The fastest possible marathon
I came across this article in the BBC this morning, which posed the question “when, if ever, will humans run a sub-2-hour marathon?”.
Expert opinion seems to be somewhat divided on this question. The runners themselves seem to think that it’s possible, but not likely within the next few decades. One of the “leading authorities on marathon running in the US” says that it isn’t, while a kinesiology professor from the University of Montreal used some extrapolation formula to predict that the 2 hour mark will be broken in 2028. Just about everyone seemed to agree that 2 hours, 2 minutes is within reach (the current world record stands at 2:03:59).
I’m certainly no expert on distance running, but I did develop something of a method for addressing this question that I used to predict the “fastest possible mile” time (3 minutes, 39 seconds by my estimation).
So I decided to apply the same method here. My conclusion, surprisingly, is that even a marathon time of 2 hours, 2 minutes is far from given. In fact, my prediction is that the “fastest possible marathon” is 2:02:43, only 76 seconds faster than the current world record.
Below I quickly repeat the arguments/procedure I used for the mile and I show the graphical results. (Warning: If you haven’t read my earlier post, the following might not make very much sense).
Here is the progression of the marathon world record over the past 100 years (data from Wikipedia):
If the marathon world record is plotted as a function of “person-years” since 1908, when the world record was first kept, it shows a pretty convincing exponential decay to a particular value: 2:02:43.
Translated back into real time, the progression of the world record marathon time looks like this:
It’s not a rock-solid analysis, but I think the data is actually pretty convincing.
So count me among those who are skeptical that a 2 hour marathon is possible. In fact, count me among that rare (nonexistent?) group of people who are skeptical that a 2 hour, 2 minute marathon is possible.
I hope I’m not right — I love watching humans break records as much as anyone else. But either way, you should take a moment to enjoy watching Haile Gebrselassie’s record-setting performance from 2008. He may have been running to within 1.01% of maximum human capacity.
You need to re-graph this with steroids.
Shouldn’t the world record data points be monotonically decreasing with time? Your plot shows them going up some years…
Good observation. The discrepancy has to do with different races being certified by some athletic federations and not by others (the Wikipedia article explains it more fully: http://en.wikipedia.org/wiki/Marathon_world_record_progression ). I’m not qualified to judge which records are legitimate and which aren’t, so I just kept them all, even though it does look funny.
OK, let’s assume that world record progression follows an exponential curve, and only the past 100 years are relevant, and all that. I’m skeptical, but let’s assume it’s so.
Shouldn’t the logical conclusion, then, be that 2:02 is the best possible time certified by some timing association, not the best possible time a human can run?
When the IAAF and ARRS can’t even agree to within 90 seconds on who’s the fastest in a race that has already occurred, how can you use their data to predict a future race time accurate to one second?
You’re right; it’s not fair for me to claim single-second accuracy. The accuracy of this conclusion, based on scatter in the data, is probably closer to +/- 15 seconds.
Luckily, though, those terrible ~90 second uncertainties that happened a couple times in the 1930s don’t screw up the data too much because they occurred for times that were very far from any hypothetical “fastest time” (so they look relatively small on the second plot above). If the more recent times had uncertainties of 90 seconds, that would really mess with the data.
Perhaps this is true, but a similar argument using the same logic was being made for the men’s 100 metre record until a few years ago, when the record was blown out of the water by Usain Bolt.
So i’d guess you are right that it can’t go much lower on current technology and technique. It would require something new such as what Usain Bolt’s height allows him to do. I’d guess the much greater melding of East African genetics with world class techniques and training from a young age might allow a similar step change as for the men’s 100 metres.
I suppose that you already saw that Geoffrey Mutai won Boston marathon on the amazing time of 2:03:02
I did! Absolutely incredible. It’s too bad Boston isn’t world record certified.
As a means of ‘sanity check’. Would the ‘best possible time’ come out different if you had calculated it 10 years ago ? ( i.e. without the last 10 years of data ) – or 20 years ago ?
I haven’t tried it, but you can sort of see what effect it might have from the second graph above. Removing the last twenty years of data would remove the last six data points, which would more or less leave the fit line unchanged. The last four points represent the last ten years: if they were removed the predicted fastest time might increase slightly (but not substantially).
And Patrick Makau shaves 21 seconds off the world record today. I wonder whether that makes any impact on your assessment?
Also, notice that the likes of the late Wanjiru, Mutai and Makau are much younger than Tergat, Gabreselassie and other such runners. With dedication and top quality training (some of these athletes start in their teens) should we not expect that they do much better than is currently thought possible?
I’m really confused about how you’re doing the fit that you’re doing. From reading both your analyses, it seems like you’re assuming the world record time T will be related to the person-year S by T = B + exp(-aS), where a is a constant and B is the best possible time. But in this model, plotting log T against S should not give you a straight line! So what do I have wrong?
Hi Aaron. What I’m actually plotting is log(T – B) against S, which is why it looks like a straight line. (On the second graph, that’s a minus sign on the y axis label, not a dash).
My fitting method is to search for which value of B best produces a straight line on that plot, and that’s what I call the “asymptote” of the world record, or the “fastest possible marathon”.