Björgen vs Skari vs Välbe
Marit Björgen returned to action this weekend in (mostly) convincing fashion. It’s becoming very interesting to see whether anyone will be able to beat her in a distance race. She certainly has shown some chinks sprinting, with Kikkan Randall stealing a freestyle win and Petra Majdic grabbing a classic victory yesterday. But with another World Cup win this weekend, the all-time comparisons are coming out again, mostly to Bente Skari Martinsen, but really Elena Välbe needs to be in the conversation as well.
FIS likes to count the total number of World Cup victories as a sort of benchmark here, although the logic behind what they decide to count as a “World Cup race” is, well, lacking. But no matter! Despite my differences with their counting method, we certainly agree that Björgen is among the greatest of all time.
Unfortunately, counting the total number of victories is kind of a crude measure. And not many people realize this, but FIS points (or any method based on the percent back from the winner) will not be very good at distinguishing between the very best athletes. Simply put, if you win you get 0.00 FIS points, so by that measure all victories are created equal! So how to you compare one person’s 0.00 FIS point race to another person’s 0.00 FIS point race?
This problem actually extends to more than just the winners. By placing a hard lower bound on your performance measure (0.00), you end up compressing the very best athletes (say, the top 10 or so) into a small numerical range, which makes it difficult to see meaningful differences between them. For example, let’s look at the distance results using FIS points for these three ladies:
This weekend’s win by Björgen is shown in red. Granted, I’m missing a good chunk of Välbe’s early career, but I think I’ve got enough of when she was in her prime for a reasonable comparison. Notice all the dots squished down near zero? It’s really hard to tell what’s happening, although we can at least see that Välbe didn’t have a whole lot of slow races (again, keeping in mind that this might change if I had the first part of her career).
Instead, let’s look at a slightly different measure: percent back from the median skier in each race. Read more
How Many WC Victories Does Björgen Really Have?
How embarrassing is it for our sport that no one seems to be able to reliably count the number of World Cup victories of our best athletes?
Here’s the deal. Marit Björgen has attracted some attention lately for the number of total WC victories to her name, which is generally thought to be at least 40, although different people will report slightly different numbers. For example, see these Scandinavian news reports on the topic here and here.
As far as I can tell, everyone is getting the count for Björgen wrong. This is harder to count than is seems, so I’m going to discuss this in what will probably be painful detail.
First, we need to agree on what counts as a World Cup race. Now, I’m sure you’re wondering, how could we be confused about what is or is not a WC race? There are two basic issues:
- Do we count the overall results from stage race formats like the Tour de Ski, the World Cup Final or the most recent Nordic Opener in Kuusamo? Athletes receive World Cup points for the overall standings, as well as for the results of each individual stage. If you get WC points for it, isn’t it a WC “race”?
- Prior to 1999, I believe, the Olympics and World Championships were counted as part of the World Cup schedule, but that is not the case anymore. This becomes important for comparing people like Björgen to other greats like Bente Skari Martinsen or Bjorn Dählie. Why? Well, this is debatable, but skiers now are faced with more races to choose from in Olympic or World Championship years, whereas before those races were simply folded into the WC schedule. So Björgen has faced more of a tradeoff than Skari or Dählie did in choosing to skip normal WC’s in order to prepare for other major events like Olympics or WSC’s.
I’m not going to argue for a “correct” answer to either of these issues, I’ll simply count victories as best as I can and include enough information for you to go whichever way you want for the final tally. Here we go… Read more
Marit Bjoergen’s Best Freestyle Race
Marit Bjørgen commented somewhere that her win at the WC opener in Gällivare, SWE was “the best skate race of her life”. Sadly, I can’t find where I read that, otherwise I’d have a link for you. Obviously, I found that kind of intriguing. Let’s look at Bjørgen’s race in a bit more detail:
This is the difference in percent back between Bjørgen and the top thirty women at Gällivare in all skate races where they’ve competed against each other. (Since there’s quite a bit of data on Bjørgen I was able to be a bit more picky and only include skiers she’s raced against at least 5 times.) The red line indicates the median percent back difference for each season.
This isn’t a direct comparison to specific races, of course, so this doesn’t tell us directly whether this particular race (in the blue) is better than any of her past skating efforts, but it provides some useful context. The most obvious thing to note is that the seasons with the most similar looking performances are from 2004-05 and 2005-06, where Bjørgen appears to have never lost a major freestyle race against these particular skiers (all the dots are below zero). Additionally, the median percent back difference from Gällivare is quite a bit below the median from any other season.
