# The Math of the Fastest Human Alive

Last year, while watching the Beijing Olympics, I was blown away by how much faster Usain Bolt was than everybody else:

He became the first man to run the 100 meter dash in under 9.7 seconds. Now, I thought, that’s really, really fast. But then, just a few days ago, there was a race between the “World’s Fastest Men”, and Bolt said he would break his own record. The result?

9.58 seconds. An average speed of 23.4 miles per hour (37.6 kph). It isn’t like humans can’t run faster instantaneously, as Donovan Bailey, for an instant, has been clocked at 12.1 meters per second (27.1 mph / 43.6 kph), and it isn’t like we can’t run faster (like during a relay) if we get a running start. (Carl Lewis’ 8.8 second split in the 1992 Olympics is still one of the fastest relay splits ever.) But for the 100 meter dash — where you start from rest — this is unheard of. If we look at the progression of the Men’s 100 meter world record, we can really get a feel for how special this really is. Let’s take a look at how the record has changed over time:

You see, there ought to be some intrinsic limit of how fast humans can possibly run. There ought to be some physical, anatomical limit to how quickly we can — starting from rest — cover 100 meters. Luckily, simply modeling this mathematically — by an exponential — will tell us what the world record progression ought to look like, and should tell us what the theoretical limit of the human body is. Not only that, but we can predict what the future record ought to be. What do we find?

Okay, first off, mathematically, it looks like the theoretical limit of how fast humans can run the 100 meter dash is somewhere around 9.2 seconds, but it looks like we won’t get there for hundreds of years.

But second off, you can also see that Usain Bolt is running much faster than humans ought to be running right now. This should give you an inkling of just how special these performances we’re seeing from him are. We shouldn’t be seeing times like this until the 2030s. Which means, honestly, that it ought to take around 30 years for someone else to come along and break his record.

So what do we learn, practically, from doing this math? That watching Usain Bolt run is like watching Bob Beamon’s long jump in 1968; it’s a record that should stand for at least a generation.

Unless, you know, he can break his own record again.

1. #1 Joshua Ochs
August 19, 2009

The only question I have is whether or not you should be applying the statistical curve to that long a dataset. It certainly seems that we have one trend up until the mid 80’s, and then a very different trend thereafter. Unless those final four datapoints were all from Usain Bolt, then we’re seeing a new trend emerge.

Whether this is due to improved training, better living conditions yielding better athletes, or what-have-you, I think we may be artificially pushing that curve lower. 9.2 seconds may still be the limit, but I’d wager we’re getting there faster than the curve above would represent.

2. #2 Interrobang
August 19, 2009

I suspect the math behind this performance is actually chemistry…

3. #3 Alexey
August 19, 2009

Now, wait a second. You make a couple of assumptions:

1. that there should be a hard limit on how fast humans can run a 100m dash
2. that an exponential graph is the right mathematical model to describe 100m dash records

I’ve never studied sports record histories, but I can think of a number of factors that could spoil any possible mathematical model you might come up with as far as predictions go:

1. new science and technology within the rules
2. new science and technology outside the rules
3. rule changes

Those are the big ones I find help create sudden jolts in record setting. There are other factors too. People aren’t necessarily interested in setting records all the time — just winning events. Of course, occasionally a kind of outlier of an athlete might come along and dominate the sport for a while and therefore go after records as a personal challenge beyond just winning events. Again, that’s something that we may be able to model, but I have no evidence that we know how yet, as this is a tricky mix of biology, sociology and psychology.

So, here are some questions one might want to consider when coming up with a possible mathematical model for the 100m dash:

* Can we break down athelete’s performance over the 100m distance in smaller increments to see if we can isolate where improvements are being made over the years (starting gun reaction time, first couple of meters, middle, finish)?

* Can we get any indication on how the field is advancing overall behind the winners?

* Does the entire field’s performance correlate to the winner’s times? Has the level of dominance changed over the years?

* Have there been significant changes in training, materials, cheating, and any other possible technologies involved over the years?

4. #4 Mu
August 19, 2009

Any record past the 1980’s has that “performance enhancing drug” issue around, we all know how hard it is to exclude any artificial enhancements in the light of sophisticated designer drugs. I hope they keep all samples for re-analysis in 20 years to find out what really went on with these drastic changes. Just replot your line with Ben Johnson’s 9.79 in ’88, and see how drastically it changes the picture.

5. #5 Mike
August 19, 2009

If you’re interested, here’s a graph of Usain Bolts speed during his latest record:
http://i31.tinypic.com/miigw7.gif

And you can see that he slowed down at the end … if he maintained his max speed he might be able to further improve on his 9,58s…

6. #6 Sophos
August 19, 2009

Cool post. Usian Bolt is just like an outlier to me. Like Mike posted, it’d be very probable that he would break his own record again.

7. #7 Bob O'H
August 19, 2009

Luckily, simply modeling this mathematically — by an exponential — will tell us what the world record progression ought to look like, and should tell us what the theoretical limit of the human body is.

Eh? What’s your justification for using an exponential? Surely throwing extreme value theory at this problem would be better. IIRC it is even informative about the existence of bounds on the underlying distribution, which is what you’re interested in.

8. #8 Ethan Siegel
August 19, 2009

Hi everyone,

Alexey, the splits idea that you have is fabulous, if only they would have existed for a longer baseline of times. People have only been tracking race splits for the last 10-15 years or so, so there isn’t a lot of data there.

Mike, that is a fabulous link! He slowed up, famously, at Beijing, too, and so I wonder if he can’t sustain that pace? Also, it looks like he may have broken Donovan Bailey’s speed record of 12.1 m/s!

Bob and others, why use an exponential? It’s the simplest, fewest-parameter model (only 3) that captures all the relevant behavior. We have 19 data points to go on. Yes, the curve isn’t as smooth as it has been since timing, training and technology have changed.

