Statistical Skier

It’s nearing the end of October, which means that if you are a skier hailing from the esteemed institution that I do, that means its time for the Moosilauke time trial.  It’s an uphill running time trial beginning at the Moosilauke Ravine Lodge up the Gorge Brook Trail, ending around 3.6 miles later on the summit of Mt. Moosilauke.

Conveniently for me, Ruff Patterson, the men’s nordic coach, has kept copious records, so we have some fun data to look at!

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Clearly, I was a bit distracted yesterday, so the week in review is a bit delayed.

• My little guessing game this week was a bit too hard, I think.  The answers are posted here.
• We looked at trends over time in variability by athlete, comparing cross-country to biathlon, at the request of a commenter.

Finally, it appears that FIS race scheduling is again in the news, this time with discussions of some wacky ski-cross type event.  Reactions have been, well, mixed.

For my part, I’ll take this opportunity to repost the following chart showing the changes in the WC race schedule over the past 18 years or so for the men:

I sympathize with the marketing problem that FIS has.  Everyone wants skiing to be both exciting and popular.  It probably is tough to get advertisers for a product that consists mostly of long races with interval starts.  The problem is that by inventing new and ever more “exciting” events, you are tacitly accepting (and reinforcing) the idea that the more traditional events are simply boring.

It may be that it isn’t possible to win the viewing public (in Europe, mostly) back to the notion of more traditional races.  But it’d be nice if someone tried.

A commenter asked about whether I could take the data from this post and look at trends over time.  The answer, of course, if yes!

The statistic of interest here is median absolute deviation (MAD), which is a measure of variability.  In this case, we’re calculating a MAD value for each skier and each season on their percent back results.  So each skier get a MAD value for each season they compete in that measures how variable their results were.

In my previous post, I just compared the distributions of these values for XC and biathlon skiers, showing of course that biathletes’ results are considerably more variable.  My commenter wanted to know if these values have changed much over time.

What I actually did is to plot some quantiles of each distribution over time, and extended the time frame back to 1992 or so.  What this means is that each line represents the trend for a particular quantile over time.  For instance, the middle line for both XC and biathlon represents the median, or 50% quantile.  The quantiles plotted are 10%, 25%, 50%, 75% and 90% (10% is the bottom line, 90% is the top line).

Graph below the fold:

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The week in brief:

• A quick post about how much more volatile biathlon racing is than XC, due to the influence of shooting, of course.  I probably didn’t explain the actual statistics very clearly in that post, so if you found it confusing, check out the comments.  Also, I’ll follow up on commenter Bolle’s question about changes in volatility through time sometime next week.
• After that, just two posts showing the distance results for entire nations, but coloring the points by the age of the skier.  I didn’t have some big question or message, I just sort of stumbled on them while noodling around.  But it’s kind of interesting to watch the colors change for small teams with only one or two fast skiers.

Finally, you might recall the tag cloud for FasterSkier comments that I posted a while back.  I’ve been tinkering with a version of that for the right hand sidebar (scroll down a bit).  A friend helped me out with some of the HTML/Flash issues and I think it should be properly updating itself now (every 12 hours or so, which is probably more often than necessary).  So that should be a quick look at what’s been going on in the last 100 FasterSkier comments, or so.