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The fastest possible marathon

April 11, 2011

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).

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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:

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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.

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UPDATE (Sept. 28, 2014): After Dennis Kimetto’s remarkable performance today in Berlin, setting a new world record at 2:02:57, the prediction above is starting to look pretty pessimistic.  This data point is way below the trend line in the second plot (by more than a factor 4).  Re-doing the same analysis, in fact, gives me an updated projection of 2:01:53 as a “fastest possible marathon time”.

But you can decide for yourself whether that’s worth believing.

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UPDATE #2:  G&L reader Jens has created a nice infographic showing the time progression of the marathon world record.  To me, it sure looks like the men’s time is reaching an asymptote that is above 2 hours.

20 Comments leave one →
  1. April 11, 2011 3:25 pm

    You need to re-graph this with steroids.

  2. David Woods permalink
    April 11, 2011 10:16 pm

    Shouldn’t the world record data points be monotonically decreasing with time? Your plot shows them going up some years…

    • gravityandlevity permalink*
      April 11, 2011 10:33 pm

      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.

      • Haile permalink
        April 12, 2011 1:21 am

        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?

      • gravityandlevity permalink*
        April 12, 2011 11:45 am

        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.

  3. Glen permalink
    April 18, 2011 12:50 am

    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.

  4. Sam permalink
    April 19, 2011 4:53 am

    I suppose that you already saw that Geoffrey Mutai won Boston marathon on the amazing time of 2:03:02

    • gravityandlevity permalink*
      April 19, 2011 9:40 am

      I did! Absolutely incredible. It’s too bad Boston isn’t world record certified.

  5. May 24, 2011 10:41 pm

    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 ?

    • gravityandlevity permalink*
      May 25, 2011 8:51 am

      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).

  6. September 25, 2011 4:29 pm

    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?

  7. Aaron F. permalink
    December 14, 2011 11:39 pm

    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?

    • gravityandlevity permalink*
      December 15, 2011 8:28 am

      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”.

  8. August 23, 2015 5:32 pm

    Please do an error analysis and provide error bars around your estimate. Is the error bar wider than 2 minutes?

    One possible error analysis: divide up your data into N blocks and do your analysis on each subsample, taking the variance of the results to be a bootstrapped error.

    • Brian permalink*
      August 23, 2015 6:35 pm

      Hi Kshitij,

      That’s a great suggestion. There’s not a whole lot of data for dividing — only 43 data points total. But if I do what you suggest and divide the data into 3 random partitions, I get a standard error of 1m57s.

      If you decide to play with the data yourself (linked to above), I would be happy to hear what result you get!

  9. Simon Perneel permalink
    January 4, 2016 2:02 pm

    Hi,

    My name is Simon Perneel and for school I have to make a paper about records. We want to focus on the marathon sports. Your analysis is very intresting and useful, but there are a few things that are not very clear for me. Could you please give more information what person-years is, how you plotted this function and how you translated it back to real time. I hope that you can answer quick to my questions.

    Thanks in advance,

    Simon

    • Brian permalink*
      January 4, 2016 2:32 pm

      Hi Simon,

      A lot of that is explained in the earlier post: https://gravityandlevity.wordpress.com/2009/04/22/the-fastest-possible-mile/. The number of “person-years” is just the total number of people alive during each given year, added up for all years since 1908. How you plot depends on what you’re familiar with — I used Matlab, but something like microsoft Excel (or any of its freeware clones) would work too.

      • Simon Perneel permalink
        January 4, 2016 2:35 pm

        okay thanks! (i will refer to your analysis in my paper)

Trackbacks

  1. The 2-Hour Marathon: Running’s Great Debate | Dan's Marathon
  2. Running’s final frontier: Mind games and the Neur-orld Order | Blisters, Cramps & Heaves

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