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Thursday, July 01, 2010

Cycling performance: What is possible?

The limit to cycling performance: Can physiology flag doping?

Yesterday I posted on the upcoming Tour de France, and made mention of a topic that I feel is:
a) Really interesting as a means to add value to watching the sport, and
b) Potentially interesting as a means to flag suspicious performances.

And rather than wait until the Tour begins, I thought I'd take advantage of a rest day in the FIFA World Cup to get some thoughts going, since I left yesterday hanging somewhat (deliberately, but still...)

And so here are some thoughts on the ability of performance to predict physiology.

Estimation and assumption

Perhaps right up front, I have to talk briefly about estimation and assumption vs measurement.  Of course, the ideal would be to get accurate SRM data on the power output on the climbs.  Of course, it would be wonderful to know with precision what the power output was, but as I hope to illustrate, the errors in these kinds of calculations can both be minimized and controlled so that you end up with a 'best case scenario".

This is much the same situation you would find yourself in if, for example, you wanted to open a coffee shop and had to do prepare a business model.  You don't know how many cups of coffee you'll sell, you don't know how many biscuits to bake.  But if you know your market, and its people (your future customers, you hope), then you can control your assumptions and go a long way to making a conclusion.  That is, if you make "best-case" assumptions and still your coffee shop is running at a loss, then it clearly is not a viable business.  If your "worst-case scenario" (few customers, few sales) still makes a profit, then the business works.  Realistic and sensible assumptions are the key to ensuring that your conclusion is accurate, even in the absence of a crystal ball!  Similarly, for these physiological calculations, you can make "best-case" assumptions and if the picture still doesn't fit, then you have a good case for a problem.

So over the next few weeks, I think we must acknowledge right away that these are always estimations - of power output, of body mass, of bike mass, of wind speeds and directions - all these factors will affect the eventual physiological calculation, but for two reasons, their effect is not as large as you might think:
  1. We're not proving anything here - only suggesting physiology for the purposes of increasing enjoyment and stimulating discussion, and 
  2. The physiological implications are so large that even errors don't affect the conclusion.
So let's say it now, one last time - this is not proof, but an interesting exercise nonetheless, and I believe a compelling way to approach the problem.  Ultimately, people will believe what they wish to, even when presented with a 'creaking and ugly edifice'.

So let's get cracking...

An extreme case - the physiological implications of 8 W/kg for 40 minutes

Let's take a rider who produces 8 W/kg.  Assume his mass is 70kg, which means an absolute power output of 560W.  Clearly, very high.

In order to work out the physiological implication, by which I mean the oxygen cost, there are two potential methods.

The first involves the use of a published paper called "Peak power output predicts maximal oxygen uptake and performance time in trained cyclists".  This study looked at 100 trained cyclists and established the following relationship between oxygen consumption (VO2) and power output.  The relationship is:

VO2 (L/min) = (0.01141 x Power output) + 0.435

Therefore, if you take the power output of 560W, and you apply this equation, you will calculate an oxygen consumption of 6.82 L/min.  Relative to body mass, this is equal to 97.49 ml/kg/min.

The second method, just for comparison's sake, requires that you do three things:
  1. You calculate the real energy cost of producing that power, by taking advantage of the fact that cyclists are not perfectly efficient.  In fact, elite cyclists are only about 23% efficient.  What this means is that a cyclist who is riding at 560W is in fact producing 2435 W.  Clearly, we now have our first assumption - the efficiency.  Lance Armstrong's efficiency was measured as 23.12%.  Other studies find values that range between 21% and 27%, though values over 25% are hotly debated, and basically dismissed as an artefact of testing and equipment.  This is a controversial issue, but most elite cyclists seem to be around this 23% value, and since Armstrong's was measured there, I'll use it for the remainder of this calculation.

  2. The total energy can now be used to work out an oxygen consumption.  This requires that you have knowledge of the contribution of various energy stores to the physiology.  We know that every liter of oxygen used produces between 4.69 kCal and 5.05 kCal, depending on whether fat is being used, or carbohydrates.  So, this is our next assumption - which end of this spectrum do we use, the 4.69 or the 5.05kCal?  The answer is the further right extreme, for two reasons.  One is that it's physiologically reasonable - a cyclist producing maximum effort is going to be near maximally using carbohydrates.  Second, this is the "conservative" or "best-case" assumption, as explained earlier.  So we'll run with 5.05 kCal/L O2.

