For 'short' races the average speed of a world-record performance declines sharply with increasing distance. However, above a certain distance, the decline is more gentle. For both running and swimming the change in exponent occurs between about 150 and 170 seconds. This corresponds to a change from 'anaerobic' respiration - in which the body predominately releases energy without burning oxygen - to aerobic respiration, which is more suited to longer distance running. The transition occurs after a distance of about 1 kilometre for athletes and after 300 or so metres for swimmers. They also discovered that the average speeds of men and women decline at a similar rate - disproving the common belief that women are better suited to long-distance races than men.

"I was training in Munich for a swimming competition for people working in high-energy physics," says Savaglio, "where we timed our average speed for set distances and I noticed that they seem to follow a predictable power law. Carbone suggested that we should write it up for Nature, so we did." The research seemed to pay off: "Our team won that year," she says.

The power law could be used to find the best distance for a particular athlete to compete in suggests Savaglio. "Say a young person wants to train as a athlete," she says. "A coach could measure his or her average speed at set distances, work out the power law and compare it with that of professional athletes to find the best running distance."

However, the current graphs are limited by the distances used in competitive athletics, "I would love to have additional data points at 600 and 2500 metres to confirm our findings," she says. Savaglio and Carbone now plan to see if their approach works for horses.