But the major point is that the last two times — both Usain Bolt’s — are far, far faster than what you’d expect to happen. Bolt is clearly drug-free, as he has been tested strenuously. And I think that wherever his record winds up, you can see pretty clearly that we won’t expect anyone to come along and break it for a long time. I think he may get all the way down to 9.5 flat when all is said and done; remember that when Carl Lewis set the record at 9.86 in 1991, he did it at age 30! Bolt only turns 23 on Friday.

9. #9 Brett
August 19, 2009

Ethan,

I’m curious where the theoretical limit of 9.2 seconds comes from. The obvious constraints I can think of are 1)muscle coordination, 2)volume of blood pumped, 3)lung capacity, and 4)bone/tendon/ligament strength. All of these can still be improved on in most healthy humans, and (compared to the powerful runners of the animal kingdom) we are very inefficient with our movements. Hard technology (footwear, training equipment, etc.) will advance the four points above to a certain point, and there will be advances in motion – how we physically run (think of the Fosbury Flop for high jumpers) – as well. So, what is keeping humans from reaching an average 100 meter speed of, say, 45 kph. 9.2 seconds only brings it up to 39.1 kph from 37.6. I know – it’s a HUGE difference – but where’s the limitation?

Thanks!

10. #10 Stephen Downes
August 19, 2009

Of course, we all know the _other_ explanation for surprisingly superior performances…

11. #11 Dirk dB
August 19, 2009

The exponential fit might be simpler, but, as Bob O’H points out, extreme value theory might be more appropriate here.

Check out this paper (July ’09, hence pre Bolt’s 9.58): http://arno.uvt.nl/show.cgi?fid=95436
Using a dataset of personal bests from ’91 to ’08 they predict 9.51 as limit in the near future (read the paper for how ‘near future’ is interpreted). This may bite them of course when Bolt breaks 9.5 ;). Either way, the point that Bolt’s exploits are out of the ordinary remains…

12. #12 Ethan Siegel
August 19, 2009

Brett,

Physiologically, you’ll have to ask someone who knows better than I do what the limiting factor is. All I did was fit an exponential to the world record times, which will give you an initial point that slopes down and asymptotes to a finite value. 9.2 seconds is that value in this case, which is much faster than previous estimates that I’ve heard (which were around 9.35 seconds). In other words, by Bolt achieving what he’s achieved, he’s skewed our mathematical models.

And yes, it could be steroids. He could be on some undetected performance enhancers, as Ben Johnson so famously was in 1988 and as Tim Montgomery later was. It’s just that the evidence doesn’t indicate that it is; it seems to be that Bolt is simply that much better than everyone else.

13. #13 Sili
August 19, 2009

Knowing (and caring) nothing for sports, I thought drugs too.

I’d really like to see the graph with the doped records on – the ones we know about. That might perhaps give some impression of how out of the ordinary these records are.

But, yes, as a chemist I’m tempted to claim these advances for my branch of science, rather than leave them to you physicists.

14. #14 paul
August 19, 2009

I recommend reading a book by Ed Tufte, which is on the visual display of quantitative data. No personal offense, but your graphs are not fit for professional publication, yet I came to this content from SEED magazine.

15. #15 natural cynic
August 19, 2009

Brett

I’m curious where the theoretical limit of 9.2 seconds comes from. The obvious constraints I can think of are 1)muscle coordination, 2)volume of blood pumped, 3)lung capacity, and 4)bone/tendon/ligament strength. All of these can still be improved on in most healthy humans, and (compared to the powerful runners of the animal kingdom) we are very inefficient with our movements.

1 & 4 can be improved in sprinters. 2 & 3 are not very relevant. I would add that muscle strength might be the major issue, especially strength as it relates to coordination and tendon strength. Bone and ligament strength strength are important more important for injury for injury prevention – the fewer injuries you have [ligament tears and stress fractures] the more you can train. Generation of force is through the muscles [having a high %age of fast-twitch fibers helps] and through the elastic recoil in muscles & tendons.

Metabolically, the 100 meters is done anaerobically. All the force that is needed to run fast for this distance is provided by ATP, creatine-P, and anaerobic glycolysis. Probably something less than 5% of the energy immediately used is provided by aerobic respiration. Lung volume almost certainly has nothing to do with Bolt’s performance. Several years ago it was determined that West Africans and their descendants in the New World actually had relatively small lung volumes compared to Caucasians. East Africans who live at high altitudes are a different story. Aerobic conditioning would be important in a sprinter only for one reason – increasing recovery rate during training [faster recovery of depleted ATP & CP] so that a higher volume of training can be tolerated [and cardiac output stroke volume X heart rate, is a major factor in aerobic fitness].

And… are we actually very inefficient with our movements. One would thing that evolution has had a significant say in this issue.

As for Bolt slowing down at the end, I can think of a couple of good reasons that have nothing to do with tiring. One is to psych out his competitors for future races. The other is to leave a little more room for improvement for financial reasons. Competitors often get bonuses for setting world records. If he only improves a little with each important event he is concentrating on, he could conceivably make more bonuses.

Bolt, like Phelps, is probably a freak of optimal genetics and optimal training.

16. #16 José
August 19, 2009

@Paul
It’s a blog post. Ethan cranks out about 1 a day.

17. #17 Timothy Underwood
August 19, 2009

um, to point out what I’m fairly sure a whole bunch of other people have pointed out— its not actually an exponential curve. And this limiting process doesn’t actually tell us anything about what is physiologically possible.

18. #18 Keith Hanlan
August 20, 2009

This chart is only looking at record times and fails to take into account the overall increasing population as well as the increasing percentage of that pool that is able to compete.

