Statistical Analysis: Age/FIS Points Graphs

FasterSkierApril 29, 201010

Chris Grover recently mentioned a graph,

“Every athlete who is being nominated to the U.S. Ski Team this year has something in common.   They are on the path to winning a medal.  This medal could from the World Cup, World Championship or Olympic Winter Games, but they are on this path.  If we graph these athletes’ ages versus their FIS points and plot those graphs against the progress of the best cross country skiers in the world, we can see that they are on the path.”

Being a statistics and data junkie, I excitedly scrolled up and down the article looking for this graph. Alas, it was nowhere to be found! But it sure sounded like a cool idea, so I thought I’d give it a try myself. I can’t read Chris Grover’s mind and know precisely what he meant, so what follows is simply my interpretation of what I think he might have meant, with some of my own twists added in.

This is what I did:

– Only results since 2001-2002 are used. All FIS scored events that I have are used, not just WC, WSC and OWG races. Personally, I wouldn’t consider mixing races like this advisable, but it’s what the national ranking bodies do for FIS point lists, and I’m just trying to approximate what Grover seemed to be talking about.

– I cannot guarantee that I have every FIS scored race for every athlete. For instance, I don’t believe that I have each and every American collegiate race that’s been FIS scored. I have some but not all.

– FIS points are used for both distance and sprint events. Again, this isn’t my ideal way to measure athletes in all cases, but it’s what FIS, USSA, the USST etc. use and it’s what Grover referenced in his article.

– For both distance and sprint races I created three categories of racers: Podium athletes, USST athletes and “bubble” athletes. Bubble athletes are Cook, Elliott, Gelso, Kuzzy, Southam, Zimmerman, Sargent, Deyong, Mannix, Williams, Brooks, Smyth and Compton for distance and the same for sprint (minus Mannix). I got some advice from people more familiar with the domestic racing scene than myself on who to include; I apologize if I omitted your favorite racer! I didn’t have room for everyone.

– Podium athletes are further broken down into three categories: less than 5, 5-15 and more than 15 podiums over their career.

– I plotted FIS points versus age for each group with trend lines for each athlete, where possible. Dots represent a single result by an athlete, blue lines represent trends for a particular athlete. Large outlying FIS points results may not appear in the graph because I zoomed in to show the important stuff more clearly.

– The USST and Bubble panels are the same within each Distance and Sprint graph. (Eagle eyed viewers might note that this isn’t exactly true; I jittered the ages very slightly to avoid technical issues in fitting trend lines. Specifically, I needed to avoid singular design matrices.)

– The Podium Athlete panel changes each time based on the <5, 5-15 or >15 category.

– I omitted the Podium Athlete trend lines in the Sprint graphs because, unlike in the distance case, they were just a tangled mass of spaghetti. This could be due to the newness of sprinting; we might see more definite athlete development patterns emerging after the discipline has been around for some time.

– Distance event trend lines are obtained using a smooth, but robust method, to limit the impact of small numbers of unusually large or small FIS point values. Due to a general reduction in data size, I was forced to go with simple linear trends in the sprint graphs.

– I attempted to annotate each trend line for the USST and Bubble panels with the athlete’s name. I apologize if it’s a little hard to read, I did the best I could in a short time frame.

Finally, a general disclaimer: my purpose in creating this graph was simply that Grover’s comment seemed like a fantastically interesting thing to look at, and I was a bit miffed that it hadn’t occurred to me before.


Click on any of the graphs to view a larger version

Distance (<5 Podiums)
Distance (5-15 Podiums)
Distance (>15 Podiums)
Sprint (<5 Podiums)
Sprint (5-15 Podiums)
Sprint (>15 Podiums)


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  • Tim Kelley

    April 29, 2010 at 10:20 am

    @Joran: You say: “Podium athletes are further broken down into three categories: less than 5, 5-15 and more than 15 podiums over their career.” But how can Freeman be in the 15 category also? Logically that makes no sense.

    And – you don’t take into account time weighted podium visits. You’ve got to do that. It doesn’t make sense comparing podium visits of a young skier that has been on the national circuit for a handful of years against a veteran like Freeman who has many years under his belt. The younger skier has not had time to rack up the podium visits.

    Bottom line: You are mixing apples (podium visits) and oranges (FIS points) over time and not accounting for time weighting with both variables. Break podium and FIS data apart separately and you might have statistical results that may be remotely useful.

  • Tim Kelley

    April 29, 2010 at 10:23 am

    Correction: The sentence in the first paragraph should have said: “But how can Freeman be in the less than 5 and greater than 15 category also? Logically that makes no sense.”

    Note: Using greather than and less than symbols on this site doesn’t work well as they are HTML tag delimeters. I’ve been bit by this before. 😉

  • FasterSkier

    April 29, 2010 at 10:28 am

    It is possible that my labs confused the issue when I posted the article. I think Joran makes it clear that the US portions of the graphs are the same in each of the three categories. Only the “international” portion (far left graph of each category) changes.

