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.
Physical Science
Comments
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.
Posted by: Joshua Ochs | August 19, 2009 8:25 AM
I suspect the math behind this performance is actually chemistry...
Posted by: Interrobang | August 19, 2009 8:53 AM
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?
Posted by: Alexey | August 19, 2009 8:54 AM
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.
Posted by: Mu | August 19, 2009 8:56 AM
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...
Posted by: Mike | August 19, 2009 9:23 AM
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.
Posted by: Sophos | August 19, 2009 9:29 AM
Posted by: Bob O'H | August 19, 2009 9:31 AM
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.
Posted by: Ethan Siegel | August 19, 2009 9:40 AM
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!
Posted by: Brett | August 19, 2009 10:06 AM
Of course, we all know the _other_ explanation for surprisingly superior performances...
Posted by: Stephen Downes | August 19, 2009 10:10 AM
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...
Posted by: Dirk dB | August 19, 2009 10:14 AM
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.
Posted by: Ethan Siegel | August 19, 2009 10:16 AM
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.
Posted by: Sili
| August 19, 2009 11:47 AM
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.
Posted by: paul | August 19, 2009 1:43 PM
Brett
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.
Posted by: natural cynic | August 19, 2009 9:03 PM
@Paul
It's a blog post. Ethan cranks out about 1 a day.
Posted by: José | August 19, 2009 9:06 PM
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.
Posted by: Timothy Underwood | August 19, 2009 11:56 PM
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?
Posted by: Keith Hanlan | August 20, 2009 4:26 AM
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.
Posted by: John | August 20, 2009 6:15 AM
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.
Posted by: Peter C. | August 20, 2009 9:19 AM
sorry - it's the performance-enhancers...
and they all brought this cynicism on themselves.
Posted by: john | August 20, 2009 11:05 AM
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.
Posted by: Isis the Scientist | August 20, 2009 1:49 PM
Shorter Isis: Are physical scientists really unable to grasp multiple variables contributing to a single endpoint?
Posted by: BikeMonkey | August 20, 2009 2:22 PM
I'm a Jamaican. Usain Bolt has been a wonder since he was 15 years old. Was he on steroids then?
Posted by: Oz | August 20, 2009 2:29 PM
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.
Posted by: daedalus2u | August 20, 2009 4:27 PM
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.
Posted by: Markk | August 20, 2009 5:22 PM
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? ;-)
Posted by: Redwood | August 20, 2009 6:43 PM
The curve looks more like a logistic function than exponential since it's tailing off so steeply in recent years.
Posted by: Brian | August 20, 2009 8:13 PM
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.
Posted by: toby | August 21, 2009 1:09 AM
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.
Posted by: Enoch | August 21, 2009 5:31 AM
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.
Posted by: IanR | August 21, 2009 6:22 AM
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.
Posted by: David Steadson | August 21, 2009 6:29 AM
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).
Posted by: Hanspeter | August 21, 2009 7:55 AM
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.
Posted by: stats question | August 21, 2009 9:05 AM
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".
Posted by: Mu | August 21, 2009 9:09 AM
First of all, this fixation on the 100m misses the point ...
Look what this dude has done to the 200m record!
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?
Posted by: dhogaza | August 21, 2009 9:34 AM
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.
Posted by: Markk | August 21, 2009 11:23 AM
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 start with an initial "best time by the best human".
-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.
Posted by: Ethan Siegel | August 21, 2009 3:55 PM
" 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."
Posted by: jim | August 22, 2009 6:18 AM
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.
Posted by: Mickey | August 25, 2009 1:08 AM
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..
Posted by: Jon D | August 25, 2009 6:23 AM
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
Posted by: Jon D | August 25, 2009 6:25 AM
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.
Posted by: BC | August 26, 2009 8:05 PM
the third commentor, "alexey" is a faggot
Posted by: max | October 5, 2009 3:49 PM
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.
Posted by: ben | November 3, 2009 2:38 PM
yep, "alexey" is definately gay
Posted by: joe | November 9, 2009 8:11 AM
Anyone could run those times with the anmount of doping the Jamaican athletes do.
Posted by: HH | November 30, 2009 5:30 PM
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
Posted by: Thomas Stanhope | December 22, 2009 5:19 AM