Tag: Statistical Skier

  • Trends in Age and Ski Performance: A Second Look by Ella DeWolf and Andrew Siegel

    Trends in Age and Ski Performance: A Second Look by Ella DeWolf and Andrew Siegel

    Norway’s Therese Johaug celebrates her final 30 k race at Holmenkollen, before retiring at the end of the 2021/22 season at age 33. (Photo: NordicFocus)

    This article was submitted by a reader. To pitch a story or article to FasterSkier, reach out to info@fasterskier.com.

    In 2010, FasterSkier published an article titled “Analysis: Performance and Age”, written by Joran Elias, or as he is otherwise known, “The Statistical Skier.”  The piece attempted to parse the relationship between age and performance by comparing the ages of some of the world’s top skiers to their FIS points in a given year.  Elias was quick to acknowledge the limitations of the analysis, primarily that the data appeared to exhibit selection bias.  The oldest skiers on the World Cup, still racing well into their 30s, were likely still racing precisely because they were the best of the best, while those who were not performing as well retired sooner, and weren’t reflected in the data.  These data appeared to show a trend of improvement associated with getting older, but to what degree was this apparent trend a result of the selection bias?

    Elias’ original figure showing distance performance by age, published on FasterSkier in March, 2010.

    In the now hallowed annals of the FasterSkier comments section, a commenter with a name none other than Dakota Blackhorse-von Jess, a veritable force in U.S. skiing for over a decade, posed a potential solution.  He asked, “Can you filter the dataset so that only athletes that are still competing at some reasonable later stage (say 30 or 32) are represented?” 

    It was a great question.  What would happen if we were able to look at careers that spanned a longer period of time and plotted the trajectories of those careers as the athletes aged?  This would mitigate the effects of attrition on the data and hopefully give us a clearer picture.

    The question of what happens to the performance of cross country skiers as they age has personal significance to the authors of this article.  Both of us are solidly into our 20s and deeply invested in the project of being competitive at the highest levels of ski racing.  At the University of Wyoming, we are both involved in furthering the development of a growing program which serves college graduates, many of whom are pursuing graduate studies alongside elite ski racing. 

    Athletes at this age often have the unenviable experience of watching as some members of their age cohort find success on the world stage while others do not.  It leaves us to wonder what is possible and what is likely for us to achieve as we move from teens to twenty-somethings to thirty-somethings.

    The recent success of Rosie Brennan on the World Cup and at the Olympics has contributed to reigniting a decades old conversation about age, skier development, and team selection.  One has to imagine that this “conversation,” at times less than cordial (as evidenced by archived comment threads on this website), has ended friendships, and who knows, maybe even a few marriages.  Brennan, who has seen striking improvement in her 30s, skied in college despite the U.S. Ski Team’s erstwhile insistence that promising young skiers should “strike while the iron is hot,” eschewing school and taking on international ski careers full time.  After Brennan’s 4th place in the 30km at the Beijing Olympics, U.S. Ski Team Head Coach Matt Whitcomb acknowledged that the previous development strategy may have been short sighted.  At this point, many of America’s most standout skiers have chosen to ski in college, adding renewed urgency to the question of age and development.  At the risk of adding fodder to an already crowded debate, let’s get into the data. 

    ***

    In hopes of combatting the potential selection bias of slower skiers retiring earlier, we focused on skiers that stayed in the game for at least 20 years, or at least held a FIS license and skied in 5+ FIS races per year for that long. To put that in perspective, the FIS points system has only been around since 1994, or 28 total seasons. As you can see in the figure below, the vast majority of skiers who ever hold a FIS license only hold one for a few years.  Those that continue to ski seriously enough to buy a FIS license for 20 years are a tiny, tiny fraction of the skiers. On average, these “20-season skiers” get their first FIS license around the age of 19 and continue past 40.  Additionally, every member of this group happens to fall loosely into the category of “professional skier,” having received at least one World Cup, World Championship, or Olympic start at some point in their career.

    We used FIS distance points from the last period of each season from 1994 to 2022.  While it would have been interesting to track sprint points as well, the more recent arrival of sprinting makes a long term analysis less feasible.  In the graph below, each black line represents the career trajectory of a “20-season skier.”  There are 40 athletes represented, 23 of whom are men and 17 of whom are women.  Interestingly, the ratio of men to women who hold FIS licenses for at least 20 years is more or less consistent with the ratio of men to women who have ever held one, suggesting that one gender does not have significantly more “staying power” than another in the highest levels of the sport.  The blue lines represent the overall trend.

