Caster Semenya cleared? Is this finally the verdict?

Caster Semenya to return to competition: Reports from the IAAF

It is being reported that Caster Semenya, South Africa's 800m World Champion, will be given the all clear to return to the track.  Before getting carried away at the conclusion of what seemed a never-ending saga, let's remember that on no fewer than three occasions, the SA government have organized triumphant press conferences only to cancel them at the last minute to delay the announcement further.

However, on this occasion, a reputable source, the Telegraph, are reporting that the IAAF will make the announcement and not the SA government, which gives one more confidence that perhaps, this is the final decision.  The story from the Telegraph can be read here.

If it is indeed the case, then it will bring to an end 10 months of speculation, rumour, accusation, and denial.  We've tried to follow the story, from its beginning in August last year, and there is not too much more to be said about why it has taken this long, and what may have happened over the last 10 months.

In the report by the Telegraph, I feel the most telling paragraph is this one:

"Her coach, Michael Seme, has admitted that she has not been training at 100 per cent due to the uncertainty over her future, while it is also believed that she has been undergoing medical treatment for an inter-sex condition."

That alleged treatment, which I also believe to have taken place, holds the key to why this has taken so long.  The IAAF, you'll recall us discussing before, find themselves in a difficult situation of having to avoid discrimination against ANY athlete (not only Semenya, as the SA sports fraternity wanted to believe).  So their obligation was to ensure equality of competition without discrimination.  And there are a range of issues about this, from social to cultural, even religious, all of which have been had in various forms over the last 10 months.

However, from a sporting point of view (and my bias here is sporting performance), the requirement is to manage the case to ensure that all athletes receive fair competition.  Therefore, treatment, to lower the testosterone levels and attempt to reduce any advantage as a result of high testosterone, would have had to take place, and that may be the reason this has taken so long to resolve.

Legal Tug of War

Because make no mistake, actually diagnosing the condition is a relatively simple procedure.  Knowing what to do about it, not as simple.  So over the last 8 or 9 months, the issue has probably been how to treat (if at all) to ensure competition.  The legal teams on both sides would have had their requirements.  I've no doubt at all that the IAAF would have been pushing for surgical removal of testes, where Semenya's camp would probably have resisted this.  The IAAF will probably have pushed for surgery as a key requirement for Semenya to continue her career in athletics - I'm not sure of the legal issues around this, but that is likely to have been their desire.  Semenya's team may have argued against this as an infringement on her right to decide on her medical treatment, and also to compete without that surgery. 

The eventual compromise may have been medical/hormonal treatment, and the process of the treatment and monitoring the response to that treatment would take time to track.  Hence the delay.

Will the details of the process be announced?  Or does speculation continue?

Of course, this is all speculation, and hopefully, further announcements will clear it up.  Here again, we have another fierce debate - should more detail be disclosed, or does "medical confidentiality" dictate that no announcement is made?  I've felt since the beginning that once the first leak happened, it would be in Semenya's best interests announce as much detail as she could without compromising herself too much.  In fact, if I think about it, the more she discloses the better, even at the risk of giving away too much information.  Better to control the facts than allow them to be made up or to sow mistrust and suspicion that it was a 'technicality' that got her cleared.  Simply returning to competition with no announcement will create mistrust and another round of speculation as the rumour mill begins to spin.  On the other hand, one can appreciate Semenya's desire for privacy, but this will be interesting to follow. 

The impact of reduced testosterone on performance?

The other very interesting thing to observe is whether Semenya's performance levels will remain where they were.  This is what most athletics followers will now be looking at.  If it is true that her testosterone levels have been reduced, even chemically, then it will certainly have an impact on performance, mostly because of the effect it will have on her training adaptation.

Athletes use testosterone as a drug primarily because it enables a higher level of training performance and more rapid recovery post-training.  The combination of the two equals improved performance.  A removal of testosterone would impair both direct responses and recovery capacity, and I feel that the recovery is the more crucial of the two in the larger scheme of things.  The immediate effect of 'testosterone withdrawal', in an athletic sense, is to reduce the level of training the athlete can manage without either running into injury or overtraining.

Therefore, if Semenya is to return, what is more telling will be how she adjusts her training, and not necessarily her race performances, because these are the result of her training performances, and whether her coach is able to manage an athlete who may very well be going through substantial physiological changes.  That will be the first big hurdle to overcome.

The East Germans had previously calculated that a doping programme (primarily with anabolic hormones, of which testosterone is one) could improve performance in shot put by 17% in one season!  That is not an acute effect, mind you.  Rather, it is the cumulative effect of the training that is done while doping and benefiting from higher testosterone levels.  The east Germans also worked out that doping was worth between 5 and 10 seconds in an 800m event for women.  In fact, for those who are interested in this research, you can read that post, based on the secret documents uncovered by Werner Franke, here.

Is the "loss of performance" when reducing anabolic hormone levels the same as the gain from increasing them?  Honestly, I don't know.  I don't think anyone does, and this case has no precedent.  So there are no answers.  Some of the physiological and anatomical changes induced by testosterone during puberty will never be reversed, others will.  How performance, the sum of all these factors, is affected, remains to be seen.

Of course, all of this is speculation, because we still don't know the details.  And so we're back again to the issue of whether anything will be said, other than that "she is clear to compete".

The next steps will be interesting.

Ross

Football analysis: Altitude and goal scoring

The effect of altitude on the 2010 World Cup

Amazing to think that we're now done with 60 out of 64 matches, and by this time next week, the World Cup will have left South Africa.  It's been a month-long celebration here in SA, and while the disruption to work and traffic and general life will be over, we're bracing ourselves for the mother of all hangovers down here!

