## 2.15

Jake Hofman writes that he saw my recent newspaper article on running (“How fast do we slow down? . . . For each doubling of distance, the world record time is multiplied by about 2.15. . . . for sprints of 200 meters to 1,000 meters, a doubling of distance corresponds to an increase of a factor of 2.3 in world record running times; for longer distances from 1,000 meters to the marathon, a doubling of distance increases the time by a factor of 2.1. . . . similar patterns for men and women, and for swimming as well as running”) and writes:

If you’re ever interested in getting or playing with Olympics data, I [Jake] wrote some code to scrape it all from sportsreference.com this past summer for a blog post.

Enjoy!

1. Brent Buckner says:

I see that your article uses time versus distance, as opposed to your previously expressed preference (respective of plotting) for speed versus distance (per your old blog post ). Works for me!

2. derek says:

Only the power of 1.1 or 1.2! I’m surprised, I would have thought people would tire more with distance.

• Andrew says:

I remember being amazed to realize that top marathoners’ times are equivalent in speed to 5-minute miles.

• Phil says:

Yes, an entertaining exercise (to some of us) is to calculate how far we can run at the pace of an elite runner at various distances. “I can run 100 meters at a pace that an elite runner can maintain for 1500 meters”, that sort of thing. It is a good way to appreciate how fast these people really are.

It may be worth noting (or perhaps it’s obvious) that the world record at 100m and the record at 5000 meters are set by different people, so it’s not like any single person can run twice as far in only 2.1x the time.

• Anonymous Rex says:

With regards to your final comment, that’s less true than you might think. Haile Gebrselassie previously held the marathon record (at 2h03:59, now the third-fastest) but also has a good time for two miles (at 8:01.08, the second-fastest ever). The latter is a rarely-contested event, but it’s still impressive.

Consider Gebrselassie’s best times in the 1500 meters and marathon. With respect to distance, that’s a factor of 28.13 (about 4.8 doublings). With respect to time, he has a factor of 34.81 (about 5.1 doublings). This corresponds to an exponent of 1.06, or a factor of just over 2.09 for every doubling.

3. Nameless says:

The fundamental underlying parameter is mechanical power output vs. time. It is not well known to runners or to the general populace, but it is very familiar for serious cyclists (because one can get a highly sensitive power meter built into the bicycle for <\$1000 and it's considered to be a good training tool).

There are basically three zones, which, for simplicity, we can call anaerobic, mixed and aerobic. In ballpark numbers, an average moderately trained adult male can produce 1000 watt of power up to about 15 seconds (anaerobic zone). Beyond 15 seconds power output rapidly declines to, say, 500 watt for 1 minute, 250 watt for 5 minutes, and then there's a much slower, possibly logarithmic decline from that point. If you can do 250 watt for 5 minutes, you can probably do 200 watt for an hour or 180 watt for 2-3 hours without stopping.

In running records, this picture is complicated, first, by the one-time cost of acceleration from the start (big part of the total energy budget in sprints), second, by increased contribution of aerodynamic drag at sprint speeds. Running is generally so wasteful that even a sprinter spends at most 20% of his power output on air resistance, but it's still a lot more than what a marathon runner spends (aerodynamic drag scales as a cube of speed).

Finally, to compare power output of an average Joe against a world-class endurance athlete. Using maximum power output that can be sustained for 1 hour as a benchmark, an untrained adult male can do ~2 W/kg; a serious recreational cyclist can manage ~3.5 W/kg; and a world-class athlete can do ~6 W/kg.

4. […] Andrew Gelman writes for the New York Times on how fast we slow down running longer distances and comments on his blog on where one might get the data. […]

5. […] “How Fast We Slow Down Running Longer Distances” http://nytimes.com/… see also http://andrewgelman.com/… […]