    Whereas Elias’ 2010 analysis shows a continuing downward points trend even as skiers reach their 40s, ours shows more of a u-shaped trend.  Skiers improve in their teens and 20s, reaching a peak around 30, then begin to experience an increase in points in their late 30s and 40s. This seems to suggest that athletes improve until they hit some peak age and then stop performing as well when they get older.

    We can, in fact, fit a trendline and calculate that peak age at which the average skier (or at least the average skier who skied seriously for 20+ years) hits their lowest points. That magic age based on these data happens to be 31.5 for men and 32.0 for women. However, the striking story shown by the mess of black lines is that no one is “the average.” There are clearly many other factors at play in determining a skier’s performance. Some athletes have their worst seasons in their late 20s while others have stellar seasons in their late 30s and even early 40s.  At nearly 41 years old, Italian Giorgio Di Centa stood at 2.9 FIS points, notching multiple top tens on the World Cup.  At 38, Marit Bjørgen stood at 0.9, never leaving the podium at the PyeongChang Olympics in 2018.  There is valuable information to be gleaned from both the aggregate and the individual. 

    These results were surprising given the disparity between the 2010 analysis and our own. Why did Elias find a continuing downward trend where we found an upward slope after 30? Was it possible that his results were driven strongly by attrition and selection bias as he suggested?  We went back to the data, this time including everyone with a FIS license, regardless of how many years they held one. We saw the same u-shaped trend as before.  Skiers continued to improve until their late 20s to early 30s before an upward slope in points as they reached their 40s. This was not just the case for elite world cup skiers, but more casual racers as well.  A similar trend is present whether exclusively analyzing skiers with points under 50 or over 500.  Additionally, the age of peak performance stays in the range of 29-32 regardless of the chosen points tier.

    Instead of analyzing within point tiers, what if we returned to our “20-season skiers” and segmented each athlete’s career into two pieces–one before their last World Cup, World Champs, or Olympic race–and one after?  This way we would be able to see the difference in performance between skiers at the height of their professional careers in comparison to the years that followed.

    The results of this breakdown make sense intuitively. When we separate the careers into “World Cup” and “post-World Cup” segments, the upward trend coincides with retirement and is much steeper for those athletes who have stepped away from World Cup racing.  People don’t ski as fast after their last season on the World Cup as they did before.  One possible explanation for this is that many athletes retire from the highest levels of international competition, stop training as seriously, and begin to perform worse as a result.  Another explanation is that athletes continue to ski on the World Cup until their performance stops improving, and then retire (or are forced to retire) as a result. 

    While our results alone can’t distinguish between these possibilities, it seems likely that some combination of them are responsible. Regardless, we believe including serious post-World Cup racing in our analysis allows us to gain valuable insight into the effects of age on performance and supports our conclusion of a peak age around 32. It is also important to reiterate that there are athletes for whom the trend is not representative in the first place.  Nothing about our analysis suggests the inevitability of career decline by the age of 32.

    The decorated Dario Cologna and his Swiss national teammate Jovian Hediger race the Pro Race Sparenmoos in Zweisimmen, SUI, part of the Swiss Championships, following their retirement from the World Cup in March, 2022 at ages 36 and 31, respectively. (Photo: NordicFocus)

    These results do seem to partially explain the discrepancy between our analysis and Elias’, but isolating the World Cup portion of their careers does not fully eliminate the trend of skiers eventually slowing down.  The graph is still “u-shaped.”  It appears that a reason for this is that the landscape of professional skiing has changed since the initial 2010 analysis.  Additional comparison of data before and after 2010 indicates that the phenomenon of points swinging upward with age is a relatively recent one, in part the result of a growing number of skiers continuing to race very seriously at older ages.  In other words, the effects of attrition have become less prominent since 2010 because there is simply less attrition. 

    Perhaps the more interesting question here is, what circumstances and structures have allowed this subset of skiers to race at such a high level for so long, while the majority of elite skiers have far, far shorter careers?  It may be worth asking how many people are forced to quit before their potential has been reached because they lack opportunities and support.  Prior to 2010, individuals over the age of 40 only made up 0.4% of total FIS license holders.  In the period since then, that proportion has more than doubled and there are over five times the total number of license holders over 40.  Athletes who are deemed too old to present the shimmering possibility of medals and crystal globes may not be getting as many resources, but they are showing up to train and race in increasingly high numbers anyway.  There are, after all, reasons to race besides winning medals.

