Anyone who has ever tried to get in better shape knows that there is a law of diminishing returns for exercise.  The harder you work, the better you get.  But the better you are, the harder you have to work to improve.

This law is particularly evident to me lately, as I try to train for a marathon this summer.  I’ve watched myself get progressively faster ever since I started running a year and a half ago, but it’s getting harder and harder to improve my times.  It makes me wonder: what’s the fastest I could ever hope to be?  For that matter, what is the fastest any human could ever hope to be?  In this post, I’ll try to answer those questions.  I’ll focus specifically on the mile run, where data from the world record over time provides surprisingly compelling evidence that the fastest possible human mile time is extremely close to the current world record of 3 minutes 43 seconds.

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The hypothesis

First off, I should justify my assumption that there is a “fastest time”.  Why can’t the world record for the mile get progressively faster without limit?  Well, if you want to take the argument to an absurd limit, you can say that no one will ever run faster than the speed of light, meaning the mile world record will always be faster slower than 5.37 microseconds.  More seriously, though, it’s probably safe to assume that no one will ever run as fast as Usain Bolt for an entire mile (16 times longer than his 100m race), which puts an upper limit of about 2:36 on the fastest mile time.  The world record stands at 3:43 right now.

My goal is to find this lower limit on the fastest possible mile time, both for my own self and for humans in general, by looking at the data for progression of the record.  In order to do so, I’m going to have to make an assumption that can be translated into a mathematical statement.  I’ll assume that halving the difference between your current mile time and your hypothetical best takes a constant amount of work.  For example, if your hypothetical best is a 4:00 mile, then improving from 6:00 to 5:00 takes the same amount of work as improving from 5:00 to 4:30.  It’s an unjustified assumption, but it’s fairly easy to believe.  Moreover, it’s easy to check.  If the assumption is true, then we should see the mile record decaying exponentially in time to some characteristic value.

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My own personal best

I’ll test out my method first using data (as I remember it) for my personal best mile times when I was on the track team in high school.  There are only five data points, but the data does seem to resemble exponential decay (see the graph below).  My apparent asymptote (fastest possible time) is about a 4:28 mile, with a “half life” of about 1 and a half seasons.  Not too bad!  I can even predict that I would have run about a 4:43 if I had stayed for one more season of track.  Of course, the data also suggests that I had no real hope of making the state championship meet, which had a qualifying time of 4:25.

My personal best mile times (black points) and a fit line showing exponential decay

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The fastest runner in the world

If we can figure out my personal fastest possible mile time, why not do the same thing for the world as a whole?  Data for the world record time in the mile is readily available, so it should be possible.  When you first look at the data, however, one major problem appears.  The world record in the mile has been decreasing pretty much linearly ever since 1913, when such things were standardized by the IAAF.  There is no real lower limit in sight.

This would seem to contradict my original assumptions: either there is no lower limit for the mile, or there’s no way we can get it from the data.  However, there’s something that the data is not showing.  The population in the year 2000 was over 6 billion, while in 1913 it was less than 2 billion.  There were many more runners in the 1990’s than there were in the 1910’s, so the fact that the world record was not falling more quickly in the 90’s suggests that it was getting significantly harder to beat.  In other words, we have hope of finding a “leveling off” in the world data, the same as we saw in the data from my own personal bests.

What we need to do is redefine time.  What we want is a plot of “world record mile time” as a function of “amount of work”.  To figure out my own lower limit, I plotted my mile time as a function of seasons on the track team.  To find the world’s lower limit, I need to plot the world record mile time as a function of the number of “person-years” that have elapsed since the mile world record was kept.  A “person-year” is like a “man-hour”: it’s the number of people that were alive at a given time multiplied by the number of years they lived.  So the year 1913 represents about 2 billion person-years, whereas the year 2000 represents about 6 billion.

Plotting the world record vs. the number of person-years since 1913 gives us exactly what we were looking for: a beautiful exponential decay to a particular value: 3 minutes, 39.6 seconds.  (Note that in the plot below the y axis is in log scale, meaning that a perfect exponential should end up looking like a straight line).

Exponential decay of the world record mile time to 3:39.6

The fact that all the points in this graph lie so close to the fit line is very strong evidence that the world record in the men’s mile is decaying exponentially to a particular value, just like our hypothesis.  More importantly, we can deduce the fastest possible human mile time: 3:39.6.  If you want to translate back from “person-years” to real time, this is what it would look like:

Predicted progression of the world record for the men's mile. The dotted line is at 3:39.6.

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A few comments: have we reached the end of the exciting days of distance running?

The prediction of the last section looks exceedingly bold.  The mile world record has improved by more than 30 seconds in the last hundred years, but I’m saying that we should never expect it to fall more than 3.5 more seconds, not in the next hundred years or in the next thousand.  That would mean that when Hicham El Guerrouj ran 3:43.16 in July 1999, he was running to within 1.5% of maximum human capacity.  Is it really possible?

Well, the short answer is that I wouldn’t have written this post if I didn’t think so.  If you don’t believe me, maybe you can consider this for evidence: the current world record has stood for almost 10 years.  That’s the longest the mile world record has ever been unchanged, despite the fact that the world has more runners now than ever before.  So maybe we are “levelling off”; maybe it is becoming almost impossibly hard to beat the world record.  I think it is.  The early days of track and field were full of record-breaking distance running performances, and I think those days are coming to an end.  If my predictions here are correct, then the world record will pretty much stop being broken within my lifetime (or, at least, it will stop being broken by more than tiny fractions of a second — much less exciting).

