Running: What’s The Relationship Between Distance And Pace?

I’m breaking the rules and posting about running instead of skiing.  But skiers spend quite a bit of time running, and I’ve developed an interest in ultrarunning, so I thought this might be fun.

I was reading about the Comrades Marathon recently, and was suitably impressed that those runners are stringing together roughly 55 sub-6 minute miles in a row.  So I thought it might be fun to look at how distances affect running speeds.  Not a new idea, for sure, but fun nonetheless.

I grabbed some records from here and here1.  Most are for set distances, but some are records for specific times (distance travelled in 12 hours, 24 hours, etc.).  I only used verified records, nothing that was “pending” or noted with an asterisk.  Obviously, when you get up above 10,000 meters, many of these races aren’t taking place on tracks, so the course and surface type will play a role.  Where possible I noted whether the race was on road or track (IAAF has some 100km records that I can’t quite discern whether they are road or track).  The chart is below:

Updated: Fixed y axis labels to read “Average Pace” rather than “Average Speed”.

The speeds are recorded in minutes per mile.  The distances are in miles, but I’ve plotted them on a log scale, since they vary so much.

Something appears to happen at around 30 miles.  Also, just eyeballing the graph, it appears that when you increase the distance travelled by a factor of ~1000, the average speed over that distance decreases by about a factor of 3.5 or 4.  However, your body doesn’t really know how far you’ve gone, just how long and how hard.  So it might be more relevant to look at the same plot but with the total race time on the x axis:

Since all I’ve changed is the scale, the shape of the plot hasn’t changed, just how we interpret the x axis.  Now we can see that the “bend” is happening at around 100 minutes for both men and women.  It appears that when the length of effort increases by a factor of 10 you sacrifice a bit less than 1 minute per mile until your total length of effort reaches 100 minutes.  Then for each increase in race time by a factor of ten you lose closer to 2-3 minutes per mile.

Before extending this too far, keep in mind that these data represent the very fastest human beings at these distances, so any relationship we find here really only applies to the very limits of human running.  What you or I experience may differ dramatically.

Still, I’d say human beings are well adapted to running long distances.


  1. I wrote this before the 800m men’s record was broken recently.

Prediction Game: Who’s Gonna Podium In Their Very Next Race?

Five mystery skiers, all women.  For each skier, their very next  (distance) race is a WC, OWG or WSC race.  Which of them are going to finish on the podium (top 3) in their very next race?

To make things a bit more challenging, I’ve omitted the x axis labels (which is date, not age), so you can’t work backwards from what season I’ve stopped each graph in.  Update: Just to clarify, the tick marks on the x axis represent a time gap of about five years. But I will tell you that the races that I have plotted aren’t limited to major international competitions (WC, OWG, WSC); I’ve plotted every distance result I have for each skier.

Update2: Apparently I can’t seem to write very clearly this morning.  It should also help to know that the “next race” each skier is about to do is potentially a completely different race.  So it’s not like they (or any of them) are about to compete in the same race against each other.

I will also tell you that there is at least one skier who podiums and that for those who do podium, it’s their first career podium.

Leave your guesses in the comments!

I’d say I’m going to post the answers tomorrow, but my traffic probably isn’t high enough to warrant that quick a turnaround.  How about we leave this open until Friday?

Update 3: Yet another reader requests a hi-re version of the graph.  Honestly, I don’t think it will help much.  But I am nothing if not responsive to my readers (click through for full version):


Week In Review: Friday August 27th

It’s been a light week at Statistical Skier; had to move the Statistical Residence to a new (much improved) locale closer to work, so things have been a bit hectic.

  • We mucked around with the speeds that skiers travel at, looking at differences between races in Europe and the US.
  • A short not on rivalries, in which I unwittingly dissed Marcus Hellner’s sprinting ability.
  • Finally wrapped up XC skier retirement posts (really, honest!) with Tore Ruud Hofstad.


Career Retrospective: Tore Ruud Hofstad

Another helpful commenter reminded me that Norwegian Tore Ruud Hofstad also retired this past July.  My results for Hofstad stretch back to World Junior races in 1998 up to his retirement in 2010.  I think one of the reasons I may have overlooked him is that he didn’t really race much last season.  In fact, I can’t seem to find any individual races for him from the 2009-2010 season.

He won two individual medals at World Championships in 2003 (Silver) and 2005 (Bronze) and was frequently a member of the Norwegian men’s relay team, so he racked up some more medals there, mostly gold.

He also had a handful of World Cup podiums: four, by my count.  He raced almost exclusively distance events, so we won’t bother looking at sprint results: Read more


I’ve talked about the amusing notion of victims and nemeses before.  Let’s look at some extreme cases.  Remember that a victim is someone you beat by a small margin (rather arbitrarily chosen by me to be less than or equal to ten seconds).  A nemesis is just the reverse: someone who beats you by such a small margin.

If this happened a lot between two particular skiers, one could perhaps suggest some sort of rivalry is taking place. 1 So how often could this happen between two skiers?

Well, quite a lot, it turns out.  Looking at every single race in my database, Pietro Piller Cottrer has beaten Vincent Vittoz by a margin of no more than 10 seconds a whopping 26 times.  Conversely, Vittoz has returned the favor 21 times.  On the women’s side, we’ve got an intra-Italian feud with Gabriella Paruzzi edging Sabina Valbusa a total of 21 times, while Valbusa edged out Paruzzi 14 times.

Limiting ourselves to more recent territory, the 2009-2010 season, we get the rather one sided rivalry of Northug vs. Teichmann, where Northug defeated Teichmann by no more than 10 seconds seven times in just one season.  And Teichmann?  Not once.  Poor guy.  There isn’t a similarly stand-out example for the women.  Instead, we’ve got two matchups where the score is 5-0.  We’ve got Arianna Follis getting the better of Aino-Kaisa Saarinen 5 times to nothing, and also Marianna Longa tormenting Karine Philippot by the same score.

What about the apparently oft hyped Northug/Hellner rivalry?  Well, in close races (and all seasons) it doesn’t appear to be much of a contest.  We’ve got 12 victories for Northug by less than 10 seconds and only 2 for Hellner.  Someone needs to work on their sprinting.

The equivalent rivalry for the women is clearly Marit vs. Justyna.  This actually lives up to its hype somewhat, with 8 narrow victories for Marit and 7 for Justyna.


  1. And let’s be honest.  Even if there isn’t one, it’s fun to drum them up.

A Look At Skier Speeds

I was following Andrew Gardner’s twitter feed a while back during the USSA spring meetings, and he mentioned a comment by James Southam that American courses are far easier than those in Europe. 1

That got me thinking about whether there was any way I could look at this question using, you know, data.  The short answer is that I can’t.  At least not very well.  But the data I looked at are interesting in their own right, and serve as a good example for the sorts of ambiguities and mysteries that can pop up when you’re analyzing data. Read more

  1. I’m paraphrasing here; it was something to that effect.

Week In Review: Friday August 20th

Here’s what’s been cooking this week on Statistical Skier…

  • I tried to wrap up the cross-country retirement posts, was told I forgot a few and so tacked on a post for Kristina Smigun-Vaehi.
  • I snuck in a little cycling graph, showing the riders from this year’s Giro d’Italia who dropped out along the way.
  • I took another look at men’s cross-country’s rivalry of choice, Petter Northug vs. Marcus Hellner.
  • I dug a little deeper on the topic of variability in ski racing.
  • Finally, I wrapped up a long series looking at the development patterns of skiers from different nations who’ve done well (or not so well) at World Juniors.  This last one tackled Norway.


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