Sometimes people you don’t expect race very fast. A reader asked me to look into this general topic, this will be the distance race installment. I’ll do a sprint version in a few days.
I’m going to focus here on people who have won Olympic medals in distance events. To measure how “unexpected” it was, I’m going to use my power ranking methodology, which is essentially a modified ELO ranking. The only caveat there (aside from the fact that you have to believe that my power rankings generally work) is that I ran them only for each Olympic year. If I wanted to be more thorough, I’d run every season consecutively, so that the ELO rankings pass on information from one season to the next. But the results from a single season seemed plausible enough that I didn’t see the need, at the moment, to do all that extra work.
The following graph shows all Olympic distance medal winning results for the past five Olympics, and each skier’s “power ranking”, as determined by my ELO method, on the day of their medal winning result.
The pattern here is a little more obvious if you use boxplots, but it’s still visible, and I prefer to be able to see each data point. Basically, virtually every medal winner in 1994 was more or less “expected”, coming from the top five in my power rankings. The Nagano Olympics saw a slight increase in “unexpected” medalists. The Salt Lake games saw quite a few, half falling outside the top five in my power rankings for that season. Then we simply reverse the process, with slightly fewer unexpected results in Torino, and then even fewer in Vancouver. I’ll let you draw your own conclusions.
Among these, the most unexpected Olympic distance medalists include many questionable results. The two most egregious are by Mikhail Botvinov, his silver in the 30k at Salt Lake where he stood at 19th in the power rankings, and his bronze in the 50k in Torino where he stood at 22nd in the power rankings on that day. Markus Gandler and Christian Hoffman are right up there with him.
Some unexpected medalists are actually just stars being born, such as Justyna Kowalczyk’s bronze in the 30k in Torino at the age of 23. Others aren’t necessarily suspicious, but are definitely surprising: Marit Mikkelsplass’s silver in Lillehammer. A talented skier, no doubt, but her World Cup results that season were 7th, 10th, 12th, 12th, 15th, 16th, 19th, 21st and 21st.
Others are surprising perhaps because they come from talented skiers who’s best seasons might have been in the rear view mirror (Axel Teichmann’s silver in Vancouver 50k). Surprising results coming in the longer distance races is another pattern, perhaps because they fall at the end of the Olympics, and tend to see slightly smaller fields.
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.
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.
What do I notice about the men’s podium from Saturday’s 15k classic race:
Excepting Poltaranin, not much racing at this level between them. In fact, among the youngest men’s distance podiums I have on record (basically since the early 90’s):
Saturday’s race is that unusually low value in the lower right corner. As you can see, there’s nothing to suggest that this is the start of a dramatic trend, as the other ages this year have been all over the map.
More strong early season performances from some Americans in Norway this weekend. How strong? Let’s take a look.
First up is Sadie Bjornsen who had a very strong 5th in the 10k classic.
Values above zero are good. The grey shaded region and red trend line represent how she has performed against these specific skiers in the past. She had already made a big jump last season, and this race was very strong even compared to that. Next up Noah Hoffman:
This is the better of his two races, the 15k freestyle. This result was considerably better than he normally does against this crowd compared to last season. His classic race (graph omitted) was somewhat worse that usual, but not dramatically so. Lastly, Liz Stephen had a strong result in the 10k freestyle:
She’s been on an upward trend for several seasons now, and this would suggest that might continue.
This first batch of races for 2013-2014 are in from Muonio, Finland. As always, it’s difficult to read much into a single race, particularly early season races like these. You never quite know who’s still in the midst of a big training block and how seriously people are approaching them.
Still, I thought it was interesting that Russian Petr Sedov won the last race of the weekend, the 15km freestyle. He’s still fairly young, and after a promising introduction to the World Cup he kind of slipped back a little last year, I think:
He had a handful of strong races last year, but was much less consistent in general. If we look at this Muonio 15km race in particular, we can get a better sense of the quality of his race by comparing how he did to each of the top 30 skiers at the Muonio race to how Sedov has fairly against those specific people in the past:
Values greater than zero are better for Sedov in this graph. The blue dots are the differences in percent back between Sedov and the other skiers at Muonio (he won, so they are all above zero). The shaded region with the red trend line summarizes how he’s fairly against this specific group of skiers in the past.
As you can see, he generally dominated them, and then last season struggled considerably, losing to this group almost as much as he beat them. If this is a sign of things to come, we could see more of the Petr Sedov from two years ago, or perhaps an improved version.