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Thursday, August 25, 2011

Pistorius: the "12 sec advantage" and mechanical superiority

Revealing the Pistorius science part 3: "We knew all along", as the debate turns to an argument
"We conclude that the moment in athletic history when engineered limbs outperform biological limbs has already passed"
That was the concluding statement from the first of a series of back-and-forth articles that were published in the Journal of Applied Physiolgy in November 2009.  It was written, remarkably, by two of the scientists who had in fact been involved in the research that was presented to the CAS when they made the decision to legalize Oscar Pistorius' carbon-fiber limbs 18 months earlier.  A research team of seven conducted the testing on Pistorius in Peter Weyand's laboratories in early 2008, and the fact that two of them would come out with a completely different conclusion after the hearing begs many questions - why did the difference in opinion not emerge sooner?  Was that difference deliberately snuffed out and 'hidden'?

Note that neither Weyand nor Bundle were present at the CAS hearing, and that begs a question or two itself.  Why did Weyand not attend the CAS hearing, or at the very least, Bundle, since they were of the differing opinion?  Was pressure applied to ensure that CAS did not hear a word of this possible advantage, and did they rule based on incomplete and 'manipulated' information?

This conclusion is the subject of this final piece in the full review of the Pistorius evidence.

The role of the lawyers, and the scientific integrity of the process

The paper emerged 18 months late, along with a Weyand saying: "From the instant we collected the gait-mechanics data and saw how short his swing times are, we said to the group [of scientists they were working with] that it's really clear he's got an advantage".

So to be clear - the evidence existed, and so did the interpretation that it provided an advantage.  But for whatever reason, this did not emerge until a year and a half later.  The "group" had clearly reached some agreement that this interpretation of an advantage would remain "hidden", because Hugh Herr and Roger Kram went to the CAS and presented a united front, saying that there was no scientific basis for an advantage based on the IAAF testing (if you read the CAS verdict, there is not a single mention of this possible interpretation).  Where were Weyand and Bundle in this process, you may be wondering?

Even if you accept that there are two interpretations of the data, you'd think that this one should at least have presented or discussed.  It was not.  And given that Weyand was convinced about it, you really do have to wonder what happened behind the scenes, especially when you consider that the research and the resultant published research paper was done as a result of a "deal" between the scientists and Oscar Pistorius' lawyers (in all this, don't underestimate the legal and PR machines in the background).  This is the main issue about the scientific process that I have questioned, along with what I explained in the previous post.

Too narrow a question and more selective omission

There is the argument that the CAS-proceeding determined a very narrow approach to the scientific question, which had really only one goal - to disprove the IAAF's findings.  In other words, the CAS process was not interested in the entire truth, but only in evaluating the evidence gathered by the IAAF.  And there's no question that the IAAF started off with a very narrow research question.

By extension, Pistorius' scientific team were interested only in the "truth" that would, among other things, eventually see them add distance runners to the control group until Pistorius looked similar to able-bodied athletes.  Effectively, the previous research had "set the bar" and they jumped over it, using the methods I explained yesterday.  A narrow finding got even narrower, and the whole truth did not emerge when it could have.  In all this, there was reason to suggest an advantage but the scientists did not make it known at the time, even if it was only for the purposes of debate.

Taking this into account, and adding in the fact that the research to clear Pistorius had very obvious omissions and false comparisons with distance runners when they knew what the sprinter-comparison would have revealed, you start to see that things really were not what they appeared to be with this "independent scientific process".  You may make up your own minds about what it means when scientists selectively leave out able-bodied sprinters and compare a sprinter to distance runners?  Or what it means when scientists recognize the possible advantage but fail to mention it at a hearing on advantages?  It strikes me as strange at best, manipulative bordering on dishonest at worst.

