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!

Ross

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.

The scientific evidence for an advantage for Oscar Pistorius

The second research study - what it really found about Oscar Pistorius

We may as well jump straight in with the continuation of the scientific summary of the research done on 400m sprinter Oscar Pistorius.  Yesterday, I described how the first round of testing, done at the request of the IAAF in Germany, found that Pistorius used 25% less oxygen during a simulated sprint, and that his running mechanics were vastly different to those seen in able-bodied runners.

That study led the IAAF to ban him from competing, and resulted in the appeal to the Court of Arbitration for Sport.  That brings us to the second research study, led by Hugh Herr, and, at the time, Peter Weyand.  Below follows an explanation of a key part of the paper they produced a few months AFTER the CAS hearing - the oxygen uptake question, which I introduced as being important in yesterday's post.  The timing is important because one of the first key points about the CAS-process is that the research was not peer-reviewed until after the decision was made, which contrasts with claims that the decision was based on peer-reviewed research.

With respect to the CAS hearing, there were without doubt procedural errors in the IAAF process of the scientific testing in Germany.  These are legal issues, pertaining to things like the timing of making documents available, inaccurate reporting of data in an IAAF summary, and dictating testing conditions.  This procedural dispute led the CAS to declare that "the manner in which the IAAF handled the situation of Mr Pistorius...fell short of the high standards that the international sporting community is entitled to expect from a federation such as the IAAF".  Unfortunately, it wouldn't be the first time that this has happened for a major sporting federation...

However, this is a look at the science, following on from yesterday, where I explained the specific scientific issues that were taken to the CAS panel, along with responses by Bruggemann and a few quotes from other biomechanists, as well as my views and interpretation of those points.

Today, I move on to the Herr research, which I believe is equally flawed.  But I'll go through it systematically, building up the main findings and figures, and then allow you to draw conclusions about what was done to come up with this overall finding: "We conclude that running on modern, lower-limb sprinting prostheses appears to be physiologically similar but mechanically different from running with intact limbs." (Weyand et al, 2008)

The metabolic cost of running - similar?

To begin with, one of the key points challenged at the CAS hearing was the measured reduction in oxygen use during a simulated sprint (figure shown to the right).  The problem is that during a sprint, metabolic energy is provided by a combination of oxygen dependent and independent sources, so Bruggemann provided only half the picture.

You would not be surprised to learn that in the CAS hearing, the IAAF focused on the biomechanical aspects of their research, and downplayed this particular finding, because their conclusion based on the measurement of oxygen use in a sprint was always going to be challenged very strongly.

And challenged it was - it would also not surprise you to learn that the response from Pistorius' research was to repeat the above test, but this time to measure oxygen use at sub-maximal speeds, because this provides a better indication of the metabolic cost of running.  And so this is what they did - Pistorius ran on a treadmill at a range of SLOWER running speeds.

The method used was to have Pistorius run for 5 to 7 minutes at a range of speeds, with 3- to 5-minute rest periods.  The starting speed was 9km/h (a very slow jog) and Pistorius reached exhaustion (unable to complete 5 minutes) at 15km/h (which is very slow, tellingly - Pistorius did this testing at a time when he publicly announced that he was untrained and unfit.  That this impacts on the results you'll see below is important).

Using measurements of oxygen use from Pistorius during these runs, they were able to calculate what is called running economy, or the volume of oxygen used per kilogram per kilometer. Think of this as fuel use in a car - the less oxygen you use per kilometer, the more economical you are.  Remember that the hypothesis based on one interpretation of the theoretical knowledge at the time would be that Pistorius would use less oxygen, and hence less energy, at a given speed because of the reduced mass and the increased energy return of the carbon fiber limb (see yesterday's post for the explanations).

(By the way, if you adopted the exactly opposite position based on the theory, then you might hypothesize that Pistorius would use MORE oxygen and more metabolic energy because of the demand for balance and the increased work required to control the limbs - this is what his coach, Ampie Louw, explained in a TV interview in 2007 for a UK news insert.  The point is that either theoretical claim can be tested by measuring oxygen use - it is a barometer for energy use, and will either be similar, in which case the theory is disproven, or will be different, in which case one of the theories will be proven, the other disproven.)

There are a few pertinent considerations here.  First, the Cheetah blades are built for speed (the manufacturer's own claim), not slower running, and so I would argue that testing them at these slow jogging speeds (9km/h is very slow) will provide a false picture, skewed in favour of finding a higher oxygen use.  However, even without that potential confounder, the data still provide some really interesting insight.

What is more crucial, for reasons that will emerge as we progress, is the vital question of who do you compare Pistorius' data to?  The answer must surely be able-bodied sprinters of similar performance levels.  That's because the literature shows that sprinters use more oxygen (or are less economical) than distance runners.  So the "control" group would have to be able-bodied SPRINTERS.  And this is where I begin, with four able-bodied sprinters compared to Pistorius (note - the development of the graphs below (which is Figure 2B in the research paper) does not necessarily follow the timeline of the testing, but it builds the argument and highlights the key issue)

The first graph, shown below, reveals the first finding - Pistorius compared to able-bodied sprinters at the same performance level:

So, Pistorius uses 17% less oxygen than the able-bodied controls, or 2.7 Standard Deviations less.  Without going into the stats, that's a big difference - generally, anything more than 2 SD is considered an "outlier", very different.  And so on the basis of this finding, Pistorius is very different to able-bodied sprinters.  This is not different to the 25% difference that Bruggemann found during sprinting, and it's not inconceivable that the 17% would be higher (approaching 25%, maybe?) at sprinting speeds, where the Cheetah blades are more effective, doing what they were built to do.  This first finding confirms the Bruggemann research.

Yet the paper concluded, you'll recall, that Pistorius is physiologically similar, and Hugh Herr was recently quoted as saying "It is not true that Oscar uses less oxygen than a person with two biological legs, although he is very economical".

The addition of the distance runners

So how do you get to that conclusion?  Answer - you add distance runners to the able-bodied population. Herr and co decided that in order to increase the size of the control group, the next group that should be compared to Pistorius was not more sprinters, but rather a group of sub-elite and elite DISTANCE runners, who had been measured in a study in 1995, thirteen years earlier in a completely different laboratory.

Once these distance runners are added, the following graph can be drawn:

So, with the addition of the distance runners to the control group, the gap between the sprinter Pistorius and the able-bodied runners is coming down - presumably this is a "good finding" if you're involved in this research and "want" to disprove the earlier IAAF study finding.

The difference in oxygen use between Pistorius and sub-elite distance runners was 6.7%, while Pistorius uses 3.8% LESS oxygen than elite distance runners.  However, statistically speaking, the differences are 0.8 SD and 1.3 SD to those groups, respectively, and so it can now be concluded that Pistorius is, in fact, not different to able-bodied runners.  Provided those able-bodied runners are elite distance runners, that is.

