Statistical Skier

So US coach Chris Grover mentioned to FasterSkier.com that he thought that when Kikkan Randall qualifies in the top ten that’s a really good sign that she has a good chance to make the finals.

I did this once before with an interesting quote of his, and I feel kind of bad.  I’m not trying to pick on him, but this is such an obvious thing to check with some actual data, I just can’t pass it up.

Here’s Randall’s qualification and final ranks for WC, WSC and OWG sprint races:

I’ve highlighted the top ten in qualification (vertical red rectangle) and the top six (horizontal red rectangle).

This is a classic conditional probability question.  Given that Randall qualifies in the top ten, what’s the probability that she makes the final?  As far as I can tell the answer is 7/11 or around 63%.  (If you try counting the dots yourself, you won’t get these numbers, as there is some over-plotting going here.)

This is a really small sample size, so I would be loath to conclude here that Grover is right, statistically speaking.  The good news (for Grover!) is that I can’t really conclude that he’s wrong either.  On the other hand, every time (all 11 of them) Randall qualified in the top ten, she eventually made the semis (versus the 6 times she made the semis w/out qualifying in the top 10), which is about the same at around 64%.  Now the sample size is a tad bigger, so maybe Grover’s on to something here, as long as we interpret “making the semis” as “having a good chance to make the finals”, which seems fairly reasonable to me.

Just for comparison, here’s the same plot for Andrew Newell, whose qualification/heats tendencies are a subject of much debate:

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