It’s sort of a sad thought.  But for me, it’s also sort of an awe-inspiring one.  When I watched El Guerrouj break the world record as a wide-eyed teenager on the track team, I was watching something extremely close to the greatest physical exertion of which mankind is capable.  That’s pretty amazing.

UPDATE:  Apparently someone already did this kind of analysis in 2005 and reached the exact same conclusion.  Interestingly, they also predicted a fastest possible marathon time of 2h03:38.  Three years later a 35-year-old Haile Gebrselassie ran it in 2h03:59, only 21 seconds slower than their predicted “impossible time”!

April 23, 2009 4:41 am

I suggested something along these lines to a friend not long ago, but at the same time I’m not sure I really believe it. My argument was in relation to us talking about how LeBron James and Kobe Bryant would make players like Larry Bird look like high school ballers if they were transferred in a time machine to today. This is basically fact, that players from 30+ years ago simply couldn’t run as fast as and wouldn’t be as strong as players today. But my friend went on to say ‘imagine what players in 30 or 40 years time will be like…’. This is the interesting thing… It’s hard to say now, but what if Wade, Kobe and LeBron were taken 30 years into the future? Would they really be subpar athletes? I struggle to see it, I really do. I honestly believe that players we’re seeing now are near their peak in terms of what humans are capable of…

It’ll be interesting to see how right or wrong I am… Maybe in 30 years times people in the NBa will have 60 inch verticals, and will play at speeds that would make players of today dizzy…

April 23, 2009 10:48 am

I’ve been thinking about this exact question. It’s a lot harder to quantify “fitness” in basketball than it is in track and field. But I will be extremely surprised if the NBA of 2050 is populated with much better athletes than the NBA today.

It’s only been about 100 years since a person has been able to make a living just by being an athlete. And during that time we have gotten very good at maximizing a person’s athletic potential, and at finding the people with the most potential.

So I tend to agree with you, and not your friend. Unless the distant future involves genetically-engineered athletes or trained gorillas, I think the best athletes of today are about as good as the world is ever going to see.

April 20, 2011 8:21 pm

I beleive a boston marathon runner just finished the 2011 marathon in 2h3:03. That smashes the number above. With God, I believe all things are possible. The rare few that have the genetics, talent & heart are blessed with a tremendous gift. I hope these people use this gift to do more than break world records. These are the kind of athletes that have the power to influence today’s youth in a life-changing way. By encouraging America’s children to have better eating habits and routine exercise, these “superhuman” athletes can leave a legacy that can’t be overshadowed by a new world record. Thanks for the blog, it motivates me to be healthier and stronger.

June 9, 2015 2:08 am

With God and PEDs 😉

April 23, 2009 9:22 am

Wow this is waayyy too much math for a fitness post/blog.

April 23, 2009 10:32 am

Sorry James. This is really a physics blog!

3. April 23, 2009 9:45 am

Interesting post. So, if my fastest mile is somewhere around 7:10 (from a 5-K race), then I should reach 3:39.6 in about how many million years?

April 23, 2009 10:34 am

Unfortunately, 3:39.6 is the fastest time for the world at large. Most of us weren’t blessed with the genetics of an olympic athlete and have much more modest upper limits. Like I said above, my personal fastest possible mile is probably about 4:28, which wouldn’t even have been good enough to send me to the state track meet.

April 23, 2009 1:31 pm

The future of sport will lie in technology. Give it 30 or 40 years and paralympians will exceed the capabilities of the ‘abled-bodied’ in sprint events and middle distance running. It will go something like this:
The performance/times of paralympians are getting better, ‘The Games’ will be merged into one as the difference in times would be negliable. We will have a few years of todays banned performance enhancing drugs being deemed ok to use as it will be the only way to stop ‘serious athletes’ from lobbing off limbs to stay competitive. ‘The Games’ will eventually spilit again to ‘natural’ (biological only) and ‘enhanced’ (the era of bionics).
So no, I don’t athletes of today would be able to compete with the stars of 2050 as they would be obosolete.

April 23, 2009 1:42 pm

Interesting prediction. I’m not sure if I agree about performancing enhancing drugs ever being legalized, but it doesn’t seem at all unlikely that we will one day have “natural” olympics and “enhanced” olympics. Particularly because once world records stop falling, the olympics will become less exciting. Consider how much excitement there was about swimming this past summer, and almost all of it can be attributed to advances in swimsuit technology. An “enhanced” track and field meet would definitely maintain the public interest because we would still get to see “humans” do things they had never done before.

5. April 23, 2009 9:22 pm

Might be interesting to see this applied to other track/field records that haven’t been impacted too much by technology: long jump, shot-put, discuss.

Also, what about power-lifting records? (this data might be skewed though, I believe there was a former soviet-bloc male lifter who was rumored to be holding back on his lifts: just breaking his own world records by the minimum weight each competition to maximize his  bonus incentives)

Nice article and analysis overall though…

April 23, 2009 11:24 pm

I am confident that the same analysis could be done for other sport records, although they might have less reliable data, like you said.
What do you think would be most interesting?

