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Friday, July 24, 2009

Tour de France 2009: Contador VO2max

Alberto Contador - can he have a VO2max of 99.5 ml/kg/min?

I came across this interesting piece on Cyclingnews this morning. It caught my eye because it's an extension of a topic that we've been covering in the last week, analysing Alberto Contador's Tour-winning climb up to Verbier.

In the article, Antoine Vayer calculates that given Contador's power output on that climb (which he calculates as 490W for a 78kg "normalized" rider - more on that later), and with one or two assumptions to turn that power output into oxygen consumption, Contador would be riding at 5.55 L/min. The problem with this is that it implies that Contador's VO2max is about 99.5ml/kg/min!

Not that VO2max is the be-all and end-all of exercise, mind you (though some still believe it's the key variable), but that value is off the charts. Some would say preposterous. Most elite athletes have VO2max values between 70 and 80 ml/kg/min, with a few above this. For Contador to be approaching 100ml/kg/min clearly raises a flag.

And it did, with Greg Lemond calling for proof that Contador is capable of achieving these numbers without using performance enhanching products "assuming the validity of the calculations".

And herein lies the catch - are the calculations valid?

Well, first of all (and thank you to Seb for pointing this out - my French is hardly 'parfait', so I'm afraid I can't do the original piece justice!), the Cycling News article is actually incorrect when it quotes Vayer as calculating a power output of 490W. In fact, what Vayer has done is to work out a power output and then normalize it for a rider of 70kg and a bike of 8kg, so that different riders can be compared. This value of 490W actually corresponds to an 'absolute' power output of 440W for Contador. This has implications for how one discusses Vayer's subsequent calculations.

Just on this note, I still think that this calculated power output of 440W is a little on the high side. For example:

  • Last week, we looked at Contador's climbing rate (VAMs) and using Michele Ferrari's formula, arrive at a power output of 6.78 W/kg, or 420W.
  • Alex Simmons very kindly provided some calculations for the climb, given the speed and gradient, and he arrived at a value of 422 W. He went on to show that if you assume even a small following wind, this power output drops to 397W.
  • Using the same principles, but making more "aggressive" assumptions, I have calculated the power output at around 440 W - this is an upper end, call it the "worst case scenario", because I think Alex has pretty much arrived at the accurate figures using his equations (which match the estimation of the Ferrari equations based on VAMs).
The only way I can arrive at this high a power output is to assume a headwind (which is very unlikely), or that the climb was steeper or longer (or that Contador was riding a bike weighing 13kg!). The length and gradient are contentious - we couldn't find any agreement on how long it was or how high it climbed, so Vayer may well be right. In the end, the data from Trainingpeaks.com showed an 8.7km climb and 640m ascent, which seems the safest bet.

There are some other assumptions you have to make - the air density, surface area and so on. However, these have a much smaller impact on the power output than gradient, speed and mass - a lot of people wrote in about this, the effect of air density and road surface. They're factors, don't get me wrong, but they're really very small in comparison with speed, mass and grade.

So that's the first problem with the calculation. That said, Antoine Vayer knows about power output - he published the book I referred to in my previous analysis of Tour climbing power, and has a library of all the Tour climbs. He, more than anyone, knows how to look at a climb in context, and so his figures deserve more than out of hand dismissal.

Converting power to oxygen - some assumptions required

Next, you have to convert that power output into oxygen consumption. This also requires some assumptions. I don't know the specific ones made, but an interesting exercise is to go through what might be "reasonable" assumptions and see what happens. First, you have to assume the level of efficiency. The more efficient the rider, the lower the oxygen consumption at any power output. So, Vayer may have assumed efficiency to be lower than the reality for Contador - short of measuring it, you'll never know.

Next, you have to assume energy use per liter of oxygen. This is tricky because depending on how hard you are riding, the value varies - if you are burning fat, it is lower than if you're burning carbohydrates as a source of energy. For example, the oxidation of fat provides 4.69 kcal/L of oxygen, whereas carbohydrates provides 5.05 kcal/L. Because Contador was climbing at a high intensity, he'll be on the carbohydrate end of the spectrum, so the assumption would probably be around 5 kcal/L.

If you do this, and assume 23% efficiency (which is in the normal range, and I'd assume would be where Vayer would go), then you arrive at a VO2 of 88.6ml/kg/min on the climb. Next, you assume that this is 90% of the VO2max, and you have the estimated VO2max of Contador - 98.4 ml/kg/min! (note the small difference is because I don't know what assumptions he's made - if you assume even slightly more energy from fats, then the VO2max rises to 99.4 ml/kg/min, for example - I'm just using some assumptions for illustrative purposes for now)

The problem - the starting power output is calculated, not measured

The problem of course, is not necessarily these assumptions - they can be made to be conservative and work out a "worst case scenario" as I did for power output. Then they are actually very instructive, because if you are conservative and still get 'unphysiological' values, then you have a real problem! The problem is that missing one assumption can create a misleading picture.

First, you have the power output of 440W. You must remember that this is a CALCULATED power output, and is therefore the result of performance. Any factor that improves performance (like a following wind) will cause an overestimation of the power output if it is not taken into account in the calculation.

In my analysis of the climb, looking at the VAMs (which are also contentious, but minimize the requirement for assumptions to calculate power output), I went to great lengths to explain all the factors that could have contributed to the record climbing speed of Contador. These included the shorter length of the climb, the suspected following wind, the race situation (and of course, the possibility of doping, which is now receiving the bulk of the headlines in this article). Given the shorter climb, the following wind and the relatively conservative riding up to that climb, perhaps the climbing performance was expected.

On the other side, one has to also acknowledge that Contador's VAM (and hence estimated power output) would have been even higher on a steeper climb, as I tried to explain (unsuccessfully in many cases, it seemed!). Of course, this assumes you use VAMs, which is not the best for this kind of interpretation. However, on balance, it was clear that you can't take this single climb and read too much into it.

The impact of wind

For example, just to illustrate the impact of the following wind, for every 3.6 km/h of following wind (and that is a very gentle breeze), the required power output drops by between 2 and 3%. The result is that by the time the average following wind speed reaches 10km/h, the estimated power output has fallen from 422W to 387W (8%). By all accounts, the general wind direction on the Verbier was from behind or the side, so I think it's fair to assume the wind helped the climb.

Therefore, Contador's "real" power output may have been substantially lower than what Vayer has calculated. If his assumption is 440W, it is conceivable that the following wind may reduce it to around 396 W (with an average wind speed of 15km/h from behind). Suddenly, the estimated VO2max drops to 89 ml/kg/min.

Just out of interest's sake,using the same assumptions for converting power output to oxygen use, and using Alex's calculated power output of 387W with an average wind of 10km/hour, the estimated VO2 on the climb is 78 ml/kg/min, and the VO2max estimate is 87 ml/kg/min.

What can be inferred from power output and oxygen use - physiological markers of doping?

They are still exceptionally high, but are more in the realms of "normality" (whatever that means). I still have my doubts about these figures - if Contador's efficiency really is 23% (as I've assumed to work that out), then it's highly unlikely his VO2max is that high. We know that VO2max comes DOWN as efficiency rises. So the combination of a high VO2max and high efficiency is unusual indeed.

Having said all this, then, I really do believe that Greg Lemond is onto a very important aspect of performance analysis. There are upper limits to what can be achieved physiologically, there are without doubt physiological "impossibilities". Unfortunately, in this case, I think the calculation of the key parameters is too fraught with error to be truly meaningful.

What is physiologically possible?

If this kind of analysis is to be useful, then every single aspect must be factored into the calculation - the wind speed throughout the climb, the mass of rider and bike, the length and gradient of the climb. Then one might be able to make a strong case for the position that what we are seeing is impossible physiologically.

