I glanced at some numbers but I wasn’t exactly clear on what you were asking (average start per athlete? per season?) so here’s a rough idea of totals. You can infer averages yourself by dividing.

Looking at WC, OWG and WSC races, Distance and Sprint, Men and Women, the big nations (NOR, SWE, FIN, RUS, GER) tend to have ~120-160 finishes per season (excluding dnf,dsq). Then there’s nations like CAN,CZE,EST,FRA,JPN,SUI,UKR and USA that tend to have ~40-90 finishes per season. SUI, for example, is typically closer to 90 while the USA is typically closer to 50.

Then there’s lots of nations with 1-30 per year or so.

I literally just glanced at a quick summary, so don’t necessarily hold me to those numbers, but they should be roughly in the right ballpark.

I will simply reiterate what I began with before: My objective was to get a sense of how all wc skiers vary, not just a subset. So in that sense, neither one of us is wrong, we’re just asking different questions.

When you say “I don’t think that including the slower world cup skiers in the mix is the right thing to do because we are looking at what the best are doing” you’re assuming that we’re trying to do the same thing!

If I had asked your question, then yes, what I did wouldn’t be very relavent. But I did answer the question that I _did_ start with. I just didn’t answer yours.

See how we can both be right, here?

I think that a better model, would be to take the top 50 skiers in the world based on their FIS points profile, and if one of those skiers doesn’t have a minimum number of world cup starts this year, throw them out. Then find the standard deviations of that group. This will eliminate the bias of excluding bad races, and including bad skiers.

You’re right, I am capturing skiers at the low end of the world cup. I’m also capturing skiers at the high end, though. My objective was to get a sense of how all wc skiers vary, not just a subset. So in that sense, neither one of us is wrong, we’re just asking different questions.

However! I do disagree on the usefulness of looking only at sub-50 point races. I tried many different cutoffs looking for one that was reasonable (in the context of my specific question) and settled on 9 and 150.

What I found was that lowering the point cutoff has two big drawbacks: (1) you end up tossing bad races from good racers, artificially deflating their variability and (2) if you go too low, you end up running out of data.

For example, using your suggested cutoff of 50, suppose we have a racer with 9 races between 15-30 points and one race at 80 points. A cutoff of 50 seriously underestimates the real variability of this racer by simply omitting their 80 point race.

Now, the same sort of thing will happen with any cutoff, even at 150. But the higher you go, the less it happens. I was mainly concerned about a small number of very large fis points scores that would make plotting a histogram awkward.

So I went for a relatively high number of races (9) to weed out some of the sort of people you’re talking about, since people regularly scoring really high FIS points aren’t as likely to compete in a large fraction of the events in a given season, and a low point cutoff (150) to make sure I’m capturing the “real” variability of the racers.

Finally, I don’t need to redo the analysis to tell you that lowering the point cutoff will lower the SD values. What you’re suggesting amounts to saying “if we look at values in a less variable range, they will vary less”. Numbers between 0-50 will vary less than numbers between 0-150 no matter what.

I hope that made sense…

Based solely on my impressions from gathering the data, though, I’d be willing to bet it doesn’t change the picture much, at least when you’re looking at the entire group rather than a specific individual. The number of DNFs on the World Cup circuit is (again, just my impression, I haven’t counted) a rather small proportion of all the results. We’re talking maybe 2-4 out of 40-80 for perhaps one/two races in three. Well under 2-3%.

But believe me, it’s part of a quickly growing list of things I’d like to look at!

That said, one guy’s bad result is another’s reason to absorb a DNF.

Also, I specifically focused on distance events because sprinting is somewhat more confusing with qualification vs. final ranking difficulties. Also, there’s simply less data for sprinting, as it has been around on the WC circuit for barely 10 years or so.

@nexer: In general, yes. The correlation is not rock solid, though. I’ll try to update the post with some pictures showing this relationship.

@Cloxxki: As @nexer said, DNFs are tough. Obviously in some sense they represent a “bad result” but in a way that is tough to quantify fairly. I made the decision fairly early on to simply ignore DNFs, which I am mildly regretting now. I may revisit this late.