Statistical Skier

As promised from last time, here we have the detailed development plots for sprinting. First the men:

And the women: Continue reading ›

I happened to be thinking about visualizations of athlete development recently, and in the process cooked up the following graph:

What I’ve done here is to take the podium finishers in major international events for the past five seasons and recorded each person’s age when they received their first (individual) WC/OWG/WSC start, when they scored their first WC/OWG/WSC points (i.e. a top thirty at any of those events), and finally when they first landed on the podium.

The style of graph here is sort of a more informative type of boxplot. Boxplots really only show you five values, so there’s a lot of lost information. Here, each dot represents a single athlete, so we can get a sense of the entire distribution of ages for each event.

As expected, the women’s ages tend to be somewhat lower across the board; this could be development related, but I tend to ascribe it as much to differences in field depth or competitiveness. The basic story is roughly the same in each of the four panels: rarely do future podium skiers get their first “major” start after the age of 23, they finish in the top 30 after at most a year or two, and then finish in the top three maybe another 2-3 years later.

Of course, that’s what happens with the “average” skier, which doesn’t exist. We are all our own unique snowflake. So this is still masking a fair bit of variability (that I’ll delve into a bit more on Thursday). But the basic lesson I draw from this is that if there’s a threshold to be seen here, it’s at the age of 25. The best skiers seem to have established at least the potential for scoring World Cup points before the age of 25.

This post is somewhat of a teaser trailer for the sorts of things we can do once we have a complete record of major international ski results stretching back to the 70’s.

A natural and possibly controversial question is whether the World Cup field has become more or less competitive over time.  Intuitively, I think it’s clear that it probably has.  That’s just the natural progression of any sport as it attracts more money, sponsors and participants.  The skiing community as a whole simply gets better at producing fast skiers.

But this process can make it difficult to compare the results of today’s athletes to those of many years ago.

In a sort of XC skiing data fantasy world, we’d like to make direct comparisons between modern skiers and historical skiers (i.e. is Petter Northug faster than Gunde Svan?).  The only real way to answer that question would involve time travel.  We can, however, make relative comparisons about the entire field.  So we can ask the following: Is the average 30th place finisher on today’s World Cup closer to or further behind the winner than the average 30th place finisher in 1984?

To do this I grabbed some preliminary data from my big data entry project.  To keep the comparison and fair (and simple) as possible, we’re only going to look at men’s interval start classic races.  (I think it’s pretty obvious that skating comparisons are going to be problematic.)

I happened to have all the results for World Cup races from the 1982-1983 and 1983-1984 seasons, so those races will serve as our “historical” data set.  I’m assuming that all these races were classic races, which isn’t technically correct, if I have my history right.  At least a few of these races had experimental “skating zones” where people were allowed to skate for a few hundred meters at a time.  Personally, I think that’s a small enough deviation from “classic skiing” that for these purposes, we needn’t worry.

Next, we’ll take a roughly equivalent number of modern men’s interval start classic races.  The result is around twenty historical races and twenty modern ones (from across the last several seasons, since classic interval start races are more spread out in the schedule).

The following graph shows the average FIS points (calculated using modern rules for all races) for both groups versus finishing place:

I was expecting the average modern skier to be closer to the winner, but I wasn’t expecting the difference to be this large or to range across the entire field like this.

Now, World Cup point rules have changed as well.  Back in the day, only the top twenty scored points, and the point scale differed.  Still, we can make some sensible comparisons for the average 10th, 20th, etc. place finishers here.

For interval start races, FIS points are essentially just percent back times 800.  This means that the average male 30th place finisher in the early 80’s was ~2.5% further behind the winner than today’s average male 30th place finisher.  Two and a half percent!  That’s probably almost a minute in a 15km and just over two minutes in a 30km.

Obviously, the point here isn’t that the skiers from back in the day were slow.  Remember, we can’t say things like that because that would be a direct comparison.  It’s just that when the sport was younger, there were fewer people able to ski close to the winner.

The way I like to think about this is to compare the World Cup circuit to a game of musical chairs. This entails reading the above graph “backwards”. Let’s start with a 30 FIS point World Cup result. If we move across horizontally from that spot on the y axis, we see that there were typically around 15 skiers in the early 80’s who were capable of finishing that close to the leader. Continuing across the graph, we can see that that number has increased to around 25 now. So you could think of that as adding 10 people to a game of musical chairs that started with 15 people and 15 chairs.

The notion of an athlete preferring distance races of a particular length is pretty familiar, but what about sprinting? The differences between a 0.8km and a 1.8km sprint course may not seem like much compared to the differences between a 15km and 30km race. But (while I’m not a physiology expert) it seems likely to me that you could very well run into much more significant differences in the physiological demands at that smaller scale, in terms of what sorts of things your body needs to be efficient at.

That’s a long winded introduction to my having run through some simple linear mixed effects models that look at skiers who have a particular tendency to do better (or worse) in sprint races of different lengths. I’m going to start you off with the graph, which is fairly self-explanatory. But be warned, there will be quite a list of caveats…

The pool I’m drawing on here are folks who’ve done at least 10 major international (WC, OWG, etc.) sprint races. One tricky thing with sprints is what you use as your response variable. I’ve chosen four of the skiers who exhibited the strongest effect in one direction, towards better performance on longer courses. I’m using the final position (not qualification rank) here. In a lot of ways, looking only at qualification speed would be “cleaner”, but I wanted a measure that captured more than just one round of the event; a measure that reflected how well you actually performed in the sprint race as a whole.

Another big caveat here is that this graph represents all the athlete’s races, so we could be obscuring a confounding variable of changes over time. (I was particularly worried about that with Holly Brooks, but upon checking the raw data, that doesn’t seem to be the case.)

I’m going to start with Petra Majdic, because it’s a great opening into yet another factor that can be at play here. The effect of performing better on somewhat longer sprint courses for her is probably the weakest of the four. One interesting feature is the rather sharp cutoff at around 1.2km. Since Majdic is (was) one of the fields best sprinters, ever, how can we explain the apparent tendency to perform so much worse over shorter distances? Among many possible options, one things that comes to mind is that shorter courses will tend to make races more unpredictable. Being unlucky, in terms of crashes or stumbles, has a much larger effect. So we might expect less consistency from even the best skiers on shorter courses.

Holly Brooks is a somewhat dramatic example, particularly since so many of her results never went past qualification, so one could argue that we’re seeing something more directly reflective of her response to race effort length. On the other hand, our data for her are the most limited. Small sample size, and all that. The other two I’m not terribly familiar with.

On Thursday we’ll look at some folks with trends in the opposite direction…