Statistical Skier

Some comments on a recent post got me curious about the FIS points awarded at OPA Cup races. Similarly to my commenters, I’d noticed that oftentimes the top skiers at an OPA Cup race would receive very low (i.e. good) points for that race, and that this often wouldn’t seem to match up well with how they actually ski against a real World Cup field.

Here’s what I’m interested in: are the FIS points of top skiers at OPA Cups a worse indicator of performance on the WC than the FIS points of top skiers in high-level Scandinavian races (i.e. Scandinavian Cups). I think we all would suspect that the answer is yes; but how big is the difference? Can we quantify it?

Let’s take all the skiers who finished in the top ten in an OPA Cup race over the past five season and compare their OPA Cup FIS points with their WC/WSC/OWG/TdS FIS points. In the process, we obviously going to filter out some folks who didn’t participate in both types of races. Normally I just make a pretty graph, but I was feeling fancy, so here are some estimates of the difference in FIS points obtained via some simple linear modeling:

These values all indicate significantly higher FIS points against actual WC fields for these skiers. (Note: these models were fairly crude, but did attempt to account for the number of races of each type a skier did as well as general performance changes over time.) Note that generally speaking, OPA Cup FIS points are a worse predictor of WC FIS points in distance races; for the women, they are very bad, on average.

How about Scando races? Let’s do the exact same thing, but instead we’ll take the skiers who’ve finished in the top ten over the past five seasons in Scandinavian and even general FIS races held in Norway, Finland and Sweden. The estimates we get for this group of skiers are:

Holy Cow. The negative values suggest that these skiers actually have a slight tendency to get better FIS points against a WC field. However, note that only the estimates for the men are “statistically significant”, and even those aren’t really that far from zero in a practical sense. (A difference of 5-6 FIS points, on average, is not very big given how variable people’s FIS points are to begin with.)

Still, these values are definitely strong evidence that a top result in an OPA Cup isn’t nearly as meaningful as a top result in a competitive FIS race held in Scandinavia. Not a big surprise, but fun to quantify.

Finally, I should point out that all the models I ran here “fit poorly” in some senses. By that I just mean that their R-squared values were fairly low (generally around 0.3 or so). Now, R-squared isn’t really a good indicator of model fit, but it’s safe to say that while the differences we just observed do exist on average, there is a lot of variation from athlete to athlete. The somewhat mythical ‘average’ OPA top ten skier will tend to do much worse on the WC circuit, but what you see in individual skiers will vary considerably.

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