There are people (experts in the sport) who believe that the upper limit of performance should lie around 5.6 to 5.8 W/kg on a longer climb. This is well below what is being calculated for the current Tour, particularly the Verbier. However, if the wind speed is not controlled, then the calculated power output may well fall below that "ceiling". The point is, we just don't know what the wind is doing and so the margins are currently too large. Therefore, you cannot use isolated performances, lacking control over variables, to infer doping.

What we should rather do, and I hope can be done after this Tour, is to look at the average of all the major climbs - Arcalis, Verbier, Col de Colombiere, Col de Ronne, and see how the power output goes on average. Why? Because doping's biggest impact may not be on the single performance, but on repeat performances through its effect on recovery between rides. Analysing many riders over a longer period also helps to control the influence of these variables a little better. This analysis would still require accurate estimations of power output, however.

A fascinating subject, and one that's sure to get a lot of air-time, but frustratingly, too many grey areas, and "ifs" and "buts" - I look at this type of analysis, and I can see that there is something there, but it's just out of reach... For now!


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Seb said...

490W is the value Vayer et al. get assuming "standard rider" (they use the term watt étalon or puissance étalon = standard watt/power). A standard rider being 70kg body plus 8kg equipment in their papers. They use this value to compare power developed by various riders of different weights, with different bikes, water bottle, etc.

With Contador only 62kg body weight, the 490W turn into an actual power of 445W.

Anyway, standard powers only make sense for statistical studies, where you compare many riders on many races. But you know the meaning of statistics and how they must be interpreted. Taking out a single value, error bars are large, and interpretation gets tricky.

Goran said...

You all accuse Contador for taking drugs but you don't see that Andy Schleck's performance is not much worse than his. But he is second so accuse first. By the same formula you can calculate that Andy's VO2max is about 90-95 ml/kg/min. Stop writing about doping, write about performances. Why do you follow sport if you doubt in every better achievment? VO2max is not very good prediction of result. My VO2max is 70 ml/kg/min, Frank Shorter had 71 ml/kg/min and he is still 28 minutes faster than me in marathon. And I know few runners who have even better VO2max than me but have worse results.

Ross Tucker and Jonathan Dugas said...

hi Seb

Yeah, I'd considered that possibility. And I think you may be right - I actually need to acknowledge that in the post. Thank you for pointing that out - I assume you've read the French? Because it doesn't come across in the cyclingnews article, that's also incorrect...

Regardless, he's still using the calculated value to work out 99.5ml/kg/min, which means the error is in the conversion of power output to oxygen consumption.

You're definitely right about the use of power output in an isolated analysis...interpretation is tricky, which is why I think the 'sample' must be expanded, as you say, to include many riders on many races. Thanks again for that info on the normalization to a 78kg rider!

To Goran:

Calm down - you haven't read this post. My post is done specifically to answer the allegation that Contador MUST be doping based on the latest analysis. I am in fact saying that you CAN'T imply that he is doping - so you've misread this article entirely.

Just to respond though, the issue about writing about performances and forgetting all about doping betrays a real naive side - you can't just say "there is no doping". You have to adopt a balanced view, which I'm trying to do. I have never, never said that you can judge doping based on a single performance - read the article fully and clearly and you will see that. HOwever, you can use performance, if variables are controlled, as strong evidence.

Failing to recognize this means you're wilfully burying your head in the sand. It's sad, but that's the reality of sport - you can thank Riis, Pantani, Virenque, Ullrich, Zulle, and about 100 other cyclists for the doubt in the sport


Jamie said...

HI Ross

Thanks for a series of thought provoking posts.

How does gearing affect power output and efficiency in cycling? I was thinking about this a lot watching the time trial yesterday and especially after seeing Wiggins eliptical front chain ring.

It seems to me that Contador generally is pedalling at a higher cadence than most of the other top riders especially up the maontains and definitely in the TT.

I know that cadence was quite widely talked about a few years back when Armstrong had his comeback from cancer and was riding up the big mountains with more revs than others like Ulric etc.

I also understand that a higher cadence is more aerobic than lower cadences but takes more focus to maintain. It seems that it is more natuaral to grind a bigger gear as the cadence is more similar to walking or running.


Alex Murray said...

Great read. This is exactly the sort of analysis that is needed on the subject.

Perhaps the only way we could get an accurate picture would be from a motorbike going ahead of a rider armed with an array of sensors covering all variables. But then you're still not going to get influencing factors like body core temperature, hydration and so on which Allen Lim seems to indicate all have a role to play.

I know Greg Lemond has a point but he has a habit of undermining his position with incomplete analysis and context. Or perhaps he is undermined by the selective use of evidence.

All in this article helps ease my frustrations a bit.

Marco said...

Yes, they use of a standard 70 kg rider with standard 8 kg equipment.

The most detailed recent article I think is this one (in French): http://cyclismag.com/article.php?sid=5184 where they explain that the mass of a rider is not known precisely and changes during a stage, so that they use this standard to compare riders.

I don't understand how these comparisons hold, and I understand even less how Vayer can make a power estimation based on a weight of 70 kg, and then use that result to estimate the vo2max/kg with a weight of 62 kg (99.5 ml/min/kg) instead of 70 kg (88 ml / min / kg)...

Ross Tucker and Jonathan Dugas said...

Hello Alex

`thanks a lot, glad you enjoyed it and appreciate it - it vindicates the time.

Yes, the motorcycle idea would work. Would be tricky to gauge wind accurately from that.

In terms of body temperature and hydration - important for performance, yes, but I guess you have to assume (barring disaster) that the athlete will optimize these provided they have enough access to fluids and it's not unbearably hot. If its 40 degrees and humid then you'll probably not see very high power outputs to begin with, because everyone would pace themselves and just ride slower! So it's a moot point!

But there are so many things, it's really difficult to say "Yes, that is the answer". And maybe Greg is looking in the right places, but not looking at the necessary detail!


Goran said...

I think Greg Lemond is one very jealous old rider who was taking doping when he rode so now think every one who is better than him must be doped. :-)

I know that you didn't accuse Contador for doping but one thing that bothers me is that non stop writing about possibility that he is on drugs. I haven't even know that Riis has doping history and now when I know it I would have different view about Schleck brothers and Cancellara because he is their sport director. So better not to know such a things and just enjoy in watching how they ride.

Jim said...

You guys are so freaking smart. Beyond my intellectual capabilities for total understanding but I truly appreciate the knowledge/researach your passing on. Please keep up the good work, it's fascinating (if sometimes confusing).

Colin R said...

Another reason the VAM/VOMax calculation is fraught with error to near-pointlessness -- Contador got HUGE pulls from Saxo Bank on the lower slopes on the climb. The peloton came in flying with Voigt and Sorenson on the front, and after they blew Cancellara (coming back from the break) put in another huge effort on the front. Contador was hardly riding a solo TT from the base of the climb.

grynde said...

Colin is right. All this would make much more sense if you could limit the analysis to the Kms that AC rode alone. I bet that the performance during his attack was inferior then than during the initial phase of the ascent.

If you cannot, I think it would be more valuable you extend your analysis to all the group so we can arrive to a conclusion about the performance of the group (Lance, Andy, ...) and see if AC really stands out.

Sigmund1 said...

How about extrapolating from the SRM data of Sørensen to arrive at a minimum w/kg estimate. Acording to the SRM blog Sørensen completed the Verbier climb in 25min 23sek. According to your article Contador completed the climb in 20min 36sek. It took Sørensen, again according to his actual SRM data 5,6 w/kg to achieve his time. Contador climbed 18,8% faster than Sørensen, and adding this results in a minimum estimate of 6,68 w/kg for Contador. Given that Sørensen rode tempo for a maximum of approximately 2 km while Contador had to take the full force of air resistance for approximately 5 km this this estimate has to be on the low side. Add on .2 for riding alone and you end up at a little under 7w/kg for 20 min.