For a great read on the process and how twisted it seems to have been, David Epstein of Sports Illustrated provides the information, and I'd highly encourage you to read it here.  When you consider this, as well as the information we discussed yesterday on how the able-bodied group was manipulated to find

It then took 18 months, but when the paper was eventually published, it revealed a big split in the camp, and a group of seven was split into two - Weyand and Bundle on one side, arguing against Herr and co.  Eventually, it got to John McEnroe-like shouts of "you cannot be serious" in a scientific journal, and nothing came of it.  But it is this debate that I will end of with in this look at the science on Pistorius.  And then we can get on with enjoying the IAAF World Champs and on-track action.

The mechanical aspect of the debate

So far, we've seen that the IAAF testing found completely different mechanics and suggested less metabolic energy demand.  The Herr-Weyand study for the CAS hearing managed to find that Pistorius was "similar" to able-bodied elite and sub-elite distance runners.  Had they compared him to other sprinters, he was anything from 2 to 7 Standard Deviations different.

And then came this debate, which moves us from the metabolic to the mechanical - as I said in the first post, I believe the mechanical data provides the explanation for the metabolic and physiological findings of reduced VO2, and the implications for reduced metabolic demand.  And so that's the context of understanding this debate.

The "12-second advantage" - Weyand's calculation and the rationale behind it

Weyand and Bundle produced an article that explained the mechanical basis for an advantage, and concluded by estimating how much slower Pistorius would run if his carbon-fiber blades behaved like normal legs.  12 seconds was their answer, and that conclusion made their paper easy to dismiss for those who wanted to dismiss it.

So with hindsight, it may have been disingenuous to try to estimate the time advantage.  You can appreciate why they'd want to do it - it makes the debate more 'tangible', easier to conceptualize, but the problem is how it was done.  It took a few assumptions, and produced an advantage of 12 seconds, which was very easy for the likes of Herr to dismiss as too large to be realistic.  And that's fair enough.  But it shouldn't stop us from looking very closely at what Weyand is saying, how that number is estimated.  In order to understand where that number comes from, you first have to understand what it was that Weyand was arguing was the reason for the advantage, which is a good place to start.

A word on Weyand to begin with.  For all Pistorius' talk about how Herr and Kram and co were the best in the world, the truth is that Weyand is the world's leading biomechanist in sprint running.  Look him up on Pubmed and it's clear that he has done the seminal work on sprinting mechanics.  He is, you might say, an "F1 Driver" when it comes to mechanics...

And one of the key articles by Weyand is this one - a paper published in 2000 on how sprinters speed up, and it contributed the first key point in the debate.  Below is the key figure from that paper (sorry for not redrawing it - not enough time)

What you are looking at above are the swing times, in seconds, of able-bodied sprinters at a range of different speeds.  Swing time is the time spent by each foot in the air.  That is, it is the time taken from when the foot leaves the ground until when it next lands.

The runners are measured at a range of speeds, from 6m/s up to 11.1m/s.  Weyand adds Olympic runners measured on another occasion for comparison, but I'll disregard these three because there are questions about how accurately they are measured.  Besides, running at 40km/h is pretty much Olympic 200m level, and much faster than a 400m runner would run, anyway.  Pistorius ran at 10.8 m/s, so you don't need those Olympic athletes to make this case. 

The thing that should jump out is that there is no change in swing time as the runner speeds up.  Whether you are running at 6 m/s (21.6 km/h) or 11.1 ms (40 km/h), your swing time is pretty much the same. Even sprinting downhill, swing times don't get faster than this.

It's extremely tight, and that's crucial, because the key point about that is that in able-bodied runners, it is just not possible to swing the leg any faster than shown in the figure above, and so by the time we run 21km/hour, we are already at this "limit" for how quickly we can reposition our legs.  In Weyand's own words:
 "Clearly, with athletes with intact limbs, there's a lower limit to how fast they can reposition their limbs"
As a result, if you want to get faster, you have to do so by applying more force to the ground.  There's a downside to this - more force means more muscular work.  More muscular work means more metabolic energy cost, and two potential limits to how fast someone can run - first is the inability to generate that force, and second is the metabolic cost of doing the work, running at a given speed.  And that brings us to the theory of sprinting, and the Oscar Pistorius finding

Sprinting mechanics, and how Pistorius is "off the charts"

There are three things that limit the speed of a runner: 1) how quickly the limbs can be repositioned for the next step, 2) the distance traveled by the body while in contact with the ground and 3) the force applied to the ground in relation to body weight.