    Ella DeWolf graduated from the University of Wyoming with her BS in molecular and microbiology and MS in botany. She continues to coach and race while working as a data analyst for an environmental consulting firm.

    Andrew Siegel graduated from the University of Vermont in 2021 and is now at the University of Wyoming–coaching, racing, and pursuing an MFA in creative writing. 

    This research was made possible by the generous support of the non-profit SNOW (Skiers Nordic of Wyoming).  

     

  • The Devon Kershaw Show: Slinging Stats with the Statistical Skier

    The Devon Kershaw Show: Slinging Stats with the Statistical Skier

     

    This week, we re-posted a great piece from the Statistical Skier (Joran Elias). Before jumping into this episode, it’s worth taking some time to digest some of the findings. He wrote the piece in response to a podcast we posted after the classic sprint in Oberstdorf, Germany. In that sprint, Norway’s Johannes Høsflot Klæbo had an astounding qualifier. In the podcast following the race, we discussed Klæbo’performance and the time-back to some skiers in the field.

    What does it all mean? Well, Klæbo still crushed it. However, the Statistical Skier’s analysis helped put some things into perspective.

    “This is one of the problems with measuring performance based on only the winner,” Elias wrote. “Devon talked (correctly, I think) in the podcast about how if you’re 15 seconds back from the winner in qualification that’s a pretty good signal that you’re not going to win. But, it is a potentially quite misleading signal about how you skied relative to your own performance history!”

    Jump on in head first.

    (This might be one of those occasions when it helps to have a computer open to the Statistical Skier piece when listening.)

    You can find more great material from the Statistical Skier here.

     

  • Statistical Skier: Unusual WC Sprint Qualifying Time Gaps

    This piece was originally was published on statisticalskier.com and is republished with permission.

    The recent episode of the Devon Kershaw Show by FasterSkier (which I’ve been enjoying quite a lot) included some discussion of the noticeably large time gaps in the men’s classic sprint World Cup in Oberstdorf, Germany. Beginning at around 25:18 they discussed a variety of aspects of the large time gaps. I thought that some of the things they noted would benefit from some cursory looks at some data. In no particular order

    “We’ve seen this before from Klaebo”

    Indeed we have. Over the past decade or so when Klaebo has won a sprint qualification the margin has averaged around 1.65% in classic and 1.12% in freestyle. His margin in Oberstdorf was 1.31%. So this was not even particularly extreme for him, in terms of a gap over second place.

    30th place is 15 second back

    That is a remarkable time gap for a World Cup sprint qualification, for sure. But how unusual is it for much of the top 30 field to be that far off the pace? Let’s take all major international (WC, OWG, WSC, and TdS) sprint races over the past 10 seasons and plot the top 30 qualifying %-back values for each race as a line.

    That’s definitely unusual. One of the things that’s interesting about gauging performance in individual sports like xc skiing is that there’s a subtle distinction between a particular outcome arising from one person skiing really slowly and another person skiing really fast. And of course it could be a combination of the two.

    Devon and Jason discussed the fact that if you’re 30th and 15 seconds back in qualification, it seems really unlikely that you have a realistic shot at winning. But I think that underplays somewhat how unlikely it is for anyone to win a WC sprint race when you qualify that slowly, regardless of the time gap.

    Over ten seasons, men qualifying in 25th-30th have reached the podium only 16 times, or around 1.92% of the time. On the women’s side, it has happened only 7 times or 0.8% of the time. Actually winning is obviously even rarer: 5 times for the men and only once for the women, for 0.6% and 0.1% respectively. So the folks qualifying in the back of the field are very unlikely to win, even with “normal” time gaps.

    Of course, it is easy to get confused about the causal relationship here. Fast qualifying times will tend to be correlated with all sorts of other fitness characteristics that lead to good performance in the heats. It’s not the fast qualifying time itself that leads to better performances.

    Let’s return, though, to the unusual time gaps themselves. Certainly, some specific talented sprinters had rough days (Ustiogov and Iversen were mentioned in the podcast). But if you’re sitting in 30th, 15 seconds out in this particular case, should you be saying to yourself, “Geez, I skied pretty badly!” or should you be saying, “Geez, the top 3-4 guys really just had another gear today!”. (Or obviously somewhere in between.)

    This is one of the problems with measuring performance based on only the winner. Devon talked (correctly, I think) in the podcast about how if you’re 15 seconds back from the winner in qualification that’s a pretty good signal that you’re not going to win. But, it is a potentially quite misleading signal about how you skied relative to your own performance history!

