I ran a race and made some graphs

The Cambridge Half Marathon was this past Sunday and I was able to race with a couple of friends. It was a gorgeous day and very nice course. As always, I was inspired by the diversity of runners.

After finishing, I was happy to see that the full results were dumped in one not-too-poorly formatted text file. I whipped it into a Julia DataFrame to do a bit of analysis.

How fast are old people?

It's a thrill to get passed by older women and men who are pacing along by themselves or running with their daughters or sons. How fast were the older runners in this race, especially compared to runners in their "primes"? To answer this, I plot the estimated distribution of pace (minutes per mile) across age groups.

It's interesting to note that, besides the literal elderly, runners from very different age groups have similar distributions of paces. Sure, there's a little more mass on faster paces for the youngest runners (20 years old or younger) and a bit more mass on slower paces for the 51-65 year old runners. But the five age categories in the middle show quite similar distributions, and the modes are almost identical at around 9:00 minutes per mile.

I haven't looked at the science for how pace changes with increased age in general — though presumably it converges to 0 when we die — nor looked at data from other races, so I'm interested to see if this phenomenon is seen more widely. I would expect that for the older age groups, there is a fair amount of self-selection in which more dedicated runners compete and the "recreational" runners stay home. This could balance out the natural decreases in pace from aging.

How fast are young people?

With those oldies speeding by, it's important not to lose track of my own peers. Below, I plot the estimated distribution of pace for the group of 23-year old males, and show the pace of several key individuals.

I turn out to not be the last of the pack for my group, for which I'm relieved. However, while I handily beat the oldest racer of the day — a 71-year old man —, I get crushed by the youngest racer of the day — a 9-year old boy, who runs an amazing 7:14 pace.

It's inspiring to take part in a race with such a diverse group of racers in terms of age, experience, and ability. A special shout out as well to the eight visually impaired runners and two wheelchair racers who completed the course.

The data and code can be seen on my GitHub.