Above, I've shown that the evidence says that the ability to swing the leg is constrained regardless of running speed - 0.373 ± 0.03 seconds was the average ± SD.  Here's what Oscar Pistorius' mechanics look like compared to the able-bodied SPRINTERS when running at 10m/s in the CAS testing (about 400m pace):

So, longer contact times, shorter swing times, shorter aerial times, lower vertical force but not lower peak vertical force.  Using the statistical method that Herr and Weyand used for VO2, where anything more than 2SD different from able-bodied runners is different, it's clear that Pistorius is mechanically very, very different to able-bodied sprinters and crucially, these differences all provide significant sprinting advantages.

First, Pistorius has stride frequencies 16% faster than any athlete ever measured (and 9.3% faster than elite 100m sprinters - data not shown, and again, not worth including because of the measurement method).  It's a mass effect - the carbon fiber prosthetics weigh 3kg less than able bodied limbs below the knee, and so they can accelerate much faster, for less force.

The high stride frequency was the result of the speed of repositioning the limb.  That is, Pistorius' swing times are so much faster than any other runner measured, that Weyand described them as "off the charts".  At top speed, Pistorius has swing times of 0.284 s, which is 21% faster than sprinters - it's also 4 SD different from the other sprinters tested in this study, and 2.7 SD faster than the entire collection of sprinters tested in Weyand's lab in previous studies using the same methods.

Being able to reposition the limb so fast (11% faster than the fastest athlete in the group tested in the laboratory) has some major theoretical advantages.  In Weyand's own words:
"Oscar is off the charts. Clearly, with athletes with intact limbs, there's a lower limit to how fast they can reposition their limbs. With Oscar, if you make that lower limb twice as light, that moves that lower limit.  He repositions his limbs so fast that he doesn't need to get his body back up into the air so high like other sprinters, and that lowers the force he needs to generate.  The muscular forces he has to generate are less than half of what an intact sprinter has to generate to go the same speed." - quoted in SI article
Then there is contact time - Pistorius spends 14% longer in contact with the ground, which means the horizontal distance traveled during ground contact is higher (see the three factors limiting speed above), and it means that the force production required to run at a given speed is substantially reduced - it was 5.2 SD lower than the able-bodied controls in this study.  Interestingly, peak vertical force was lower, but not statistically (2SD) different from able-bodied controls.

How did he estimate 12 seconds?

So the next thing is to take the above measures and ask how did Weyand estimate a 12-second advantage?  There are a few assumptions that have to be made to do this, and as mentioned, I think Weyand did his own argument something of a disservice to not make a more "conservative" adjustment.  It's much the same as when I tried recently to explain how 6.2W/kg is a limit for cycling without doping.  You have to make assumptions, but if you make them sensibly, always making the assumption that goes AGAINST the thing you're trying to prove, then they're extremely valuable (I can elaborate on this more in the discussion if it comes up).

What Weyand did is move Pistorius' mechanics back into the able-bodied group.  That is, he looked at swing times and contact lengths and asked how Pistorius would run if those were "normal", or equal to the average of the able-bodied group.  So, the average swing time for the group was 0.359s so Weyand corrected Pistorius' swing times to that value. He also adjusted the contact length to 1.05m (to match the normal leg length-contact length ratio in able-bodied athletes) and average force produced during the stance phase.

The result was that he calculated that Pistorius' top speed would change from the measured 10.8 m/s to 8.3 m/s.  Next, using a similar method to that which Herr & Kram had used at the CAS to show that Pistorius DIDN'T have an advantage, Weyand estimated a 200m time of 27.3s and a 400m time of 61.7s, which was 12 seconds slower than his lab time-trial at the time of testing (49.8s)

Now there are two reasons why this 12-second estimate may be too high, and both relate to the inputs that estimate the performance.  The first is Pistorius' speed at VO2max.  During the testing, Pistorius' speed measured at VO2 max was 5 m/s (or 18 km/h, which is a sub-elite level), and this is factored into the prediction.  An elite sprinter would arguably reach a faster speed than this, and this increase (say to 6m/s, or 20% faster) would reduce the estimated time and thus the calculated advantage.  There is no question that Pistorius was less than in peak shape at the time of the testing - he fatigued at 15km/h after only 5 minutes, for example.