April 24, 2009 7:15 pm

Seems to me you could figure out the hypothetical fastest speed a human can run using physics (assuming perfect physical fitness)

limiting constraints:
-the static friction coefficient between soles of shoes and the track surface (technology element)
-air resistance of the runner’s body cross-section (technology element: full body clothing to reduce air resistance?)
-mass of the runner
-gravity
-and the trickiest one: power/force that the runner’s body can output to the track surface … seems like it would be a question of the biophysical performance of muscles, tendons, etc.

May 2, 2009 12:12 am

I actually tried this for the other extreme of running, the 100m and the data is much more scattered. It looks like there are jumps in the data – a period of years where the record falls much faster. I suspect this will be true for any technique or equipment intense sport (e.g. starts, running form, shoes, etc). I think by picking distance running, you probably hit the event that is the “most pure” form of athletic competition, that is the least dependent on technique and most dependent on just hard training and raw ability. There have been relatively few dramatic improvements in the technique or equipment of distance running for quite a while as far as I know! The two events that come to mind that would be at the other end of the technique/equipment extreme would be swimming (recently) and the high jump (not so recently).

May 2, 2009 11:41 am

Yeah, I considered doing the same analysis for the 100m… but the data was much more spotty, and I was worried I would get some ridiculous conclusion (like an 8 second 100m). I’m sure swimming would be even worse.

6. April 24, 2009 9:38 am

Great post! I am also training for my first marathon having started running a little less than a year-and-a-half ago.

Anyway, your analysis is very interesting and I’ve often wondered about the “fastest” a human could run, swim, etc. Then Speedo gave us the LZR suit and swimming records took the largest drop accross the board in history. Perhaps that is the one missing link to your hypothesis – how will technology impact the mile record? What if Nike comes out with something that is equivalent to the LZR suit? Perhaps it IS possible for humans to run faster than the predicted 3:39.6, as long as we get some “legal” help. But of course the purist in me hates the LZR suit, and would equally dislike anything of the sort in running. I think milers should compete barefoot and naked – only then can technology play zero role in the result (at least during the race portion, if not in training).

April 26, 2009 12:43 pm

Interesting post. I have one issue with it.

You treat every new human birth equally in adding to ‘person-years,’ while in reality the majority of the additional population had no chance of being involved in “world record” running due to economical constraints. A huge percentage of the world’s population increases in the past century or so are from locales lacking in both the nutrition and training facilities to produce a top runner – this has become more true as time has passed: the “wealthy” nations have outstripped the poor nations significantly in those factors, while the “poor” nations have well-outstripped the wealthy ones in population growth.

Obviously, it’s exceedingly difficult to correct for that, but I also believe it skews the “maximum” speed that you ascertained – there are billions of potential runners out there that have never had an opportunity to reach their top potential because the economics of their situations prevented it – population growth AND economic growth should be factored in when looking to correct for the eventual maximal speed of a human, I would think.

April 26, 2009 2:04 pm

Hi Jon,

You’re right, of course. The right way to adjust time is not by “number of people”, but by “number of runners.” I’m not convinced, though, that the fraction of runners in the world is changing. In other words, I don’t see much reason to think that the world has been getting poorer over the last hundred years. Sure, there is more poverty, but is there more than can be explained by population growth alone? After all, the global economy has been growing exponentially in the last century as well.

May 2, 2009 10:11 pm

Wow, that was very interesting, I admire your intellect to be able to do that. I think I agree: the human body can and will only go so fast without the use of drugs or technology. Under 3.40, huh? Wow.

May 19, 2009 7:02 pm

I’m in the process of reading a book called The Perfect Mile. It follows the three athletes in the ’50s who had the best chance of breaking the 4 minute mile, Roger Bannister, John Landy, and Wes Santee. I thought it was rather interesting, because I knew that the world record was much faster than 4 minutes. I run the 800m in track, and I dropped nine seconds over the span of the 5 months this year. With the world records of 43~ in the 400 and 3:43~ in the 1600, I wonder if the barrier for the 800m is around 1:40~. The world record is 1:41~ set in the 90’s, and hasn’t been close to being broken since (winning time in the Olympics was 1:44~) . I don’t feel like doing the math necessary to figure that out, I was never one for statistics.

It is rather interesting to see if 3:40 will ever be broken, I highly doubt it will be within the pure human capabilities. Barring genetic engineering and neural implants, it probably won’t.

May 19, 2009 7:09 pm

Eventually I want to sit down and analyze data from a number of other track and field events. Maybe then we can see what the data says about the fastest possible 800m. 1:40 may be a pretty good estimate.

As other people have said, though, data from other events/sports is generally not as “clean” as for the mile.

May 19, 2009 7:24 pm

The top 10 fastest 800m times are only 1.5 seconds in difference, from 1:41.11-1:42.62, both in 1997. Since running a 50 second 400 is no easy feat, running two of them successively would be nearly impossible.

Guerrouj, the mile record-holder, ran an unofficial 1:42.7 800m, but the training and build for the 800 and 1600 are barely different. My coach asked me what event I wanted to train for, because he had different a “peak-week” for each event. I assume that when he ran it, he wasn’t peaking for it, but being a slightly longer distance runner, he may not have had the raw speed necessary to run the 800.

August 2, 2009 12:45 am

I don’t follow the assumptions connecting the individual-level model (e.g. the model in which you assume that halving the distance takes a constant amount of work) and the global model. You could derive the global model directly by assuming that this assumption holds globally, but this is no better than simply saying, “I’m going to fit an exponential curve to the data, it seems to do pretty well!” This is not a particularly promising method.