For good measure, they also add John Ngugi and Zersenay Tadese to the sample, and the graph is now complete, as found in the research paper (Figure 2B on Page 906):

Just a word on the Tadese value shown above: this is a study that I actually wrote quite a bit about back in 2007, and the main reason was because Tadese was the most economical runner in history, but there was something not quite right with that running economy value.  His economy, measured at 150 ml/kg/km has some bizarre implications - it means that running at world record pace for the marathon (2:56/km), Tadese would be using only 51 ml/kg/min of oxygen.  Take it from me, that's just not possible, especially when you consider that Tadese's VO2max was supposedly 83 ml/kg/min - his marathon world record pace would be an easy jog!  My point is - something didn't add up, and I'd be very cautious about accepting that Tadese value.  And this illustrates just why you should not take data from other labs and use it as part of your data set as was done - you simply cannot guarantee the validity of that data.

To do this, to borrow from other research, where methods are different, equipment is different, and athletes are different, is to violate a key concept in the control of science.  It's the same thing as if I want to test the effects of something like compression socks on muscle pain after running, and I make a few runners do a trial, and then compare them to a study done in a different lab with different methods.  Certainly, you will use other studies to explain your data and provide context in the discussion, but to borrow data like this is extra-ordinary.

Having said this, I can appreciate why it was done - the time was limited, and the research had to be done for the CAS panel.  The control group was small initially, and had to be increased in size.  So given the time constraint, I can appreciate that this would be an exceptional circumstance.  But the question is this:  Why compare a sprinter to a distance runner in one of the key variables (running economy) that is known to be very different between them, when data on sprinters exist for a more valid comparison?  At the very least, show BOTH distance runners and sprinters...

Why compare to distance runners, when data for sprinters is available?

The question is so important, I repeat it - why would Herr and co have chosen to compare Pistorius to elite and sub-elite DISTANCE runners, when the data exist for sprinters' running economy?  It's not as though we don't have the data for sprinters - it exists.  But the research chose to ignore these data, and instead focus on distance runners, both elite and sub-elite.  Why?  I hope it's becoming clear in your minds as you read this.

But before continuing, take a look at this sentence from the research article, in the discussion (pg 909):

"However, his values were 17% (2.7 SD) lower than those of the intact-limb 400-m specialists tested here and two or more SDs below the means reported for four other groups of subelite male sprinters"

In other words, the authors are aware of FOUR studies on sprinters that could have been used to expand on the subject numbers used in the very first graph I showed above.  Four studies that would have increased the size of the able-bodied control group and allowed a VALID comparison of a sprinter (Pistorius) to other sprinters, rather than elite distance runners.

One acknowledged consideration is that the sprinters in these studies are not elite, but then neither are most of those in the distance group used in their place.  The sprint data could, at worst, have been included in the analysis.  But instead, they chose to ignore the sprint data on athletes who were, at the time, at more or less the same performance level as Pistorius.  Rather, they presented the distance data, which conveniently supported the ultimate finding of physiological similarity.  Perhaps the comparison with other sprinters produces a finding that you'd rather not show...

The graph that compares sprinters to Pistorius - the real finding and comparison

So I went and found the four studies in question, and I've redrawn the graph, this time showing the oxygen use of Pistorius compared to other sprinters and middle-distance runners, rather than elite distance runners:

So, that graph looks a little different to the one shown above, the one that was eventually published in the research paper (Fig 2B), comparing the sprinter Pistorius to the elite and sub-elite distance runners.  Here, when you compare Pistorius to sub-elite sprinters, you get a very different picture.  I've shown in red below each bar the difference in percent between Pistorius and these sprinters, and in black, the difference in Standard Deviations.

So 17% or 2.7SD is the Weyand et al finding (comparing Pistorius to performance matched sprinters).  13% or 7.2SD is the difference to 400m sprinters (performance time 50s). It's 3.2 SD to 800m runners, 5.1 SD to 1500m runners, and overall, Pistorius uses 14% less oxygen than able-bodied sprinters and middle-distance runners.  That's 2.3 SD and a difference that, according to the definition set out by Herr, would have led to the conclusion that "Pistorius is physiologically different"  And importantly, it's a difference that strongly supports the hypothesis of advantage.

Again, these are sub-elite athletes (50sec 400m time, for example), but they do include middle distance runners who would be expected to have better economy than sprinters (remember, Pistorius is a 200m-400m sprinter), and they are close to the performance level achieved by Pistorius in the actual testing protocols (they actually exceed his level - remember, he hits a peak sustained speed of 15km/hour - some of the above runners were measured at 20 km/hour).

Conclusion - look at what is included as well as what is not

So the point in all this, I would hope, is obvious.  The selective addition of distance runners to the able-bodied group allowed the physiological differences to disappear (statistically speaking).  Meanwhile, selective omission was happening - there were at least four studies on sprinters that would have confirmed the Bruggemann finding, and even the Weyand 2008 finding that Pistorius has significantly different physiology and metabolic cost compared to other sprinters.  This would go a long way to confirming the initial hypothesis, and so it's not a trivial matter at all - it is in fact the crux of the issue.  The question is why make this selective addition and omission?

One answer may provided by the background to the research.  Pistorius has the Bruggemann research, he knows the methods and the results, and knows why he has been banned.  He now has to cast doubt on the Bruggemann research, showing the CAS that there is insufficient scientific evidence to ban him.

The first point to challenge for the CAS hearing, arguably the "weakest point" in the IAAF case, was the issue of energy use, or metabolic cost of running.  So the researchers Pistorius works with, one of whom is a big recipient of funding from Ossur, who make Pistorius' blades, are tasked with disproving the Bruggemann findings.  That means one thing - show that Pistorius uses similar volumes of oxygen compared to able-bodied runners.

Unfortunately, he doesn't.  At least not compared to sprinters, who train like he does, who share the genetic make-up of being a sprinter rather than a distance runner - he's 17% different despite everything being in his favour - he's untrained, he's running at slow speeds on equipment designed for higher speeds.  I dare say that three months of training would reduce Pistorius' values even further.

But when distance runners are added, the control group changes sufficiently so that even though Pistorius uses less oxygen and energy than them, he is statistically similar, and it is concluded that he is physiologically similar.

CAS accepted this (which defies belief, but anyway), and so the key barometer in the debate, the key variable that allows one to evaluate whether the theory is correct regarding the reduced energy cost of running on the carbon fiber blades, suddenly appears questionable.