  3. We can now work out the oxygen consumption for a given power output at a given efficiency.
In our example, 560 W produces an oxygen consumption of 6.91 L/min, or 98.71 ml/kg/min.

You'll note that this is similar to the value of 97.91 ml/kg/min that we calculated using Method 1.  This suggests that the above assumptions of efficiency 23% and energy use per liter of oxygen are correct.  I must point out that we haven't yet considered the contribution of non-oxygen dependent pathways (the so-called anaerobic contribution) to energy.  This is of course important, but I would also point out that we are talking about a cyclist who is producing this power output for 40 minutes at the end of a 5-hour cycling day, and so the assumption on energy demand, given the length of exercise, is still valid (in my opinion).

Now, what do you make of that oxygen consumption of 97.9 ml/kg/min?  If I measured it in the lab, I'd be checking my equipment...clearly, something is wrong.  And if a cyclist were able to produce that power output (8 W/kg) for 40 minutes, with that physiological implication, then you'd be calling him out (or you'd be looking for the electric motor in his pedals).

If you assume, for example, that a cyclist can maintain 90% of their maximal level for 40 minutes, then this oxygen use of 97.9 ml/kg/min corresponds to a VO2max of 110 ml/kg/min.  The red flag is clearly waving.

So when is it possible for a cyclist to ride at 8W/kg, assuming they have a VO2max of 80 ml/kg/min?  Well, their cycling efficiency would have to be around 32% - many percent higher than anything ever measured before.  9 W/kg, which I throw out only because it was suggested is possible on a chat forum, would require that a cyclist with a VO2max of 80 ml/kg/min is 35% efficient.  Either that, or a cyclist with an efficiency of 23% would have to have a VO2max of 123 ml/kg/min.  It simply doesn't happen, and therefore, neither do 8W or 9W/kg for 40 minutes.

Now, let's look at a much more conservative assumption - the decent level cyclist...

The "low end" - 4 W/kg for 40 minutes

Most trained cyclists would be able to produce this power output.  In our lab, we test the range of beginners to elites, and this what you would expect of a decent level cyclist.  And we know that a decent cyclist will produce a VO2max of around 60 ml/kg/min.

Using the same method as before, we can estimate that the oxygen consumption associated with this performance of 280 W is equal to 51.9 ml/kg/min.  If you prefer method 2, using an efficiency of 23%, then you'll calculate 49.4 ml/kg/min.  The reason this is lower, incidentally, is because this person is unlikely to have an efficiency of 23%, but one that is lower than this.  If we use 22%, for example, we calculate 51.6 ml/kg/min.  Again, this shows that 23% is a pretty safe "best case" estimation.

Again, if you assume that a rider such as this is maintaining 90% of max, then the inferred VO2max would be equal to 57.6 ml/kg/min.  That's a perfectly reasonable value.  If anything, it's on the low side, which I again point out shows that the assumptions I'm making for all these calculations are "conservative".

The key assumption in this regard is the 90% of maximum assumption.  In reality, a good level cyclist will ride at 85% of maximum, which means our inferred VO2max suddenly rises to 61 ml/kg/min.  I also maintain that a Tour rider, on the final climb of the day, will be closer to 85% than 90%, given that they've been riding for five hours.  However, this assumption is debatable.  My point is, if the physiology is still unrealistic with these safe assumptions, then you know you have a problem.

So now, we've looked at two extremes - the high, which simply doesn't exist, and the low, which is safe and clear and maybe even a little conservative.  There is a point in between, where elite Tour riders exist, where the really interesting questions begin.  So let's look at a Tour rider...

Bjarne Riis - 6.8 W/kg for 35 min on Hautacam.  Or Armstrong - 6.6 W/kg for 38 min on Alp d'Huez

Bjarne Riis is estimated to have produced 6.8W/kg (480W) on Hautacam when he won the Tour in 1996.  Armstrong's estimated power output on Alp d'Huez was 6.6 W/kg (465W).  This is Vayer and Portoleau's estimation, and I believe it to be accurate.  I actually saw a PhD student from Texas present a similar analysis at the ACSM conference in 2005, and he had worked out 495W (7 W/kg), taking into account the gradient every 100m as well as wind speeds.  If anything this is more accurate.  But as I mentioned, we'll be "conservative" in our calculations, so let's take the lower option and see what it means, physiologically.

