Optimal Norwegian Women’s Relay Team

Now that I have some nifty code for analyzing the optimal relay team given a set of skiers to choose from, I thought I’d have some fun by looking at the Norwegian women.

Now, clearly on some level it almost doesn’t matter which folks you put on this team in addition to Bjorgen and Johaug. But I thought it would be an interesting exercise to learn a little about what my methodology is actually measuring.

Recall that what I’m doing is evaluating each skier against only the other potential relay team members. The idea being to identify who is the most “valuable” given the set of possible replacements. So each matchup between a pair of skiers is recorded, and weighted based on how recent it was. Then each combination (and order) of four skiers is evaluated comparing each leg to the potential replacements who aren’t on the team. I have no way to numerically evaluate who might be particularly suited to scrambling or anchoring, so that simply isn’t accounted for. But differences in technique are included.

My starting pool of skiers for the Norwegian women was essentially their first two teams in Lillehammer, plus Kristoffersen. This results in a bit more than 3000 relay teams, about a quarter of which are actually distinguishable by my methodology.

When I say that the composition of the Norwegian women’s team doesn’t matter much, this is what I mean:



The drop off in scores for the Norwegian women just isn’t very steep at all. The Norwegian women are a deep, deep team.

What’s more interesting to me is that my analysis strongly implies that the Norwegian team would actually be quite a bit stronger if Bjorgen skied a classic leg. The logic here is that the difference between Bjorgen and her teammates in classic is considerably larger than in freestyle, so they’d have more to gain by having Bjorgen crush everyone in one of the classic legs. The three best teams all put Bjorgen on a classic leg. The 4th/5th best shift her to skating, but then the 6th has her on a classic leg again.

The top team according to this analysis would put Bjorgen and Weng on classic legs and Johaug and Jacobsen on the freestyle legs. The 2nd best team simply swaps Steira for Jacobsen.

It’s more ambivalent about where to put Johaug. In the ten best teams, she is placed on a classic leg 4 times and a freestyle leg 6 times. For comparison, Bjorgen is placed on a classic leg 7 times and a freestyle leg only 3 times.

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.

Race Summaries: Introduction

This is type of graphic that I hope to do on a semi-regular basis once the World Cup season gets rolling.  These easily fall into the “fun” rather than “serious” category.  If you hadn’t already guessed, I like making graphs.  So these entries will be race summaries, but in graph form.  They are fairly labor intensive (manually scraping PDF files for split times, push the data around and annotate it by hand, etc.) so I’m going to pick and choose when I do this, ideally focusing on races that are interesting for some reason.

Here’s an example using the Men’s Olympic Relay from the Vancouver Olympics (click for a larger version):