If you want to derive the pattern of world records from assumptions about individuals (a “microfounded” model), it seems like what will be crucial are assumptions about the distribution of hypothetical bests from which each individual is a realization (ignoring as other commenters noted the possibility that technological advances such as PEDs, genetic engineering and cybernetics will continue to shift this distribution).

A key factor is the number of people with potential access to state-of-the-art training. If population were the only relevant variable, India and China would dominate the world record lists. The problem with using population as a proxy for “number of runners with access to state-of-the-art training” isn’t malnutrition, but rather the fact that only a few countries specialize enough to produce people near the global frontier in any given event. This point also underscores the key role that technological progress, as opposed to just a greater number of person-years to draw from plays in driving world records. Even absent game-changing events like the legalization of steroids, the evolution of better training methods is a crucial factor. We could model this as shifting hypothetical bests, or as allowing for more efficient training – in either case, it is a crucial factor omitted from your current model.

August 2, 2009 1:30 am

Hi Jason,

The most sensible way to interpret this analysis is not as a proof of anything, but rather a piece of statistical sleuthing that showed an interesting correlation. I made a guess that seemed reasonable and it worked surprisingly well. As you rightly point out, my guiding assumptions here are too vague and ill-founded enough to draw any strong conclusions about why the world record mile is trending in this particular way.

Nonetheless, the data do seem to suggest that the mile world record is decaying exponentially with “person-years”. That doesn’t mean population is the only relevant factor, just that the number of truly great runners produced by the world is scaling directly with integrated population. It may be that the most significant effect of those person-years is in the building of athletic technology, as you suggest. It seems a little difficult to believe in the case of distance running, though. I’m not sure how large an effect new running shoes and training methods have had. I also don’t see much reason to think that the availability of world-class training should be changing dramatically over time — it seems mostly an issue of your culture and your personal wealth.

August 2, 2009 10:38 am

Let me pose my question a different way: let’s pick any monotonic time series which you know has an absolute lower bound (e.g. the Usain Bolt extrapolation or zero). I’d expect there are many cases when an exponential fits pretty well, especially if you allow yourself the additional degree of freedom of finding the appropriate units for the X-axis. If you had some theoretical motivation for the person-year model, we could evaluate the underlying assumptions and attempt to determine whether they are likely to continue to hold in the future, but absent this, I’m skeptical.

The person-year hypothesis has other implications than the exponential curve: for example, it predicts a certain distribution of world-records across countries (and a certain change in this distribution over time due to differential population growth). Is this prediction born out by the data? Is there some easy way to tweak the model to explain both the cross-country distribution and the time series? If person-years are just a proxy for the building of athletic technology, it’s very unclear why adding person-years in India and China should contribute (and this is a large fraction of the additional person-years in your chart).

p.s. I’m not a physicist, but it’s possible that this sort of procedure is much more likely to produce correct predictions in physics than in the social sciences. In physics, there often really is an underlying simple mathematical process guiding the results. With a few rare exceptions (perhaps Zipf’s law for cities is one, arguably Okun’s law), trends in the social science are frequently upset by changes in parameters of the underlying process, which is why it is crucial to understand this process to make correct predictions.

August 2, 2009 2:01 pm

Your point about “physics reasoning” vs. “social science reasoning” is well-taken. In a sense, my physics training has only prepared me to deal with large systems of things about deterministic laws, so you are right to be skeptical.

You are also right that there is no good correlation, in general, between a country’s population and its propensity to produce great runners. But that isn’t a reason to discard the “person-year hypothesis”, as stated here. Imagine, for example, that all runners come from Kenya. Then the world record in the mile should depend only on “person-years for Kenyans”. But if the proportion of Kenyans in the world remains more or less constant, I can still draw up a correlation between the mile world record and global person-years. There’s nothing inconsistent about that, even if it misses an important microscopic detail.

August 7, 2009 5:43 am

Jon,

I completely disagree with the notion that persons from developing countries with poor nutrition and lack of training facilities have a worse chance of breaking long distance world records.

In fact, ill argue that the analysis should focus on persons from eastern Africa, since this peoples are renowned for long distance running and currently own the world record, currently we know that very few of these peoples are exposed to good training facilities and world class athlete diets. In the future we expect that more of them will have access to better training facilities and better diets and this should help identify more “super human” athletes within their population and in turn lead to a significant decrease in both the mile and marathon WR times.

• August 10, 2009 9:59 pm

There is a remote but real chance that the “pattern” will be broken by major breakthrough in training technique (think swimming records broken in Beijing with latest swimsuits) .

Its impossible to predict, by definition, what it might be but consider how high jump world records were shattered after someone invented back flip instead of front jump. I speak from experience as I improved by hard earned mile PR from 6:50 to 5:52 by switching from regular running shoes to barefoot running. One possibility is, genetically selected kids picked up early in the development phase and trained scientifically to be running machines.

(btw, minor technicality, second half of 200m for Usain Bolt is faster than his 100m record so its not necessarily safe to assume multiple of 100m time is upper limit.)

• September 1, 2010 2:09 pm

His second half of the 200m is faster than his first because he is already at top speed. The first half includes his acceleration from 0 m/s to top speed, while the next 100m begins with him already moving. Thus, the fastest 100m a person can run would be measured from when they have already achieved top speed, not including acceleration.