We again assume 23% efficiency (in Armstrong's case, this is not an assumption - it was measured by Coyle), and we can calculate that the oxygen cost of producing 465 W is equal to 81.96 ml/kg/min.  Using method 1, the equation from the published literature, we find oxygen use of 82.00 ml/kg/min, pretty much identical.

Now, is it possible to ride at 81.96 ml/kg/min for almost 40 minutes?  If you are at 90% of maximum, then it means that the VO2max must be equal to 91.07 ml/kg/min.  If you are at 85% of maximum, then the maximum must be 96.42 ml/kg/min.  Given that by the time these performances happen, the cyclist has been in the saddle for five hours, not to mention about 2 weeks before, I feel pretty safe in saying that you're projecting a VO2max that lies somewhere between 91 and 96 ml/kg/min, probably closer to 96 ml/kg/min.

Another example comes from Armstrong's own words.  In this interview, he says "I also cranked out 495 watts for more than 30 minutes".  495 W is about 7W/kg, and applying the same equations as I've done throughout this post, you can work out that it requires oxygen consumption of 87 ml/kg/min, and a VO2max of 97 ml/kg/min (and that's at 90% of maximum.  If you go with 85%, you get 103 ml/kg/min...).  

Is that realistic?  I suspect that your answer to that question depends not on what you know, but rather on what you want to believe.  I don't believe that it is possible, because the combination of high efficiency (and 23% is high) and high VO2max doesn't seem to exist.  In fact, Lucia et al showed that there was an inverse relationship, so that those with the best efficiency had the lowest VO2max. So the problem is that if you suggest that we increase the efficiency to make the predicted VO2max come down, you're chasing the pot of gold at the end of the rainbow, because the possible VO2max is coming down anyway!

However, people will draw their own conclusions.  I am of the opinion, like Prof Aldo Sassi, that a value above 6.2 W/kg is indicative of doping.  And in the coming weeks, I will post more on this, including graphs that hopefully illustrate this point even more clearly.  But, as always, there is likely to be debate.

Next up - the Quarterfinals

That's it for cycling for now - during the course of the Tour de France, we'll return to this kind of approach and look at some of the performances, and compare them to historical numbers.  As always, the discussion is welcome.

The cycling now gets put on hold for a few days while the Football World Cup Quarter Finals take place!  I am sitting on piles and piles of data about how far players run at different altitudes, and even how goalscoring seems to be affected by the altitude.  But perhaps for two days, I will be a fan, and then resume the analysis next week!

Oh, and there's Wimbledon!  And the start of the Tour!  Enjoy it, and we'll be back soon!



matt said...

Again, great article and great series. I have two questions. First, how is efficiency measured on a bike. Second, how is the 560W max power output for a 70kg rider calculated.

Ross Tucker and Jonathan Dugas said...

Hi Matt

Thanks for the comment and the question.

Regarding the efficiency, best bet is to refer to this article:


It talks about the measurement. As I said in the post, it's a tricky one, because of equipment issues. Basically, it's the ratio of how much work is being done to power the bike over how much work is being done metabolically.

So, a rider may be producing 200W, but his energy use is 1000W, which means he is 20% efficient.

The 560W is an arbitrary value - I was giving a high extreme here, so I used 8W/kg to illustrate the high end of the extreme, and 4W/kg to illustrate the low end. On the bike, that power output might be measured using an SRM device, or it can be estimated if you know mass, gradient, time and rolling/air resistance. This is what was done for the Tour rider example in the post. I hope that clears it up a little...


Steve said...

I remember reading in Lore of Running (and probably your book, too) that V02max is less of a performance limiter than efficiency (at least for running). Is that also believed true for biking? The page you linked to about the inverse relationship between V02max and efficiency was a news article, not a peer reviewed journal article. It would be interesting to read the latter if you have access to such. And/or if you could explain in more detail why there would be an inverse relationship there, that would be helpful. Also, I had heard speculation that Armstrong may have a "natural" performance enhancement as a consequence of having had testicular cancer, possibly resulting from higher-than-normal testosterone production. Here's the source: http://www.medical-hypotheses.com/article/S0306-9877(06)00633-5/abstract Maybe you've already commented on this, but it would be interesting if you had any insights on it. Finally, it seems likely that after 5 hours of racing a cyclist would lose some weight; I wonder how much weight loss it would take to affect the calculations significantly.

Anonymous said...

