Statistical Skier

With the first period of WC racing in the books and the next one just around the corner, I’m going to look back at the results of the North American skiers so far this season.  The theme of this post is context and expectations.

One of the reasons that I started this blog was that I felt as though the tools we use to measure performance in skiing don’t always match up with our expectations and this can lead to a lot of needless frustration.  The general paradigm for measuring performance in XC skiing is to examine only an athlete’s best few races over some time period.  FIS averages your best five races over the previous calendar year for their point lists; EISA picks out each skiers best two classic and freestyle races (if I recall correctly), and so on.

We may not be explicitly aware of it, but this methodology stems from an important observation: once in a while good skiers can have truly terrible races.  Averaging is particularly sensitive to extremely small or large values, so one terrible FIS point race could have a huge effect if we were to look at all of someones results.  This is an excellent observation, but I don’t think people are necessarily aware of the consequences.

Performance measures that look only at an athlete’s best few races are a terrible indicator of how well they typically ski.  Instead, it’s measuring how well they have skied at their very best.  It’s an estimate of an upper limit, not a “typical value”.

This, combined with short memories, leads to some strange tendencies, I think.  When we think about how good a skier is, we tend to think about their best results: Kris Freeman’s 4th place finishes, Kikkan Randall’s sprint podiums, etc.  But those aren’t necessarily indicative of how well they ski from week to week.

With all that in mind, let’s look at some graphs.

Note the slightly unusual scale on the y axis.  I’ve been tinkering with this for a while now, and I’ve grown to like using percent back from the median skier.  Negative values are good (ahead of the median skier) positive values are bad (behind the median skier).  It turns out that it mostly (but not completely!) eliminates discrepancies between mass start and interval start races, it’s easy to interpret, and there are some technical mathematical reasons why I like it as well.

The red dots are this season’s results.  I’ve highlighted last year’s Olympic results in blue, which I’ll return to in a moment.  I will also point out the one instance here where percent back from the median doesn’t capture everything as we’d like: Devon Kershaw’s 5th place in the Olympic 50k last year.  His percent back from the median skier isn’t all that low, for a 5th place finish.  This suggests that (a) the pace might have been fairly slow and (b) as with all 50k’s, the field was likely somewhat reduced. Continue reading ›

This is a follow-up post to an earlier entry where I noted an off-hand comment by US coach Chris Grover that when Kikkan Randall qualifies in the top ten in a sprint race, that this is a good sign that she has a good chance of making it to the finals.

I looked at some data and concluded that it mostly supported his claim, but that the sample sizes were small enough to not mean much, from a statistical point of view.  It was suggested in the comments that I look at this overall, for all skiers and see what, if any, relationship there might be.

Generally speaking, I think we shouldn’t be terribly surprised about a correlation between one’s performance in qualification and one’s performance in the heats.  It just makes sense that, on average, the faster sprinters will do better in qualification.

What we’re interested in here is in quantifying this somewhat arbitrary, but interesting, cutoff of finishing in the top ten in qualification.  First up is a modified version of the plots I made for Kikkan Randall and Andrew Newell in the previous post: Continue reading ›

Just as I did yesterday, let’s take a closer look at the results form Saturday’s World Cup mass start race in La Clusaz, France, this time focusing on the North Americans.  As I discussed yesterday, we’re going to use percent-back difference plots from mass start or pursuit races to evaluate each skier’s race, since the FIS points awarded in mass start races can be a bit misleading.

Starting off with the Americans, Morgan Arritola:

Both Arritola and Stephen seemed to have excellent races if you go by their place (18th, 19th) but pretty terrible races using FIS points.  Clearly, the FIS points are misleading in this case.  While the entire range of dots from Saturday’s race (blue) doesn’t seem markedly different than last season, what interests me is the median (red), which was almost 5% points better in that race than what Arritola typically managed last season (or ever, quite frankly).  And if you think that’s a big jump compared to last season:

Granted, this is looking only at mass starts and pursuits, which happened to coincide with some truly horrible races for Liz Stephen last season.  But Saturday’s race still looks about as good, or slightly better than what she was managing the previous two seasons.

Men’s post to follow later today…

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Saturday was the first long mass start race of the World Cup season in La Clusaz, France, and along with mass start races come difficulties in measuring performance in a sensible manner.  The women’s field didn’t help matters by having the top three ski away from the field.

So you end up with some odd stuff, like Elizabeth Stephen and Morgan Arritola have seemingly some of the better races of their careers (18th, 19th) with FIS points near 100, which would only just barely put them in the top ten in last weekend’s Nor-Am race in Canada.  As I’ve pointed out before, over the course of a season or an entire career, these sorts of things tend to even out and not be such a problem.  But in situations like this, where we’re looking at a single race and we want to know what it means, it’s a problem.

One way we can get around this is by comparing a skier directly to the other skiers in this particular race, using a percent-back difference plot looking only at mass start and pursuit races.  The fact that the entire field’s FIS points may be inflated (or deflated) artificially won’t matter, since we’ll only be looking at the relative differences between a particular skier and the field.  Sometimes we get a different answer, sometimes not.  As an example, let’s look at a handfull of skiers who appeared to have particularly good or bad days on Saturday.

First up, Curdin Perl (SUI):

Compare this with how his race looks in my snapshot graph.  In that version, Perl had a career race, as the black bar represents the middle 50% of his results over the past several years.  While the percent-back difference plot above suggests a good race, it doesn’t look mind-blowingly good.  The difference in percent-back between Perl and the other top 40 skiers or so is modestly better than last season.

Another skier who seemed to have an unusually good race was Sweden’s Daniel Rickardsson (who also, I believe, is also more known for his classic skiing, but I haven’t checked that): Continue reading ›