13. August 11, 2009 8:40 pm

There are problems with this model.
1. You use the example of the 1600 (while of course a 1500 would give you much more data). This arguably the lowest of the distances. In track there is a variety, and the short sprints data per record performance is a HUGE skew. It serves to predict nothing about the upper end of performance.

2. Recordbreaking in track tends to a different pattern, and that pattern is more like punctuated equilibrium and NOT a gradual tapering. Athletes perform at a particular plateau-like level for years, then a standard is broken, then the average elite perfomance is bumped up for all for a long period, and then another jump, and so on.

3. Above, you say “meaning the mile world record will always be faster than 5.37 microseconds. More seriously…” I think you meant “slower than…”?

4. Three years later a 35-year-old Haile Gebrselassie ran it in 2h03:59, only 21 seconds slower than their predicted “impossible time”!
—21 seconds is a HUGE margin, not a small one.

An interesting piece!

August 17, 2009 6:22 am

An interesting article. After having seen how Bolt broke his record once again in the 100m race I kept wondering what the physical limits of humans are. I believe that there are limits to what humans are capable of, but it seems hard to impossible to determine what those limits really are.

Apart from the technological advancements, there are simply too many parameters to take in consideration: What’s the perfect height one must have to practice a specific sport, what are the absolute best conditions in which that person should race/run (wind, air density etc), at what age does that athlete reach the absolute maximum of his abilities, what’s the best possible fat/muscle/water ratio for him, what’s the best diet etc, etc. You could keep going on and on in finding things that need to be considered. If one would know every single parameter that’s relevant for a better performance, would it then be possible to calculate the absolute limit? I mean calculate that limit unambiguously, without having to make any assumptions. Is it possible for one athlete to meet all those predetermined conditions at the same time?

Of course one could also argue that humans, like any species, evolve. Meaning that even if we were able to calculate an absolute limit for a certain sport today, that this limit may no longer hold true in e.g. 1,000 generations from now . Or am I being a bit naive here?

October 18, 2009 8:48 pm

interesting article, however you should have just taken the world record for the 400 and multiplied that by 4, i’d say that is the upper limit. I’m young but i highly doubt that the world record will get below 3:35 in my lifetime, if that.

November 26, 2009 2:02 pm

It’s really a bummer that I read this article because I wanted to set a mile world record of 3:38 but I guess I could suffice with a 3:39.6. I am a freshman in high school and have a fastest mile of 5:14, so so I was just wondering if you could give me some information on what my fastest mile ever could be. I have been running competively for 1 1/2 years.

November 26, 2009 2:56 pm

5:14 is pretty fast. I’d say your chances of breaking the world record are pretty small… but the great thing about running is that you always compete against yourself, and you can feel amazing every time you improve on your own personal best.

If you want to get a taste of what your own “fastest possible mile” might be, try making a graph of your PR mile time as a function of time (say, semesters since you started running); something like the first graph of this post. If the graph looks like it’s leveling off somewhere, you can use that as an estimate of your fastest possible mile. If it’s not clearly leveling off, then that’s a good sign — just keep running hard and getting better!

February 5, 2010 12:42 am

You know what would be neat? If we applied this to some intellectual ability lol. Like the abiility to make the most accurate stat-plot as we learn more about our enviroment and elimate variables, what happens when there is nothing else we are capable of learning?

April 11, 2010 7:11 pm

Hey man I saw the post and thought I’d comment. I think you’ll see the world record down under 3:30 if not under 3:20 in this lifetime. Here’s why:
First, let me say your graphs are well researched and legitimate as a scientific study, but they only measure the limit of human potential while using the same major muscle groups and technique as elite runners currently use. If an athlete was to choose a different set of muscles to use as the engine of their running, their potential would change, whether for the better or the worse. Your limits are based on the assumption that the chosen method of running is in fact, the best method available; or at least that it will remain the same through your whole lifetime. I agree we’re close to the potential of human ability so long as we continue trying to refine the same old running style. The reason I think the record will fall by 10 or 20 seconds is because of a recent breakthrough in running technique that eliminates the need for oxygen guzzlers like the hamstrings and tensor fascia in favor of deep muscles in the back like the Illiopsoas group, obliques, and the Lumborum group. This keeps oxygen circulation in the core close to the heart for greater VO2 efficiency, and, with proper flexibility, the stride length can extend by 3 inches or more which will put future athletes 2200 inches (about 62 meters) ahead after 750 strides (typical mile). So, yes there’s a limit, but it’s based on taking the best running technique to the limit, and I don’t believe the one being used by elites today is the best technique possible; only the best one known.
Best of luck on your marathon.

19. April 26, 2010 2:52 pm

I run at a four minute mile at present, and I think it could be possible to break your barriers, when people say never they are just asking for it to happen.

May 20, 2010 7:42 pm

Well first of all that’s a very interesting article. It’s hard to believe that it would be impossible for someone to beat that time by even a hundredth of a second therefore, I don’t think that that is the exact fastest time possible, but I think it’s very close. I’m in 8th grade and I’ve run a 4:57 1500 which is pretty close to a 5:17 mile. Im going to plot my times and see what it comes up with for my expected improvement now. Great work!