Great article Ross. thanks.


Thomas said...

If we take Armstrongs own words for granted he would have ridden the Col de La Madone with a relative power of 6,6 W/kg in 99´ before the tour. Lets say he was weighing 75 kg at the time. That would give an power output of 497 watts. Just as he is saying in the article. Scary to think that Armstrong tweeted he was close to that earlier in this week. Last year Armstrong often rode at 6,2 W/kg

Kevin said...

I'm always skeptical of peoples inferences drawn from VO2 values. In new running science (more street talk than literature, but indicative of something) VO2 should be taken with a large grain of salt because of the test's reliance on the athlete deciding when to call it quits. I make this distinction because of the central governor theory of fatigue suggests that an athlete, especially an elite athlete, (and more especially the lance armstrong-attituded athlete) will push so much harder on the pavement than the lab. (A citation for the street talk: http://www.scienceofrunning.com/2009/12/fallacy-of-vo2max-and-vo2max.html)

Besides, extraordinary athletes are just that, extraordinary. Sports science has a tendency to disprove what happens anyway. Bannister's Mile is the easy example, but I'll excuse the 1950's science. But Bubka's vault despite physicist saying 20' vaults are impossible, or Even Solinksy's feats, among other examples, demonstrate that science should realize they are dealing with those 1 in a million, (actually, 1 in 6 billion) kind of people.

Ryan said...

Good news for the brains out there! Looks like you'll have all the data you can handle from team HTC.

Giovanni Ciriani said...

Great article!
I'm a little rusty on my statistics. The study you cited says Wpeak explained 94% of the variance in measured VO2max. Doesn't that entail that there is a good probability of being 6% away from it, and still be OK? (or something like that)

Anonymous said...

Interesting article. A good point was made about the science in the 50's saying no human can run 4 quarter miles at 60s each to go sub 4min for the mile, yet it was done and is quite common today.
I also noticed you give a one to one relationship between work output (W) and VO2 when working at greater than 90% VO2. I would think the increase in Watt output declines drastically once you are past this threshhold, along with efficiency
Also, there are documented cases where individuals have greatly exceeded the norms of human capability under emergency conditions. This would indicate there must be an untapped source of power within the human body that we don't understand.
Not all performances follow the laws of science as we know them. Just look at the bumble bee???

David Guedalia said...

Great article, made me think, then it made me go calculate my own stats.

So, about a year ago I did a VO2 max test and came up with 43. I then did a short time trial ~24 minutes up a hill, where I averaged ~250 watts.

I weighed ~75 kilo at the time.

Following your calculations, I get by method 1:

VO2 (L/min) = (0.01141 x Power output) + 0.435

4.0375/75 = 53ml/kg/min

method 2 gives me:
250 watts at 20% (since I am not a trained athlete) is = 1250 watts = 1074 kcal; 1074/60 = 17.9; 17.9 / 5.05 = 3.5; 3.5 / 75kg = 46ml/kg/min

now given the 90% rule, my VO2 max should be: ~50 -> ~58

but it is not.

-- my basic ability to produce 250 watts, is challenged by my measured VO2 max of 43.

Now maybe you can say that a 24 minute time trial is not a good measure.

So, recently I went up Mount Ventoux, 1:51, which I worked out to be roughly 250 watts (a little less)

So, maybe my measurement of wattage is not accurate (since it is calculated), well, in between I have measured myself in a gym, and found myself producing 250 watts reasonably well on a stationary bike.

So I am stuck. Either I have been doping or I am able to tap some other source of energy. Or my VO2 max was not accurately measured in the lab or something else.

Like any good scientific theory, there is a thesis and then empirical evidence to prove/disprove the thesis.

I invite everyone else to post their numbers. Lets gather data.

Ross Tucker and Jonathan Dugas said...

Hi Steve

Sorry about the link - I pasted the incorrect one by mistake. I've gone back and fixed it, I hope. But here it is anyway:


Re the inverse relationship, the best analogy I can think of is that a car that is more fuel efficient will burn less fuel at top speeds than another, less efficient car, but the speed it can reached is limited by something else (aerodynamics).

So a cyclist with higher efficiency, using less oxygen, will reach a peak power output using less O2 than another cyclist, but ultimately both are limited by factors other than VO2max. Muscle fatigue, mechanical strain, for example. The result is that a highly efficient cyclist will use less oxygen at a given workload, right up to the maximum, and so is likely to have a lower VO2max. Key is that he is not necessarily limited by the VO2max - this is another debate entirely. But basically, the VO2max is the consequence of the workrate being achieved and the efficiency of the rider doing it. Hope that makes sense?