The pool for potential record-breakers is growing. The question that needs to be asked now is how much of the improvement in speed is due to training, nutrition, and environment and how much is due to genetic predisposition?

19. #19 John
August 20, 2009

As a former sprinter from the days before anyone had broken ten seconds for the hundred meters, I think this whole notion of finding an ultimate limit is downright silly. A greyhound dog can easily break Bolt’s record. Why? The animal is biologically different. Different genes. But sprinters have some different genes from ordinary humans, too. Hence the high percentage of fast-twitch muscles and the powerful upper leg muscles. But isn’t it possible that some new sprinter might be born with just the right mutation(s) to hit a top speed ten percent higher than Bolt’s? A new outlier, if you will, but one that would screw up any calculations we make today.

20. #20 Peter C.
August 20, 2009

I think it’s also worth looking at this in terms of wind speed as well as the differences between each subsequent record. I made this visualization: http://bit.ly/p2T73
I’m curious what folks think about it.

21. #21 john
August 20, 2009

sorry – it’s the performance-enhancers…

and they all brought this cynicism on themselves.

22. #22 Isis the Scientist
August 20, 2009

Ethan’s analysis is an inappropriate application of an exponential model to these exercise physiology data. If you look at the data, you’ll notice that data before about 1975 does appear to follow a single exponential trend, but the data after the late 1980s do not follow the same trend. If you remove these data and repeat the analysis, I suspect your answer would be different. The application of this model also requires an assumption of stability of other confounders (diet, training programs and technology, supplement technology). These things changes drastically in exercise training in the 80s. I think what you are seeing there us the introduction of novel technology. It is impossible to know the limit of human performance when we don’t know the available of remaining untapped resources to recruit. Still, the fact that these background confounders are not constant makes a single exponential even more inappropriate here.

A more appropriate, and potentially more interesting, analysis would be to bin the data, regardless of world record status, and compare the functions between bins.

23. #23 BikeMonkey
August 20, 2009

Shorter Isis: Are physical scientists really unable to grasp multiple variables contributing to a single endpoint?

24. #24 Oz
August 20, 2009

I’m a Jamaican. Usain Bolt has been a wonder since he was 15 years old. Was he on steroids then?

25. #25 daedalus2u
August 20, 2009

Bike monkey had a post about body weight and how losing it improves hill climbing.

http://scienceblogs.com/drugmonkey/2009/06/sports_doping_via_elective_sur.php

Losing weight in the upper body would help in acceleration too. Losing muscle, liposuction, breast reduction, osteoporosis limited to the ribs, arms and skull, stomach reduction, tooth extraction, nose job, all would help reduce his mass a little bit and provided it didn’t interfere with training might improve his acceleration and his times.

I think what we are seeing is the acceleration of technology. The “true” parameter that the time should be correlated with is technological advancement, not calendar time.

26. #26 Markk
August 20, 2009

In regards to doping – 13 of the podium finishers since 1995 in the Tour de France have been caught for doping offenses. They all were under a stricter test regime than track athletes. Despite the stories, cycling has lead the way in testing for the last 10 years or so. Despite this, only two of those people ever tested positive for anything from the race, and one of those was because the drug company finally helped the testing (CERA). Drug testers have been bribed to test samples so that athletes know what they can get away with. Localized injection makes it even tougher. Tests are only now starting to catch up, but the whole process is politicized and opaque.

Based on this information, to me, any unusual results in athletics that depend on muscle and metabolism in the last 15 years always mean Physically Enhancing Drugs. I have no evidence except all the other past dream performances that proved to be drug aided, and I kind of feel sorry for Bolt because he can’t really do anything personally to dispel my beliefs, but personally I believe he is using PED’s. Until the test regime is open, clear and technically powerful. I’ll continue to believe this. It is just too bad. The drugs are too good, the physiological knowledge of their use and effects is so much better than it was. This isn’t the speed use by the old runners and cyclists from the 50’s and 60’s this stuff makes you percentages faster.

I love the fact his tall body has changed the way people think the fastest sprinters will look.

27. #27 Redwood
August 20, 2009

Ethan may or may not have used the correct mathematical model in this analysis, but you gotta give him props for triggering one helluva discussion.

Markk, if you’re never going to change your mind about PED’s, does that make you a PEDophile? 😉

28. #28 Brian
August 20, 2009

The curve looks more like a logistic function than exponential since it’s tailing off so steeply in recent years.

29. #29 toby
August 21, 2009

One explanation for Usain Bolt I have heard is that he is a physical outlier – he has two characteristics that are rare in sprinters – his enormous stride that comes from his height & sheer muscular power.

Tall men are usually gangly and awkward, unable to attain the metronomic stride corodination required to be world-class sprinters. Historically, great sprinters are usually more stocky, muscular, medium-sized men and women. It would be interesting to do a count of the number of strides it took Bolt to cover the distance compared to his opponents.

Might it be possible that he learnt his stride discipline by rigorous training from his youth?

All the great sprinters of recent years are descended from West African stock, suggesting a genetic component to their success. However, few from come from West Africa itself, but from the diaspora in the US and British Commonwealth where there is a strong tradition of athletics competition starting at schools level. France and French West Africa have produced few top-class sprinters, but a lot of great soccer players!

There seems to both nature and nurture at work here, which should not surprise us.

30. #30 Enoch
August 21, 2009

Toby, according to what I have read he took 41 strides to get through the race on Sunday. Tyson Gay took 44 1/2 strides to come in second place. Bolt is a rare one as you mentioned. He has the stride frequency of someone shorter with a longer stride. It has also been suggested that his running style is still very raw and can be improved.

