A little later than I’d intended, but here it is. Instead of just the previous season, this is a view of the difference in median FIS points in Europe versus in North American for all North American athletes, in all events. Since we’re looking at multiple years, the graph is a bit different. For each season, we have the center of the distribution of median differences (the median of the medians, if you will) and the bars represent the middle 50%.
This is interesting on a few levels. First, if you looked at just last season, and saw the the North American female sprinters were getting better points in Europe than in North America, there would be a temptation to attribute that to the increased success by folks like Kikkan, Jessie Diggins, Ida Sargeant, etc. But here we can see that the points for North American female sprinters have pretty much always been better in Europe!
The other three panels all to some degree show a shift away from good points in Europe towards better points in North American. It’s a weak trend for the male sprinters, but much stronger for both the male and female distance events. The other interesting difference is that there seemed to be a sharp jump for the men’s distance skiers in 2010-2011. Normally that would make me wonder about changes in the population (i.e. a sudden jump in the number of non-USST folks racing in Europe), but the fact that the other panels look so different makes me skeptical.
Last week I wrote about how US and Canadian skiers fared last season, in terms of FIS points, when racing in North America versus in Europe. That included a rather almost too perfect looking symmetric, normal distribution for the men’s sprinters. On it’s face this suggests that the difference in median points earned by North American sprinters in Europe versus at home, while possessing a fair bit of variation, is basically centered perfectly at “no difference”. A reader complained about this apparent statistical anomaly, so I offer the following:
This is the exact same plot, only instead of a density estimate I’ve used a simple histogram (yes, yes, I know, a histogram is a sort of density estimate). I suppose if you wanted to get all shamanic and read the tea leaves on this, you could argue that the four short bars on the extreme left of the men’s sprint panel argues for a less symmetric distribution than the density estimate showed. But I think we’re splitting hairs at that point.
The sample size here is what I’d call medium-ish, at around 75 individuals for the men’s sprint panel. I think the best argument against what I posted last week is not that the distribution appears remarkably symmetric, but that perhaps my choice of smoothing parameter for the density estimate (in truth, I simply used the defaults for my software) were perhaps a bit….aggressive for 76 data points.
Later in the week I’ll update this with a look at how these values have changed from season to season.
I thought I check in on the most recent season and compare the point availability for North American skiers in Europe versus at home. This was a pretty simple approach, I just took all US and Canadian skiers who raced in both North America and Europe last season (any race type) and calculated the difference in their median FIS points for the two locations. Finally, I did a simple density estimate on the difference to get this:
The x axis here is relative, not absolute. So -100 means a person’s median points in North America last season were 100% better than their median points in Europe. I’ve omitted the y axis labels entirely, since the idea here is to simply look at the shape of the curve, and where most of the area is located.
The men’s sprint panel sticks out like a sore thumb for being so damn perfect looking. This strongly suggests that as a group, North American male sprinters weren’t really any more likely to score better FIS points in Europe or “at home”. As the distribution makes clear, though, there is plenty of variation between individuals and how their particular races went at home and abroad.
While we’re on sprinting, my next biggest surprise was the women, who appear to have had a moderate trend towards scoring better sprint points in Europe. Before you start saying that Kikkan Randall is driving this, keep in mind that Kikkan only contributed a single value to that density estimate. Each individual skier only counts once in each graph. So maybe between Kikkan, Jessie Diggins, Ida Sargeant, etc., one might have expected some good points in Europe, but I wasn’t quite expecting it too be that clear.
The distance panels aren’t too surprising, I think. Even with the recent improvements for the US women in distance events, US and Canadian skiers are still much more likely score lower points in North America than in Europe.