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.
Travel is a big issue for cross country skiers, particularly those of us living in North America. Flying back and forth to Europe can be both time consuming and exhausting for athletes. Obviously, this can have some serious effects on performance. Of course, this works both ways. Presumably it’s difficult for Europeans to travel to World Cups in North America as well.
Let’s see if we can see any general trends in the data. Read more
In a post last week I talked about how I felt that a single early season result wasn’t necessarily a great predictor of how someone will tend to ski (on average) during the rest of the season. I feel like most people would accept that this is, in principle, generally true. Just because you pop a great race in November doesn’t mean you’ll be killing it in February.
A commenter pointed out, though, that while that person with a single great early season result might have worse results in an absolute sense for the rest of the season, they might still do better than everyone else. And that’s really all that matters if you’re selecting people for an event. That’s a good point, so I went for a somewhat more specific comparison and found that my statistical intuition wasn’t quite as correct as I had thought.
The following plot shows the the ranks of the minimum FIS point result versus the rank of the median FIS point result for US juniors:
So the people with the best minimum early season FIS point race really do tend to have the best median late season FIS point results. I was not expecting these to line up nearly this well at all.
Of course, there’s still some variability here that means it’s not perfect. (What in life is?) So you can see several instances where the person with the best FIS result in the early season only had the 4th-5th best median FIS point races for the rest of the season. But it’s much more highly correlated than I would have thought based solely on my mathematical intuition. Chalk one up for my commenters!
For WJCs, the FIS point cutoff has been lowered to 50 for both men and women (it used to be higher for women than for men) and it can come from any FIS sanctioned race between Nov 1st and Dec 31st.
Generally, I’m skeptical of the wisdom of allowing people to automatically pre-qualify based on a single race (albeit a good one). But I’ll come back to that issue in a subsequent post. For the moment, I was curious where US juniors might be able to find races with penalties under 50 during that time of year (excluding WC races, of course). So here’s a summary of all such races that fit that bill for recent seasons:
This is showing the number of FIS races in each country within those dates with a penalty less than 50. (Of course, this doesn’t reflect how many skiers in that race broke 50 points, just that someone did.) I wasn’t expecting there to be such a big disparity between the distance and sprint races, to be honest. Part of me is wondering if this rule change will favor juniors who make the effort to get over to Europe during the fall in the hopes of popping a great race. Now that I write that, it occurs to me that encouraging juniors to “go to Europe for their points” might be part of the intent here, but that’s just speculation.
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.