31. #31 IanR
August 21, 2009

I certainly understand the idea behind this discussion, but of course it’s not a valid mathematical model, as it’s a bit dubious that world record time will be correlated in any way to the year it is in; the causes of the world record time are complex and do not provide a direct, smooth function the the effect. (And, likewise, the extrapolation to 9.2 seconds is dubious as well, because of the error bars in the data.) That’s not to say the data are not provocative and interesting.

August 21, 2009

Hi think Toby hit the issue here. Usain Bolt may not be an outlier but more a paradigm shifter. Athletes of his height weren’t supposed to be able to sprint that well. Now that he’s so dramatically changed that view the hunt will be on, and there’s every possibility other sprinters of his stature will be discovered.

33. #33 Hanspeter
August 21, 2009

If available, how about plotting the average of the 3 podium winners at each Olympics and World Championships? This should help clean out the curve (if it is a curve).

34. #34 stats question
August 21, 2009

One thing that I’ve always wondered about records like this is whether they reflect 1) an shift in human abilities over time or 2) random sampling.

you can imagine that human 100m dash times are normally distributed across the population, and each year we sample n of them at officially sanctioned events. Even if the population mean doesn’t shift, overall minimum value will slowly decrease over time as more samples are taken.

this suggests that the number of race times recorded each year should affect the rate of decrease in the record, no? I’ve never seen the two plotted together.

35. #35 Mu
August 21, 2009

Regarding the comment that Bolt has been a phenomenon since he was 15 – Ben Johnson admitted to having taken steroids for 7 years before he was caught in Seoul. Testing today might be tougher, but it is always for known compounds. If I develop something new today and keep it to a select few, I might be able to prevent detection for decades. Just look at the East German swim “girls”, with all their admitted doping they got rarely caught due to a sophisticated regime of internal testing before events, if anything showed, the athlete was “injured”.

36. #36 dhogaza
August 21, 2009

First of all, this fixation on the 100m misses the point …

Look what this dude has done to the 200m record!

One thing that I’ve always wondered about records like this is whether they reflect 1) an shift in human abilities over time or 2) random sampling.

Well, before Beijing, Michael Johnson’s 200m was a huge outlier, I remember the NYT plotted the 50 fastest times ever run in that race, and the result was 49 bunched together with Johnson’s Atlanta record off by itself.

Within the 49 bunched together I think your random sampling point holds. On any given day, have two of those folks race each other, and each would have a chance to win.

When Johnson broke the record, the old one had held for 17 years. Johnson’s held for 12 years, and Bolt only beat it by 0.02. At that time, given slight improvements in track surface and footwear and training methods, you could imagine that just maybe, in a head-to-head race, Johnson might beat Bolt. Though Johnson, who was doing commentary, when asked if he wished he were down there racing said something like “the view’s better up here, down there all I would see would be Bolt’s back!”

29 years, two records set before Bolt. Now Bolt has set the record twice in two years, and has lowered the time 0.02 in Beijing and 0.11 in Berlin – 0.13 seconds in two years.

Yesterday, Bolt could’ve turned around and run the last few meters backwards and would’ve won the race.

What’s really scary is that he’s only run one 200m this year and hasn’t been training much for it … what happens when this dude matures and gets 100% serious about his craft?

37. #37 Markk
August 21, 2009

I’ll change my mind about whether I think people are using PED’s when the testing is out in the open, the methods are clear and in the open, and the tests are technically good enough to catch people even if they know when they will be given. Something like the biopassport in cycling is a start. It doesn’t catch people directly, but when you see results that don’t match anyone else, then it helps direct the more expensive looks.

PEDohile? Just the opposite I guess. I do wonder sometimes if things like HGH that could perhaps eliminate the need for most reading glasses, don’t get the money put in that perhaps they should. I do think there is a reluctance to make available the latest PED’s because of this and older peoples lives aren’t as “enhanced” as they might be.

38. #38 Ethan Siegel
August 21, 2009

Hi everyone; thanks for the interesting comments and discussion!

As you all know, I did not make the most rigorous mathematical model possible for this. What I did was take the record times and fit the simplest curve that would model the following properties:

-You assume that there is a maximum theoretical limit. In other words, picture the ideal human being for sprinting in terms of musculature, bone structure, lung capacity, oxygen transport, tendon structure, body fat, limb length, etc. But the person still needs to be human.
-You assume that, as human train better and learn more about themselves and their racing potential, they become closer to the ideal human.

While an exponential will not capture many of the things that many of you have articulated, such as cheating, population growth (in the number of sprinters), and the sporadic rate of improvement. When Jesse Owens ran 10.2, he really outclassed his peers. When Carl Lewis ran 9.86, the second place finisher, Leroy Burrell, ran 9.88, also in sub-world record time. What we’re seeing with Bolt is clearly someone who, for whatever reason, is simply more advanced than his peers. And this article, and the math behind it that I showed you, I think really helps to illustrate that.

And yes, more complex functions that better account for the systematics involved will, indeed, be a better short-term model for the data, and may even indicate a different asymptote/limit than 9.2 seconds. But, that’s still pretty damned fast.

39. #39 jim
August 22, 2009

” It isn’t like humans can’t run faster instantaneously, as Donovan Bailey, for an instant, has been clocked at 12.1 meters per second (27.1 mph / 43.6 kph)”

Actually, to run 27.1 mph instantaneously would be to go from standing still to 27.1 mph in an instant, which only Superman and the Flash can do. I think you mean “for an instant.”

40. #40 Mickey
August 25, 2009

SUPERMAN was written as a comic book which cannot be feasible
even with today’s drugs Nor could the FLASH, since instantaneously
and the word simultaneously are two different meanings.