Go right back to the hypothesis - either Pistorius has a metabolic advantage because of the reduced mass and the elastic energy return, or he doesn't.  Measure the oxygen used, and it will decide for you - the measurements of oxygen used confirm the metabolic advantage - across a range of speeds, from barely a jog to a 400m race, Pistorius uses significantly less oxygen than able-bodied sprinters.  Even dipping into previously published literature confirms this.  My take - hypothesis proven.

The mechanical debate and the "10 second advantage"

There is still the issue of mechanical advantage.  But it's late here in SA, and that is an issue for another day, when I'll look at the split that occurred between Pistorius' own scientific team, leading Weyand to publish a letter to JAP suggesting a 10-second advantage.  That is the final piece of the puzzle.

Thanks for the comments to yesterday's piece, it's good to inspire debate and as mentioned, in all this, there's allowance for disagreement.  I mean, we can't even agree on something as basic as whether dehydration causes heatstroke, I don't expect consensus on this.  But I've seen more ambiguous data, that's for sure - this is, I suggest, pretty clear cut.

Ross

The scientific interpretation of Oscar Pistorius research

From the go-kart racer to the F1 driver: The  scientific interpretation of the Pistorius research

The possibility that Oscar Pistorius has an advantage from his carbon-fibre blades is a topic that I honestly wasn't going to cover on this site.  For one thing, I've covered it already, dating back to 2007 when the story first emerged.  And secondly, it inspires in people a reaction that buries the scientific question/debate in a tsunami of emotion fueled by social and political correctness.  Even in a recent scientific debate between two camps that formed with Pistorius' own team split turned into name-calling, and the ghost of John McEnroe was called upon in a "You cannot be serious barb".  And that was in a scientific journal... 

However, I've received about a dozen emails in the last few weeks (most of them surprisingly supportive) and a lot of people have asked about the scientific discussion around the blades.  There are a lot more readers now than before, and so the "old news" may not be that old to many.  And then I got to thinking - The Science of Sport began specifically to provide a more detailed analysis of sports news, with a special focus on how sports science might add to our interpretation of what we see.  As we say in our "Mission", we're about the how and the why of sports news.  And there can be no bigger current sports story involving sports science than the Pistorius one.

Added to this is that the media seem scared of this issue - or at least, that's the only reason I can think of for why some of the facts haven't emerged, or why they never challenge the claims made by those associated with Pistorius, and most recently Hugh Herr.  Every claim made is accepted as fact without actually looking at what is being said, and some of the counter-points border on ridiculous.  And so this series of posts is the result - they will summarize my views on the science, the scientific process and the misdirection that has characterized what is one of the most controversial illustrations of science applied to sport encountered since this site started (with the exception of Caster Semenya in 2009 and 2010)

And it will be controversial.  Those who have followed the site for a while will know that I believe there is an advantage, and that is a conclusion based on ALL THREE scientific papers published about Pistorius, as well as the years of hypothesis and discussion, and the known theory of sprinting.  But it would be a glaring oversight to ignore it any longer.  (It's a long, and technical piece, so I may break it up into parts)

Being right vs being correct - the concession, and agreeing to disagree

Let me start off by saying that even once all the science is considered, and even if you arrive at the conclusion that Pistorius has an advantage, your response to that may not necessarily be to stop him competing in able-bodied races.  The more I think about it, the more I can appreciate the views of those who may be saying that he should run regardless of the possible advantage.  They have a point - it's possible that his "rarity" and the fact that he is such an inspirational figure outweigh the potential advantage and future implications of allowing him to compete. 

I'm not one of those people - my interpretation, having followed this from before the hypothesis-generation stage to the research studies, is that he has an advantage.  And because I come at this from an athletics standpoint (as opposed to the human interest side of it), my opinion is that he shouldn't be allowed to run regardless of it.  However, I bring this up counter-point to emphasize that this controversial issue may not have a "right" solution.  It may be a matter of being "correct" (with regards to the science) but not "right" (with regards to his participation).  So while I disagree, I can respect and appreciate a balanced view that says "there may well be an advantage, but given the circumstances and bigger picture, allowing him to run is the right thing to do".  All I ask is the same respect and courtesy, free of emotional name-calling!

What I do take exception to, however, is the dishonest scientific process in this story, and the lies that are actually shown up by data - that's where my criticism is leveled.  This is therefore not only a post about Pistorius, it is about the scientific process behind him.  My criticism is directed primarily at the science that, I believe (and as I'll describe) was twisted and manipulated to create the desired finding.  It is not at Pistorius personally.

However, I do also want to use these posts to respond to some personal comments made by Pistorius at me - unfortunately, journalists don't allow for opportunities to respond to being called a "kart racer" and accused of hunting publicity.  These are minor issues, so I leave those for a footnote at the end of this post.

The bigger issue is some of the claims being made in this debate, which are outright lies, to the point of deliberate dishonesty.  The media of course don't challenge these statements - they accept every claim at face value and instead prefer to sensationalize and create "hero vs villain" sagas.  But the claims that the science proves that there is no advantage demand a response.  And since the media are not bothering to question them, someone else has to.

Right back to the beginning: The starting hypothesis

Before looking at the evidence, it's important to understand WHY specific things were being measured, and what the basis might be for saying that Pistorius has an advantage, because this will help explain the implications of what were later found.  As far back as 2007, it was possible, on a theoretical level only, to debate whether the blades would provide an advantage.

The key points suggesting advantage were:

1. The reduced mass of the carbon fibre limbs
   
   The ability to accelerate the limbs faster is the first theoretical advantage.  A study had previously found that in distance runners, athletes with smaller calves (by mass) were more economical.  And while economy isn't as valuable for a 400m sprinter, the reduced mass is a potential advantage because it allows lower forces and work to be done in accelerating a smaller mass.  Conceptualize this by imagining how your 400m performance would be affected if you raced with 1.5kg strapped to each foot, and then imagine taking that mass away - that is the mass advantage of the carbon-fibre Cheetahs.  This would be detected in a reduction in the work or cost of running at a given speed, and is potential difference number one.
   
   
2. Enhanced energy return from carbon fiber
   
   The company that manufacture the blades, Ossur, make the claim that the carbon fibre blades return around 80 to 90% of the energy they store under compression.  That is, land on carbon fibre that is specially designed and shaped to compress under the body, and more than 80% of the energy will be returned on recoil. 
   
   In contrast, human tendons are relatively poor at returning energy - estimates vary depending on the way it is measured, but energy return ranges between 30% and 70%.  Greater energy return would reduce the need for muscle work, further reducing the "cost" of running.  There's no question that 400m races are metabolically limited.  The details are debatable, but key is that every 400m runner is regulating the rate of metabolite accumulation or energy depletion.  They are limited/regulated by the consequences of metabolic energy use, and anything to lower this (as carbon fibre blades would, according to the theory) would be advantageous.
   
