How Useful Is A Single Good Result?

Following up from last time, we’re still discussing the recent USSA rule changes for qualifying for WJC/U23s. Now, it’s not like USSA has a ton of options here, but I would like to point out a few difficulties with pre-qualifying an athlete using only a single result.

Being a stats guy, I always think about things in terms of variability. So when I think about a skier’s performance, I visualize it as having a distribution. An athlete’s best races come from one extreme end of that distribution, but they are necessarily fairly rare. So to my way of thinking, a skiers best race isn’t a good estimate of how well they’re likely to ski. Rather, it’s a good (-ish) estimate of how well they might ski, if we’re really lucky.

To give you some context on this, I took all the FIS point results for Americans since 2006. Then I counted up how often each skier matched (or bettered) their best FIS point race from the early season (11-01 to 12-31) during the rest of the season. I counted this separately for men/women and sprint/distance and only kept folks who had at least 4 early season results, and at least one result from the remainder of the season. Here’s what we have:

I’m not quite so interested in the sprint numbers, since FIS points are such a dicey way to measure performance for sprinting. But if you look at the men’s distance panel, what this is saying is that they ski as well (or better) than their best early season result at most once more that season around 60% of the time. The drop-off is a bit less dramatic for the women, but still it is much more likely that you aren’t going to see a race with FIS points that low for the rest of the season.

And this trend is even more stark when we focus in on just the group of skiers who’ve managed a sub-50 point race during the early season:

Granted, this simple method of counting the number of results at a certain level may obscure some things. For instance, maybe folks don’t race quite that fast ever again, but they come pretty close fairly often. That will require a different sort of analysis that we’ll delve into next week.

Related posts:

  1. Kershaw’s Volatility
  2. Participation Rates
  3. Some context for Skofterud’s late season troubles
  4. Thanksgiving Turkeys
  5. Week In Review: Friday Jan 7th

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2 Responses to “How Useful Is A Single Good Result?”
  1. Fiona says:

    The question, though, isn’t “how likely is someone to beat their early season best”, it’s “how likely is someone to do well in a later season race”.

    Even if the 50 point skier never beats their early season best, a 60 point race might be better than the 100 point skier could do.

    • Joran says:

      You’re right, except that wasn’t exactly the point I was trying to make. (Which I obviously didn’t do a great job of.) My point was supposed to be that a skier’s best result isn’t a great predictor of how they’ll ski generally.

      In particular, that means if you have a skier who’s best result is 45 FIS points, and another who’s best is 65 FIS points (in a short 2 month time period), that isn’t really necessarily much of a signal that one of them will tend to ski faster than the other, in general. Showing how often a skier matches their best early season result was meant to demonstrate that, but perhaps a better way to look at it would be to directly examine a skier’s best vs median result.

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