Will respond to the others shortly!


Ross Tucker and Jonathan Dugas said...

To Anonymous at 5:06am

You're right about science being wrong about the limits to performance before. I know that it was once predicted that women would soon beat men in the marathon, based on mathematical analysis of times, and that clearly didn't happen!

So point taken. But I think this is different. What this exercise is trying to show is that if a cyclist is able to produce 8W/kg, then they are doing so with physiology that doesn't exist today. Sure, in 50 years, 100 years, it might well (though I must say, gene doping is the only way it will). However, right now, you don't find cyclists with this kind of oxygen carrying capacity. Or with the efficiency required to produce that power output. As I've said on some chat rooms, if I discover this rider, I pack my bags and head to Europe, because he'd dominate the Tour!

It simply doesn't happen, so as we stand, and if we look backwards to the Tours of the early 2000s, I believe we can say that nobody would have been capable of 8W/kg, and no one would have been capable of 7W/kg. Maybe in 2065, it will be possible, but not now, and not back then...

As for the untapped source, yes, sure, but day after day, every day, on demand? And this is a bike race, not that kind of emergency situation, which usually leaves the person "damaged" in some way. That reserve exists for a reason, which makes it something of a "moot point", a reserve without being a reserve, and the only way to access that reserve would be doping. It's like saying that someone can commit suicide by holding their breath. It doesn't matter how badly they want to die, physiology will stop them...

Finally, re the bumblebee, I disagree. The bumbledee doesn't do the impossible, it is just that we don't understand that what the bumblebee does is possible.

This of course means that in this current example, the same may be true, that we don't fully understand the physiology. We certainly have a lot to learn, I concede that point. But again, this is different, because we do have data on "clean riders" and we do have the ability to compare their lab tests to their race performances, and we do know and understand what the body is capable of. We also have historical data, and I guarantee you that the performances today are slower than what we saw in the 90s and up to about 2006 - the biological passport has done a great deal to "control" doping. So overall, the collection of data, the fact that we've SLOWED down, suggests that doping drove the peloton and the winners in the 90s and 2000s, and now it's less severe. Not absent, but less severe.

Your argument is a philosophical one, and it's impossible to prove as either correct or incorrect, because it's an argument that WANTS to believe. Which is fine, but the data suggest otherwise. Perhaps in 50 years, I'll be shown to be incorrect!


Ross Tucker and Jonathan Dugas said...

To Steve

A similar response to the one above this one. Fair points, but I disagree that you're looking at 1 in a billion athletes.

You're looking at physiology. And physiology dictates performance capacity. It's not some supernatural ability, it is measurable and quantifiable. I am revealing my biases here, but I base this on the literature (and I did my PhD on the Central Governor and so I can assure you, I'm the last person to base everything on VO2max - I think you have misread the post if you believe this to be the case).

The reality is that the Tour is slowing down. In the Giro this year, the power output is substantially lower than in previous years, right from the winner to the autobus. And this is a sign of the success of the biological passport. This fact, plus the fact that physiologically, a cyclist cannot ride at 7W/kg for that length of time, means you're not dealing with these "alien" species who defy all physiological belief.

I've tested some of them, they're normal athletes who obey the same physiological rules as you or I, only at a much higher overall level of performance.

I'm not sure where this notion of "super-athletes" comes from. It's PR and marketing, a dream-like state that has us believe we're watching the impossible. We're not. They are amazing athletes (even with doping, I have to say), but physiology explains what they do.


Ian said...

Basset et al published a really interesting paper in MSSE 31(11): 1665-1676, 1999 tiled "Comparing world cycling records, 1967-1996: modelling with empirical data". If you take their data in Table 7 and apply a 4% absolute error to their power data, power outputs are generally lower than 6 W/kg. Only more recently have riders been able to ride for an hour at >6 W/kg.

