Marathon data show gender patterns in runners' performance

On Monday 20 April the Boston Marathon takes place, with tens of thousands of entrants expected to cross the finish line.

Marathons are rare examples of sporting events where performance data are often available for elite and amateur competitors, providing large and diverse data sets for exploration.

Last year more than 30,000 took part in the Boston event, split broadly equally by sex, and spanning an age range of 18 to 81.

Unsurprisingly, the top performers were in their late 20s, where most of the elite field were found, but the interesting patterns lie in the male-female distributions.

As the left plot shows, a significant number of elite women crossed the line with similar times to the better-performing men. This in itself is no surprise; what's interesting is how quickly that pattern peters out further back in the field.

The explanation is all about how finishing times varied between and - more importantly - across genders.

There was a greater range of completion times among the men than the women, but at the fast end of each sex's distribution, the pattern was reversed - women showed a far higher variance in pace. In other words, the top 1 per cent of women ran faster than the next 1 per cent by a bigger margin than was the case among the men.

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