It would be really interesting to try and put together an estimate for Contadors absolute power for the ITT. In my opinion his result there is simply insane and way stronger than his Verbier climb.

Eric C. said...

The original paper is here :

"Alberto Contador a été merveilleux avant-hier. Il a escaladé Verbier en 20’55’’, à 24,38 kilomètre/heure de moyenne depuis le Châble sur 8,5 kilomètres à 7,6 % de dénivelé moyen. Soit 490 watts en puissance étalon… "

"Puissance étalon" does mean, as Seb wrote it in the first comment, that it has been computed with a standard weight of 78 kg.

And Marco is right when he points out the inconsistency with the weight used for the vo2max/kg figure ...

DrTim said...

Hi guys,

I must really compliment you on your excellent blog. I will be a regular reader!

And don't fret too much about the negative posts, I ran a public site for years and while you will always get detractors they are outnumbered and self-regulated by the positive contributors.

Now, on to my topic for today ... I had told to me a good approach to predicting the likelihood of whether an athlete was doping. It basically came down to how they answered the questions around doping, cause in most cases (Marion Jones excluded) athletes don't want to straight out lie and perjure themselves.

The taxonomy goes something like this ...
1) I have never taken drugs = you can be pretty 'confident' they haven't in the past and are unlikely to in the future,
2) I don't take drugs = you can be pretty 'confident' that they actually don't right now but they did in the past and got away with it,
3) I don't take performance enhancing drugs = they take cocaine, ecstasy now ... a la Tom Boonen ... and probably did take performance enhancing drugs at some point in their career,
4) I don't knowingly take performance enhancing drugs = my manager/coach gives me a whole lot of pills to take and plugs drips into me and takes my blood off somewhere but I don't ask any questions,
5) I have never tested positive for performance enhancing drugs = I know I am taking them but I am one-step ahead of the testers.

If you watch the career of the dopers you will see them slide down this scale as it all unravels. It's like clockwork everytime. I'll leave it to you guys to put the various TdF guys into these classes.

And rather topically, I think Contador was rapidly scrolling through these options and the best he could do was say 'next question' ... I think that 'No comment' might be option 6 :)

Keep up the good work!

Dr Tim

Anonymous said...

When are Lance's old tour numbers going to be recalculated with his real weight?

Ross Tucker and Jonathan Dugas said...

Hi everyone

Thanks for the great comments - they really are helpful and very constructive. Much appreciated!

To Goran:

I think those are sentiments that a good many sports fans share, you're not alone! Sadly, one must be realistic about it. I have moments where it detracts from the performances, others where it doesn't. What bothers me most is the deception. I guess we just have to accept the fact that these questions will be answered, and our approach will always be to find the balanced approach, and rather than just fling the accusation out, to evaluate the evidence and try to be realistic, though of course our opinion will show through!

To Jim:

Thanks, that's very kind! I bet some would disagree, but I'm very honoured, and thanks for reading!

To Colin R and grynde:

100% correct - the first 4 km of the climb were very fast and he definitely benefited from the draft. Size of that effect? At speeds of around 28km/hour, which is what it was for 4km, probably 20 to 25%. That is substantial.

So you're right. Unfortunately, it was difficult enough to get the figures for the whole climb, let alone working out accurately what each part comprised! When I first tried to analyse it, that was the idea, to look at it kilometer by kilometer, but that was doomed by how incongruent the information was - for the life of me I could not figure out what each kilometer's gradient should be given the overall climb! Used google, Tour site, other sites - all disagreed with one another!

In terms of what it would reveal, you're right - I think one would find that the lower slopes, particularly from 2km to 4km in, were very fast (power output wise), even though Contador was sitting in the group benefitting from that pull effect.

So that's why one has to adopt a conservative approach to the analysis, and as I said in the post, try to control or at least account for all these factors - I omitted this one from the list, thank you for bringing it up!

As for whether AC really stands out, another good point. Of course, he still does, because his was the fastest climb, but the gaps are small enough that you have to bracket all the climbers together. The cycling news article reports that everyone up to about Armstrong would be calculated as having VO2max values of 90ml/kg/min, which is unrealistic. So you're right, he doesn't stand out like say Yao Ming at a children's party (joke), but I guess since he's the winner, he will be the focus of the analysis.

But just as Lemond might ask Contador to "prove it" (which is unrealistic, as I've said), one might be compelled to ask the same of all the top 10!

To Sigmund1:

That's a really interesting approach. Interestingly enough, the calculations for Sorensen also give a power output of 5.6 W/kg, which means his measured power output and calculated power output are pretty similar! That is the first time I've noticed that - perhaps the wind wasn't that big a factor? It's intriguing just for that reason!

It would suggest that the 6.78W/kg we calculated for Contador might be appropriate. I'll have to think that one through!

As for the time-trial, absolutely, that would be a very interesting analysis. He was mighty impressive, certainly a stand out performance given the expectation difference!

FInally, to the last anonymous:

You mean the weights as reported by Coyle? Or lighter ones? Not sure I follow which "real" weight you're referring to?

Thanks again everyone!

Sigmund1 said...

Coming back to the TT again. I mean he was faster than Larson and Cancellara, TT specialists of 80 kg and 80+ kg on a predominantly flat course and we know that one of those riders have a threshold in excess of 450W (in a TT position). This has got to be the biggest feat in cycling ever!

I have been toying with the thought of a rough approximation of Contadors power output using Gustav Larsons SRM file from this years Tour of California. Using that as a starting point results in an FTP for Larson of approximately 460W at that time. His bodyweight in those files were set at 80 kg and thus an FTP of 5,75 W/kg. This as a result of having an average power of app. 470W - 475W over 30 minutes in Solvang.

I think it is a fair assumption that Larson, given his 4th place yesterday has at least as good form now as he had then (this is after all the Tour de france and the highpoint of the season).

Now obviously Contador is a lot smaller than Larson, and I have no idea of how to estimate the difference in CdA between the two riders.

Maybe you guys have an idea here?

Ron Wolf said...

all very interesting.... BUT there is a BIG PROBLEM with this whole line of thinking. not too long ago 'experts' were CERTAIN that the 4 minute mile couldn't be broken or that women could not run a marathon. what's interesting about barriers is that we keep breaking them, isn't that what sports 'science' is all about? so the BIG PROBLEM is that this line of thought leads to suspicion of ALL high performing athletes. what's next? a speed limit maybe? if you finish this climb faster than xx minutes then we DQ you. come on now....

Alex Simmons said...

Just what would be a reasonable % of VO2 Max to *average* on a 20-min climb done "au bloc" / "at full gas"?

Given top riders can approach 90% VO2 Max average for a longer TT (~ 1 hour), I guess that a rider would, at least for the latter stages of a shorter 20-min effort, be riding far closer to 100% of VO2 Max, bringing their overall 20-min average up, perhaps to some what beyond 90%.

Given a typical ratio of 20-min to 60-min power is in the range of ~ 107% +/- 4% (where in that range depends on a few things, such as contribution of anaerobic work capacity), then wouldn't be an unreasonable assumption.

Anyway, the various charts on these matters really should have assumption/estimation ranges or error bars included. Then I suspect we'll see there's insufficient precision to draw too many conclusions (or for some, to draw far too many conclusions).

BloggingLance said...

Hi. Interesting article. It should still be fresh in our memories that a bitter Fabian Cancellara said that Alberto Contador beat him by three seconds in the Time Trial because of two motos ahead of Contador.