   There was a lot of confusion about this, with some people saying that carbon fiber was only passive energy return and thus a disadvantage.  The reality is that human muscle can return energy, but it requires muscle contraction twice - first to store energy AND then to release energy.  Therefore, there is a cost to energy storage AND return in human muscle and tendon.  The fact that carbon fiber releases energy stored under compression is thus an advantage - there is no cost. 
   
   Once again, this would be reflected in a reduced energy cost of running - same effort, faster speed, or same speeds with less work.  On top of this, there is the matter of fatigue, which causes the force-producing properties of muscle to decline, whereas carbon-fiber never fatigues (in an athletic sense).  The result may be less fatigue at the same speed or for the same effort, over time.

Given those two theoretical considerations, the hypothesis before testing was that the metabolic energy cost of running would be substantially lower compared to able-bodied controls, and that the mechanics of running would differ significantly.  The word "bounce" came up many times in the initial debates.  The question remained, however: Had anyone collected data to confirm these hypotheses?  The answer, until 2007, was no.

The summary version of the evidence

Then, over the course of about 6 months, that evidence was gathered.  It took a while for it to emerge, but when it did, it confirmed much of the above.  This is a summary of the findings, and if you don't have the appetite to go through the detail and you trust the summary, then this is where to stop!  Or read on for the detail of the first study...

1. Pistorius used significantly less oxygen than able-bodied sprinters.  25% less during sprinting (the IAAF Study) and 17% less during jogging (the Herr study), to be specific. Therefore, his metabolic cost of running was lower.  This was true at all speeds, from jogging to sprinting, and of course the carbon-fiber limbs are not designed for jogging in the first place, so one can question how valid a measurement would be during jogging.  It was still found that he used 17%, or three Standard Deviations, less energy when jogging than able-bodied sprinters.
   
   
2. When you add in elite distance runners, then Pistorius becomes "similar" to other runners.  Herr et al conveniently did this when they found that Pistorius uses 17% (or 3 SD) less oxygen than able-bodied sprinters.  Rather than actually testing runners themselves, they turned to the literature and found fifteen-year old research studies on elite distance runners, and sure enough, when they added other people's data to their sample, it helped bring the average down and he became statistically similar to distance runners.  Even then, he used 4% less oxygen than the elite distance runners, which is quite remarkable.
   
   
3. Pistorius had significantly lower vertical ground reaction forces and horizontal braking forces than able-bodied runners.  That means less braking force, but interestingly, the same propulsive forces.  This in turn means less work at the same speed than able-bodied runners.  There is however a disadvantage of lower peak vertical forces, compromising the acceleration from the start.
   
   
4. The energy return from the carbon fiber limbs was 92% compared to 59% for the able-bodied runners.  This, in part, explains the reduced physiological cost compared to sprinters.
   
   
5. Pistorius' rate of fatigue was similar to the able-bodied sprinters, using running trials to fatigue.  This is interesting, and I have my doubts about whether testing an untrained athlete who knows the hypothesis reveals anything of value.  It is also questionable as to how relevant it is to a self-paced 400m race, but this is the only one of five findings that doesn't suggest advantage.

Now, for more on the findings, as well why they were so hotly debated, read on.

First testing - the IAAF study in Germany: Bouncing locomotion with lower metabolic cost

The first round of testing was conducted on behalf of the IAAF by Pieter Bruggemann in Germany in October 2007.  Below is a brief explanation of the three key findings from that paper, the reasons it challenged by Pistorius' science team (led by Hugh Herr, and at that stage, Peter Weyand), as well as some responses from other biomechanists to those challenges.

1. Oxygen use 25% lower = lower metabolic cost of sprinting

First, they measured his oxygen uptake during a simulated 400m sprint.  It's really important to understand that measuring oxygen is done because it's a "barometer" of sorts for the cost of running.  It's not because oxygen is limiting to a sprinter or because a sprinter needs a high VO2max (as was alleged as part of the normal obfuscation of the issue), but rather because much like fuel use in a car, oxygen measurements give an indication of the energy requirements for running.

So if you recall the hypothesis and the theoretical background to the question, measuring oxygen is important because it allows you to establish whether the work requirement is in fact different for carbon-fibre compared to able-bodied limbs, and not whether the runner has a better cardiorespiratory system.  The hypothesis was that Pistorius would show a reduced metabolic cost of running.

Below is a graph of oxygen use during the 400m simulated trial:

So, Pistorius uses significantly less (25% once up to speed) oxygen than able-bodied sprinters during a 400m race.  Also of interest is that he uses the same volume of oxygen over the first 15 seconds, when the balance problem (which many have said would increase his metabolic cost) is theoretically greatest.  Once up to speed, balance is actually not as much of a factor as some suggest - if you want to test that claim, jump your bicycle and ride at 2 km/hour, and then at 20 km/hour, and you soon realise that movement assists balance.

The mechanism for this reduced oxygen, and hence energy cost would be two-fold, and goes back to those two points raised earlier - increased energy return and mass of the limb mean less work, and that means a lower metabolic cost, indicated by lower oxygen use.

However, there was a problem with this conclusion, and the research was not complete in this regard.  That is, when someone is sprinting, energy comes from oxygen-dependent and oxygen-independent sources.  Measuring oxygen uptake during a sprint means that both are contributing, but only one is being measured.  The graph above thus gives an incomplete picture, and the conclusion that the metabolic cost of running is lower was challenged at the CAS.  There is a counter-point, and that is that if he uses less oxygen and thus less energy from oxygen-dependent sources, then there's no reason to suggest that his oxygen-independent contribution would be higher.  But only part was measured, and this would go on to become perhaps THE key point that was challenged in the CAS hearing.

The mechanical energy - 41% vs 8% energy loss

The other Bruggemann finding is summarized by the quotes below.  All are drawn from the report after testing and from a great piece by Edward Ovadia on the issue.

"The energy loss in the blade during the stance in sprinting was measured at 8% and is significantly lower than in the human ankle joints of the controls (41%). This results in a mechanical advantage of more than 30% (it is reported as a 7-fold greater energy return elsewhere in the paper) when the leg is substituted with the prosthesis" - Bruggemann report

Bruggemann attributed most of the 41% energy loss to heat.  This was disputed by Hugh Herr, on the grounds that a) the energy loss in able-bodied runners cannot be that large, that it is not possible to dissipate that much heat in a 400m race, and b) that measuring energy loss in joints is extremely complex, and that there is a possibility that some of the energy in the human joint is not lost, but rather transferred across the joint.  This would bring the energy loss down from 41%.  Bruggemann however disagreed, saying that firstly, the frictional energy loss is as high as claimed, and secondly, the energy transfer across joints is very small.

