For the last few months I have been tossing around the idea of analyzing data sets sourced from my hobbies: endurance sports (triathlons and marathons), sailing, and mountaineering. Athletic endeavors lend themselves quite well to statistical analysis (see Moneyball and Nate Silver's NCAA tournament predictions), but such careful and thoughtful scientific investigation rarely reaches the realm of less commercial sports. I've often been frustrated because speculation, anecdotal heuristics, and qualitative arguments dominate most discussions about factors which influence athletic performance in amateur sports. I hope that in this series of posts I can bring some clarity to these debates. This is a work in progress, so if these analyses pique your interest or you have comments, please send feedback my way!
In this post I attempt to ascertain how much the wind affected the results of the NYC Marathon earlier this month. On marathon Sunday runners were battered by a 11-21 mph headwind with gusts of up to 36 mph. The wind made running tough. I would know. I was one of the marathoners. During the first two miles of the marathon, runners summitted the Verrazano Narrows Bridge. Racing 150' above NY Harbor, there was no protection from the breeze. Runners dashing down the bridge at 7:00 min/mile pace were often blown sideways by sudden puffs. I found a sad humor in the image of my fellow runners stumbling down the course towards Brooklyn looking as if they were all racing the marathon in a drunken stupor. I probably didn't look much better.
Despite my enthusiasm for my charity (City Harvest) and my teammates, I did worse in this year's marathon: In 2013's marathon I finished in 3:27:48, but this year, I (quite literally) limped across the line in 3:37:30. So what happened? At the conclusion of the race my coach Liz Corkum consoled me saying that the wind probably added 8:00 minutes to my finish time. Is there any truth in that? We'll see.
For this analysis I scraped data from the NYC Marathon website for finishers in the men's 20-29 year old age group for the 2013 and 2014 races (3129 finishers in 2013 and 3043 finishers in 2014). Here's a plot of the distribution of finish times in both marathons:
Over-populations in the distribution just before half-hour boundaries in finish times are immediately obvious (at 3:00, 3:30, 4:00, 4:30, and 5:00). These half-hour boundaries are very common target finish times for marathoners, so it's not surprising that on race day competitors push themselves to meet their training targets. Interestingly, there isn't a large spike just before the Boston qualifier time of 3:05, another common goal for marathoners in NY. I guess that if you're going to run a sub-3:05 marathon, you're most likely fit enough to go for a (much more fashionable) sub-3:00 marathon time.
Looking at the distribution, we see that the 2014 distribution (blue) often exceeds the 2013 distribution (orange) for finish times slower than the mode (just before 4:00:00). The opposite is true for times faster than the mode. This would seem to imply that that people ran the 2014 marathon more slowly than the 2013 marathon. Let's examine this next.
By comparing the finish time at the boundaries of every 5th-percentile interval (groups of ~150 runners), we see that the percentage difference of finish times across all runners is remarkably consistent: For all but the top 5% and bottom 5% of runners in the age group, the 2014 marathon times were on average 2.44% slower than 2013 marathon times. In the top 5th percentile and bottom 5th percentile, the runners are probably running an entirely different race than the rest of the pack. The runners in the bottom 5th percentile are probably walking and just struggling to finish; while the runners in the top 5th percentile (3:01:52 or faster) are probably fit enough to deal with whatever race day might throw at them. Thus, I think it's acceptable to throw out both groups when computing this average.
At this point you might object that if wind resistance is the cause of the slow down, then we'd expect to see a greater decrease for faster runners. After all, the simple act of running generates its own headwind on a calm day, and wind resistance increases with the square of velocity. However, for an ultra-competative marathoner running 6:00 minute miles, a 15 mph headwind accounts for 84% of the wind resistance experienced by the runner. This percentage increases for slower runners, so wind-generated wind resistance is the dominant factor for strong headwinds for most runners in the analysis. (Fun fact: For our same 6:00/mile runner, a 4.2 mph headwind is all that's required for the wind-generated headwind to begin to dominate wind resistance.)
Assuming a 2.44% slowdown as a rule, the following table gives the projected slowdown for a range of 2013 marathon times:
|2013 Finish Time (hh:mm:ss)
||Predicted Amount of Slowdown (m:ss)
For me, a 2.44% slowdown would have meant a 2014 finish time of 3:32:52, indicating that about half of my slowdown (5:04) was due to wind and half (4:38) was due to my lack of training. (I was a bit light on long runs in my training program this year. Life got busy.)
This jibes with conventional academic analysis of the effect of wind on runners. A calculator from renowned running coach Dr. Jack Daniels indicates that a ~5 mph headwind is enough to produce the 2.44% slowdown observed in the results. Indeed, the headwind experienced by the marathoners might have been closer to 5 mph rather than 11-21 mph because of the wind shadow created by buildings and other structures along the running route. A paper by C.T.M. Davies in the Journal of Applied Physiology indicates that a world champion runner would experience a 3.9% decrease in their time if they could run a marathon in a vacuum.
Finally, while I have demonstrated that 2014 marathon times were slower than 2013 marathon times, it's worth noting that I haven't proven why the times were slower. Besides the wind, other factors could also be to blame:
- Weather conditions in the months before the marathon might have been less conducive to training;
- As the economy strengthened, perhaps people were more busy at work and had less time to train;
- The course might have been slightly altered; or
- A timing error might have occurred.
I've seen no evidence to support the final two possible causes and the first two statements don't seem likely. Having run both the 2013 and 2014 marathon, I believe the wind was the only significant factor that could induce such a consistent slowdown over the entire population of runners. Let's hope for a tailwind next year!