In an interview after the now controversial Verbier climb, Andy Schleck complained that the race vehicles weren't far enough ahead of Contador and that Alberto was able to draft. He said it wasn't Contador cheating, but the Race Director needs to do a much better job to make sure that sort of thing doesn't happen.

The guys on Versus routinely toss out the figure 30% as the amount of energy conserved by traditional drafting behind another rider. Maybe some of the power you're looking for could come from a vehicle trying to cut through a wave of fans. Cheers. John Calliott

Anonymous said...

Excellent articles. Couple of things to remember re. Verbier climb include:
In Contador's favour compare with other riders - as previously said here, Andy Schleck was not far behind. However, factor in Contador's performance after his attack at 5km to go and then what is the difference? Until then he was just 'idling' with the pack.
More suspicious than these figures for complete climbs are the brutal accelerations. Like Di Lucca there seems to be no limit to the number of jumps Contador can manage. In the past the riders used to get tired and could not respond after a 2 or 3 efforts.
Some educated words on what factors are at play every time an acceleration is made would be welcome!

Karol said...

Hey guys, Digger here from CyclingNews forums. I was engaged with you both and a few others in the debate with Andrew Coggan.
I am a big fan of your work in general, and whilst my academic research is in another area, I find the concepts covered here to be fascinating. The idea behind the site itself is very commendable, and is really reaching a far wider audience than 'just' academic papers and journals for example. Only for Michael Ashenden and yourselves, a person such as myself, who does not specialise in this field, would not have become acquainted with the inadequacies of the Coyle paper.
People like Allen Lim and Antoine Vayer are the way forward in the fight against doping. This is how we should be target testing....Aside from this though, do you have a rough calculation of Andy Schleck's figures on same Mountain?
I think people need to realise, and is something which you've alluded to, is that Antoine Vayer is a seriously knowledgeable guy in this field. For example, he was one of the first physiologists to point fingers at Ivan Basso at the 06 Giro.
And secondly, I accept that this site is not about doping, but what is your opinion on Alberto not releasing his VO2Max figure?

Anonymous said...

I would just like to critique a bit of your presentation writing here if you don't mind. I would love it if you stop putting bold lettering in every other sentence. Its actually distracting me.

Anonymous said...

You may also need to title this blog as "Sciene of Human Performance".... there is more science in sport than you try to cover. You're just doing the human aspect of it.

Ross Tucker and Jonathan Dugas said...

Hi Karol

Thanks for the comments and questions - good to have you here, thanks for your inputs on that cyclingnews forum as well! Always good to engage with people who approach sport with a similar logic!

You're right that performance analysis is a very definite component of the anti-doping battle - I think once it is refined, and people buy in (that is, the authorities), the it will become a very effective part of the bigger picture. It was a long time ago now, but I once did a few posts on where doping control is going, and I think it's heading the same way as the criminal justice system. That is, it will one day involve "cases" that sum up the available evidence and then deliver a verdict based on reasonable doubt. What we have now - the requirement to "prove" doping by means of a positive test, has been shown to be quite ineffective. It is, returning to the criminal defence analogy, the equivalent of trying to prove a crime by capturing the accused in the act of committing it on a video tape!

So I think we'll one day get to the point where evidence from a number of sources is collected and evaluated, and performance analysis will be part of it.

However, and herein lies the key, and you've probably picked it up, this requires that the measurement of performance be tightened up a lot! At the moment, we can have these fascinating debates about Contador's VO2max, the climbing rates in the history of the Tour and so on, but it's all assumption-based. It will take a while to "remove" (or at least, account for) those factors that affect how we interpret information.

Now, to answer your questions:

First, Andy Schleck's climbing rate was 1801 m/hour for the Verbier (using the same parameters as before). Given his weight, Ferrari's calculation puts his relative power output at 6.55W/kg, compared to Contador at 6.78W/kg.

If you use a formula (like Alex has, or Escarabajo back at the forum), then you get Andy at about 444W and 6.63 W/kg, compared to Contador at 435W and 7.01 W/kg.

So those are the basic calculations, again acknowledging the number of assumptions you have to make. Factoring in a following wind, as mentioned in the post, reduces the power by 1% for every 1km/h wind.

Just to pick up, Vayer is very good, very knowledgeable and so yes, I'd certainly pay more attention to him, based on his history of analysis.

Finally, regarding Contador and the VO2max. I can kind of understand why he isn't keen to divulge it - the riders are probably quite nervous about things like this being used against them, possibly out of context. I think there is a mistrust of science, and so his refusal is not necessarily an admission of guilt.

However, if the calculations of Vayer were fully transparent, and agreed on by all experts (because at the moment, they aren't), then a rider should embrace this approach. I can see it being a way to clear yourself. At the moment, I suspect Contador is treating his VO2max a little bit like a hostage, because he doesn't trust what it will be used for if it is released! If his performances are physiological, then science will prove it, but it requires trust, and obviously good science, otherwise the science can equally be used to "prove" that he dopes! So as with testing, it must be made more transparent, open to review, and then agreed upon.

Thanks a lot for the discussion!

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

Thanks for the input! No one ever brings stuff like that up, so I certainly appreciate it! The bolding is done specifically because I've done a lot of work in presentation and proposal writing (for sponsor or marketing purposes) and the use of bold is used specifically to highlight important aspects because of the short attention spans and overload of information from marketing execs!

But I take your point and can see how it might be distracting. Perhaps the compromise is less bold, which I have been thinking of anyway, so that's the way forward.

Thanks for that!

Next, I'm not 100% sure what you mean by "more science in sport". We've done posts on running shoe technology, the physiology of sport, analysis of performance, topics like dehydration and fatigue (what I would call more general physiology topics). We have done a number of posts on swimsuits, impact on performance, doping.

I'm not sure what aspect we are missing...? Obviously, our main focus is on how humans are affected by all these things - technology, doping, physiology.

But that's hardly a reason to change the whole title. That's a bit excessive...


Anonymous said...

Enjoyed the post, I think that Contador could be both super efficient and have a high VO2max. I know the Lucia article you are refusing to, and there is one person that does have a high VO2 and efficiency. Maybe Lance and Contador fall in that category. Or maybe not, either way makes for interesting stuff to think about, and good entertainment.

Ross Tucker and Jonathan Dugas said...

One last thing to the anonymous poster

If you're suggesting "Science of Human Performance", then you're saying that it's because we don't cover "sport".

So I don't follow - I think the title is entirely appropriate. I'm not sure how much of it you've read, but unless you've read it all, you're basing your suggestion on incomplete info...

Anyway, thanks for the suggestion

Conrad said...

Dear Ross and Company:

I think we would all agree that this is a fascinating conversation and one worth pursuing. Thank you Ross for your continued diligence in posting scientifically. Unfortunately, in my opinion, there is a sad unpinning to this thread.

Though the battle of doping will go on for some time, the Lemond statements is borderline libelous. Libelous b/c Lemond – forever in search of a sound bite as the cycling world chooses to ignore his rantings – as leveraged his media opinion of Contador’s potential doping on accusation rather than proof.

Equally sadly is the observation is that cycling innocence is based on the accused proving their innocence rather than the accuser providing solid proof. Accusation appears to be enough.

As Ross and others have introduced is the tremendous potential for error in the calculations used to platform the current doping allegations. As a scientist, I have no problem with scrutiny, skepticism, doubt and investigation; however, I do not think that a tabloid accusation/intimation does anything more to promote cycling than doping.

Perhaps it is my altruism gene hyper-expressing itself and perhaps it is the “era we live in” where tabloid journalism is synonymous with truth, but introducing a doping accusation to this years Tour was a shameful bit of a “cry to be noticed” by GL.
I do not know Greg personally and he may be a very stand up guy who is obviously passionate about his quest to combat doping.

