# Power of running world records

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Followinga few entries on sports here and there, I was wondering what kind of law follow the running records with respect to the distance. The data are available on Wikipedia, or here for a tidied version. It collects 18 distances, from 100 meters to 100 kilometers. A log-log scale is in order:

It is nice to find a clear power law: the relation between the logarithms of *time T* and of *distance D *is linear. Its slope (given by the *lm* function) defines the power in the following relation:

Another type of race consists in running backwards (or *retrorunning*). The linear link is similar

with a slightly larger power

So it gets harder to run longer distances backwards than forwards…

It would be interesting to compare the powers for other sports like swimming and cycling.

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**Statisfaction » R**.

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