November 29, 2010 9:52 pm

Nice analysis (I just stumbled across this while looking for something else), but there’s a problem. You took population into account, but you didn’t include participation. Not only were there fewer people alive in 1910, a smaller percentage of them engaged in athletics. This would be particularly important if you did the same calculations for the women’s records. The important thing is not how many women were alive in 1950 (say), but how many actually considered taking running seriously (damn few).

Still, I’m very intrigued.

June 7, 2011 12:34 pm

no someone could go faster

September 2, 2011 1:13 am

Interesting.. I was just thinking about the fastest possible mile time and decided to do a little concluding of my own before stumbling upon this. One of the fastest athletes in the NFL runs 25mph, if you formulated an answer to how fast his mile would be at a continued pace it came to approximately 2.4 minutes. Definitely probable, especially with the future generations and their competitiveness – pushing one another for the title as the greatest whether it’s the fastest or strongest.

September 4, 2011 7:21 am

Like all statisticians you have absolutely no idea what it takes to reduce the world mile record….and rest assured it ain’t graphs of world population. For example during the second world war the worlds population of young athletic males was decimated…yet the world record for the mile improved…the offspring of all those athletic males killed were never produced…yet the mile record still improved.
Let me cut to the chase. The world mile record will be reduced to 3.20 over the next 100 years. There is only one limiting factor stopping it’s reduction now, and that is lack of motivation. When payments were introduced for winning marathons the world best time was reduced from 2.10 to 2.03…critical mass and financial reward will see the marathon time go under 2 hours within the next few years.
Here’s how to reduce the mile to 3.20…put up a billion U.S. dollars for anyone running 3.20…and 1 million for anyone breaking the previous W.R. by more than a second on the way to 3.20.
Make it financially attractive for Usain Bolt to stop running 100m and get him to run a mile…make it financially attractive for all those people who do other sports to run the mile.
Usain Bolt can run 43 odd seconds for the 400m…but he doesn’t train for it…cos it’s too hard…to run 3.40 he only has to run 55 seconds per lap…to run 3.20 someone has to run 50 seconds per lap. For someone like him 3.40 is do able even now…all you have to do is over ride the psychological barriers that limit performance.(pain is the greatest barrier to performance, immune system strength, comes next…( training suppresses the bodies immune system…so a strong immune system is paramount to hard training)..competition over rides pain…so you need a critical mass of men capable of running the time.

In conclusion… it’s got nothing to do with world population..cos it only takes one person to run 3.40….and critical mass (the competitive level required to overcome the limiting factors to reducing the previous best time) can be produced by as little as 10 people
It is not a case of physiology because there are people alive today who are capable of running 3.40…
Oh,and as I write this the Jamaicans have just broken the world record for 4 x 100m with 37.04 at the IAAF champs in Daegu..This is an average of 9.24 per 100m….now if we could just get a couple of them to train for the mile !!
regards
Don Jacobs

October 11, 2011 4:39 pm

Challenge Accepted

November 7, 2011 6:41 pm

hahahaha don usain could not break 5 in the mile

August 3, 2012 11:19 pm

This is fascinating work that you did. This is a question I have pondered from time to time as a former distance runner. Beautiful, accountable, analysis

August 6, 2012 6:30 am

Phenomena you did not factor in your analysis is the change in people themselves. There are performance enhancing developments that will occur we cannot predict that could blow this analysis away. Also people themselves will change. Evolution may either enhance or detract from human performance. But if we emphasize performance then people will mate accordingly. One day a record will be set that no one thought would be possible.

January 6, 2013 11:58 pm

Mike Boit already ran the Queen’s Street Mile (down hill most of the way) in a time of 3 min 28 sec in the Auckland, NZ in 1983!!!

29. February 27, 2013 9:31 pm

Peter had it right back in 2012. What changed the most between Hitler’s 1936 Olympics with Jesse Owens and the current world record was more Jesse Owen types running. Once all races and nationalities were in play the records began falling at a faster pace as the overall runners increased in pace. It was a function of a wider variety of human beings playing the game, being in the race. It was a social revolution. Blacks and others had been running fast all along, you just did not see them participating in the Olympics as much.

Now that we have broken that barrier we may have reached another barrier. With every race being represented the next barrier to be broken will be genetic, aka evolutionary. That takes much longer than social change. It will not happen in the lifetime of anyone reading this post and probably not their grandchildren, or even their grandchildren. That is barring a genetic freak of some sort.

To break the three minute mile s going to be one of the longest runs in the history of man.

June 17, 2013 12:48 pm

At first I thought this was extremely true, and at the individual level I think it is true. But I don’t think the data you use to make yor best fit line for the world is fair. Back in the early 20th century people didn’t run miles much, nor was the training very efficient. With distance running training plays a huge part. As training got better and more people started running the miles times dropped faster, which accounts for the much larger slope. Now that training has reached a high level of efficiency I think the slope on the graph is still going downwards as human capabilities improve and will continue to argon sly decrease, but with the large slope before it appears its stopping instead of nearly slowing down. Also I do feel that there will be some breakthrough in training causing the slope to pick up a little also. But maybe I’m wrong and you have the right.

31. July 11, 2013 6:15 am

I think athletic timings could increase a lot further. You have discounted evolution and genetic manipulation, which could allow humans to run much faster. Nobody predicted Usain Bolt’s world record before he started to run. Bolt is much taller and his muscles have developed to allow such a tall person to run faster. I am sure the future could see people over 7 feet tall reducing sprint and distance running times further than current predictions.