This has implications for both the findings of the study (Pistorius probably uses even less oxygen when highly trained than in the study, and that makes him even more different than was measured), and for the 12 second advantage.

The actual advantage - smaller than this, but nevertheless present

I think it's important to realize that the problem may be the INPUTS into Weyand's equation, and not the concept of the calculation.  If Pistorius had been 10% fitter, then those predicted times would drop, and the advantage predicted would be much smaller.  But given his state of training, it's actually not an unreasonable projection. 

The other issue is whether it's appropriate to correct Pistorius highly different mechanics to the average of the group.  It would perhaps have been better to correct them to say 2 SD from the average, so that he's still statistically similar, but at the extreme edge of the normal range.  If that had been done, then instead of adjusting his swing time to 0.359s, they would have made it 0.321s.  That calculation would produce estimates for performance that are closer to Pistorius' current times, but still faster.  I don't have the formula (or time) to make all these inputs now, but if the VO2max speed was 10% higher, and if the corrected mechanics were 10% lower, then the calculated advantage over 400m would drop considerably from 12 seconds.  And that is not nearly as easy to throw out as unreasonable.

Weyand didn't do this, and unfortunately the size of the advantage he did calculate gave ammunition to shoot the theory down.  That would wrong - the theory is correct, and the evidence based on mechanics is very strong, all that needed to change were the adjustments, the inputs to the equation.

So how large then might the advantage be?  Obviously, it's impossible to say, unless there is more testing.  That's not going to happen because Pistorius would never agree to it now - the science was only important until it cleared the blades for use.

I'd suggest another method that would give a good indication, using Pistorius' 400m and 200m race times, and then comparing them to other 200-400m athletes.  This works because the performance at one distance is a great predictor of performance at the other, and so when you look at this, compared with pacing, you get a good idea of how much he GAINS overall in a 400m race.  That is is, net loss would be canceled by net gain.  But not to leave you hanging, but I'll save this for another occasion, in the interests of time (it's a lengthy explanation of pacing strategy).

The rebuttal

Herr and the rest of the intial group produced a counter-point, and there were two main "points of attack".  One was video footage of other runners, to show that Pistorius was not really as different as Weyand claimed.  The problem is, you can't use normal video footage to make this case, the resolution is just too low to be accurate - that's the reason why I wouldn't include the Olympic or World Champion level runners in the control group.  Weyand did this in his subsequent response to Herr, and it saw the debate get a little side-tracked - the truth is that every finding in Weyand's initial report, and what I've summarized above, was produced in the laboratory, with very high resolution cameras, whereas Herr's rebuttal was based on inaccurate video footage.

Then Herr also reveals the hypocrisy of the statistical method used when it suited the desired finding earlier in the CAS process.  He writes:  
"Pistorius’ leg swing time of 0.284 s at 10.8 m/s is nearly 3 SD faster than that mean (It's actually 4 SD from the mean, but who's counting?).  However, leg swing times as low as 0.31 s for Olympic 100-m medalists at top speed have been reported"

So firstly, the Olympic runners were measured with low-resolution video, and Weyand responds to this with the example of the same athlete measured in the lab and on TV, and the TV times are 16% faster than the accurate lab times.  Clearly, you can't base an argument on TV footage.  The case I've made in the post above doesn't use TV footage, and is very compelling.

But more than this, having set up the 2SD requirement for difference, Herr now disregards it, and instead wants to compare Pistorius to the minimum value in the control group.   Even here, though, the difference is enormous.  The top graph in the post above shows some of the athletes who can be validly compared to Pistorius - yes, one athlete has swing times of 0.315s at top speed.  But Pistorius was 0.284s, and that is fully 11% faster than the next fastest swing-time ever measured - it's a whole 1 SD between the fastest swing-time and the next fastest. Weyand was quite correct in his response to say that "the double-artificial-limb value is not simply an outlier; it is quite literally off the biological charts".