What is significant is that other studies of energy in joints support the Bruggemann evidence, showing that energy loss ranges between 70% and 30%, depending on whether the person is walking, jogging or sprinting.  The 41% energy loss found by Bruggemann is thus not unrealistic - he may have overestimated, and at the time, a group of biomechanists did debate the model he'd used, but concluded that even with certain small imperfections, the general conclusion was correct - human tendon returns only around 60% to 70% of its energy, compared to 92% for the carbon fiber blades.

However, this discussion was another point of contention for the CAS hearing, who said that the uncertainty re the exact energy loss could not be confirmed. The paradoxical thing about this, however, is that if energy is transferred from the ankle to the knee, as Herr and Kram argued to the CAS, it is not actually an advantage. The problem, as Bruggemann explained, is that this would be "a disadvantage for the able-bodied athlete, because this energy will bend the knee in a phase when the knee is in extension. It's an argument against Pistorius" (Bruggemann, quoted by Edward Ovadia)

Ground forces - less energy loss and less work required

The third finding is that Pistorius had very different ground forces during running. His vertical forces were 20% lower and the horizontal braking forces were 50% lower than those measured in able-bodied controls. Interestingly, the horizontal braking force is reduced, but he doesn't lose anything in the propulsive component of the horizontal force. This is shown below:

To Bruggemann, the reduced vertical force was a distinct advantage, because it was measured at a constant speed, similar to that of able-bodied runners, and meant that Pistorius would do less work to run at the same speed, a finding that is supported by the lower oxygen cost shown earlier.

Herr however argued that this would be a disadvantage during the acceleration phase of running and that faster runners would need more force. There's no question that this reduced vertical force would be detrimental to the start, and goes some of the way towards explaining Pistorius' relatively slow starts.

However, the debate about peak forces and acceleration typically obscures the real significance of Bruggemann's finding - it's a false comparison because we should not be comparing runners at different speeds, but rather comparing Pistorius to other runners at 46 second 400m pace. The comparison to people running faster is irrelevant. As Bruggemann explains: "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.”

These sentiments were echoed by Benno Nigg, one of the world's leading biomechanists (if not THE leading biomechanist of running):

"He needs less vertical force as well as less horizontal braking and propulsion force – which means he has to work less at the same speed than the control subjects. Pistorius lost less energy and had to produce less work during each [instance of] ground contact than the athletes in the control group.” (as quoted in Ovadia's article)

Conclusion from the first study


The ultimate conclusion reached by Bruggemann, as you all no doubt know, was as follows:

Sprinting with the artificial limbs (Cheetah) is – from a biomechanical perspective – a “bouncing” locomotion and is significantly different to sprinting of able-bodied athletes on hard surface. It is a different kind of locomotion at lower metabolic cost.

This was however challenged at the CAS for the reasons explained above - the metabolic cost was challenged because of the method of measurement, and the mechanical/kinetic data on the basis of alternative interpretations.

I think it's clear that when trying to model the joint loads, the forces, the energy turn, much is model-dependent.  The biomechanical model used by Bruggemann (called inverse linear dynamic model) was questioned by biomechanists, but they nonetheless agreed with his overall conclusions.  So too, as shown for a specific part, did Nigg. 

The importance of the physiological data 

The challenges made by Herr & Weyand were of course equally unprovable.  They offered no alternative to the 41% energy loss, only a question about frictional heat loss.  Of course, this was all that was required, because the CAS hearing only asked for doubt to be cast on Bruggemann's findings, and not proof of a lack of advantage (the context would have been significantly different then).  The result is that the biomechanics part of the debate reaches a stalemate, and finding "conclusive proof" for either position would prove impossible.  CAS of course required conclusive proof and perhaps it is not surprising that they ruled the way they did, on this question anyway.

However, it is for this reason that I would suggest that the physiological data, and not the biomechanical data, hold the more important information.  That's not to say the mechanics are unimportant - the case made by Bruggemann, both in his research and in his responses to the questions, is, I believe, compelling and correct.

But it's when you look at the metabolic factors that things become really insightful, because metabolic cost is a symptom of the mechanics, and so given that there are two ways to interpret Bruggemann's kinetic and energy data, the way to test the options is to use metabolic cost.

And so what was needed was a comparison between Pistorius and sprinters at sub-maximal speeds to ascertain whether that oxygen cost would be lower even then.  That is, repeat the experiment but at slower running speeds.  And this is where Herr enters the picture with a research study that can only be described as "manipulative".  It was, to be blunt, one of the most astonishingly selective research articles I have ever seen, to the point of being dishonest.

But that is the topic of tomorrow's post, when I'll consider Herr's evidence, and some of the claims made in the media about what he showed, and more importantly, what he chose not to show for the sake of the finding.  I realise there are many unanswered questions - but this is only the first part - the analysis of the Herr paper reveals much more, including why I believe the CAS process was so farcical.

More to come.

Ross

The fineprint

And finally, because the tabloid journalist did not allow a response, I must make the following statements, which I do at the end of the piece because they are a footnote, not necessary to the debate, but need to be said.

First, at no point, not even once, have I contacted a journalist to "push an agenda".  Ironically enough, the fact that I have conducted no "pertinent research" on Pistorius is in fact because Pistorius didn't want research.  Back in 2005, I offered to do the research, but he was not interested enough in the science.  Then in 2008, he requested help from SA sports scientists, but again, he would not work with us because of the likelihood that we would confirm the Bruggemann findings.  Ultimately, Pistorius went to Hugh Herr because Herr was going to find what Pistorius wanted.  In tomorrow's post, I'll explain how they did it. 

When you stop to think about it, any person who says "Oscar Pistorius has an advantage" is walking into unpopularity and guaranteed hostile reactions.  That is hardly the way to raise your profile.  The reality (and this is a direct message to the Pistorius camp) is that the journalists are contacting me with questions, and I am answering as honestly as I can, about the evidence and the CAS process.  The alternatives are to lie ("there is no advantage), or to say "the evidence is unclear", but it's not.  It clearly points in one direction.

Secondly, when Pistorius personalizes the issue by calling me a "kart racer", it reveals one of the key problems in this issue - this is not an issue of personalities and of WHO is saying what.  It's about the evidence, independent of the people.  I don't care that Hugh Herr got a write-up in Time, what concerns me is the distortion of the evidence (again, see tomorrow's post).  I also care to point out that Herr is a big recipient of funding from Ossur - the idea of "independent research" from him is utterly false.  There are vested interests everywhere on this one, and it clouds how the media are reporting it. 

That's all, an unnecessary distraction from the evidence.  I'll get back to it tomorrow!

Performance implications of Pistorius advantages

Pistorius Part IV: The performance implications complete the picture

I was going to delay this analysis until after the IAAF World Champs, which got underway this morning with a dominant Kenyan display in the women's marathon.  Later today sees the women's 10,000m, and there's every chance that Kenya will have claimed the first four (or maybe even more) of the medals at this year's Championships, with Vivian Cheruiyot the favorite for gold.  Ethiopia will again have something to say about this, so that should be a great race.