A little editorial comment here. Statisticians tend to react to extreme events differently than other people. The typical response is to assume that this sort of thing is going to keep happening, whereas statisticians will tend to assume it was a rare event, unlikely to happen again. In this case when Bjørgen opens the season by absolutely crushing the field, there’s a natural tendency to begin to expect Bjørgen to destroy the field like this all season long (or at least to seriously suspect this is going to happen). My reaction was more along the lines of “There’s no way she can sustain that level of dominance for any length of time.”
Now, Bjørgen may well continue to win races, perhaps most of them. But I doubt we’re going to see her rack up margins of victory above 2.5% on a regular basis. Unless, of course, she does, in which case I’ll eat my words.
But how about a more direct, simple comparison? How did that victory compare to Marit’s other WC/OWG/WSC wins?
Prediction Game: Results!
Back on Monday I posted the graph shown below and posed a question:
It turns out I didn’t ask my question very clearly, because I had to keep updating the post with clarifications. So that’s my fault. Maybe this time I’ll do better. What I did was plot a part of the time series of FIS points for these five women. The x axis is time, and the large white grid lines represent around five years. So the “next race” for these five skiers will not be the same race. They’re not all about to race against each other.
My question was for you to pick which of the five would have a top three result in a WC, WSC or OWG in their respective next races. I provided a few more pieces of information: at least one of the women will succeed (so the answer isn’t “none of the above”) and the one(s) that do, it will be their very first career podium.
Here’s the answer in graph form:
Head-to-Head: Marit vs Justyna
This is the head to head matchup that was runner up in my recent reader poll. No reason not to keep everyone happy by tackling this pair next!
Per usual, what I’m doing is taking races where Marit Bjoergen and Justyna Kowalczyk have both participated and plotting the difference of their FIS points (distance races) or the difference of their finishing place (sprint races) versus time.
Victims & Nemeses: Marit and Justyna Edition
Earlier this week I described the notion of victims and nemeses, and showed you who Petter Northug’s were for the 2009-2010 season. You can check back at that link for a description of victims/nemeses. The basic idea is to count up the number of times you beat someone by a narrow margin (they become a victim) or are beaten by someone by a narrow margin (they become a nemesis).
This time let’s look at two of the fastest women around today: Norwegian Marit Bjoergen and Poland’s Justyna Kowalczyk. Only this time, instead of limiting ourselves to just a single season, let’s look over their entire careers.
First Justyna’s victims and nemeses:
| Justyna Kowalczyk's Victims | Value |
|---|---|
| STEIRA Kristin Stoermer | 10 |
| KUITUNEN Virpi | 9 |
| ROPONEN Riitta-Liisa | 9 |
| BJOERGEN Marit | 8 |
| SAARINEN Aino-Kaisa | 8 |
| BOEHLER Stefanie | 7 |
| Justyna Kowalczyk's Nemeses | Value |
|---|---|
| SAARINEN Aino-Kaisa | 11 |
| BJOERGEN Marit | 10 |
| ROPONEN Riitta-Liisa | 10 |
| LONGA Marianna | 9 |
| KALLA Charlotte | 8 |
| KUENZEL-NYSTAD Claudia | 8 |
Marit Bjoergen actually isn’t in the lead here in either case. Instead it’s Kristin Stoermer Steira who’s been edged out by Kowalczyk the most. Interestingly, it’s Finnish skier Aino-Kaisa Saarinen who ends up being Justyna’s biggest nemesis, not Bjoergen, although just by a hair.
Next up Marit Bjoergen’s victims and nemeses:
| Marit Bjoergen's Victims | Value |
|---|---|
| STEIRA Kristin Stoermer | 14 |
| PEDERSEN Hilde G. | 13 |
| SAARINEN Aino-Kaisa | 13 |
| HAAG (HANSSON) Anna | 10 |
| KOWALCZYK Justyna | 10 |
| SACHENBACHER-STEHLE Evi | 10 |
| Marit Bjoergen's Nemeses | Value |
|---|---|
| MAJDIC Petra | 10 |
| SMIGUN-VAEHI Kristina | 9 |
| KOWALCZYK Justyna | 8 |
| JATSKAJA Oxana | 7 |
| PALUSELLI Cristina | 7 |
| SAVIALOVA Olga | 7 |
Once again Kristin Stoermer Steira gets the win in the victims category. For some reason I wasn’t expecting Petra Majdic to pop up as Bjoergen’s top nemesis, but there she is.
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