Statistical Skier

If you hang around skiing in North America long enough you will eventually hear people talking about point differences between races in Europe and North America (or the US in particular). One of the most common forms of this is the complaint that penalties (and hence points) are artificially high in the US, compared to Europe.

While I’m certainly sympathetic to criticisms of the vagaries of FIS points, I’ve always felt this complain was a bit short on data. It’s certainly plausible that race penalties are systematically lower in Europe, but that doesn’t necessarily mean that the differences are in some sense “wrong”.

The most direct way I know of to examine these sorts of issues is to isolate individual skiers who raced in North America and in Europe in a given season, and compare their points. If the North American races are seeing artificially high point levels, you would expect the average skier’s points to be systematically higher in North America than in Europe. (If FIS points worked perfectly, they’d be roughly the same.)

Doing this raises some sticky questions of which racers and which races to include. Since this is most often raised among North American non-World Cup level skiers, I think it’s most instructive to restrict ourselves to just that category of skier. So we’re only going to compare points from non-World Cup level events.

Here’s our first graph:

Each dot represents a single skier. Specifically, the difference between the median FIS points for North American races minus the median FIS points for European races. (Obviously, only skiers who competed on both continents are considered.) Clearly, this shows that there is a lot of variation from skier to skier, as we would expect. Someone might be killing in the US, travel to Europe and get sick and race very poorly, or vice-versa.

But it’s the blue trend lines that we’re really interested in here, since they are what will measure systematic trends. Given the scale of these plots, it’s a bit of a challenge to interpret. So let’s redraw just those four lines on a common scale:

Remember, the y-axis is North American points minus European points. If North American races systematically have higher points, we would expect these trend lines to be solidly above zero. And some of them are! Or at least, they have been in the past.

The line that stands out as the most different here is the men’s distance line. For a while it flirted with approaching zero in the mid-00’s, but has spent most of its time at around -20 FIS points. This means that US/CAN men, on average, get FIS points that are around 20 points lower in North American than in Europe. This is the exact opposite of what we’d expect if North American races had artificially high FIS points.

The other three lines have generally been above zero, sometimes by quite a lot, sometimes just barely. But all three have dropped dramatically over the last 3-4 seasons. This past season, the only one still above zero is women’s sprinting.

The other thing to note here is that FIS points for sprinting only captures qualification speed, nothing more. Any differences in competitiveness in the heats would not be captured here.

Earlier this week I tweeted a little nugget I stumbled across: that Jessie Diggins now owns around half of all top 30 results for US skiers 21 years old or younger over the past two decades. In contrast, the most any single Norwegian contributes over the same time period is around 10% of all their top 30 results by skiers 21 or younger.

That fact illustrates two things to me: (1) Jessie Diggins may be the best talent the US has seen since in a long, long time, and (2) the US is really quite bad at developing skiers at younger ages. Usually, our best skiers are well into their late twenties or even thirties.

Among young World Cup skiers, how does Diggins stack up? Well, of her 16 starts, she was in the points over half the time. This is well behind the likes of Krista Lahteenmaki, Maiken Caspersen Falla and Heidi Weng. But it was better than Finn Hagen Krogh, Gleb Retivyhk, Petr Sedov and Hanna Kolb.

This all got me wondering what the age breakdown has been more generally for top thirty finishers, so I made this following graph:

(The handful of bars that don’t reach all the way to 100% are due to a small number of skiers, mostly Russian, from the 90’s who I don’t have a year of birth for.) Not surprisingly, the under-21 crowd is more strongly represented among the top sprinters.

I received an email recently from a reader who pointed out to me that Marit Bjørgen completed the 30k classic mass start in Oslo this season in 1:26:09.8, last year at World Championships Therese Johaug did the same course, mass start, skating in only 1:23:45.1, which is only a difference of about 2.8%. Surely, skating is more than 2.8% faster than classic?

Now, there are all sorts of reasons why unusual differences like this could occur. Strange weather and snow conditions, obviously, is the major culprit. My memory for those things isn’t so good, but my correspondent assured me that the classic conditions for Bjørgen were not favorable, which should have made the gap much larger, one would think. (I’m also assuming that the course really is identical, which is another factor that I have very limited knowledge of, being many thousands of miles away with limited TV coverage.)

As a first pass, let’s just look at the average speeds for the winner of all recent women’s 30k mass start races:

Now we can see that the average speed difference does appear to be quite large, but that my correspondent happened to stumble across a particular pair of races that weren’t that different. But clearly I can’t stop here.

Before going any further, let me be up front that there are numerous important variables that influence average skier speed that I can’t control for simply because I don’t have the data. Weather and snow conditions, as mentioned above, but also the fact that I collapse race distances down to their “advertised” distance. For instance, if the schedule says it’s a 15km course, that’s what I call it. The PDF race results will typically have a more accurate number, but pulling data out of PDFs is just more trouble than it’s worth.

With those caveats in mind, I went ahead a fit a big complicated model. Well, it’s not really that complicated, but I’ll spare you most of the details. Basically, it models average speed among the top 30 skiers as a function of gender, technique, race type (mass start vs interval start), race length and time (to account for changes in speed between, say the mid-90’s and now). There were a little over 16,000 observations in the data set used for this model.

Then we can look at the model’s estimates for the average speed of skiers in various types of races. First, the men: Continue reading ›