Statistical Skier

I know the Moscow city sprints were exciting and all, but I’ll have some posts on them and the Rybinsk races next week. For now, as promised we have the follow-up for sprinting from Wednesday’s post.

These are the folks with the largest improvements in performance (within season). As before their results from this season are highlighted in red. I’m most interested in following up on Devjatiarov, since his trend seems so stark.

As for the folks with the largest declines in performance:

Not who you were expecting, eh?

So once again we have some Americans, who possibly do slightly worse late in the season do to increased travel demands. But how do we explain that the others here are some of the best sprinters, ever?

Well, keep in mind that saying that these skiers see the “biggest declines” during a season is a relative claim. So in Bjoergen’s case, she has had some poort sprint races, but never before January, basically. The trend for Matveeva I’m less likely to dismiss as a fluke since the difference in her case is so stark (although I don’t know her injury/health history, which can affect these things).

For Angere, Bjoergen and Pettersen I really want to think of some other explanation. But their bad races are certainly not evenly spread throughout the season.

Since I feel bad picking on Vibeke Skofterud twice now, I thought I’d follow that up with a look at that kind of trend among all skiers. Today we’ll look at distance results, Friday we’ll consider sprinting.

I hauled out my favorite statistical canon for this one, a mixed-effect model that compares each skiers results to the time during the season, estimating a separate slope for each athlete. Then I can quickly sort skiers into those with a large positive slope (get slower as the season progresses) and those with a large negative slope (get better as the season progresses).

Here are the six skiers, active in 2011-2012, with the largest declines in performance (at least, as measured by this model) over the course of a season:

I’ve highlighted each skiers results from this season in red. Also note that while I’m using standardized percent behind the median skier, the scales on each panel are different, for readability’s sake.

Surprised to see Kikkan Randall here? Note that she has had a large number of poor races in Feb/Mar. But just as influential are the current season’s result (which isn’t finished yet). Since they’ve all been rather good, they will tend to pull down the estimate of her early season performance. Once I made this plot, I realized that it would make more sense to fit the model on only results from completed seasons. For many skiers (indeed, most of the ones I’ll show you) it wouldn’t make much of a difference, but it clearly would with Kikkan. Consider this your daily glimpse into the iterative process that is “statistical analysis”.

Notice also that Skofterud isn’t at the top of this list. So perhaps we shouldn’t be quite as hard on her for tailing off as the season progresses.

How about the folks that see the most significant improvements over the course of a season?

These tend to be skiers with considerably more races under their belts. Oxana Jatskaya is an interesting case, as her current season seems to be playing out right on cue: some “normal” early season results, followed by the terrible results mid-season. What will she pull off in February…?