You might like to read Bioenergetics and Racehorse Ratings by Bob Wilkins who investigates human and horse running times using bioenergetics.

October 3, 2013 7:42 pm

Someone broke the hypothetical fastest marathon!! Wilson Kipsang with a 2:03:23!

33. September 17, 2014 12:28 am

You know, I like the idea of messing around statistically with the “record hasn’t been broken in BLANK number of years.” Except for counting all the people on Earth, it seems like that might produce a good guestimate in many human-powered endeavors.

For half a moment, I thought about any endeavor made by mankind. But technological ones would not work. I love history, and watching the highest speeds of airplanes starting in 1903 would show records being broken constantly (well, starting a few years later). But it’s not apples to apples: Too many mechanical breakthroughs. Single prop vs single prop, fine. But then you add in twin engines, lighter and stronger airframes, better wings and props, and, only about 40 years after Kittyhawk, jet engines. Then turbo jets and jump jets and rockets and who knows what else.

Hmmm. Maybe you could do it for tech. It would have to be on a much larger time scale, though.

Hey. Damn blogger. Stop making me think!

September 24, 2014 10:09 am

I don’t agree with the upper limit being 2:36 based on Usain Bolts 100m dash– this dash includes him accelerating from 0-25~ mph so basically the 100 meter dash could be faster with a full running start. Secondly creating artificial situations tha stress the muscles beyond what could naturally be achieved will really tell the story of the limits of the human body. So being slightly facetious eating the Jamaican yams coupled with jet pack training (this is a reality–see university of arizona engineering student) then I believe the 3 minute mile is a real possibility.

January 12, 2015 8:45 pm

The biggest problem I have with your comment about how long the record has stood is that the mile isn’t really included in many high-level meets. I’d argue that the record’s longevity is more a product of the decreased prevalence of the event than of human limits. I also think it’s a bit much to give an exact number in anything like this.

February 10, 2015 11:13 am

There is a psychological factor involving the goal and other options. As is probably known to all runners, this theoretical bound (mine is 3:37 likely in the next 35 years) becomes part of the folk-lore for aspiring milers. If your model is correct, based on the span of records and population statistics, the new runner is faced with information (understanding it or not) that the absolute best that could hoped for in their wildest dreams is to cut about four seconds off the mark. This is not incentive, when the effort is so supreme. What is the reward, when for an aspiring athlete there are now many other outlets for their talent at speed? Thus, there is a diminishing return in the face of the quest. It is more likely there will be a “fluke” factor down the road, the black swan of excellence, despite the training, and this will ever so slightly lower the minimum time possible. Also possibly lower the best time will be newly created methods for both physical and psychological training.

February 18, 2015 1:09 pm

What formula did you use to find your fastest possible time? I am attempted to find my human limits in swimming and relate it to analytical limits. I am doing this for an IB math project. Any insight on what formulas you used to determine you fastest possible time would be greatly appreciated. Thanks!

February 18, 2015 3:24 pm

Hi Claire,

I think you’re asking about the blue fit line on the first graph. Is that right?

The data in that plot is my own personal mile time (y axis) versus the amount of work put into training, which in my case is measured as the number of seasons on the track team.
I fit the data to the form:
y = A exp(-x/x_0) + B.
You’ll notice that in this equation, y –> B at x –> infinity. This means that B is my “fastest possible time”, which I would approach only after an “infinite” amount of training.

So if you do the fit, then the coefficient B that you get from the best fit represents your fastest possible time. Of course, this is just an educated guess for what the curve y(x) should look like, so there’s no guarantee that the answer you get for B will be literally correct.

Hope this helps!

• April 9, 2015 3:29 pm

Hello, I’m trying to figure my fastest possible times as well, but I’m having the hardest time trying to figure out this equation. Could you please explain how you did this step by step (If this is too much to ask, I understand)
Thanks

April 9, 2015 3:39 pm

Hi Riley,

You might find this website useful: http://mycurvefit.com/

Enter your data, using x for something like “number of seasons of training” and y for your time. Then enter a user-defined formula formula that looks like the one I mentioned above: y = A exp(-x/t) + B. The website will tell you the best fit for B, and that will be an estimate of your fastest possible time.

Hope this helps.

April 15, 2015 12:48 pm

I agree with the premise, but consider this, in the late 20s and early 30s, a study showed that the fastest a human can run the mile is 4:02. Now, 90 years later, you are trying to use the same science to prove somthing that has been proved wrong by over 15 second.

April 16, 2015 12:16 pm

Your comment is most interesting. My preliminary estimates using the exponential model previously cited give the lower limit on the best estimate are about the same. However, you have touched on the important point of data and what data and how do you use it to predict the future. The simple fact is that when one uses the data available, one is captured by that which is. This implies that predictions can be terribly wrong. This implies that reliance on data can be terribly wrong. This implies that the model can be fully off-base. In summary, the use of data must be carefully scrutinized, particularly for new factors (such as new genetic stock such as in the marathon) and the actual model used.

It certainly would be of some value to know what models predicted the 4:02 time based on data from the 20’s and 30’s.

June 26, 2015 12:16 pm

This is faulty because Hicham already beat that by about 17 seconds in 2001 running the mile in 3:26. There could be a lower limit to how fast the mile can be ran but I don’t see it any time soon. The lower limit would need a genetically gifted long distance runner train at the highest altitude on earth then race at the lowest altitude under the best circumstances with a little luck. There is also the improvement of sports science and improved training techniques that have yet to be perfected. I’m sure we couldn’t see someone run a mile in 30 seconds but maybe under 3 minutes, some day.