    Kris Freeman has never been on a World Cup podium, so wouldn’t be on any of the podium graphs…

    I am not speaking for Joran in any way, but my understanding was that he was trying to replicate the graph that Chris Grover described – which was simply age vs. FIS points. He looked at three classes of skier – the moderately successful through the very successful. Since age is part of the graph, age adjusting podiums doesn’t make any sense to me, but I am sure Joran can provide a better answer.

  • JoranElias

    April 29, 2010 at 11:25 am


    I think you might just be misunderstanding what I’m graphing, which isn’t surprising, cause these are kinda “busy” graphs and I may not have done a great job of explaining them.

    I realize you don’t like FIS points, but as I pointed out, I’m just trying to recreate something like what Grover was referring to, so your beef is with him on the choice of using FIS points, not me.

    Fasterskier is correct that the left panels contain the FIS point vs. age graphs of athletes who have attained the indicated number of podiums since 2001-2002.

    The other two panels contain graphs of FIS points vs age for USST and “Bubble” athletes, and these are the identical set of data points for each of the three distance and sprint graphs.

    The graph does not compare podium visits to fis points, or anything else for that matter. It compares the fis point to age relationship of athletes, across different sets of racers grouped by the number of podiums they’ve won.

    There are two levels of comparisons taking place in these graphs:

    (1) Comparing FIS points to age within each athlete
    (2) Comparing the relationships in (1) between sets of athletes

    The “podium athletes” category is simply one of the sets of athletes I chose for the comparison. But the thing being compared is the relationship between age and fis points, not podium visits.

    Sorry for the confusion.

  • darlene

    April 29, 2010 at 11:31 am

    What if you took data just from WSC and OWG medalists, and from the top 3 sprint, distance, and overall WC skiers at the end of each season? It seems like what the country has been stiving toward.
    You could take the FIS points for a medalist at a given age, and multiply by the # of medals or final podiums she won. You add this value to that of all the other winners values at that same age, and divide by the possible # of podiums, and you’d get an average of the FIS points for medalists at that age. You’d have to adjust # of possible for each age, as a number of winners are still young (and it’s possible that some older winners started their WC career late). You could then compare any athlete to this average at a given age, and see how close they are to that average, and if they are within a statistical range. I have no idea if that is how Chris is doing it, but it makes sense to me.

  • darlene

    April 29, 2010 at 5:47 pm

    I found the data looking through fis-ski and calculated the average FIS points for all OWG and WSC medalists and World Cup overall top 3, and WC sprint and distance top 3. I couldn’t get the points for Pedersen, Ohrstig, or Burukina. Also I couldn’t find data for Moen, Paruzzi, or Belmondo when they were under 25. These are the results for women:
    30.16 for 22 yr olds (146 podiums)
    21.92 for 23 yr olds (142 podiums)
    9.14 for 27 yr olds (132 podiums)

  • nexer

    April 30, 2010 at 10:29 am

    Just by looking at the trend lines it seems that Simi and Hoffman are heading down a steeper slope (don’t kill me) than Andy Newell, although Newell may be just at the bottom of the parabola.

    Care to do some curve fitting there Joran?

  • JimGalanes

    April 30, 2010 at 11:48 am

    I beleive this is useful information in that it provides a baseline of where US skiers are relative to a deinfed group of top skiers in the world.

    From a distance racing perspective the picture is not very promising. One critical piece of infomration this data is illuminating is the performace curve of successfull, podium finishers and a pattern of yearly progress. Improvement comes faster from 18-20-22 and then over the balance of the years the rate of progress slows dramatically.

    Pretty clear to me that at 20 years old men women need to be in the 50-60 point range if there is to be a reasonable expectation of long term success. Guess who the only distance skier listed onthese chart fits that profile?

  • JoranElias

    April 30, 2010 at 12:07 pm


    Not sure if you’re referring to the sprint or distance graphs. If you mean the sprint ones, technically speaking, straight lines are “curves” too. 😉

    In either case, I’d be careful about reading too much into an athlete’s “trajectory”. Athletes who begin their racing with 250 point races are going to have an extremely easy time improving down to 100-150 point races, whereas moving from 100 point races to 30 point races is probably way more than twice as difficult.

  • teamepokeedsbyn

    April 30, 2010 at 5:52 pm

    I agree with #8…if one wants to develop a ski racer who will be a reasonble challanger to top 10 for a 1 or more season-long competition during their carreer, than the gentic gift will reveal itself by age 20-22.

    Stringing along athletes who race WC for 2 + seasons/15+ starts, and who still have not broken into say 3-4% behind podium, year after year hoping for 1 “good” race, is not very productive, in my opinion. If one has entered 1 distanc races, and not broken to top 15 by age 22, move on i say.

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