But then I made the "error" of posting a Tweet about Pistorius' race times,which I believe are very significant and complete the picture of the advantage, and it started something of a debate, because I think people misunderstood what I meant by performance comparisons.  So I felt it necessary to post this, Part 4 of the Pistorius series, now, rather than delaying it until after the World Championships.  I must make the point that the first three posts in this series explain the scientific evidence.  They are the basis for the advantage, NOT this post.  This post is merely to contextualize and to explain an observation about performance that further consolidates the picture, not to bring evidence to the debate.  It's a small piece of the puzzle, but it fits in at the end of the three-part debate we've been having.  By itself, it's not proof, but when you look at the whole picture, it is in place.

The whole picture - a recap to begin with

The missing piece in the debate so far is the performance implications of those metabolic and mechanical advantages.  It's really important to keep the WHOLE PICTURE in mind as you consider this question - each line of evidence by itself is important and telling, but when the pieces come together, only then you do see the full evidence for the advantage.  And the one piece that I've yet to tackle is performance.  To recap, this is the picture so far:

1. The theory that Pistorius has an advantage is a result of two factors.  First, the significant reduction in mass of the carbon fiber blades means faster limb movements, and less work to accelerate the limb.  Second, the significantly higher energy return from the carbon fiber blades means less energy needed as the investment.
   
   Now, BOTH of these theories predict the same thing - a reduced metabolic cost of sprinting, and a performance advantage.  The problem was, back then, there was no research.
   
   
2. Then the research came along and it confirmed the theory.  It showed:  1) Pistorius used 25% less oxygen during sprinting, and 17% less oxygen during slow running than other sprinters.  2) His mechanics were very different to those measured in able-bodied runners, and suggesting less work required to run at a given speed.  These were enormous differences, making him statistically way off the charts.  They also implied advantage, because oxygen use is a barometer for metabolic energy cost.  Herr and the team that tested him eventually resorted to comparing Pistorius to elite distance runners, and then he started to look similar, but it is remarkable that was still more economical than distance runners.
   
   
3. Then came the explanation - Peter Weyand showed how Pistorius' running mechanics were off the charts.  His ability to reposition the limbs was 4 SD faster than average, and a full 11% faster than the next fastest runner ever measured.  This advantage means more contact time, and also reduces the need to generate forces.  The result is that he has to produce half the muscle work compared to able-bodied runners.

So, in a nutshell, you had a theory, confirmed by the findings on physiology and metabolism, and then explained by the findings of his running mechanics.

All told, that's a compelling and almost complete picture.  But the question is, what does it do to performance?  Obviously, it's impossible to know with certainty.  Weyand tried to quantify it, but as I explained in the previous post, I think he made some excessively "liberal" assumptions about how to adjust Pistorius' values.  The result was an over-estimate.  But I still believe it's possible to narrow down how large the advantage may be, and that's what I want to do in this post.  

I'm going to go through this very slowly, systematically, but bear with me - past experience has taught that this pacing concept is tricky to explain, there are lots of gaps to fill!

The theory - an abnormal performance relative to other performances

And we begin again with a hypothesis:  Pistorius' reduced metabolic cost of sprinting and those mechanical advantages lead you to the theory that Pistorius will be able to sustain a higher relative speed over longer distances than able-bodied controls.  The advantage, in other words, will be seen if Pistorius is able to slow down less as he moves up in distance.  I hope that is clear?  He will run at a higher speed (relative to his OWN performances) than any other athlete, and that will reveal that the metabolic and mechanical factors we've explained are 

Why would this be the case?  To understand this, ask yourself the following question:  Why don't 400m sprinters run faster in a 400m race?  The reason this seemingly obvious question is important is because it's clear that every 400m runner COULD run faster, based on their performance over 200m, and the question is why don't they?

Take Michael Johnson, for example.  Over 400m, he ran 43.18 seconds, and in that race, his first half was run in 21.22 seconds and the second half in 21.96 seconds (Ferro et al).  His 200m PB, as you know, is 19.32s.  

That means that his first 200m is 9.8% SLOWER than his best 200m, and his second 200m is 13.7% slower than his best 200m. Even if his 200m best is adjusted slightly because he wasn't quite in that shape at the time, he's still about 7% and 11% slower over 200m splits in a 400m than in a 200m race (bear with me as I try to evolve the argument - I have to labour the point because people may misunderstand this concept otherwise). I've shown this in the graph to the right.

Why pace a 400m race?  And doing the impossible

So, it's quite clear that the 400m event is paced.  This is obvious, but it's important to understand WHY it has to happen.  The reason the race must be paced is because there is a significant metabolic cost to sprinting at 200m pace.  If a runner does this, then factors such as metabolite accumulation (think H+ ions, phosphates, ADP) and failure to provide energy rapidly enough will force them to slow down too much.  Start too fast, try to run a 400m race at your 200m pace, and you will pay for it big time and slow down in a big way in the latter part of the race.  As it is, every single 400m runner in history has run the first 200m faster than the second 200m in a major race.  It's just not possible to negative split and still run fast

What is impossible to do is to race a 400m race at anything close to your 200m pace.  Rather, you pace yourself and still slow down in the second half of the race.  Below is a graph showing that in elite 400m running, the only way to race is to run the first half between 2% and 6% faster than the second half.  This happens without exception - 16 athletes in an IAAF final, every one did it.  It even applies to the 100m segments - the slowest 100m segment in 16 out of 16 elite races is the final 100m, and by a long way.

The average breakdown in both men's and women's races is that the first half is 47.7% of the race, the second half is 52.3%.  So, if someone is running a 45 second 400m, then the typical way of putting it together is to run the first half in 21.46s and the second half in 23.54s.  

And before you say that not every athlete has to be "typical", look again at the graph above - Michael Johnson is the only "non-typical" athlete, because his split is 49%-51%.  Even he, the outlier, is 1.7% faster in the first half, and that's about the limit for what is possible in terms of pacing a 400m race "evenly".  But as I mentioned, he still runs the first half a full 10% slower than his best and the second half 14% slower than his best (see the top graph)

I must just make the point, that it's possible to run the second half faster than the first, but then you'd have a huge overall under-performance.  Michael Johnson could run the first half in 25 seconds and then blast a 20.5 second second half, but the time he'd produce is not optimal.  And that's key.

Now, what's the significance of this?  It's very significant, because once you understand this concept, you realize that this method of looking at how a race is constructed is a very important and meaningful way of understanding Pistorius' performances. 

