Statistical Skier

I’ve fussed in the past about the weaknesses of FIS points in distance events, but they really are quite useful.  Sprint events, however, just don’t have an equivalently simple and useful numerical summary.  I’ve resorted to using the final finishing rank (i.e. what place you came in, after the elimination rounds), but I’ve never been particularly happy about it.

Currently, FIS awards traditional FIS points for the qualification times only.  After that, all that matters is what place you come in.  This means that I end up tracking three different values for each sprint result: FIS points, qualification rank and final rank.  None of these are particularly easy to combine in a sensible way.

For bird’s eye level analyses, just using the final rank is generally sufficient.  But when you start drilling down to the level of individual athletes, or small groups of athletes, it doesn’t work very well.

As an example, consider my posts looking at season to season improvements by individual skiers in distance events.  You’ll notice I haven’t given sprint racing the same treatment.  Modifying my script to do roughly the same analysis using finishing place in sprint races was easy, but the results didn’t make much sense.

The problem is that finishing place pretends as though each result (1st, 2nd, etc) is uniformly spaced along our range of performances.  But this just isn’t true.  The difference between 40th and 32nd may represent a legitimate improvement, or it may not.  You’d have to look at the time and FIS points, since neither result led to participation in the elimination rounds.  On the other hand, the difference between 35th and 27th is potentially quite large, since at least we’ve moved up into the realm of qualifying for the elimination rounds.

My ideal system would

• give you credit for being closer to qualifying, proportional to your percent back
• give you credit for qualifying
• give “bonuses” for each elimination round you survive

I’ve concocted something simple that does these three things.  It’s by no means perfect, so I fully expect tons of legit criticism.  But I do think that a measure like this is at least potentially useful for some specific purposes.

The way it works is this:

• Skiers not qualifying for the elimination rounds are simply assigned their FIS points
• Skiers qualifying for the elimination rounds are assigned “alternate” FIS points, evenly spaced from 0.00 to the qualification round FIS points of the 30th place skiers, with gaps inserted corresponding to each elimination round.

It’s much easier to show you this than explain it in words.  Here’s a table with the Men’s Classic World Cup sprint in Canmore on 2/06/2010.

[table id = 12 /]

The columns should be fairly self explanatory.  Notice that the first 6 places have points that are evenly spaced; then there’s a gap, and then 7-12 are evenly spaced.  13-15 are evenly spaced, then a gap, and so on.

I realize this doesn’t perfectly reflect what happened in the elimination rounds, particularly near places 13-15.  But I can’t really reconstruct lucky loser information from the data I have.  Nor does it reflect how close a particular heat was.  For instance, the top six are evenly spaced, even if they didn’t finish with equal gaps.

Still, I kind of like this.  It gives me a number I can use that is roughly comparable across those skiers who qualified and those who did not.  The numbers get smaller as you move through elimination rounds, with a built in “bonus” that reflects the fact that advancing through heats is not really a linear performance function [1. That is, the difference between 6th and 7th places is not the same as the difference between 7th and 8th places.].  The numbers for non-qualifying athletes are proportional to how close they were to qualifying.  Even the values assigned to skiers in the heats reflects, to some degree, how difficult it was to qualify: if the 31st place FIS points value is very low, the values of the top 30 skiers will be more compressed, and hence smaller.

One (of perhaps many) downsides is that these new values don’t have much concrete meaning, other than “lower is better”.  If you finished 5th, and are assigned 3.54 “points”, this number has no valid meaning in terms of traditional FIS points or percent back.  Still, it will allow me to do some most improved/unimproved posts for sprint racing down the road…

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