Statistical Skier

Can you name a Polish men’s cross country ski racer?  Hmmm.  Poland has certainly been a one woman show of late, thanks to Justyna Kowalczyk.

Which makes the following graph (a continuation of the graphs in this post) not terribly surprising:

So here are some Polish men for you: Janusz Krezelok and Maciej Kreczmer.  Who was that older Polish woman who clearly retired in 1998?  That would be Malgorzata Ruchala.

Poland is another extreme case.  Germany is another team that’s been getting older, despite being a much bigger program:

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Yes.

That whole shooting bit.  Tricky, isn’t it?

So maybe a bit more discussion would be good.  This graph shows the distributions of the median absolute deviations (MADs) by athlete and season, for those athletes who competed in at least five major competitions in that season.

Biathletes, due to wild swings in shooting performance, are much more likely to have results that bounce around from good to bad.

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When most people say that World Cup skiers are animals, they probably mean they are fierce, strong competitors.  I got my PhD in statistics in a department that found itself working quite often with very strong wildlife biology and ecology departments, so for me that reference leads me to think, “Well, what if they really were animals?  What sorts of statistics might I end up doing on these data?”

A common statistical analysis when your subjects actually are wild animals is called survival analysis.  Very generally, the aim is to determine what factors influence the survival of, say, bears[1. Usually, the organism isn’t nearly this exciting.  Typically I’d see data on something like the western spotted shrew, or the golden mantled ground squirrel.  One of those animals I made up, the other I did not.].  The poor biologist would spend countless hours over multiple summers capturing, tagging and then tracking and recapturing the shrews or slugs or whatever[2. Stats grad students would frequently talk about how grateful we were that we didn’t have to do field work.].

The end result would be a bunch of lifetime data (along with other variables) on individual organisms.  Then the question is, which variables seem to influence survival rates?  There are all sorts of technical details with this kind of data (censoring, mainly) on how to model it that I’m not going to get into here.  If some nerdy biologist is reading this and wants more details, let me know, and I’ll put them in the comments.

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With more North Americans sojourning over to Europe to participate in high-level European racing that isn’t quite World Cups, I thought it might be interesting to take a closer look at the OPA (or Alpen) Cup and Scandinavian Cup series in a bit more detail.

As the name might imply, the Scandinavian Cup races are in, well, Scandinavia.  The racers are nearly all from Norway, Finland and Sweden (although Estonia has a large showing as well).  The OPA Cups are more continental European affairs, with racers coming mainly from Italy, Germany, France, Switzerland and Austria, among others.

Both circuits are, to my knowledge, generally considered a sort of “minor league” racing circuit just below the World Cup.  To get some sense of the competitiveness of these races, here’s a plot of the FIS points awarded to the top five finishers in distance events in each circuit:

For the men, the two series seem roughly on par while the women’s Scandinavian Cups appear slightly more competitive.  Of course, this assumes we trust the system of assigning race penalties to accurately gauge the strength of the field on a particular day.

For comparison, the US SuperTour series (probably the highest level racing circuit in the US) has in recent years seen penalties (i.e. the FIS points awarded to the winner) averaging in the neighborhood of 40-60 FIS points for men and 80-100 FIS points for women.

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