The force production - advantage or disadvantage, cause or consequence?

The second big point of contention is the importance of the ground forces.  To repeat, Pistorius' average force production is 23% lower (5SD) than that of able-bodied athletes.  Hugh Herr argues that this reduced force production is a disadvantage, whereas to Weyand, it is a huge advantage (See quote above).

In trying to sort out this issue, the important point is that Pistorius' reduced force is present and measured during running at the same speed as the able-bodied runners.  That is, they're all going at 10 m/s when these huge differences are measured (see the graph above), and they persist at top speeds.  When you have fixed the speed, then the ability to increase the force is irrelevant.  In Bruggemann's correct words: "If we look at subjects running at different speeds, it’s logical to say that the higher the force, the higher the speed. But with all subjects running at a given speed, lower force is an advantage.”

On top of this, Herr looked at it 180 degrees backwards.  The 2000 finding by Weyand showed pretty clearly that the first limiting factor to sprinting was the ability to swing the leg faster.  This is "maxed out" fairly early, and then the ability to produce force separates those who can achieve Olympic-like speeds and those who cannot.  So there is an order - first you exceed the limits of moving the limbs faster, and then you have to apply more force to get faster.  And so when you have the ability to move the limb that fast - fully 11% faster than the next fastest person measured, and 33% faster than average), then the changes in force are the result.

As a result, the lower force production measured in Pistorius is the consequence of the reduced swing times.  The muscle force production requirement is thus lower - "half" according to Weyand, and that has some obvious benefits.  Add to this the higher energy return, the fact that less mass is being carried, and that carbon fiber does not fatigue during a 400m race, and you have explained why Pistorius uses much less energy at all speeds than other sprinters.

Advances in technology - have the blades really stayed the same?

The final point, before we get on to the IAAF World champs and leave this for now, is the issue of technological progress.  In a recent interview, Pistorius said the following:  
"My prosthetic legs have stayed the same for seven years, down to the bolts and the lining"

Hugh Herr, meanwhile was interviewed in a piece where he says that the "Cheetah blades have been available to athletes in their current form for 15 years, and that Pistorius has run on the same blades for the last seven years." 

Now, if you do believe that a company like Ossur, which operates five R&D departments, files more than 300 patents per year, and spends millions of dollars every year on product development (6% of total sales in 2007 was spent on R&D) would not change the blades over more than a decade, then you are more gullible than the Pistorius PR team would even have dreamed.

The reality is that technology evolves all the time - and in this particular segment, prototypes are produced, and tested by athletes who then have them customized.  Take the following, from an article where the journalist actually accompanies Pistorius (with his permission) to Reykjavik to test the latest prototypes in 2007:
"But last September [in 2007], Pistorius and Brauckmann went to Reykjavik to test prototypes designed for double amputees. The new ones, which Pistorius hasn’t debuted at a major race yet, make just one smooth curve, an arc of pure engineering.  Ossur’s R&D team met them at the company’s workshop and unveiled the prototypes. Brauckmann attached the blades to the sockets, and Pistorius walked around on them, testing the design".
So, in 2007, a prototype or two was tested.  Read further and you discover that each blade is customized for the athlete.  Add to this that these companies (and there are a few) regularly send their engineers to the athletes to 'test-drive' limbs that have a different stiffness, and you realize that the technology is not as stagnant as you may be led to believe.

Finally, I also know that a simple thing like changing the stiffness of the blade makes a big difference to  performance.  One case - a single-leg amputee tries out a range of different blades.  They are the same product, but with subtle differences in stiffness, curve etc.  The result is a variation in performance that is not hundredths or even tenths of seconds, but seconds.  That's a bigger effect than a year of training, than nutrition, I dare say, even doping will provide.  The simple reality is that the technology IS evolving, and there's no way to police it.