However, a headline based on one scientists calculations without more investigation is not only lazy “journalism,” but also disingenuous toward fighting doping without proof in hand.

Unfortunately, guilt by association seems to be qualifying doping criteria. Armstrong and Ferrari, Contador and Operation Puerto, Manolo Saiz. If this is true, then is not Lemond equally “guilty,” despite (apparent) denial due the company he kept? He can deny all he wants, but according to his “association criteria,” he may be equally culpable? Please not that I am not accusing Lemond of doping, merely pointing out that he fails many of his same “criteria.”

At the end of the day we are stuck with several flavours of reporting:
[1] The eternal skeptic who would rather accuse than obtain facts,.
[2] The eternal altruist who would rather believe in innocence, despite the facts.
[3] The enlightened skeptic who is capable of doubt but reserves judgment until the facts are in.

Ross and Jonathan have provided a great platform for #3. Good for you guys. I hope this does not erode into a finger pointing contest. (I am pretty sure Ross won’t let this happen).

On that note, thanks Ross for spearheading a logical and cogent approach to this question. Thanks also to those that have posted in a logical manner. At the end of the day, everyone is guilty and everyone is innocent. Hopefully, we will let facts (positive doping tests, accurate modeling) determine who falls into which camp and disallow innuendo and accusation as a viable means of assigning “guilt.” Like doping, I am afraid the latter will always be with us.


Anonymous said...

Of course doping will be always with us in sports. But are we willing to admit it?

For example: the winner of the Tour '99 delivered 6 positive Epo tests for this race, though not official ones. He was then 28 years old, an age considered the best for this sport.
Now, 10 years later, the same athlete is more or less still on the same level of performance. How plausible is the assumption that this performance is now produced without any similar techniques?

Karol said...

Thanks guys for taking the time to answer my post in such detail. Very much appreciated. And I agree with you both on so many levels - in essence I believe that, whilst you are both highly educated (obviously), you take a very common sensical approach, which is refreshing to people like myself.

Talk soon, K

Ross Tucker and Jonathan Dugas said...

Fantastic comments all around, everyone, and when we see this kind of discussion we are so chuffed because it showcases our readership!

To respond to Sigmund and the thread-within-a-thread discussion about COntador's TT performance, way back in 1979 an Italian scientist (no, not one of the two doctors you are thinking of!) published a paper called "Equation of motion of a cyclist:"

di Prampero et al., Journal of Applied Physiology, 1979.

In it they derive an equation to calculate the power output as a function of the air and ground speed. The mathematics of the paper are a bit beyond my abilities, but someone with an interest in this plus the math skills should be able to calculate the power outputs of Cancellar and Contador and really any of the guys from the TT.

If you do not have access to the article, please just email us and I will send you a copy!

Kind Regards,

nechai said...

Would it be interesting to do same calculations on the 91° GIRO D'ITALIA - 16° TAPPA - St.Vigil in Enneberg/Kronplatz? I have two GPS tracks to calculate the gradient, recorded by hike and bike. It was an Uphill TT, which should eliminate another gray areas. There are also some after the race positive tested participants as comparison.

Ross Tucker and Jonathan Dugas said...

Hi Jamie, and thanks for your comment about gearing and power output.

The interesting thing about cadence is that when we measure people in the lab we see that there is an "optimal" cadence that produces a lower HR and VO2 given the same power output. If I recall correctly this is around 80 rpm. However most cyclist choose a slightly higher cadence, say around 90 rpm.

Without getting too much into gearing ratios and things like that, my simple understanding is that to produce the same power output one must increase cadence as you select a lower (easier) gear. So one can cycle at 300 W in a 53:20 at say 100 rpm, or 85 rpm in a 53:13---that is the general idea.

Which is easier? Not sure, because the funny thing is that in he lab we can find that "optimal" cadence but then hardly any athletes seem to choose this as their self-selected cadence. It is a classic example of how what we measure in the lab does not always translate into something meaningful in the field.

I suppose the short answer to your question is that it does not matter, because the cyclist will choose which one feels best to the according to how they are trying to pace themselves and dole out their effort over a given distance.

Anyone who had done any riding at all will probably report that slightly higher cadences are "easier" because sitting in a big gear means you have to push down a bit harder with each pedal stroke, and the feeling is that your quads get tired more quickly, and then you want to shift down.

Kind Regards,

Ross Tucker and Jonathan Dugas said...

Hi Conrad

Well, thank you so much for the comment, it is a fantastic and objective piece. Thanks for taking the time to put it together so thoughtfully. All I can say is that I agree wholeheartedly with you on your message.

A couple of specifics: I think Lemond is passionate and believes very strongly in what he is saying, but yes, it's been based on what is imperfect information and some bad journalism (which was propogated from one to the next - the reports on the original French piece were also inaccurate). So while I'm not sure it's tabloid all the time, this occasion allowed "due dilligence" to take a back seat to thorough investigation.

ANd also note that like you, I don't think we can conclude either way whether Contador (or anyone else, because they're all so close that if Contador is implicated as having impossible physiology, pretty much the top 10 are too) is doping or not. I think what you're saying, and this post was saying is that if we want to take this performance analysis approach, let's do it so that it is watertight!

That brings the next anonymous poster's comments into play - you're right, it does seem implausible. but evidence is needed, it would be great to have it, instead of having to rely on "worst-case vs. best case scenario".

Then finally, in the sport of athletics, we're about to see the rumour mill kick into gear with the announcement that 5 Jamaicans have tested positive. It's now being reported that one of them is Yohan Blake, a training partner of Usian Bolt. By association, Bolt will come under even more suspicion.

I agree it's unfair, but I guess it's the climate we live in. Hopefully, as we debate issues like this, it will become clear that if factors are controlled, we can use performance analysis as a tool against doping!

Thanks again for the great post, Conrad


Rosemary Barnes said...

I really appreciated this article's efforts to explain all the possible errors in a VO2max calulation based entirely on estimated parameters. Most other articles I have read on this topic simply take it for granted that Vayer's analysis proves that contador is on drugs.

I simply do not agree that this sort of analysis has any value in the fight against sports doping. I don't uderstand the obsession with calculating whether it is physiologically possible for someone to ride that fast up the Verbier. No matter how hard you try to make it accurate. Obviously it is possible - Contador did it. And several other riders were not much slower.

The second part to the question: "is the performance possible without drugs?" should be answered by drug testing (which they are doing), not by trying to force Contador to "repeat" his performance in the lab. As an athlete myself, this idea is hilarious to me. Why should you have to be able to break a record twice for it to count? And no one performs their best on an ergo in a lab anyway! It is much easier to push yourself hard on a real bike than on an ergo in a lab, and there is a lot to be said about adrenaleine in a race situation. Use VO2 test results to compare with other VO2 test results, not with race performances.

Imagine if this type of witch-hunt was applied to non-athletes, e.g.: "your IQ result was higher than we've ever measured before. Therefore you must have cheated, and you don't get the job (and you also have a 2 year ban from any work at all)...

Let's leave the job of finding drug cheats up to the anti-doping agencies.

Ross Tucker and Jonathan Dugas said...

Hi Rosemary

Thanks for the comments - interesting perspective. Certainly, I'd agree that many have accepted blindly the initial report. But this is nothing new - it happens for every topic, it seems (Pistorius for example).

Where I disagree is that this kind of analysis has no value - I think it is very valuable, just not in the manner it is currently being done. There are too many unaccounted for variables, but the principle is very sound. That's not to say the rider should be asked to reproduce the performance in a lab - I agree 100% with you there, it has been done on the road, and to ask for a lab to confirm it is asking a lot more than in reasonable.

However, the point behind this performance analysis approach would be very much the same as the blood passport - it is a tool to develop a "blueprint" for the sport, to grow the body of understanding around what an athlete is capable of (or is physiologically made up of, in the case of the passport) and then to use this as one of a few lines of evidence to discuss the doping claims.