With that aside as the comment posted should be, all of you
might be overlooking something very obvious. In that last one hundred
years, THAT WE KNOW OF, RECORDED– men and women alike are proving what
the HUMAN body can do. CAN DO, when pushed to its workload of
rate of speed. Strength plus speed equals a lot of power. Come on people, didn’t any of you take physics? At least didn’t you pay attention in mathematics? It’s simple logic! Drugs or not, steroids or not, the HUMAN BODY can do fabulous things, THAT WE KNOW OF.
Hint hint. Imagine what our kid’s kids will be capable of.
Are we suppose to assume that in our future, our grandchildren will
have “medicinal drugs” so they’re brains will run electrical and
non electrical things, to enhance they’re personal psychic strengths
and weaknesses? Come on ladies and gentlemen. Running the hundred meter dash is like drawing on a canvas with no prior training.
Everyone’s abilities depend on their bodies and their brains.

41. #41 Jon D
August 25, 2009

I was reading recently about how the athlete’s distance from the starting gun could mean up to a 150 millisecond difference in their time, due to the time it takes for the sound to travel to their position. The volume of the sound can also create a quicker ‘startle response’ in the athletes closest to the gun, giving them up to 18 milliseconds advantage.
Recently, of course the starter gun is electronic and there is a sounder directly behind each runner to make everything as fair as possible, but try as I may, I cant seem to find when this started happening..

42. #42 Jon D
August 25, 2009

found this, regarding the advantages of being close to the starter gun:

http://www.newscientist.com/article/dn14183-olympic-start-gun-gives-inside-runners-an-edge-.html

I suppose that as long as the placements on the starting blocks are random, or properly rotated, the advantage would average out though

43. #43 BC
August 26, 2009

Re: Comment 24:
I’m a Jamaican. Usain Bolt has been a wonder since he was 15 years old. Was he on steroids then?
Posted by: Oz

No one is claiming that Usain Bolt is just a typical joe enhanced by steroids. The claim is that he’s a top-level athlete (or “a wonder” in your words) who is ALSO enhanced by steroids.

44. #44 max
October 5, 2009

the third commentor, “alexey” is a faggot

45. #45 ben
November 3, 2009

I think that Usain bolt is possibly cabable of breaking the 9 second mark in the next 7 years. He will have the next two olympics and the real prime of his athletic career to work with assuming he doesn’t have any major injuries to hold him back. And after that who knows, someone could come along and break the 8 second mark in the next 100 years.
If statistical modelling were something we could rely on then the above graphs might be believable. However what happens in the real world and what the so called ‘experts’ predict often turn out to be two different things.

46. #46 joe
November 9, 2009

yep, “alexey” is definately gay

47. #47 HH
November 30, 2009

Anyone could run those times with the anmount of doping the Jamaican athletes do.

48. #48 Thomas Stanhope
December 22, 2009

Ethan may or may not have used the correct mathematical model in this analysis, but you gotta give him props for triggering one helluva discussion.

Markk, if you’re never going to change your mind about PED’s, does that make you a PEDophile? 😉 freelance writing jobs

49. #49 Jason Gitters
February 16, 2010

Thomas, so you think you are Mr.Know-it-all?
@Brian, “The curve looks more like a logistic function than exponential since it’s tailing off so steeply in recent years.” This makes no sense.Go on ahead and write my essay, because it won’t be any better. And it;s all about the “biological help” hint hint not the fact that people are more developed.

50. #50 GaryT
March 24, 2010

I certainly understand the idea behind this discussion, but of course it’s not a valid mathematical model, as it’s a bit dubious that world record time will be correlated in any way to the year it is in.
Gary Wii softmod

51. #51 Carol Cline
March 31, 2010

That is a great post and shows you more of what our mind is capable of than anything else. Once something becomes achievable for the first time you will see more and more people break the record because in their mind they know it is achievable.
Carol Cline: Potty Training Pro

52. #52 ChrisYan
April 17, 2010

Great Post!The comments helped with my assignment as they examined how valid an exponential model is when examining 100m sprint history. I’m wondering why a logistic model won’t work. How about a Power Function? Thanks.

53. #53 Castor
April 27, 2010

this prediction is tricky.how many steps, what is the frecuency, how much force apply in the millisecons of contact with the track,how much foward motion from that contact. usain bolt is not the fastest, he is the more efficient 100 meter.less steps, less frecuency, but more distance cover per steps. see if have faster frecuency less time in contact with the track, equal less foward motion. what you thing.

54. #54 Foster
May 8, 2010

Interesting stuff, what I do notice is the career of a runner is very short. 5 years maximum at the top but more like 2 or 3 years. Fosters Beer

55. #55 Anonymous
May 18, 2010

I’m a Jamaican. Usain Bolt has been a wonder since he was 15 years old. Was he on steroids then?
Posted by: Oz ..frozen shoulder

56. #56 jermy
May 18, 2010

the record, the old one had held for 17 years. Johnson’s held for 12 years, and Bolt only beat it by 0.02. At that time, given slight improvements in track surface and footwear and training methods, you could imagine that just maybe, in a head-to-head race, Johnson might beat Bolt. Though Johnson, who was doing commentary, when asked if he wished he were down there racing said something like “the view’s better up here, down there all I would see would be Bolt’s back!apartamentos panama

57. #57 Dallas
May 21, 2010

The graph would be better understood as having two curves rather than one curve with anomalies. The first curve runs from 1910 to about 1985. That curve would suggest a maximum speed for a human running 100 meters at about 9.9. This I believe is the maximum speed a human can run unaided by technology.

From 1985 on, a different trend emerged. The different curve that emerged suggests that world-class sprinters from 1985 to present are using technology to increase their maximum speed. Technological enhancements would include not only illegal practices such as using steroids, but also legal practices such as neuromuscular electrical stimulation and consumption of scientifically optimized nutrient cocktails.

