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Optimal US Women’s Relay Team

Since we in the US now have a relay team that’s doing quite well, that also means we as fans have something new (and fun!) to argue about. Namely, what is the best team we can put out there?

Let’s assume that there are seven women who could potentially be placed on the US women’s relay team in Sochi: Kikkan Randall, Liz Stephen, Jessie Diggins, Sadie Bjornsen, Holly Brooks, Ida Sargent or Sophie Caldwell. I suppose Caitlin Gregg is another possibility, but let’s keep it at these seven for now.

Some very simple math tells us that there are actually not that many relay teams you could construct from seven people. 840, to be exact. That includes every possible combination of four people, and every possible ordering of those four.

That got me to wondering if it were at all possible to somehow assess the quality of each relay team versus the others. I don’t track relay leg results, so I only have individual distance results to work with. But if we limit ourselves to a pool of seven athletes, then for a given relay team, we really only need to know how each skier performs against the three folks left off, in whatever technique their leg is.

For example, let’s imagine a relay team of Diggins, Caldwell, Stephen and Brooks, in that order. Then we’d look at how Diggins and Caldwell have performed against the remaining three in classic races, and how Stephen and Brooks have performed against the remaining three in freestyle races. What I settled on was taking the weighted average of the difference in percent back between each pair of skiers, with races weighted based on how recent they are.

So using the above example, we’d take Jessie Diggins and look at the difference in percent back between her and Randall, Sargent and Bjornsen in classic distance races, and then take the weighted average of those values, weighting recent events more heavily. Repeat for each Caldwell, Stephen and Brooks and then add up those four numbers. Voila! One way to think about this is that it is similar in spirit (though not in the technical details) to VORP in baseball.

Some obvious caveats: this methods cannot distinguish between the two classic legs and the two freestyle legs. So you don’t get any special consideration for skills at scrambling or anchoring. In that sense, order is only very loosely evaluated, amounting to just comparing techniques. In fact, once you decide who is doing the classic legs and who is doing the skating legs, my method will give you the same “score” for all of the four different orderings you could use. But it will help sort out issues of whether someone like Randall is more valuable skiing a classic leg or a skate leg.

Still, it’s fun to play with, and now that I’ve built it I can start using it on skiers from other countries…

The results are pretty unsurprising. The best team is basically what we saw last weekend: Randall and Bjornsen on the classic legs and Stephen and Diggins on the freestyle legs. The next best team simply swapped Randall and Diggins, having Randall skate and Diggins do a classic leg. The third best team starts to get kind of interesting. It has Stephen and Bjornsen doing the classic legs and Randall and Diggins skating.

You can also ask fairly fine grained questions, like “What’s the best team with Ida Sargent on it?” The answer in this case would be the team with Bjornsen and Sargent taking the classic legs and Randall and Stephen skating. Similarly, if you require that Holly Brooks be on the team, then once again you have to remove Diggins, but this time unsurprisingly you have to keep Randall on a classic leg and Brooks gets the freestyle leg vacated by Diggins.

Finally, one slightly surprising tidbit that fell out of this was that of the three (Brooks, Sargent and Caldwell), if you have to sub one of them in at the moment, the best option is Brooks.

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