Rider W/kg (W/kg-4%; W/g+4%)
Bracke 5.6 (5.3; 5.8)
Ritter 4.9 (4.7; 5.1)
Merckx 4.9 (4.7; 5.1)
Moser 4.6 (4.4; 4.8)
Moser 4.7 (4.5; 4.9)
Moser 5.3 (5.0; 5.5)
Obree 5.1 (4.9; 5.3)
Boardman 6.0 (5.8; 6.3)
Obree 5.4 (5.2; 5.6)
Indurain 5.6 (5.4; 5.8)
Rominger 6.9 (6.6; 7.2)
Rominger 7.4 (7.1; 7.7)
Boardman 6.5 (6.2; 6.8)

Riding at >=6 W/kg at the end of a Tour de France mountain stage...

Ralph said...

The other day we were talking about technology in soccer - now here's a thought: to what extent may the Johan Bruneel's be guiding their riders through their 2-way radios to slow up a bit on the climbs (based on the telemetry in the car) so that these superhuman performances can be held back just enough so as to reduce suspicion..?

fxg said...

Let’s look at the problem another way. In your analysis, you keep the threshold and the efficiency fixed and allows VO2max to vary. I understand you do this because doping changes VO2max, but this value is not supposed to vary much in clean well-trained athlete. You also do this because efficiency is not supposed to change and this was one of the arguments put forward against Coyle’s study on Armstrong. But there is now a new paper on elite spanish cyclists (some winners of the three big tours), which followed a much more rigorous protocol than Coyle’s, that shows a significant improvement of efficiency over 5 years (DE23 to 27%), which is higher than the improvement measured in Armstrong (Santalla et al., 2009). This lend strong support to Coyle’s study because if elite spanish cyclist can improve their efficiency, the best cyclist ever certainly did improve his also! So let’s assume for one second that the results in Coyle’s study were correct (you do the same with the 23%). There is no reason to suggest that the improvement of Armstrong’s efficiency stopped in 1999, so let’s assume that it continued to improved at the same rate from November 99 (date of the last test) to TDF 2004. Let’s also assume that his VO2max and his racing weight did not change and remained at 85ml/kg/min and 72 kg respectively. Using the same calculations, but a slightly more conservative fuel consumption of 5 kCal/L of oxygen, it is possible to predict the range of possible power developed by Armstrong in each TDF assuming he would climb at 80-90% VO 2max. Here is what one obtains :
TDF99 : 396-445W
TDF00 : 400-450W
TDF01 : 405-455W
TDF04 :419-471W
Now let’s compare these values with the range of calculated power presented on this website :
TDF99 : 387-436W
TDF00 : 406-457W
TDF01 : 411-452W (Plateau de Bonascre at 475W)
Alpe d’Huez04 : 465W
Owing to all the uncertainties in calculations, the match is quite remarkable. With all your respect, there is less arbitrary assumptions in this analysis than yours and although spectacular, this steady improvement can all be explained by an improved efficiency without doping (unless the 6.1L/min measured in 1993 was achieved by doping, which is quite possible!).

Byron said...

Hi Guys,

Love your work!

Does that mean that we're back to believing that Merckx is the best cyclist of all time?

And doesn't this article plus your other chart showing Contador at 1760 (while Riis, cheating, and Armstrong, NEVER poven to have cheated, both near 1660) prove that Contador has been cheating somehow?


Ross said...

HI Byron

Thanks a lot! Well, depends if you believe Merckx was clean! Amphetamines were the drug of choice back then - Tom Simpson's death near the summit of Mont Ventoux was attributed to his amphetamine use!

In fact, I recall that in the very first Tour in 1903, cyclists used strychnine and wine to dull the pain!

I think doping is still rife in the peloton, yes, but certainly coming under control. If one compares this year's Giro to previous years, you see a massive drop in power output on the climbs. If memory serves me, the winning time from the Zoncolan this year was only 30th best the last time they did it, despite what are being reported as better conditions - cooler and with less wind! So yes, I suspect the top riders are all still doping, but it's a 'controlled doping' rather than what we had in the 90s and up to about 2006. I think the biological passport is a big weapon that has helped bring it under control, as we discovered with our interview with Yorck Schumacher.

As for proving it, unfortunately, no, because with Contador's performance, if he'd had a tailwind on that climb, then his power output comes down to 6.2W/kg, or thereabouts, and as you saw yesterday, that's what I would deem suspicious but not proof of doping. It's in that grey area. Like I said yesterday, 7W/kg starts looking ridiculous - guys would have a max of over 100ml/kg/min. And 5W/kg is entirely reasonable. But in the middle, at 6.3W/kg? That's a grey area!