It is impossible to predict the limit on speed of technologically enhanced athletes. That would depend on what technologies were used. some technologies could radically enhance human capacities. If, for example, nano-technology and genetic engineering ever enter into professional sprinting, then we could see humans running much faster than we do now, perhaps a sub-5 100m would even be possible.

58. #58 haunted places
June 4, 2010

um, to point out what I’m fairly sure a whole bunch of other people have pointed out— its not actually an exponential curve. And this limiting process doesn’t actually tell us anything about what is physiologically possible.

59. #59 reduce cellulite
June 22, 2010

The reason why we achieve lesser time in the 100-meter run or any runs there is from the past years until now is on the capacity of humans to develop better overtime. Because of medical science, research, and technology, the lifetime health condition and capacity of humans do really improve. Performance do really improve because of rigorous trainings, and the new ways and means of bringing oneself better.

60. #60 Men cams
August 6, 2010

I think that Usain bolt is possibly cabable of breaking the 9 second mark in the next 7 years. He will have the next two olympics and the real prime of his athletic career to work with assuming he doesn’t have any major injuries to hold him back. And after that who knows, someone could come along and break the 8 second mark in the next 100 years.
If statistical modelling were something we could rely on then the above graphs might be believable. However what happens in the real world and what the so called ‘experts’ predict often turn out to be two different things.

61. #61 HGH reviews
August 25, 2010

Physiologically, you’ll accept to ask addition who knows bigger than I do what the attached agency is. All I did was fit an exponential to the apple almanac times, which will accord you an antecedent point that slopes bottomward and asymptotes to a bound value. 9.2 abnormal is that amount in this case, which is abundant faster than antecedent estimates that I’ve heard (which were about 9.35 seconds). In added words, by Bolt accomplishing what he’s achieved, he’s skewed our algebraic models.

And yes, it could be steroids. He could be on some undetected achievement enhancers, as Ben Johnson so abundantly was in 1988 and as Tim Montgomery after was. It’s aloof that the affirmation doesn’t announce that it is; it seems to be that Bolt is artlessly that abundant bigger than anybody else.

62. #62 los angeles graphic design
September 27, 2010

It is a new line in my life and it is so awesome to find on the topic I want to deal for the rest of my life. Hopefully, I am the one that will be on one wave with you.

63. #63 joshua
September 30, 2010

Hmm…this looks like one of the medicine essays on the Olympics! but I think there’s more to that than just math! I mean,if we think about it,over the last few years we have seen a real great deal of cheaters in such competitions. Now,I’m not stating anything, personally I ,believe that the human body can improve and we will see guys breaking their own records over and over again! But I can’t help but wonder whether there was some modern technology used in order to receive such a result…I guess,it’s pretty possible…

64. There ought to be some physical, anatomical limit to how quickly we can — starting from rest — cover 100 meters. Luckily, simply modeling this mathematically — by an exponential — will tell us what the world record progression ought to look like, and should tell us what the theoretical limit of the human body is.

65. #65 Body Detox Diet
November 3, 2010

This is a very interesting observation. Looking at Bolt’s record, I think he will break his own record again soon. His name is just coincidence or what. Just like lightning bolt.

66. #66 Sam
November 4, 2010

I was reading recently about how the athlete’s distance from the starting gun could mean up to a 150 millisecond difference Google Redirect Virus in their time, due to the time it takes for the sound to travel to their position. The volume of the sound can also create a quicker ‘startle response’ in the athletes closest to the gun, giving them up to 18 milliseconds advantage.

67. o material de nteresting, o que realmente noto é a carreira de um corredor é muito curto. Máximo de 5 anos em cima mas mais como 2 ou 3 anos

68. #68 woodworking plans
November 10, 2010

Nice post. Usian Bolt is just like an outlier to me. Like Mike posted, it’d be very probable that he would break his own record again.

November 13, 2010

really nice post, the picture actually reminded me of said aouita

70. #70 classification essay
November 24, 2010

After Haile Gebrselassie ran the marathon in 2hr 3min 59sec in 2008 there was renewed speculation over whether anyone could run the distance in under two hours…

71. #71 Billiard games
December 4, 2010

Usain Bolt is going to stay the fastest men on earth for the next few years. But I’ve read he wants to become a soccer player in the future. I hope not!

72. #72 Don
December 4, 2010

I think he’ll be the world record holder for a very long time. This guy is just owning all the rest. I guess it will take some time before he can be beaten. Maybe they can try billiard games? 🙂

73. #73 Ted Sneebs
December 14, 2010

I remember watching Usain Bolt(great last name by the way,eh?) break his own record in the 100 Meter dash. It just seems like that guy has no limit to how far he can push his body. It would be interesting to track the advances in running tech and performance enhancers(legal of course) over the same amount of time. I would not be surprised if the graphs were correlated. Thank you, by the way, for doing the math on the graphs and coming up with a reasonable “fastest time” for the 100 meters. I could see how 9.2 would be possible. Given the smaller increment decreases we are seeing now, we most likely have reached a plateau for now. It may not be in my lifetime, but I am certain that record will be broken. That’s how it has always worked . . .kind of like the golden rule of records. Do unto others, ya know. They are set in order to act as a carrot. Why else would we keep track of them?

74. #74 samsung blu ray disc player
December 15, 2010

Usain Bolt stands up for his name – a bolt of lightning. He’s going to break his own record because he’s still young and got a lot of time to improve. That guy is simply amazing!

75. #75 samsung blu ray disc player
December 15, 2010

Usain Bolt stands up for his name – a bolt of lightning. He’s going to break his own record because he’s still young and got a lot of time to improve. That guy is simply amazing!

76. #76 samsung blu ray disc player
December 15, 2010

Usain Bolt stands up for his name – a bolt of lightning. He’s going to break his own record because he’s still young and got a lot of time to improve. That guy is simply amazing!

