The unexpected silver and bronze medals for US cross country skiers Diggins and Gregg, respectively, in the 10 km freestyle race at the recent Cross Country Skiing World Championships in Falun Sweden has raised eyebrows and fueled much discussion both in the US and among others in the global cross country skiing community. Much of the discourse has centered on the effects of dramatically changing weather conditions on the ski speed of the later starters in this interval start race.
The (relative) poor performance of favorites Bjoergen (bib 65) and Johaug (bib 63) (both of Norway) who started in the last group of seeded skiers has been put forth by some as evidence that the deteriorating conditions played a dominating role in the final results. Others point to the winner, Kalla (bib 49) (of Sweden), who started just seven minutes before Johaug and and eight minutes before Bjoergen as support that start time was not deterministic for performance. Presented here are a few observations on and analysis of various available data types for the race as it played out.
Diggins (bib 37) started 13 minutes before and Gregg (bib 3, in the first group of unseeded skiers) started 30 minutes before Johaug (bib 63). Review of the video of the race and other on-the ground reports reveals that at the start the conditions were 1.1 C air temperature, -0.4 C snow temperature, 86% humidity, and overcast with no actively falling snow. At about 5 minutes after the start of the first skier, light snow was falling (starting at about bib 10), at 10 minutes a rain-snow mix was coming down (about bib 20), and by 20 minutes into the start it was snowing heavily with very wet (free water) conditions (starting at about bib 40 onward). A significant layer of heavy wet snow had accumulated on course by about 30 minutes into the start order (bib 62).
The winning time was 25:08.8. A simple calculation of percentage of skiing time spent with an accumulated heavy, wet snow layer on course shows that Weng (of Norway, another favorite), Johaug, and Bjoergen all spent about 100% of their skiing time in these conditions whereas Kalla spent about 85% of her skiing time, Diggins about 50% of her skiing time, and Gregg about 0% of her skiing time battling the adverse ski track conditions.
All who ski regularly and/or in circumstances where the conditions are changing to heavy, wet snow accumulations know how drastically ski speed is depleted from an otherwise optimized ski flex/grind/structure/wax for non-actively snowing, high humidity conditions. I have personally measured diminished ski speed well in excess of 10% in tests after such accumulating wet snow conditions prevailed. Although wax will play a relatively minor role, ski flex and grind are particularly critical to attaining ski speed in the conditions facing the late starters in this race. So if the late skiers had selected their skis based on conditions at the start of the race, they likely had skis with less aggressive grinds and stiffer forward flex. Such a selection would lead to ski speeds many percentage points slower than skis optimized for skiing through heavy, wet accumulations. That Norway made an errant selection for skis is supported by remarks of their skiers in the race who have been quoted as saying that “our skis were ass”- which is apparently Norwegian-speak for “our skis sucked”.
It is not difficult to anecdotally explain the unexpected results from this race based on the analysis above. Johaug and Bjoergen both finished about 9-10% back from the winning time. Given that Kalla had about 15% of her skiing time with less challenging conditions, one can staightforwardly account for about 1.5-3% of the 9%-10% deficit in finishing time using a linear function for decline in speed with conditions*. That still leaves a hefty 6% or so of deficit to account for. Using prior performance as a guide, it is clear that both Johaug and Bjoergen should have been much closer to Kalla and it is possible that after being given increasingly positive splits off Kalla (not to mention off of Diggins and Gregg as well) there may well have been a “limit losses” posture taken by the athletes to ensure their performances under better conditions later in the week. Kalla also likely had a very good day.
In the case of Diggins, she finished about 3% back of Kalla and about 6% in front of Johaug and Bjoergen. Once again using a linear approximation, just about all of that 6% could be accounted for based on the difference in skiing time in the difficult conditions (50% for Diggins and 100% for Johaug and Bjoergen). Obviously one can account for all of the difference (and more) between Gregg and the Norwegians with the same reasoning.
Next let’s take a look at the splits at 1.5 km into the race, at a point where the wet snow accumulations for the late starters were still manageable. At this checkpoint the following are the splits:
1. Kalla 3:51.0
2. Johaug 3:59.
3. Niskanen 4:02.4
4. Jacobsen 4:02.8
5. Bjoergen 4:03.0
15. Diggins 4:08.7
20. Gregg 4:09.2
This sequence looks “normal”, i.e. it is what would be expected (except that Bjoergen and Johaug would not be so far behind so early). Things unraveled from here as the wet snow accumulated. Johaug dropped from 2nd at 1.5 km to 26th at 5 km, similarly Bjoergen dropped from 5th to 32nd. Unheard of, but let’s also take a look at some more analytical data and at how astonishingly different this race is when compared to other, similar races held in more constant conditions.
One of the basic expected functionalities in timed event athletic endeavor is that history is a very good guide for expectations of performance in individual events. This holds true for cross country skiing just as it does in track and road running, cycling, and numerous other sports. The basic premise: past performance is highly correlated with performance for a given event.
Presented below is a plot of the FIS Distance Points (as of the race start) versus percentage back from the winning time. Only those competitors who have finishing times within about 10% of the winning time are included in the cohort as these athletes represent the “elite” population in the race. FIS Distance Points are an acceptable surrogate for an historic performance metric for the current season. It is expected that such a plot would yield a high positive slope as past performance (FIS Distance Points) is a good predictor for individual race performance. Application of a simple linear model to the data shows that there is essentially no correlation whatsoever of finishing time to FIS Distance Points for the Women’s 10 km FS World Championship race. A highly unexpected result- an ink splatter, a sneeze!
Now let’s take a look at the same type of data for another, typical, interval start race from the 2014-2015 season. In this case we use the Davos Women’s 10 km CL interval start race from December. Presented below is the same plot as above but with the data from the Davos race also plotted (in green). The equations for the fitted linear models are shown on the graph. Note the high positive slope of the fitted line and high (greater than 40%) correlation between FIS Distance Points and finishing time for this race (note: Bjoergen won this race with Fessel (GER) 2nd and 1.3% back, Weng 3rd, Haga (NOR) 4th, Nystad (GER) 5th, and Johaug 6th- Diggins was 27th and 6% back and Gregg finished this race in second to last place, over 16% back (and therefore is not a part of the analyzed elite population)).
The Davos race is exemplary of what is normally seen with such cross country races. In fact, of the 20 or so races that I have analyzed from the past couple of seasons, the correlation was positive in all cases and had R^2 values from about 0.38 to 0.60. For instance presented below is the data for the Women’s World Championship Skiathlon a couple of days before the 10 km CL race showing a similarly positive slope and high correlation.
The lack of any correlation with FIS Distance Points as seen in the Women’s 10 km CL World Championship race sets this race apart as not “normal” nor even fathomable from a performance perspective. Clearly the conditions played a primary, controlling role in the outcome. Ski flex and grind/structure choices (not wax) were dynamic during the race and the Norwegians likely screwed this up. At the same time Kalla likely made a good ski choice and also had an outstanding day. Diggins and Gregg benefited greatly from start time and this combined with hard efforts lead to their surprising results.
In the end a race is a race (even if it is interval start and the weather goes wacky) and a World Championship medal stands as a significant achievement. Congratulations are well placed with Kalla and the US skiers. However this race will forever have an asterisk and will not be a good source for prediction of future performances.
*From a physics perspective it is not difficult to argue that ski speed is actually non-linearly affected, i.e. the faster the speed the higher the percentage declination in speed. So in a sport where winning times are often only tenths of a percentages faster than other skiers, the increased percentage speed declines for faster skiers is even more impactful than for the slower skiers.