Thanks for the feedback, and let's hope this Tour is drug free! Though I suspect "drug-free" is not the same as saying "without the use of drugs"!


Anonymous said...

I'd like the sport to clean itself up as much as the next man, but I really dislike this line of argument - how are extraordinary, clean athletes supposed to compete in a sport where performances beyond a certain fixed level are considered proof of doping?

Ross, what studies have you got that prove anything about clean, elite cyclists? Presumably you don't have any, because you say yourself that they have all probably been cheating since the '60s. Therefore all your assumptions are on shaky ground, especially the maximum pedalling efficiency but also the maximum VO2 max possible.

Finally, one thing that always amazes me on this subject - why is so much "sports science" based on these kind of back-of-the-envelope calculations when cheap and easy experiments seem to be available? VAM is utter rubbish, championed by a dodgy doctor with a known history of producing superhuman performances. Alpe d'Huez (along with most others) is a public road - why not take a motorised bike with measuring equipment up there in 38'40" and find out what the power output actually is, instead of all the guesswork?? (or just get hold of some truthful power numbers off the TdF bikes)


Ross Tucker and Jonathan Dugas said...

HI edb

Good questions.

To respond to the first one - this line of thinking is useful if you assume that performance limits can be calculated based on physiology. You don't, which is why you're suggesting that extra-ordinary clean athletes will be discriminated by it.

Also, please read the post again - I have explicitly stated, at least three times, that this does not constitute "proof" of doping. I appreciate that it is implied, but I'm trying to move away from that definitive approach, precisely because there is room for error.

However, I still maintain that the error in the calculations can be worked around - I have made some ridiculous assumptions in my estimates. For example, the notion that a guy can ride 90% of max at the end of a 5 hour day, is a stretch, in my opinion. Similarly, the caloric breakdown is assumed in the rider's favour. Yet it still produces what is clearly an unrealistic physiological picture, and that is telling.

As for the question about elite cyclists, I think your point only re-inforces the fact that Tour performances are suspicious. Because if lab studies are being done on doped cyclists, and they're still only getting VO2max values in the low 80s with 23% efficiency, then what does it take to produce either VO2max of 95ml/kg/min or efficiency of 27%?

However, this is a moot point, because there are plenty of clean riders. I'm not sure where you get the idea that I've said they have "All" been cheating since the 60s. I've certainly never said that. What I have said is that the sport has had a problem since the 60s, that most of its major champions have doped, and in particular, I don't believe there has been a clean champion since the 1990s. However, that's different from saying "All", and I do believe there is enough data that we know the physiology of cycling well enough to say with high accuracy what is possible and what is not.

The assumptions are thus not shaky. In fact, if doping has been prevalent, then those assumptions are even safer than before,because doping would shift

Finally, fair question about the actual measurement. The reasons it's very difficult are numerous. We know exactly what power output would be required to climb Alp d'Huez in 38:40 on a still day, no wind. However, it gets much trickier because wind factors in, plus drafting, plus the pacing of the climb (power is not distributed evenly) as well as the weight of the rider which is not measured at the bottom of the climb.

So when a performance of 39 minutes is recorded, you can't simply scale it down using your motorbike as a 'benchmark' - the wind, the mass, the drafting, must all be taken into account.

The only way to get accurate data then is using SRMs, which many teams are now doing, so that should help resolve that issue to some extent.


DrTim said...

Let there be light!


Nil said...


Just to follow-up on the stats question: I believe you are thinking of a confidence interval, which this is not. This number suggest that 94% of the variance of VO2max is explained by W peak and 6% of the variance can be explained by other variables.

Hope this helps-

Anonymous said...

Thanks for coming back with responses - I find it to be a very interesting area of discussion.

I do agree with you that performance limits can be estimated based on known physiology, sort of, but only in the way that invites a freak of nature to break the mould. For example it would have been easy to use similar logic a few years ago to prove that even the ideal athlete (a short, stocky one for faster striding pattern, of course) was not likely to get the 100m record much below 9.8sec. Someone has already mentioned similar ideas around the 4 minute mile in the 1950s. So overall I'm not sure the analysis proves anything apart from providing another obstacle in the path for a genuine new talent of the future who can climb at 7W/kg clean.

I take your point that studies on possibly-doping elite cyclists are more likely to skew the data in a favourable direction for your analysis - but I think this is still problematic when it comes to analysing that data. For example confessing dopers have been known to say that the main problem with using EPO is that you have to go easy sometimes in races so the jump in performance isn't too obvious. Surely their test results are just nonsense.

