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:
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: