Tuesday, February 15, 2011

The slowdown factor

Every runner who has toed the line over any distance is all too familiar with the inverse relationship between the distance of the race and the speed of the runner. In other words, inevitably the longer the race, the slower the runner's speed. But how does this relationship play out among the pros? I have been meaning for awhile to plot velocity versus race distance for the world records, male and female in the various road and track distances. Today I am home with food poisoning and unable to concentrate on much between trips to the bathroom (rancid horse chestnuts... ohhhhhhhh) so I thought I would finally get to this post.
Here is the big picture:

A couple of things I find interesting, first the long held belief that the performance gap narrows between the genders at longer distances appears to be absolutely true. It would be nice to have some data points between the marathon and the 100 km to see the progressive narrowing but it is already evident at the marathon distance and even more so at the 100 km distance. As an aside, I thought it was strange that wiki did not post records beyond 100 km - I guess the longer ultras are not IAAF events? Incidentally, at the oddball distances of 15 km, 20 km, 25 km 30 km I could chose from the track or the road record and I thought it was really interesting that the road record was always faster, by a lot! Often more than a minute faster... this is probably due to how rarely these distances are raced on the track versus the road. The 20 km world record road performances were, for both genders, the split on the way to the half marathon world record.

There is also a popularity effect evident in this plot. The marathon data point is out of line with its less glamorous cousins (30 km, 25 km, 20 km, 15 km) to the left. Clearly being a premiere event that is often raced by the fastest of the fast has an important effect on the world record. This effect is also evident in the shorter distances, if we zoom in on the women's data we see that the velocity for the 3 km world record (6.17 m/s) is actually higher than the velocity for the 2 km world record (6.14 m/s) which, even given the huge differences in how frequently these two events are run, is pretty amazing. After all, the 3 km is 1.5 X longer than the 2 km and also at these distances we are on the steep part of the velocity curve:

We also see that the effect of distance is equal between the two genders. Let's get rid of the 100 km data point and look at the two genders together again:

In both cases the big drop off in velocity occurs after the mile, I guess this bend in the curve represents the transition from one metabolic system to another... anaerobic to aerobic? It has been forever since I read about the physiology of running... Also the effect of race distance is very predictive of velocity for both genders. For the men, 95% of the variance is accounted for by the equation 7.991x power -0.103 whereas for women 93% of the variance is accounted for the by the equation 7.1545x power -0.105. Or, for those not familiar with modelling, in plainer terms, say you wanted to know at what velocity the world record would likely be run for some random distance like 18 km for women, you could plug 18 into the above equation which yields 5.28 m/s (NB it would take 56:48 to run 18 km at 5.28 m/s). 93-95% of the variance explained is pretty darn good (at least compared to the data I am normally work with), I guess this means the effect of distance on velocity is governed by very rigid physiological principles. Or something like that.

Finally, for my own entertainment:

Yup, I seem to be governed by a similar yet slower equation. 


  1. Clearly you are bored...
    Interesting stuff though. However I would be interested to see what it looked like couple decades ago. Let's say 30 years back. Because 800m record is almost 30years old, however longer distances at that time were much slower than they are now, and shorter distances were not that much off, weren't they? I think that the deviations from the regression curve were greater, so it seems to be evolving and deviation is getting smaller, which probably means that we are indeed getting closer to reach the physiological limits. (However, I am not an expert and never really liked econometrics and statistics classes)

  2. Almost all of the female ultra world records go to Ann Trason (50 mile, 100 mile, 12 hour). I can't find the mens' equivalents, though.

    50k female world record is held by Frith Van der Merwe in 3:08:39. The male 50k world record was run by Thompson Magawana in 2:43:38. So you could add those points to your graph (really cool graph, btw!). Interesting that they both come from Claremont, South Africa.

  3. The men's ultra records are almost all Yiannis Kouros (not 50 miles or 100K, though).

    I find times up to the marathon generally fall on a line of 1.075xlog(distance)-const.=log (time). Over the marathon, it's 1.213xlog(d)-c=log(t). It holds well for world records (and age and gender records) and for many individuals as well, myself included.