I was sort of half-joking about the motorbike, and I know there are lots of confounding factors in measurement, but Alpe D'Huez is not a hugely windy place and the weight of the riders is not much of a secret. I think it should be easy to come up with some much-more-accurate-than-VAM measurements based on power. I'm amazed that discussion still centres around "so-and-so said Armstrong's W/kg was x" when it would not take much to ascertain the actual, absolute, power output of a rider of given weight climbing a given mountain at a given speed with a given drafting profile on a still day at least.


Anonymous said...

Your thoughts on this?


Alex Simmons said...

Another look at ascension rates and power to body mass ratios:

Ross Tucker and Jonathan Dugas said...

HI Alex

Thanks for the link - interesting perspective, makes good points!

Are you going to have a look at the power output estimates on today's mountain finish? Would be good to compare to SRM data from those riders publishing theirs. If you have power outputs, let us know a link too, it'll make for a great post!


Roger said...

Hi scientists,

with a passion for distance running I really enjoyed your strafing of the barefoot cult that so needed exactly what you brought to it. Kudos.

And this article is really interesting and seems pretty sensible, which I think is a less presumptious way to describe it than 'correct'. But I'd really like to see your response to idavidg's comment, as to whether he's wrong in his equations or his assumptions and why, or whether he might have a point.

It would be interesting to see how teams offering more data fare within this question of peak vs improbable performance. Phil Liggett the British commentator was talking the other day about their energy consumption in the mountains being around 6000kCal per day, which is just a brutal figure to match 3 days in a row. If there are already article here about the science and strategies of endurance athletes working at such a level they'd be well worth a search. If not already , in future maybe?

Ron George said...

A similar wind and density effect analysis from me can be found here, (except I didn't go to the extent of breaking down a climb into so many finite sections as Simmons did. Having quickly calculated the increase and decrease in watts/kg demand due to wind and altitude, I must say that it is entirely plausible that a performance can be clean and still hover around the 6.2 W/kg barrier.

Anonymous said...

question for Ross.

Assuming the data and calculations we can apply now are pretty accurate (which its fair to say they seem to be).

If we set a limit based on best performances measurable now, whats the effect on longterm chance of exceptional athletes being born? Ie can we assume that in the 10 years or so we have good data / estimations for the natural performance ability spread of athletes cycling covers the whole range possible within the human genome?
In other words is 27% efficiency (or pick your number) an absolute impossibility for a human being? And how can we estimte that? Or do you recon that in the next 100 or 200 years someone could naturally achieve that?

Or really what I'm saying is - shouldn't we focus on how to detect cheating better (seems the science of testing protocols and lab work ability is kind of crap at that today) rather than set physiological limits that are arbitrary and could cast suspicion without proof?

I know its interesting and may help 'target' certain riders, but surely thats largely common sense and also what the passport system does??

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

You're 100% correct, and you put it very well. This is why you can't use this approach as proof, but rather as one bow in a quiver full of them, in the fight against doping.

The biological passport remains the key, and I am convinced it is having a positive (pardon the pun) on the sport. Certainly, I don't believe the climbing power outputs are as high as they've been in the past, based on the SRM data published so far. They are also physiologically 'reasonable'.

As for the 'freakish' athletes, of course there is this possibility. Equally, there is a chance of a once-off freakish performance, like that of Bob Beamon, who was a great athlete who produced a freak jump at that time. Perhaps Bolt is the same. I certainly hope he is - it would be a massive blow if he weren't.

But this is why I'd also be cautious about exclusively singling out individuals - to me, performance analysis should be applied to the entire peloton - if a winning performance of 2010 is comparable to a 20th best performance 10 years ago, then that's very meaningful. If the average of the top 20 is now similar to the average of the top 50 from 10 years ago, then it's a sign of progress. And the physiological implications help to explain this, and they're interesting (to me, anyway!).

But yes, absolutely, and I'm sure that if Yorck Schumacher reads this, he'll agree - the priority must be on the testing, with physiology creating context and better understanding.


Giovanni Ciriani said...

Great article!
I'm a little rusty on my statistics. The study you cited says Wpeak explained 94% of the variance in measured VO2max. Doesn't that entail that there is a good probability of being 6% away from it, and still be OK? (or something like that)