There are three things to consider:

1. This method allows you to compare the first 200m of a 400m race to a 200m time.  This deals with the start issue, because both races include the start.  So you can see how he paces himself relative to a valid and reliable anchor - his own performance.
   
   
2. The method also allows comparison of the second 200m to the best 200m, which gives an indication of fatigue over the course of a race.  Importantly, here the 200m race has the start, whereas the second 200 of a 400m race doesn't, and that makes the difference even greater.  When Michael Johnson is running a 21.96 s second half, it's a) much, much faster than anyone else has run, and b) it's still a full 14% slower than his 200 and would be even larger if you accounted for the start.
   
   
3. You can also compare the halves of a 400m race, first to second 200m.  That is significant because it's known that the 48%-52% is pretty much universal.  However, in Oscar Pistorius' case, this comparison is not meaningful because of his affected start.
   
   This is important, because one can be misled if you just look at his first and second halves, because we don't know the time loss at the start.  I've heard Pistorius say it's 2 seconds, which is ridiculous, because he runs 100m in 10.9s, and so if he's losing 2 seconds, he's basically saying that he'd be a 8.9 second 100m runner without it.  So moving on from that...
   
   The point remains that Pistorius has an affected start, and that's why the first and second points above, where you compare his 200m race to his 200m splits gives you value AND accounts for any differences in the start

The key requisite is that the runner must have valid 200m and 400m times, and I'm happy to concede this point in this illustration. Many 400m runners race over 200m early in the season as part of their speed training, but that's different from recording a 200m in a targeted competition.  So the comparison will only work when the runner is racing 200m and 400m in targeted races, like Johnson, Felix, Perec and Richards-Ross did.  The issue is one of "capacity".  It does get trickier when you look at the 400m specialists (as opposed to the "double runners") who dip down only occasionally.  Then there is the variability in performance - these are not robots, and there is variability in performance that means you never really compare like to like.  Again, I concede this point, but this is why this illustration is not "proof", but comes at the end, almost an addendum to the three posts I've done on the science of Pistorius.  There will be disagreement, and that's fine, this is not proof, only an extension of previous explanations.

So I hope it's clear what the approach is - it's to compare an athlete over 200m and 400m, but not simply to look at times (which is what a lot of people missed in the tweet.  Fair enough, it's only 140 characters!)

The key is to look at how the race is constructed relative to that athlete's 200m race.

Oscar Pistorius - an increasing advantage as distance increases

So let's start with the simplest illustration, and then get increasingly more advanced.  The simplest thing is to take Pistorius over 200m and find similar performances in other athletes.

Pistorius' best 200m is 21.41s.  There are no male 400m runners with a 200m best as slow, so the best comparison comes from women runners. Allyson Felix has a PB of 21.81, and she's a great comparison because she's also focused on 400m events, like Pistorius (who races 200m seriously at the Paralympic level - it's important that the runner has to be competitive over both distances).  Then you can take Mari-Jose Perec, another 200m-400m combination runner.  Her 200m PB was 21.99s.  And Sanya Richards-Ross, a current 400m star, and her 200m PB is 22.17s.

So these three athletes are close to Pistorius - about 0.4 to 0.8 seconds slower than him over 400m.  But what about at 400m?  The image below summarizes the differences at the 200m and 400m distances:

So, those small differences over 200m, which you'd expect to be more or less doubled over 400m are suddenly much, much larger.  The Felix comparison is especially obvious - 0.4 seconds apart over 200m, and 4.6 seconds over 400m.  That is partly the result of Felix perhaps still underperforming over 400m, but you can't say the same about Perec, or Richards-Ross.  Their better performances are over 400m, and they too have a huge deficit at 400m, but not 200m.  

That's telling to begin with.  But, it's not a definitive point - you can counter this by saying that Pistorius loses maybe 0.5 seconds at the start.  And you'd be right - that accounts for maybe 0.5 seconds of the difference, but not all three to four seconds.  You could argue that Pistorius' 200m would come down, maybe to 21 seconds.  Fair enough, that accounts for 0.5 seconds, but not all three.  My point is that the differences are just so large that they are compelling.  (You can do the same for men's runners, but in reverse.  Find other 45 second guys, and you will find that all of them are more than 1 second faster than Pistorius over 200m, assuming they run 200m often enough to have decent times there, like Pistorius does)

Pistorius - putting the race together, racing 400m at close to 200m pace

But the picture crystalizes when you look at pacing and how the race is put together.

I've already showed Michael Johnson's performance - a 43.18s which was made up of a 21.22 and a 21.96s.  To the left is a figure showing the performance of each half compared to MJ's best, as well as a "conservative" assumption that he might have "only" run 19.8s in 1999.

So, 9.8% slower for the first half, 13.7% slower for the second half.  To repeat, the reason this has to happen is because the starting pace must be conservative to allow for distance, while the second half is slow because of a combination of pacing and fatigue.  Even if you make the adjustment, the pace is still 7.2% and 10.9% slower, first and second half, respectively.  

And remember, Michael Johnson is the exception to the rule - in most situations, you'll see an even larger difference than you see in this figure.

Perhaps you're dismissing Michael Johnson because he's such a great 200m runner, one of the greatest ever.  I'd argue that he's the greatest 400m runner ever, so his 400m to 200m comparison is, I believe,valid to compare to Pistorius.  But let's look at a few other runners.

First, back to the women - Felix, Perec and Richards-Ross.  Here, we don't have split data for their 400m PBs.  So, it needs an assumption.  And in in the interests of making the "conservative" assumption, we assume that their race is 48-52 split (remember that above, I showed that the average for women is 47.6%-52.4%, so this assumption is valid.  The graph below shows their projected splits, relative to their 200m bests.

So Allyson Felix, who I think is the best comparison by virtue of the fact that she's the 200m runner going up and still improving over 400m like Pistorius, runs the first half at a similar relative speed to Johnson (9.4% vs 9.8% compared to 200m times), but then her second half is very slow relative to her best.  Perec and Richards-Ross, slightly different runners in the sense that they were 400m runners going down in distance, start and finish closer to their 400m speed, but it's still a big gap - 5.5% on the first half, 14% on the second half.  Remember that their 200m PBs may be under-performances, much like Pistorius' may be this season.  But these are typical race patterns, relative to the 200m races.

Remember also that if you want to change the assumption of pacing from say 48-52% to 49-51%, and make them run faster in the second half, then you'll find bigger gaps in the first half of the race, relative to the 200m PB.  This is the strength of comparing to 200m PBs - the assumption over pacing and the split is actually not that crucial. All it affects is the relative size of the difference between first and second halves. The "weakness",which I freely admit, is that it uses 200m times, and assumes that they're max performances.  For Perec and Richards-Ross, I dare say they are not, and that they would be even faster over 200m.  Which of course increases the percent differences you see in the figure above.