June 28, 2015 2:11 am

El Guerrouj ran 3:26 in the 1500m. Usually, “the mile” refers to a race of 1600m. (Even though, technically, a mile is ~1609 meters.)

Interestingly, if he could have maintained his 1500m pace for 100 meters more, he would have run the mile in 3:39.72!

July 2, 2015 6:05 pm

very interesting. I believe there is a lower limit but I think it is lower than 3:39. With the population being so high there is bound to be the occasional human who is just built slightly different(ex. muscles, heart, lungs) that allows them to move faster.

August 13, 2015 12:49 pm

Well, a marathon has now been run in 2:02:57 by Dennis Kimetto, which blows the prediction out of the water. I think there are two things really wrong about this model. First, The effect of doping means that it is possible that beating a record is comparatively harder in 2015 than in 1984 when doping detection was just getting started.

Secondly, in the early 1900s only a small percent of the human population was involved in sports. What we have seen is that certain parts of the world, for whatever reason, excel at certain distances, as with the Kenyans and the marathon distance. If this is due to the geneology of the runner then I propose a different model: each individual has a top potential performance, but it requires cultivation in order to be realized. The decrease of the world record time is due to the increasing variety of runners that are given the chance. Therefore the curve should in some way follow the total number of professional athletes and distribution of personal optimal times. Once these are fitted to the observed personal best times then you can give probabilities on the occurance of an athlete with any given personal best time.

August 19, 2015 8:06 pm

UPDATE: to your UPDATE: that marathon record has been broken already. 2:02:57

September 13, 2015 7:34 pm

yea but this just means that women sports will start to accelerate faster than men’s and we will see more competition in 20 years in women’s sports

September 28, 2015 1:51 am

Im curious as the actual math to figure it out so i can find out my fastest mile time.

September 28, 2015 8:59 am

You might want to see my comments above to Claire McClelland and to Riley.

September 28, 2015 1:52 am

Also i agree with what your saying. Human beings have reached our peak as of now.

November 18, 2015 8:56 am

The extreme difficulty of running a sub-four minute mile requires extraordinary athleticism. To run at 15 mph for four minutes is a truly amazing feat. It is as difficult today as it was when Roger Bannister became the first individual to do so in 1954 with a time of 3:59.4. Only a very small percentage of the global population have the genetic ability to run a sub-four minute mile.

September 14, 2016 7:42 am

I like your mathematical approach to this subject. However, there is one flaw. Maximum human capacity is dynamic. Mankind is constantly evolving. With internationalization of the world, the gene pool is ripe for change. Evolution is not always the slow lumbering process that most people believe. Rapid evolutionary bursts, especially when isolation of a gene pool ceases, has often happened. Time will tell.

47. September 14, 2016 8:27 am

I like the mathematical approach. The flaw is assuming maximal human capacity has a limit … that it is static … a mathematical constant. It is not. It is dynamic … a variable. The question is how fast or much can it change? That is up to two factors: 1) the evolutionary process of man. Not always the slow lumbering change over eons that it is typically pictured to be, evolution has happened in bursts for a variety of reasons. With the ever increasing internationalization of the gene pool, it is happening already. 2) exercise physiology – we are not even close to the limits of what this field can do. Most believe incorrectly that this discipline will only increase the percentage of maximum human capacity, as you put it. But it likely has and will continue to increase maximum human capacity, not at the genetic level, but at the physiological and biochemical level. Dynamic changes in muscle fiber characteristics, once thought to be static, is but one example.

March 23, 2017 5:09 pm

3:08 1500, 11:37 5000, 24:12 10000, 1:56 marathon. With perfect form, and × FACTOR. Did the study using secretariat model in horse racing. Once per 91 years. Supper heart factor which peaks in occurance only once per decade.

March 23, 2017 5:15 pm

Mathmatics works only to the point of the genetic abnomalities, which is how we evolved and everything else. The issue is not everyone runs so he may have already existed? Sprinting is far more lickly to reach a limit because of kinetic limits. I would say it may stay pretty close on all fronts. V02 max has more wiggle room in the distance events. I dont think we are as close to limit as we think. I go those numbers in an unlickly experiment.

April 10, 2017 6:29 pm

Hate it for you, part of your proof has been decimated, the world record for the marathon is now under 2:03 by about 3 seconds, thus the impossible has been done.

May 12, 2017 7:49 am

eliud kipchoge

51. August 15, 2017 12:04 pm

March 4, 2018 10:58 am

Great post. How do you think random improvements contribute to this? Even if the population remained steady, random mutations probably help/hurt performance; also just random environmental things (what you eat growing up to where the race is held). Assuming that ever highly trained runners are still have a percentage of things produce a good performance, if someone gets an outlier level performance, what would that look like and take (maybe based on increase in population) of like 1, 5, 10, 50, or 100%? To be blunt, maybe averaging takes all that into account, but I assume not fat-tail events. non-math person here.

May 20, 2018 10:49 am

Someone will break the 3:40 barrier in the next 15 years. 3:30 will be broken someday … not in my lifetime. Remember that humans evolve. Roger Bannister believed as an old man before he died that 3:30 would be broken in the distant future. As a fellow physician, I like his optimism and respect his opinion.