Head-to-Head

Ranking athletes based on FIS points, or some other measure, is relatively easy.  Sometimes rankings are fun, because they give sports nuts something to argue about.  Sometimes, however, things devolve into annoying arguments about the specific measure you’re using to rank the athletes with.

Any such measure has flaws, and FIS points are no different.  So if we want to compare two athletes, what’s the gold standard metric to use?  The most unequivocal measure is simply their head to head results.  That’s easy enough to do if you only want to compare two skiers at a time, but what if we wanted to think bigger?

Suppose we took several top athletes and looked at the difference in percent back for each time they raced against each other directly.  Then if we averaged1 these differences we’d get a grid of numbers that we could display like this:

You should read this graph using the rows, not the columns (it’s symmetric, but I think focusing on rows is easier).  The darker the square, the more the row skier beat the column skier.  So, moving across the first row we see squares representing how Marcus Hellner did versus himself (blank) and then Northug, Bauer, etc.

I ordered the names a little differently, just for fun.  The order is determined by the (weighted) average of the darkness of the squares in each row.  This means that you get more credit for beating faster skiers.  Using this measure, Hellner just barely edges out Northug, but most of the rest of the ordering is basically unchanged.

Here’s a similar graph for women:

One thing that’s fun to do with these is look for squares that stand out as being darker or lighter than their surroundings…

Another nice aspect of this is that you no longer need to worry about race penalties.  You can take any race whatsoever where two skiers went head to head, whether it’s a World Cup, OPA Cup or just a plain old FIS race.

  1. I’ve actually shrunk the differences somewhat, non-linearly, to limit the effect of small numbers of very bad races.

Related posts:

  1. Daehlie vs. Smirnov
  2. Gadflies & Punching Bags
  3. How Well Prepared Are World Cup Rookies? (Part 1a: Distance)
  4. Introducing: Biathlete Rankings
  5. Performance vs Age Redux: Grover’s Graph

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