Pistorius case

So let's now look at Pistorius.  The first issue is to ask what his splits would be?  We don't have his splits from the 45.07s race,  but from all reports, that bizarre negative split strategy that he used in Rome in 2007 has now been replaced by a more optimal one.  The fact that he could run a 46.78s with a negative split and a second half of 22.72s tells a story of its own, of a runner who doesn't fatigue normally, but for this discussion, that race is not relevant, because it is four years old and he's improved by seconds since.

So there are a few options.  One way to do it is to give him the "typical" race allocation of 47.8%-52.2%.  I've shown that on the far left in the figure below.  The problem is, Pistorius loses time at the start, and so his breakdown is likely to be more even.  So then we might make his race similar to Johnson's a 49%-51% split (the 'outlier' by comparison to other 400m races, as you saw in the figure above), and you see the figure in the middle is the result.  This would be the case, by the way, if Pistorius loses 0.5 seconds at the start.

And then a final option, just to make the point, is to assume that Pistorius does a 400m race with a 50%-50% split.  That is shown on the far right.  The reality is that this pattern would be highly, highly unusual, even given a slow start.  Remember, the normal pattern, the universal pattern, is that the second half is 2 seconds slower than the first half.  Even a full second lost at the start would not produce this pacing strategy.  Here, we've made every assumption possible IN FAVOUR of Pistorius, and the figures below are the result

In the figure above, it doesn't matter much which comparison you choose, there are some enormous differences between Pistorius and able-bodied runners, and they all suggest an advantage in terms of the relative pace that he runs a 400m race at compared to his 200m race.  And to repeat, this includes any time lost at the start.  For comparison, here is Pistorius compared to other able-bodied athletes:

So, the average, across able-bodied runners, is to run the first 200m 7.5% slower than the best 200m, and to run the second 200m 15.2% slower than the best 200m.  Pistorius runs both halves significantly faster than this, to the tune of anything between 2% and 6% faster for the first half, and 6% to 10% faster than the second half, depending on what the pacing strategy you assume. 

Take the 50-50 split example (bottom right graph).  Here, Pistorius runs the first half 5.3% slower than his 200m PB, which is the same as Perec and Richards-Ross.  However, then the second 200m is remarkably different - 5.3% compared to more than 14%, a 9% difference.  This the value of segmenting the race.  If you go with the typical strategy, then he is 4.2% faster and 8% faster than able bodied runners for the first and second halves, respectively.

Now, I realize there are assumptions here, but I hope that I've covered the range of possible inputs, and illustrated that if you assume a slow start, then the implication is a faster finish (both in time and relative to the 200m PB anchor), and in both instances, he stands out because of his performance over 400m segments relative to his 200m.  I would put the net size of that advantage between 3% and 8%, or around 3 to 4 seconds in a 400m race.  I dare suggest that if Weyand were to adjust his estimate based on the points I made in the previous post, he'd produce a similar number.

Some of you may be thinking that his 200m is a huge under-performance, explaining these findings.  I disagree - that PB of 21.41 is only a year old, and so it may certainly be up for revision, but only slightly.  You might improve it by half a second (based on the 400m improvement seen - it may not change at all, of course), and I'd invite you to look at what that does to the performance comparison.

In fact, there's only one way to make assumptions that don't give Pistorius an advantage - you have to assume that his 200m PB drops to 20.20 (a full 1.2s faster).  Possible?  Sure.  But overall, there are perhaps 10 assumptions you'd have to make, and the only way to NOT show an advantage is to make 10 out of 10 in one direction.  And yes, there are ranges (that's why Usain Bolt who is fastest over 200m is not guaranteed to win over 400m - he'd slow down more than others), but even with the ranges, you see an outlier. 

All told, what is the conclusion?  The conclusion is that Oscar Pistorius runs a 400m race at a speed that is much, much more like his 200m race pace than any other 200m-400m runner in history.  Why might this be?  Remember the big picture - you have a theory, you have evidence, and you have a mechanism. All these factors suggest that Pistorius sprints at a lower metabolic cost, with less work required, and therefore, the implication is that as distance increases, his pace declines less than for other athletes.

The key to this debate is by no means this observation.  The key is the evidence gathered, which I've explained in the previous three posts.  I post this because it's a compelling observation that lends further support to the theory.

Now, let's go onto the athletics and leave this issue behind!  

Ross

Appendix: Performance analysis - key to make the prudent assumptions

I foresee some comments about the idea about making assumptions.  It was the same when I tried to explain how performance analysis can help identify and explain possible doping behaviour.  So the first response is to emphasize that I'm not making these assumptions to PROVE a point, but rather to add to an already existing set of findings.  The evidence is there already.  I do the post above because it gives context to the evidence, a practical illustration of what the evidence suggests might be the case.  To me, it adds another "brick in the wall" in the issue of Pistorius' advantage, but it's not proof, and please recognize this before labeling as absurd any of the estimates.

But more than this, I'm a big believer in performance analysis, as regular readers will know.  I believe that if you are SENSIBLE about how you analyze performance, you can glean enormous quantities of useful information.

The key is that you have to be prudent about what you assume.  Before dismissing an illustration based on assumption as flawed, just remember that assumption is often valuable in evaluating options.  For example, in business, you always develop business cases based on assumption before making business decisions.  You make a "best case" and "worst case" scenario, and if the "worst case scenario"  still succeeds, then the business will likely succeed.  I used to do this all the time when I worked in sports business because for example you have work out if a sports event is viable.  So you assume how many tickets you'll sell, what the costs of staging the event are, and so on.  If you make all the worst assumptions, and succeed, then the event works.  And that's the principle here - reasonable assumptions show what is feasible and what is not.

In the Pistorius debate, Peter Weyand tried to quantify the size of Pistorius' advantage by adjusting his mechanical advantages and making them equal to those of able-bodied athletes.  The result was his estimate of a 12 seconds advantage, which is probably an over-estimate.

But the point I made the other day is that it was the assumptions that may be incorrect, not the principle, and the same goes for any performance analysis.  So above, I have tried to make the equivalent of "worst case" scenarios.  Don't just make Pistorius equal to the "typical" case, because clearly he is not.  Rather make him the outlier and see what happens then.  So don't give him the 47.8%-52.2% split which is typical, show the 49%-51% and the 50-50 splits as well.  Reduce the 200m time to see how it affects the pace.  And when those are all done, then you start to see the picture.

There are perhaps 10 assumptions you can make - if you make all 10 in the "favourable" direction, then you find that Pistorius is getting an advantage of around 15 to 18% (7 to 8 seconds in a 400m).  If you make all 10 in the "unfavourable" direction, then you can estimate the advantage at around 3 to 4% (about 2 seconds).  The reality is that it's likely to be a moderate version.  But the advantage is still there.