It may be instructive to look at it the other way - there are tests one can do in a lab (VO2max and cycling efficiency) that would easily allow a cyclist to prove that their on-road performances are reasonable, thus refuting doping claims. So it can work both ways, and I do believe it will be valuable. However, it is a tool, not a silver bullet, which is how I think you're construing it a little. I think the confusion stems from the fundamental flaw in the whole debate, which is the false starting point (Contador's power output).

There are a few other cases of performance analysis in doping, and I believe it will gain popularity in the coming years. As I've said before (last year), the fight against doping MUST move away from simply asking for positive tests - I think it's pretty clearly been shown that doping controls do NOT detect many doping practices! Therefore, an integrated approach, where performance analysis is ONE OF MANY approaches might be the way of the future!

Of course, all this must be done by the anti-doping agencies, but they must, I believe, expand their approach, because their current ammunition (doping tests), while stronger with the passports, is still relatively thin.


ihavenolimbs said...

What about the effects of altitude?

A study published (available on Pubmed) shows that VO2max drops 6.3% for every 1000m of altitude. The Verbier climb went from ~900m to ~1500m? This means that estimates here for VO2max are about 7% too low?

Magnus said...

Hello I have one question and a comment.
How is the influence of doping on VO2max? Is 99 a value that is "normal" / plausible for that?

To get the exact grade you just have to ride the climb and record it with a gps with barometric sensor.
There is a track at http://www.gpsies.com/map.do?fileId=rlywrabqunqytvgq&referrer=trackList
but he seems not to ride exactly the race cource and there are some deviation in the altitude data so probaly there are not from a barometric sensor.

Ross Tucker and Jonathan Dugas said...

To ihavenolimbs

Not necessarily - Vayer is not saying that Contador's VO2max on the climb is 99.5ml/kg/min, he is working out what his VO2max might be at sea-level, based on his power output on the climb. That said, altitude does have to be considered, because it would affect that measured power output, and would also impact on the VO2 that one estimates for Contador on the slopes. That is, in my assumptions (which I think are close to Vayer's), Contador is riding at a VO2 of 88ml/kg/min. This value (and not the max) should probably be increased by a small factor, and that would have implications for the estimated VO2max. Hope that subtle difference makes sense?

To Magnus:

I think that's what Greg Lemond is getting at and is implied by Vayer's analysis - doping would allow a higher power output, and remember that the VO2 is estimated based on the power output. So that is where the "red flag" is raised - I think the implication is that Contador's power output is so high that it predicts a VO2max that is unphysiologically great. It's not necessarily the effect of doping on VO2max that is in question, but rather doping on performance (and hence estimated VO2max).

That said, what would VO2max do with doping? It would increase, because the power output achieved would rise, and VO2 is a function of work rate.

As for the grade, it's not quite as simple, because you have to know exactly where the climb starts and ends, and it has to be the same as what the organizers used, otherwise you can't match the times to the gradient! Also, if you don't match the start up to the official route, then it's difficult to work out kilometer by kilometer what is going on.

THanks for the comments!


Pim said...

Two weird assumptions: no correction for altitude (which inevitably means less oxygen/L of air so per mg/ml/kg as well).

Secondly, resistance & wind aren't of influence to the _power_ output. To speed or cadance it can be; not to power (since power's the only invariable factor, it's just how hard you can put the pedals down).

Contador weighs way under 70kg as well, so instead of correcting you'd better use the kw/kg numbers for the total combination (since his 6.8kg bike is a relatively larger part of man+machine combined than the 70kg guy, being more non-functional mass (muscular tissue 'makes up' for its own weight).

And that's not even accounting for bidons (2x 500ml), which means bottom/top varies with about a kg.

Bottom line: unless you've got AC's SRM-data and correct intervals for weight it's no use.

Ross Tucker and Jonathan Dugas said...

Hi Pim

A couple of responses:

First, both your assumptions are not entirely correct.

Firstly, if you correct for altitude, the estimated VO2 goes up and not down. You are right that VO2 is lower at altitude, but that means the estimated value is an under-estimate. I explained this in a response to ihavenolimbs, who pointed this out - the reason is that the VO2 that Vayer has estimated is based on power, and altitude would affect the power output which you calculate based on the performance. If anything, then, VO2 rises if you try to factor altitude in, it doesn't fall.

Second, the wind and resistance are very important for the calculation of power. You are misunderstanding the whole method by which the power has been worked out. That's actually the crux of the argument. The power output that Vayer uses is not measured, but calculated. So you've assumed that it's invariable, when in fact it's not. If you measure it, it's invariable. If you estimated based on speed, which is what everyone has done, then wind is very, very important - I tried to explain that in the post, emphasizing that these power outputs are not measured, but calculated based on performance the given paramters.

Finally, you're addressing your specific concerns to the wrong people - it was Vayer who made the calculations, we are trying to analyse why those estimates and their implications are not 100% correct. So we agree with you that power must be measured - again, I tried to emphasize this in the post (refer to the sub-heading 'The problem - the starting power output is calculated, not measured')


Supertramp said...

Is there any rider in the tour that has power figures for the Verbier climb available?

Even if that rider did the climb at a lower speed, that data could still help to improve the accuracy of the estimated average power of Contador.

Rob, NY said...

I find this kind of analysis, silly and a pointless waste of time.

After digging through all those numbers and facts and data your final answer is...MAYBE.

IF you suspect drug use, the ONLY way to catch a cheat is to keep testing.

If you want to analyze power output, VO2 etc, then do it in a lab and not waste peoples time.

Besides that, I do enjoy reading your website regularly and have found many useful tidbits of info.

Ross Tucker and Jonathan Dugas said...

Hi Rob

Thanks for the comment

I just have to defend this article by pointing out that our analysis was never intended to answer the question "did contador use drugs?". That was not the point of the post, if you read it, you'll see that this particular post was written to analyse the comments made by Lemond in response to Vayer's calculations, which implied doping.

The cyclingnews.com article was rather more vague, and given the fact that this topic was bound to cause some debate, it seemed worthy of further analysis.

So when I conclude "maybe", it's NOT to the question of Contador using drugs, it's to the issue of whether this kind of performance analysis could be valuable in the battle against doping.

And I do believe it is. Rather than being silly and pointless, this kind of analysis is part of the future of doping control. As much as I'd love to say that they should just keep testing, it's not enough. So this will be important, definitely not a waste of time, but just has to be done comprehensively. That's where "maybe" fits in.

I think the view of science being confined to a lab is quite narrow, and it's not wasting people's time at all.

Anonymous said...

"Alex Simmons very kindly provided some calculations for the climb, given the speed and gradient, and he arrived at a value of 422 W. He went on to show that if you assume even a small following wind, this power output drops to 397W."

Hmmmm. At 20 km/h (roughly climbing speed), (still) air resistance is about 25W for Contador.
Even with a small following wind, there is no air resitance left? And if true, what about heat dissipation if there's no air cooling left?

Am I wrong?

Anonymous said...

Ross and Jon -

Thanks for a great site. Like you I believe that this type of analysis, given its limitations, is valid.

I find it very interesting that if you calculate W/Kg for a number of "clean" professionals you come up with around 5.6. I'd be very interested in Mercks, Boardman's, and Miller's (recent) numbers for TT's.

There is enough data to establish reasonable statistically derived control limits that would show cyclists and equipment have not evolved enough to produce a 20% improvement. The hour record is pretty much proof of this.


Frans Rutten said...

