Tuesday, June 21, 2016

Grandma's Marathon 2016: How much did the heat slow your time? A statistical analysis


Photo: Drew Geraets
The 40th annual Grandma's Marathon was held this past weekend in Duluth, Minnesota.  Grandma's is a staple of the Midwest marathon scene and is perennially praised as one of the best races in America.  The point-to-point course is a beautiful route that starts in the north woods of Two Harbors and follows the shore of Lake Superior into downtown Duluth.  With a slight net elevation loss and very few hills, the course is also usually a fast one.

This year, however, many participants were disappointed with their times.  Warmer than average temperatures and clear, sunny skies caused many runners to finish well back from their goals.  Since several runners that I coach or advise ran the race, I was curious to see how much of an effect the temperature had on their finish times.  So, as I often do, I started crunching some data.

Fortunately, I was able to stand on the shoulders of some Big Running Data giants—a 2012 scientific paper by Nour El Helou and other researchers in France already laid the groundwork for disentangling the effects of climate on marathon race times.  In their paper, El Helou et al. analyzed ten years' worth of results from six World Marathon Majors (London, Berlin, Paris, Boston, Chicago, and New York), resulting in a data set of 60 marathons.  These totaled almost 1.8 million marathon finishers.  El Helou et al. ran statistical analysis on each year's results, trying to find the correlation between ambient temperature during the race and the distribution of the finish times.

El Helou et al.'s methods

Because El Helou et al. (correctly) hypothesized that temperature would have varying effects on runners of different abilities, they analyzed several levels of performance for the top one, 25th, 50th, and 75th percentiles of male and female finishers.  So, for example, if the 2010 Chicago Marathon had 21,000 male finishers, the authors looked at the finish time for 210th place—that's the "one percentile" time.  This marker is more useful than looking at the winning time or 10th place, because those can be affected by things like the quality of the elite field, the tactics employed by the lead pack, and so on.  After extracting the various levels of performance for the 60 marathons in the data set, El Helou et al. then consulted meteorological records to find the ambient temperature midway through each of the 60 races. 

Doing regression analysis allowed El Helou et al. to correlate the ambient temperature with the distribution of finish times.  The broad trend in the results was not surprising: marathon times are slower when temperatures are too hot, and they are also slower when temperatures are too cold.  What was surprising, at least to me, was the optimal temperature for marathoning.  El Helou et al.'s data robustly shows that the ideal temperature for running a marathon is pretty chilly—39 degrees Fahrenheit (3.8° C) for a 2:40 marathon! Race times follow a parabolic curve, slowing significantly on either end of an optimal temperature. 

Click to enlarge