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.

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

Related posts:

  1. Most Improved: Women’s Distance
  2. Most Unimproved Women: Distance
  3. Prediction Game: Who’s Gonna Podium In Their Very Next Race?

About Joran

Comments

7 Responses to “Running: What’s The Relationship Between Distance And Pace?”
  1. Anthony Bramante says:

    Could there be a selection effect in racing competition that accounts for that bend? The bend seems to happen right at 26.2 miles. I’d guess a huge proportion of running competition happens at the marathon-and-less distances compared to the greater-than-marathon distances. The greater competition at those lesser distances / times could be driving the average speed of the world record holders lower than ultramarathon world record holders. So, Joran, you could still have a ten-hour 100 mile in you. ; )

    • Joran says:

      I need to graduate from 50k’s to 50 milers before I start thinking about 100 milers. Even then, I think my top three goals for a 100 miler would (1) Finish, (2) FInish and (3) Finish. Honestly, though, having run between 30-40 miles at a time on numerous occasions, I simply can’t comprehend 100.

      I think you’re right that the increased participation/competition at <=marathon distances probably has a stronger downward effect on records. But I'm pretty skeptical that this alone could account for the magnitude bend we're seeing, or even a significant portion of it. Part of it, sure. But my wild-ass guess would be that human physiology and maybe the inherent hilliness that creeps into the courses over 26.2 miles are the big drivers here.

      I seem to recall learning about how 100-120 minutes is sort of a sweet spot regarding glycogen storage in the liver, which means that north of two hours you simply have to switch to fat (or, god forbid, muscle). Ever looked at world class marathoners lately? Ultrarunners aren't fat, but you'd be surprised at how "chunky" a lot of pretty good 100 milers are compared to elite marathoners. The conventional wisdom that I've heard is that the scary-thin builds of elite marathoners aren't always great for ultras because that extra body fat becomes pretty damn important after 80 miles.

      Maybe someone who actually knows some human physiology would care to weigh in here…

  2. Joe Howdyshell says:

    Hey Joran,
    I think this might interest you:
    http://jap.physiology.org/cgi/content/abstract/95/5/1955

    It’s work done by my advisor, he works mostly with sprinters, but developed this model for overall performance. I’d be very interested to see how this relates to your work above.

    Joe

    • Joran says:

      Well, calling my post “work” is pretty generous. All I did was grab some data off the internet and make a graph! ;)

      That paper is pretty interesting, though I’m certainly not qualified to comment on much of it. The quickest connection I could make based on a quick read is the following: if you look at panel A of Fig. 1 in the paper, and imagine using a log scale on the x axis, you’d likely see a linear relationship sloping down. My graphs suggest that if you continued that graph from the paper out to durations of 100-120 minutes that linear relationship would suddenly “hinge” even further downward. The idea being that for some reason, after 100-120 minutes, human runners are sacrificing speed at a faster rate as duration increases. Each piece is roughly log-linear, but with (very) different slopes.

      But I’m not physiology expert, and so I’m just talking out of my you-know-what here…

  3. pheski says:

    I think it is possible that this relates in part to the physiology of fuel, as follows (done from memory, not with literature in hand, so feel free to challenge me, but be nice).

    For most long distance runners, usable glycogen stores increase with training and can provide a maximum of 110-130 minutes of fuel for moderate to strenuous exercise. As the end of glycogen stores is neared, the body is forced to switch increasingly to fat as a source of fuel. Fat is more dense, allowing longer term (days or weeks rather than minutes or hours) storage, but is also less ‘liquid’ in that it is not as easily and quickly mobilized. As the remaining glycogen is depleted, there is less and less of it available to prime the fat burning cycle and one transitions to an energy source that will provide hours and hours of fuel – but with a smaller pipe.

    Many of us have experienced this as ‘the wall’ .

    I wonder if what we are seeing is two different energy or fuel supply systems. I also wonder if there is data to look at to see if there is a similar – and likely more abrupt – transition between 60 and 180 seconds, when one transitions out of stored ATP and glucose to glycogen. I believe I have seen data about this with individual athletes, including supportive information using blood and muscle studies.

    I will see if I have some of the studies I remember this from lying around somewhere in my office.

  4. Gerry says:

    I agree with Pheski’s idea, as it fits nicely with past experience. I would expect to see a couple more kinks in the curve for the very short sprints. The short sprints have a strong pace effect from the standing start, however, causing a competing kink.

    Most skiers have a time limit for good performance without fuel intake. If the race goes over that magic number, they either eat throughout the race or (probably more common) ski distinctly slower at the end. In my experience with masters, that time limit is commonly between 1.5 hours and 1.75 hours. This graph may justify that anecdotal ‘evidence’.

    Cycling used to have six zones (thirty years ago), but it seemed to fit experience. Time in zone was based on elite (and possible drug enhanced) athletes. Masters may find themselves at the shorter end.
    Z6: 4 to 10 seconds. This was also used as an explanation why most 100m runners struggled at the end, and why the 200m run is totally different: after about 6 seconds, most athletes fall to z5.
    Z5: 2 to 4 minutes.
    Z4: 15 to 30 minutes.
    Z3: Until the ‘wall’ suddenly appears. The actual time was highly dependent on fuel intake and pace variation.
    Z2: Until boredom or sleep strikes.
    The first two boundaries were unmistakable. The Z3 to Z2 boundary was harder to pin down, but seemed to be real all the same.

    Another great one, Joran!

  5. Ashkhen Sahakyan says:

    the graph shows the relationship between time and distance run two horses

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