Running by Numbers

I participated in my first Half-Marathon, the Airtel Delhi Half-Marathon, on 23^rd November 2014. Over 32,000 people participated, with around 12,000 for the half marathon, and another 20,000 for other races.

Well aware of being all of 44 years old, I was thrilled that not only was I able to complete the half marathon, I did that within 2 hours – the best that I could have hoped for. This set me thinking on the age vs half-marathon performance issue – was I justified in patting myself on the back?

I leeched all the summary data that I could from the organiser’s website, and this is what I found: 

The visualisation above shows the half marathon performance of 7 different age categories, 18-25, 25-30, 30-35, 35-40, 40-45, 45-50 and 50-60. For each age category, the relative % share of people completing the race in four different time slots is shown, Less than 1.5 hours, b/w 1.5 and 2 hours, between 2 and 2.5 hours, and between 2.5 and 3 hours. The darker the colour (red), the better the performance.
As can be seen above, and true to my expectations, the best performing age group was 18-25. And after that- nothing made sense. The data shows that the older you are, the better is your performance in the half marathon. This is how the weighted average time for the different age group looks:

Why would this be happening?

Not willing to accept that endurance performance can improve with age, I hypothesized that this is an example of self-selection bias. The half-marathon participants in the older age groups were the ones who were fitter than average, who had probably run half marathons in the past, and were confident of their ability to compete in this event.

To test this hypothesis, the simplest way I could think of was to compare the percentage representation of each age group in the marathon with the general population.I figured that if there is some kind of self-selection, then the older age group would be under-represented in the marathon. 

Here is the visual display of this data:

India is a young nation, and the % of population in each age group only decreases with age. However, the difference in the age profile of half-marathon participants and Delhi does not appear significant enough to explain the improved performance with age. Except for the youngest age group (18-25) which is under-represented in the marathon, rest are largely in keeping with the population at large.

Probably, the self-selection would be visible in some other attribute - income, education..

However, the census data for Delhi did show something interesting:

The saw-tooth like distribution of population by age is obviously wrong, unless somebody hypothesizes a link with 5-year plans. A simpler hypothesis is available - each peak in the graphic above is at a round number: 30, 35, 40, 45..... Maybe, there is a learning for the census surveyors, don't ask people their age, ask for their year of birth.

(I checked a few sites on age versus marathon performance. It appears that there is no significant impact on performance till about the age of 50. Here is one interesting article: http://www.runnersworld.com/masters-training/age-matters 
However, I doubt whether any amount of trawling the web would find a paper supporting the data of marathon peformance improvement with age all the way upto 60)