, who take turns choosing players until everyone is assigned to one team or the other. Call this the ABAB algorithm. Donald B. Aulenbach suggested a very easy modification that produces more closely matched teams. Aulenbach’s proposal is the ABBA algorithm, where A gets the first pick in the first round but B goes first in the second round, and they continue alternating in successive rounds. (Another way of describing the same process is that A begins with a single turn and thereafter both captains take two turns in a row.)
Hayes then shows some simulation results confirming that the ABBA algorithm does indeed divide up the players more evenly than ABAB. He concludes,
Going back to my own childhood, I don’t think the kids in my neighborhood ever discovered the ABBA algorithm. We did recognize the inherent advantage of choosing first, and we compensated by adopting a separate ritual to decide who got the first pick. In baseball, this involved a hand-over-hand struggle for a grip on the bat. Sometimes I think the preliminaries were more fun than the game.
Another interesting mathletics tidbit was buried in a recent University Week article about Generation IX, a documentary on the University of Washington women’s volleyball team:
In the documentary, the viewer sees the team statistician toting up every play in practice as well as in games. As one of the players puts it, “If your numbers aren’t there, you know you’re not going to start.” The women say they like this objective system, because nobody can say, “Oh, it’s because [Coach McLaughlin] likes her better.”
The idea of determining playing time by objective statistical criteria is appealing to me. Could this approach be used in every sport at every level?
In disciplines like cross-country, of course, assessing performance is extremely straightforward — you just line up your runners and yell “Go!” and see who gets to the finish line first. But I wonder whether there are adequate statistics for quantifying the success of, say, football linemen or soccer fullbacks. And even if there are, what sample sizes would be necessary to determine that one person is “significantly” better than another? For example, if two shortstops are equivalent defensively, should you play the one with six hits in 20 at-bats over the one with four hits in 19 at-bats? I’m not so sure.
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