77. #77 samsung blu ray disc player
December 15, 2010

Usain Bolt stands up for his name – a bolt of lightning. He’s going to break his own record because he’s still young and got a lot of time to improve. That guy is simply amazing!

December 15, 2010

Usain Bolt will go on winning games after games. No one can beat him at the rate he’s running.

79. #79 hannah
December 20, 2010

yeah, he’s the fastest running man alive in the whole world, well as you can see on the pic, almost .05 or .10 sec is the distance of the other runners. Meaning they need more rice to eat to surpass him..lol

Hannah
emr systems

80. #80 PMP
February 2, 2011

I was the fastest among the 30 students in our class- that was before when I was in grade school.

81. #81 lean consulting
February 2, 2011

Oh yeah.. Great.. I agree with you hanna. He’s the fastest of all.

82. #82 aluminium carry cases
February 6, 2011

Nice post. Usian Bolt is just like an outlier to me. Like Mike posted, it’d be very probable that he would break his own record again.

83. #83 art research
February 21, 2011

This is really amazing! I would never consider about using math towards sport results. We really can make a suggestion about humans body limits.

84. #84 regenerectusa.com
February 22, 2011

Usian Bolt is the fastest man I have ever scene. I remember how fast Maurice Green was and he blows him away. I can’t wait for the next Olympics.

85. #85 essay help
March 3, 2011

This is really unbelievable when i see the records, but at the same time i feel sad when few of the fastest human being are charged with the steroid and other medicines allegations..

86. #86 copywriting nottingham
March 3, 2011

He will have the next two olympics and the real prime of his athletic career to work with assuming he doesn’t have any major injuries to hold him back.
Phil @ Copywriter Nottingham

87. #87 online class
March 7, 2011

wow,, great,, Congratulations to the winner of the fastest human.

88. #88 Noah
March 10, 2011

It would be interesting to track the advances in running tech and performance enhancers(legal of course) over the same amount of time. I would not be surprised if the graphs were correlated. Thank you, by the way, for doing the math on the graphs and coming up with a reasonable “fastest time” for the 100 meters. I could see how 9.2 would be possible. Noah @ orkut scraps

89. #89 ppc account management
March 16, 2011

The charts are amazing too see how quickly (pun intended) times have reduced in such a short time period. We have learned so much about the physical human body. Why can’t we beat Cancer or figure out how to use the other 75% of our brains. Great post. Thanks

90. #90 Houston Lawyer
March 18, 2011

Whether this is due to improved training, better living conditions yielding better athletes, or what-have-you, I think we may be artificially pushing that curve lower. 9.2 seconds may still be the limit, but I’d wager we’re getting there faster than the curve above would represent.

91. #91 bail insurance
March 21, 2011

Not sure I agree that “better living conditions” has yielded better athletes. Kenya certainly does not have great living conditions and they still produce unbelievable runners. I think it’s our better understanding of the human body limitations, or in other words, pushing our bodies’ limitations. Thanks.

92. #92 Self Storage Buisness
March 21, 2011

I love the math and agree that their has to be a physical limit to a man’s speed regardless of conditions. Considering that cheetah is physically built for speed and has been consistently documented at achieving tops speeds within a close range for decades instead of getting faster through evolution, thus showing that speed for all things has its limits.

93. #93 akon 2011
March 28, 2011

Whether this is due to improved training, better living conditions yielding better athletes, or what-have-you, I think we may be artificially pushing that curve lower. 9.2 seconds may still be the limit, but I’d wager we’re getting there faster than the curve above would represent.

94. #94 plastic enclosures
March 29, 2011

It’s amazing that in this generation they are hitting these speed numbers. Typical food is not healthier, it’s hormone injected. I wonder when the next world class champion will come from a world power nation….they won’t.

95. #95 Key Essay
April 8, 2011

Being someone who is chasing after three world records and being very close to break them myself, I can say that records are constantly changing.

They are changing because training methods have improved and are now more efficient because we understand the human body better, and nutrition has gotten better with the introduction of high-quality supplements that, when combined with the right food, will enable the human body to grow and become capable of things we can’t imagine.

96. #96 Jessica
April 8, 2011

Quite interessting to read about about the fastest human. I think that there this a big role of genetics in play. However it is fascinating to see what people can do if they live up to their potential. Jessy from reisegutscheine finden team

April 20, 2011

omg, very fast!
great post! favorited 😀

98. #98 jovani prom dresses
May 4, 2011

This is quite interesting to learn. How amazing this man to run that fast. He should be gifted.

99. #99 web design chicago
May 4, 2011

I wish I can run as fast as this man. He is really a legend in track & field event, most especially for this 100 meter-run.

100. This is amazing! Thank you so much for sharing this article! I can’t believe that human bodies are capable of such records….makes you want to work out a little more often!

101. The mathematical presentation of the first man to run the 100 meter dash in under 9.7 seconds is incredible. I ‘ll like to quote him with a title of CHEETAH or LEOPARD.

102. #102 Equine Antibiotics
May 19, 2011

This man is truly amazing. Hope I can be like him soon.

103. #103 Marco
May 27, 2011

Very Interesting Post!
When it comes to drugs lets assume innocence until proven guilty.
With that said
You have the invention of:
starting blocks (instead of dirt holes)
track spikes (which keeping getting lighter and different spike locations under the shoe)
mondo tracks (even faster)

Bolt is an outlier because of his combined height and speed.
Speed for humans comes from stride length and stride frequency as well as energy forced into the ground to propel a runner forward. Bolt is a very tall sprinter, and mondo track surfaces rebounds the most energy back into a sprinters legs. (I run track and there is a huge difference in mondo and a regular track)

Other points

the world record would likely be faster if every person in the world trained and ran the 100m dash.
For example California and Texas produce the most athletes in the US do to the huge pool to draw from versus New Mexico or Nevada.