Antoine Vayer and particularly Greg Lemond were IMO too eager to get a quick reference scoop. An analysis on www.cyclismag.com of the fierce battle clearly states the dramatic (beneficial) group surge (550W* for 5:57), which was going on in the initial first 2,7km. Which was followed by the real acceleration of Alberto Contador (2,7-4,65km) at 535 Watts* compared with Andy Schleck at 490 Watts*. Then however, 2km consolidation of Contador with 5:32 at 450 Watts*. And finally the last 1,85km in a rather modest 4:51 at 430 Watts*. Extrapolating this further to the much longer exploits of both Riis (34 min Hautacam) or Pantani (37 min L'Alpe d'Huez) wouldn't result in better performances. So what's "the fuzz all about". * (calculated 70+8=78kg)

mayayo said...

Thank you for trying to provide true insight into the sports backstage. ¡Superb info!
I trust it that the more we learn about phisiology and performance, the better we will be able to understand the true value of the "mental" side to sports.

Regardless of the VO2 max performance analysis (fascinating and most interesting, yes) I would like to pay homage to the top-3 TdF riders willpower:

1. Contador: The 4-time "Grandes Vueltas" winner took on terrible pressure from 7-times TdF winner and marketing legend LA playing the upper hand in his own team.
And came through the fire alive. Compare to Ulrich´s mental melting in previous Tdf vs LA. New experience for LA, no doubt. ¿Met his mental toughness match at last?

2. Armstrong: Impressive. Superb mental stamina, coming back at his age and in such a level is surely not just about power output. Pschicologically, too heavy a hand he tried to play vs teammate Contador. Training together, he definitely knew the better rider from the start. Should not have tried to keep up his alpha-male stance so long. Did so, perhaps, looking for a AC mental meltdown...
Not a nice try, nut no luck.
Yet, thanks Lance for showing all willpower as key driver can achieve.

3. Andy Schleck: Keeping up his steady progression, despite being sandwiched by two of the toughest cycling minds ever. His mental resilience at the Ventoux climb, once and again, and again, yet waiting out for Franck is also inspiring.

I already look forward to these three superb cyclists fighting to outwill each other in 2010 :-)

And thank you Ross & Jonathan for all the superb info on technical aspects of training and competing.

Perhaps, the sport champions we admire most beyond their times, are those able to blend together BOTH body and soul to achieve unforgettable performances.

Theo said...

you are writing:

"On the other side, one has to also acknowledge that Contador's VAM (and hence estimated power output) would have been even higher on a steeper climb ..."

I understand, that the VAM on a steeper climb would be higher under the assumption that Contador would have the same power output than up to Verbier. But what do you mean with : (and hence estimated power output).


Pierre said...

Great information, thank you very much!

To me, you are showing that the accuracy of the criteria calculated a posteriori to define how good the performances of a climb were, is not very good.

So rather than trying to calculate such criteria, why don't we simply measure them? It seems to me that we could just have a device on the bikes to measure the watts for example. Of course we would still have to figure out "what is right or wrong" but it would factor one side of the equation out. The wind would necessarily be taken into account for example, the fact that some riders may be more areodynamic than others, the actual length and gradient of the climg would be accounted for.

It could tell us that Contador should not, thanks to his low weight for example, be suspected. In fact it may even show that some of the other riders are more suspect...

So would that work or would there still be too many issues to judge those performances?

Kup said...

First time reading through here. Fantastic resource--you guys are doing great work.

As an adult-onset cyclist and, by extension, cycling fan, I, too, share the interest in the application of science to measurement of physiology in sport, if only from the lay person's desire to know that what I see in great events like the Tour is "real" and correlates, in some way, to the efforts that I make on those weekend group rides. Otherwise, pro cycling is, as sometimes claimed, little better than pro wrestling.

Your extensive analysis here of the Verbier climb is great. Some of the previous comments have mentioned the ITT as deserving attention. I agree. As a casual--but from bitter experience, skeptical--fan, I am flabbergasted that someone like Alberto Contador, whose time trialing was by comparison so much weaker just two years ago, can "miraculously" appear to recover from several consecutive hard efforts in the mountains and then proceed to better some of the best time trialists of the current generation. That, even beyond his exceptional performances in the mountains, raises substantial suspicion in my mind.

Are there just too many additional variables relating to aerodynamics, frontal surface area, and the like, to make a similar analysis? It would seem that much of the same data might be available.

Anonymous said...

I don't know why some people are so surprised with Contador's performance in the ITT. he has been improving significantly over the past two years. earlier this year he either won or finished very high in the ITTs at several races before the tour. it was a great performance, but it should not be shocking to anyone following Contador's races closely.

Much more surprising is to see Bradley Wiggins climb mountains with the best of them when he never could in the past. Everyone is happy with his explanation that he lost 6 kilos and is more serious about racing. No one is suggesting he is doping. And there's no reason to think Contador is, either.

And what about Lance? 38 years old, retired several years, broken collar bone a few months before the tour...and he finished third and he did not suck wind up the mountains either. No one is questioning his podium.

there's as much reason to doubt lance, contador or wiggins. I happen to think they are all clean. Contador might be getting critiziced because lots of people wanted Lance to win.


Anonymous said...

It is not likely 99,5. Here is why. First, Contador is 60-63 k, rather than 78. So we are not talking 490watts at anarobic treshold anyway. In reality we are closer to 400+w of power. Second, a rider like Contador can get 75w pr liter o2. 400w/75w = 5 liter 02/min at anearobic treshold. Third, Anaerobic treshold sets in at 90-95maximum 02 uptake for higly trained riders. So Contador has a vo2 max og 5.5 liters. With a body weight of 60K that equals vo2 max of 83 ml.o2/min.

Andrew said...

This is fascinating stuff, and an area that I know nothing about.
Nonetheless, I have a question, and it's one that's been alluded to above a couple of times. The thrust of this article seems to be that hard conclusions about the result of V's calculation cannot be drawn because there are many variables that may affect the result.

Seeing that these are the results of passing a series of input variables through some standard calculations, then why not take into account the error of measurement of each of those input variables, and propagate these through the calculations, coming up with a final error bar on the end result? This will also affect the precision with which the result can be stated.

Thus "AC has a V02 Max of 99.5 ... shock!" may become something like "AC has a V02 Max of 100 +/- 30 ... meh"

You'd probably come to the same conclusion as your original article, but with some figures to back up your uncertainty.

Or am I being overly simplistic here?

When I did my degree back in the stone age we were constantly hectored about quoting uncertainties, and ensuring that they were propagated through all calculations. I still bear the scars. As I say above, know nothing about this field - this is a question rather than a criticism.

Frans Rutten said...

Last monday, Michele Ferrari commented on his website www.53x12.com the rancid suspicions (his words) raised by the "experts" Antoine Vayer on Liberation and Greg Lemond on LeMonde based on the power value for Alberto Contador as false valuations.

This evening Frédéric Portoleau, on his behalf, detailed his calculation method(!), on www.cyclismag.com. He used his method to calculate Chris Anker Soerensen's ride of 25:32 for the 8,8km climb and confronted this with the values of the SRM device.
The result was an overestimation of 8W or approx. 2,5 percent: 365W vs 357W. He admits, that there's an overestimation, which also can be applied to the power values published for Alberto Contador, but gives also a couple of elements, which could have lead to changes in the equation, one way or another.

Ross Tucker and Jonathan Dugas said...

HI Andrew

Thanks for the comment - you're 100% right. The post was really written to point out the numerous assumptions, ranging from the starting assumption of power output, to the efficiency, the drafting effect, the calories per liter and so on.

So you're not being over simplistic at all - that's pretty much it in a nutshell. The uncertainty is the problem, and until this can be reduced through direct measurement and known parameters, it will always be a grey area!


Ross Tucker and Jonathan Dugas said...

Hi Frans

Thank you for pointint that out - very interesting.