And to say, like Herr and Pistorius are both saying, that the blades are unchanged over 7 years is to say that the BMW that is driven by a friend of mine, a 2004 model, is the same as the 2011 BMW that he would like to upgrade to!  They're both BMWs, they both have four wheels, an engine and a steering wheel, but they're nothing like the same car.  So sure, the blades are the same.  But they're a world apart.

And the implication of this is that performance improvements, so coveted at the elite level, are now accessible through acts of engineering, subtle changes like stiffness, where there are many options within the same product.  Remember that a 0.1 second improvement is valuable in a 400m race.  0.5 seconds can be the difference between being fifth in your own country and top 10 in the world.  The margins are so small that it is unnecessary to talk about revolution - all that is needed is progression and prototypes provide this.  The CAS verdict applied to the blades that were used, but how is that even enforceable when you have subtle changes that can produce

Conclusion: Skillful but with an advantage

One final quote, again from the Wired article:
"To give me a sense of how they feel, Ossur’s engineers bolt a pair of Cheetahs to the back of two rigid plastic-and-leather motorcycle boots. I clamp in and trot across the room a few times. The Cheetahs seem to bounce of their own accord. It’s impossible to stand still on them, and difficult to move slowly. Once they get going, Cheetahs are extremely hard to control."
Legs that "bounce of their own accord" supports the conclusion of a "bouncing locomotion" made by Bruggemann in his research.  They must be very difficult to control and let me emphasize this point - Pistorius' unique performance is the result of his skill levels in using that equipment.  In the way that Roger Federer, Rafa Nadal or Novak Djokovic are elite because of their ability to use their equipment, or in the way that Sebastian Vettel is a superstar because of his skill with his equipment, Oscar Pistorius is skillful.

But every line of evidence - the metabolic, the mechanical, the physiological, the pacing - points to one thing - substantial advantage.  Of course, there is so much that has gone unanswered as a result of the narrow questions asked first by the IAAF and then by the Herr/Weyand research.  Would it not have been great to look at things like how much time may be lost at the start, whether running the bend is a disadvantage (I have data showing that Pistorius runs the bend faster than the straight)?  To test whether increasing the mass of the limb removes these mechanical advantages?  The narrowness of the research means we'll never know and there won't be more testing unless the IAAF demands it, because Pistorius has nothing to gain from discovering the truth, whatever it may be.

But the Weyand research, where Pistorius is off the charts, and the metabolic finding (which is explained by the Weyand conclusion, thus supporting it further) all say advantage.  Again, remember that this begins with the hypothesis that there is an advantage as a result of energy return and mass.  That hypothesis was confirmed by the metabolic measurements, and then explained by the mechanical differences.  It's difficult to see it any other way, as I read it.

Next up:  IAAF World Champs

And on that note, I leave this and look forward to the action on the track - IAAF World Championships start this weekend and there are countless stories that will add to the drama.  There is Semenya in the 800m, returning to World Champs after the 2009 saga.  There is Rudisha.  Bolt vs Powell.  Bekele vs Farah and Kenya. Galen Rupp and the possibility that either Kenya or Ethiopia might not get a medal.  There is Allyson Felix attempting a double.  There are dozens of great match-ups and stories and we'll cover them all in the next few weeks!


P.S.  A final point on the Herr-Weyand research, which I put as an Appendix of sorts because it's of interest but peripheral to the evidence...

Why was it not peer-reviewed?

One of the most common retorts to the Weyand argument about advantage is that it was not peer-reviewed.  That has come from both Herr and Pistorius, who dismiss it because of this failure to get it peer-reviewed.  The problem is, that research will never be peer-reviewed, because it belongs to BOTH Weyand and Herr.  They collected the data together, and so any research paper that gets written has to have all seven of the scientists agreement in order to be published.

Quite clearly, that was not going to happen - Herr was not going to put his name to a paper he so clearly disagrees with.  And therefore, it is not possible to be peer-reviewed.  That is the reason why the debate took place the way it did, as a point-counterpoint.  The irony then is that Herr (and thus Pistorius) are the very reason it isn't peer-reviewed.