It would also be amazing how fast humans would get if we were still evolving through survival of the fittest. Through technology we keep the weak and strong in our gene pool. So we lack continued drastic improvements. If Bolt had Children with Veronica Campbell-brown (a top female sprinter) and their children had children with another very fast people and so on, someone in their gene pool would easily break the record.

Bigger money sports take away track athletes. Many football/tracksters quit track for football when going to college even if they post similar times to bolt when he was 17 or 18.

Trial and error coaching. track workouts are for the most part educated guesses on how to make someone faster. if tyson gay and bolt switched coaches they both could switch places in with their times or both be running slower. As time progresses more workout ideas are used. Some kept some trashed. Even then a good workout does not work for every athlete the same.

I also wonder what is his top speed during the race and how long he held it. it must be around 30 mph or more
can one of you math guys create 10m splits then use its time to find his speed

104. #104 Indianapolis SEO
June 24, 2011

I think it is amazing that trained athletes can reach those types of performance thresholds. Rather or not the chart is going to be completely accurate is another story, but time will tell!

105. #105 Surety Bail Bond
June 27, 2011

It amazes me that people can run that fast, and to think that it could be approved upon is even more amazing. Not sure the graphs are 100% reliable, but when predicting future stats what is?

July 18, 2011

if tyson gay and bolt switched coaches they both could switch places in with their times or both be running slower. As time progresses more workout ideas are used. Some kept some trashed. Even then a good workout does not work for every athlete the same.

107. #107 FHA Training
July 20, 2011

Great example that should be used in text books to make learning math more fun.

108. #108 Orthopaedic Treatment
August 11, 2011

Due to the advantage technology we are having, it shows that the training program that they have made is paying off

109. #109 tim n
August 31, 2011

im working on a paper correlating chronological technology advances including track type, diet and drug usage versus official performances using a variety of precisely measured sports and a wider sample of elite competitor age ranges.

additionally im looking at the top place getters- not just the winners.

i believe that this is the key to sorting this debate out once and for all. we know in general that steroids were lpayed with in the 1930s and became popular in the late 1950s/early 1960s and were a staple by the mid 1960s and were rife in the 70s and early 80s then potency became an issue due to detectability after the late 1980s and until now, but GH also came into usage from the late 1970s. Anyways, we can only suggest that the differences between general populations of assumed non drug users and hypothetical testing of other populations would yield correlation. in other words young athlete national and world record progression over many years – other known non drug tested sports such as powerlifting, and the relative differences between genders. only then will we be able to cut through all this speculation with some more confidence. looking across the reams of data i have already it seems clear that if we continued along the drug fuelled path of the 1960s and 1970s we’d be already below usain’s performance- or arguably at it by now…that is combining the other progressions weve seen in the last 30 years of sport combined with the rapid advances- particularly in the 1970s female record sets. Youth records have gotten marginally better over the last 40 years, but the outliers havent changed much. in the mean time powerlifting has continued to improve, but shows a decreasing slope versus time- its always been drug fuelled. (im talking raw not using lifting shirts)..and so on..without writing the paper here, you get the idea. i.e. it needs a variety of data sources across a variety of relevant conditions to provide basis for argument- even before the stats and maths are done.

110. #110 spider
September 15, 2011

bolt’s a legend!

111. #111 terrence
January 1, 2012

great to know about the world’s fastest athletes, l am one of them under training jus want to come out & drop the world by a blow, ol those record ts true our generation can takle ’em, it wil be an advantage to someone who will remember the name BULS01, year 2013 m gonna scoop t, training record 09.7 in a heavy gravel road, 23yrs, 1.8m tall, 70kg weight, l train my self personally, willing trainer my number z 00263772449081. Aslong as the sunshine everything z possible.

112. #112 terrence
January 1, 2012

great to know about the world’s fastest athletes, l am one of them under training jus want to come out & drop the world by a blow, ol those record ts true our generation can takle ’em, it wil be an advantage to someone who will remember the name BULS01, year 2013 m gonna scoop t, training record 09.7 in a heavy gravel road, 23yrs, 1.8m tall, 70kg weight, l train my self personally, willing trainer my number z 00263772449081. Aslong as the sunshine everything z possible.

113. #113 Marco Capo
July 27, 2012

Quiet simplistic in my opinion…

114. #114 Chelle
July 28, 2012

I once met him a few years ago and shook hands.

… looking forward too see him break his record again next sunday.

115. #115 Jim Thornton
August 6, 2012

I really enjoyed your post. Applied statistical thinking seems to always generate questions about the model, etc. Real life seems to give us challenges about having enough data points, how controlled the conditions are, and it just isn’t as neat as pure numbers.

I appreciate the start to the process and the thought and conversation it stimulated.

116. #116 Rita
Brazil
August 13, 2012

Great post. Congratulations, the charts are amazing!

117. #117 Sandeep Sabir
August 26, 2012

Very interesting statistics. I recently watched documentary video about Usain Bolt. It is a must match documentary for those who love this legend.

118. #118 minicunas
spain
February 25, 2014

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119. #119 mURTAZA
United Kingdom
March 17, 2014

I agree with many people’s comment. A curve in the graph doesn’t necessitate anything. Bolt was taller than the average sprinter and also has long stride lengths. Compared to Donovan Bailey his top speed is not as fast or even some compared to some of his Jamaican counterparts.

120. #120 platos de ducha
September 17, 2014

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121. #121 james
June 26, 2015

Bolt is just talented, their is nothing like he is taller than the counterparts or something, this guy can sprint. i appreciate this kind of article.

122. #122 Isabell
South Korea
November 15, 2015

Where is all of this data from? It would be great if I could get a table table for this set of data that these graphs made out of.
Thx!