Just on Ferrari's comments - he's barking up the wrong tree completely, because the Vayer calculation was worked out as 490W for a normalized 78kg rider. It means that their calculation for Contador is actually 440W, so Ferrari himself is making an error!

In any event, it's very interesting that Portoleau has pointed out the specifics of the calculation and found that it's not far off what was measured directly. i think it again comes back to the point that Ferrari himself has made an error, by criticizing the value of 490W without fully understanding what it meant! Careless from the doctor...

Getting back to the comparison of Sorensen's measured power with the estimates, that's very interesting indeed. It supports a cursory analysis I did on it - I worked out that Sorensen's directly measured power output was not different to his estimate based on the Vayer method. It certainly strengthens the case that you can use performance to estimate power output...

Maybe a post on this in the future, once the swimming is out the way!

Thanks a lot for that!

richard hallett said...

Hi, great article and very interesting/engaged thread. Surely, however, you can not make many assumptions on Contador's VO2max (or that of anyone else) without knowing their pedalling economy or efficiency? I understand it is widely accepted that stroke efficiency makes a huge difference in swimming and guess gait efficiency might explain how two runners with a near-identical VO2max can post widely different marathon times. Is it not reasonable to suppose that there might be differences of several percentage points between top cyclists and even elite riders at the next level down that would partly explain exceptional performance?

Anonymous said...

Thanks for avery interesting article. I think another unknown factor must be the aerodynamics of the riders. We know that many riders can gain considerable advantage using wind tunnel tests. This would probably also be useful on the climbs. A rider holding his elbows in and lowering his shoulders a few cm would certainly have a lower power output than the same rider with his elbows splayed and his shoulders in the higher position.

Of course, this would make it quite difficult to quantify. (Most wind tunnel tests suggest that wind resistance is 30% bike and 70% rider.)

Karle said...

I'm not sure if that has been mentioned somewhere in the comments, but apparently Bjorn Daehlie, legendary cross country skier, had a VO2max of around 100. Don't ask me how clean or unclean he was though.

Rich said...

Great, great blog and blog site guys. Thanks for your tireless work.

Perhaps we're asking all the wrong questions here.

Athletes can and do cheat for a number of reasons, but in each of these cases, one thing remains the same: by definition, victory has become more important to them than fair play. And not always, but usually, it's about money.

I guess it's also true that the people who might cheat at sport are the same ones who would cheat on tests or in the workplace. It's a character flaw.

Regardless, the real problem is that what we're so often watching is a business deal, or at best an entertainment event, unfolding.

The only place where true sport still exists is on those playing fields where the rewards are limited to personal pride and a pat on the back for a job well done.

I'm a pretty serious runner and racer, but about the only person I really compete with is myself. And I'd never dream of cheating when I go up against that guy. Then again, I don't cheat in other areas of my life either. (Maybe bend the rules here or there, but that's a different discussion.)

Don't get me wrong, I love watching high-level competition as much as the next person. But I think we'd do a lot better to remind ourselves that, at the end of the day, what we're really seeing is unfortunately business/entertainment disguised as sport.

If you want to see the true exemplars of physical achievement, go seek out the men and women for whom what they do is no more or less than a labor of love: the mountain climbers, rowers, runner, cyclists, and swimmers who are weekend warriors and for whom victory, on whatever terms, is simply a matter of pride.

As an aside––and maybe this reveals a certain naivete on my part––can someone tell me how there can be so much debate about who is and who isn't doping? I understand that newer drugs may be hard to detect, but insofar as the known enhancers are concered, you take a blood sample (maybe two), send it off to a lab or two, and wait for the results. What's all the flap about?

Victor Machado Reis said...


My compliments to Dr. Tucker for his wise demystification of a possible myth that could have been created in some minds after Vayer’s article.
I have no problem with the fact that a journalist might suggest a possible VO2max of 100 ml/kg/min for Contador. Neither do I have an underlying preconception that prevents me to believe that such physiological limit can be attained by humans. Again, Dr. Tucker’s essay clearly shows why and how Vayer’s calculations are probably wrong. But for us all, exercise physiologists, who do care about the possibility or impossibility for a human to achieve a VO2max of 100 ml/kg /min, herein is my statement.
Despite the level of inaccuracy of Vayers calculations and the most probable better accuracy of those by Ross, to answer the question whether is it possible for an athlete to attain such VO2max, why do not simply measure it? Indeed, to assess an athlete´s VO2max is not that difficult. I am pretty sure that some way along Contador’s sports career he must have been submitted to such testing. So, why discuss a possible VO2max of Contador based on a number of assumptions and subsequent estimations with unknown precision? Why not simply invite Contador’s physicians or exercise physiologists or coaches to provide data that can support or refute Vayer’s calculations?
Even with a possible confirmation of such high VO2max, then we would have to discuss other issues. I have myself conducted a few hundreds of maximal tests with athletes and I have sometimes (rarely) came across peak values around 90 ml/kg/min. But do I consider those observations to reflect accurately those subjects’ VO2max? No! Issues such as time averaging procedures when filtering breath-by-breath data provided by modern high-speed oxygen sensors; the variability of records according to environmental conditions and calibration procedures; among others, may be at stake and ought to be included in a scientific based discussion of some type of unusual measurement (which is not the case yet).
In sum, I would rather wait for a more “official” statement regarding Contador’s or other top-performer athlete’s amazing VO2max (as long as provided by scientific-based sources) before engaging further in this discussion.

Victor Machado Reis
Research Center for Sports, Health and Human Development
Department of Sport Sciences, Exercise and Health
University of Trás-os-Montes and Alto Douro, Vila Real, Portugal

Matt said...

Does no one have access to Contador's lab tests to give an idea what he can do in a controlled environment? Lance's is well documented.

Keith said...

Great post. I'm a physicist and I'm often amazed that so few sciences seem to treat error bars properly (or at all), so it's refreshing to see someone try to account for them.

However, in the end I don't quite see a proper error analysis here. And I think if you did do one, you'd realize pretty quickly that in order for this method of doping analysis to have any validity beyond curiousity, the measurements involved would have to be far more accurate than you'd expect. Roughly speaking, your calculations are based on products, which means that the errors add up to first order - so a 20% error in the efficiency + a 30% error in the power calculation + a 5% error in the weight ... if a VO2M of 99.5 is not ok but 90 is, you need the total error below 10% in order to even talk about it but what you have now is something like 50+%. Even with a powermeter and an accurate scale I think you'd have a hard time getting below 10% (which is still a lot of error when you're trying to prove something).

Worse, the *actual* equations involved are a lot more complex than the simple products that are being used, and there's a systematic source of error there that's entirely unquantified.

So in principle yes, good approach; in practice, good luck!

As far as LeMond, I agree with several other posters that I wish he'd go away. GL is a tireless self-promoter and is somehow *always* there to accuse the current top riders in the sport of doping. I think someone else said it, but it bears repeating that his reasoning is not far from a tacit accusation of himself as a doper - after all, drug use in sports was rampant in the 80s and he beat all of those guys.

He also raced against his own teammate in the TdF, not exactly a classy way to be remembered. Note that Armstrong, by way of comparison, did *not* do this in 09 - and would almost certainly have been further up the GC if he had.

VO2_min said...

Several people have mentioned the complexity of the equations of motion for a cyclist. I found a nifty online calculator that's served me well and seems to produce sensible numbers for me. It's at http://www.analyticcycling.com/ForcesPower_Page.html
Enjoy !

Anonymous said...

It's definitely interesting to talk about climbing and vo2 - but how about the time trial? Cancellara is definitely over 80 ml/minkg. However, he is 78-82 kg. At the same time A.C. is maybe 2-5%worse in time trial - but weighting 61 kg. Now calculate....