Statisticians to Olympic figure skaters: Give up!

The NY Times has a clever bit of number-crunching of men’s figure skating on their website.

In figure skating, quad jumps (jumps with 4 aerial rotations) are worth a lot of points, but only if they are executed successfully. If you mess up, a quad is worth less than a successful execution of an easier triple. The Times combed through records of Olympic athletes’ previous performances and computed the points earned on quad jump attempts. They then compared the expected value of quad jumps to the value of a successful triple, and they concluded that it’s not worth even trying a quad. In the long run, a figure skater will score more points doing triples. (This assumes that the athletes in question are good enough that they could pretty much guarantee sticking a triple.)

Of course, as Keynes famously said, in the long run we’re all dead. Medals aren’t awarded on long-run averages; they’re based on a single performance. If everybody else is trying quads and you’re not, odds are that someone else will stick one. In a single performance, individuals can capitalize on chance.

But perhaps there are other hidden costs. The Times doesn’t discuss individual differences, but according to their data, Yevgeny Plushenko has a 100% success rate executing quad jumps. So if you just look at the numbers for quad jumps, you might conclude that it is always worthwhile for Plushenko to attempt quads. Yet Plushenko, who successfully stuck a high-scoring quad combo, only won the silver, and he was beaten out by a competitor who didn’t even try a quad. I’m not enough of an expert to say why that happened, but if Plushenko spent so much time practicing his quad jumps that he didn’t perfect other elements of his routine… well, maybe the Times’s conclusion is right after all (just not for the reasons they give).