    One approach I happen to like to use as an additional perspective is to calculate percent back values based on the median, or middle, skier. What do the percent back curves I plotted above look like if I recalculate them based on the skier who qualified 15th?

     

    Now which part of the red curve looks more unusual? This look at the race would at least suggest that the top 4-5 men were the ones who had unusual races, rather than the the field as a whole. The back of the qualifying field seems a bit more behind 15th place than usual, but not nearly as dramatically.

    Obviously, this doesn’t change the calculus for how close you are to winning. If you’re racing against people like Klaebo who can put down winning margins like this, it is small comfort to be told that you didn’t really ski any slower than you usually might. But it is useful to keep in mind when you see time gaps like this that it is quite possible that the folks in 25th skied just as fast as they did yesterday, a month ago, a year ago (maybe faster!). In other words, it can be a signal of how much work you have to go, but not necessarily that the work you’ve done so far isn’t helping or even making you slower.

    How fast do podium finishers qualify?

    I’m glad you asked! Let’s look at that with the following plot:

    ECDF stands for “empirical cumulative distribution function” which is quite a mouthful and isn’t a graph that normal folks interact with regularly, but don’t panic.

    This just graphs the cumulative proportion of podium finishers (y-axis) who qualify with a given percent back or better (x-axis). So if you pick a spot on the y-axis, say 25%, and move horizontally until you hit the curve you look down on the y-axis and see that ~25% of podium finishers qualified with a percent back of ~0.4% or better. Don’t forget the “or better”.

    Similarly, ~50% of sprint podium finishers qualify at ~1.4% back or better. And so on. The vertical line each curve starts with represents the fact that ~20% of podium finishers actually win qualification (0% back).

    Looking at this it seems that 1.5-2% back might be a good target to think about if you want to be landing on the podium in World Cup sprint races. If you can’t qualify at least that close, you’re probably not setting yourself up for a good shot at a podium.

     

  • Nordic Nation: Joran Elias is the Statistical Skier

    Nordic Nation: Joran Elias is the Statistical Skier

    In this episode of Nordic Nation, we tread into the world of analytics with data-analysis guru Joran Elias. You might know him as the Statistical Skier. Elias runs two websites: statisticalskier.com (which is more of a blog that has not been updated in awhile) and statisticalskierdata.com … and that site — which offers data analysis apps using FIS data —  is currently updated seasonally during the World Cup. And if you need a more regular fix of stats and skiing during the race season, Elias is active on Twitter; his handle is @StatSkier.

    Elias is 38 years old and has settled in Missoula, Montana. His Missoula day job is for the University of Montana, crunching numbers for the school’s administration. He’s also a lifelong nordic skier. Originally from Maine, Elias started skiing in the Bill Koch League and raced for Dartmouth, earning the Gebhardt sportsmanship award his senior year in 2001 (and most improved award in 2000). According to his website, he was, “at times, not entirely slow.”

    With a bachelor’s degree in mathematics, master’s in algebra and doctorate in applied statistics, Elias noted on his blog that “Graduate school taught me many things, among them that I hate academia and that I love wrangling data. Given the choice between wrangling awesome data and making tons of money, I’ll choose the former.  Hence this website.”

    Joran Elias is the Statistical Skier. He’s shown here with his son Ciaran, now 5 years old. (Courtesy photo)

    Sport is rife with those trying to understand the winning, the losing, the fast and the slow — using numbers. Elias gives us insight into how useful data analysis can be in cross-country skiing as he highlights both its limitations and benefits. Below is a snapshot of Elias’ mind craft.

    La Clusaz World Cup, Dec. 17, 2016 data snapshot: Women’s 10 k freestyle mass start. (Photo: @StatSkier screenshot)

    Have a listen.

    (To subscribe to the Nordic Nation podcast channel, download the iTunes app. If you have iTunes, subscribe to Nordic Nation here.)

    Have a podcast idea? Please email nordicnation@fasterskier.com.

  • Who’s Justyna’s Biggest Nemesis?

    Who’s Justyna’s Biggest Nemesis?

    Have you ever wanted to know how well-prepared World Cup rookies are? Or whether Axel Teichmann really is Petter Northug’s most frequent whipping-boy? Then check out FasterSkier contributor Joran Elias’s new website, StatisticalSkier.com, where he breaks down data that he has compiled from the International Ski Federation. He’s been updating frequently, so check it out for your statistics fix.