Fortunately, the Tour de France will be into its second week, and so the withdrawal will be minimal, and here on The Science of Sport, we'll keep forging ahead with the next big thing!

Today, a look back at Round 1 at some really interesting statistics, first regarding the altitude and then the goal-scoring.

The effect of altitude on physiological performance

Before the tournament began, I did a series of posts on this issue.  This level of competition in a team sport like football rarely takes place at altitude, and so the impact on the game was the subject of much conjecture, with FIFA doing their best to deny that it would have any impact.  Many people felt it would impact on players, and  I hypothesized a number of changes in matches caused by altitude.  The overall summary is that players would cover less distance and also sprint less.  The impact of altitude would be to slow the game down - the comparison I gave is that footballers in top-level competition (Italian Serie A) run and sprint more than footballers in lower level (Danish) leagues, with less rest relative to work.  The altitude would have the effect of bringing the level down.

Now, thanks to Castrol's sponsorship of FIFA, we can actually evaluate that hypothesis, at least partly.  For those who don't know, Castrol are one of FIFA's eight 'middle level' sponsors, and they have been doing technical analysis of matches as part of their sponsorship activation strategy (I won't go into the details now).

So every match is tracked using cameras and all kinds of statistics are produced.  How far players run, how many passes they attempt and complete, tackles made and missed, number of sprints attempted and so forth.  I must confess that I can't vouch for the accuracy, and I've tried to email them to find out more about how the data are collected.  I've yet to hear back, but I think it's important to stress that there probably will be some error in the data - there always is.   However, I think the data they've produced is quite compelling, and as you'll see, the differences are large.

Altitude - less sprinting, less high intensity distance

The table below is a summary of the data on distances run and sprints attempted during the Round 1 matches.  There were 29 altitude matches and 19 sea-level matches, meaning that there are values for 38 teams at sea-level and 58 at altitude (I've treated Nelspruit as sea-level, incidentally, at 600m).

The distances covered by teams in matches are looked at for TOTAL DISTANCE, DISTANCE AT LOW INTENSITY (walking and very slow jogging - the average speed in this zone is 4.5 km/h, which is walking pace), and DISTANCE AT HIGH INTENSITY.  The average speed in this zone is 16 km/hour, but in some matches, were more high intensity running was done, it gets up above 20km/hour.

So, the total distance covered per match is reduced by 4% at altitude.  What is more interesting is that the low intensity distance is only 0.2% lower (statistically it is the same), but the distance covered at high intensity is down by a pretty large 11.5%.  The distance of 25,106m at altitude is 2,750m lower than at sea-level, and assuming that the goal keeper contributes negligibly to the high intensity distance, this equates to about 275m less sprinting and high speed running per player per match.  Of course, some players will be affected more than others, and so it's quite conceivable that certain players have covered a kilometer less at high speeds at altitude.  That is a massive difference - about 30%, and may impact on match outcomes.

This is further reflected in the number of sprints - down 11.5% from 1,059 to 949 sprints per match.  That's about 10 sprints per player per match less, which makes up most of that 275m per player difference.  Note that I've cut out the medium intensity running distance from the table - the distances there were 16,890m for sea-level and 15,819m at altitude, so again, there is a reduction in distance at altitude.  I'm emphasizing the extremes though.

The point then is that altitude slows the game down at the "top end", reducing the distances covered in sprinting as well as the number of sprints by about 11%.  That is a significant difference.

What the data doesn't allow us to do, unfortunately, is to decipher whether the reduction at altitude is produced entirely in the second half as players fatigue, or whether they slow down right from the onset and pace themselves differently.  I would lean towards the latter, and suspect that the distances covered are reduced at altitude from the very first 15 minutes of matches.

Individual match variability

I must also point out that there is a chance of a false conclusion here because although the differences are large, there are many confounding factors too.  For example, the match between Switzerland and Spain in Durban produced the most running of any match in the tournament.  The Swiss covered 119,909m in that match, of which 39,256m was at high intensity, at an average speed of 22 km/hour, and consisting of 1,484 sprints!  This was the most of any team in any match in the tournament (for interest's sake, the highest total distance was by Australia in their match against Serbia - 121,506m).

However, not far behind this was South Africa's opener against Mexico, but this was in Johannesburg.  There, SA covered a total of 118,856m, and 37,312m was at high intensity, with 1,690 sprints.  So here we have two games with similar distances, but one is at altitude and the other at sea-level.  To emphasize this point even further, consider France in their match against Uruguay in Cape Town.  There, they covered only 101,499m in total, with 25,320m at higher speeds.  So, that sea-level match had 50% LESS high intensity running than an altitude match...the graph below summarizes these three teams' physiological profiles.

The point I want to emphasize is that the tempo of the match, and the distance covered is not solely determined by the altitude - the strategy of the teams and also the nature of the match influences it as much.  The France v Uruguay match was particularly "narrow" with little movement because of the strategy of the two teams, and so less running was to be expected, compared to the Swiss who chased and worked tremendously hard off the ball against Spain.  However, on the balance of 58 altitude performances and 38 sea-level performances, altitude has exerted a significant effect, 11%, on the nature of the matches.  Perhaps another 50 matches would remove this 'randomness', but I'm quite convinced by the finding.

It's especially compelling, as I mentioned, if you consider that some players will be affected more than others, and with the possibility of 30% reductions in sprinting distances, the altitude has certainly had an impact.

When are goals scored?  Could altitude affect goal-scoring?

The next question related to this is whether the timing of goals scored differs between altitude and sea-level?  The reason one might hypothesize this is two-fold:

1. There is already plenty of evidence that more goals are scored in the final 15 minutes of matches than in any other fifteen minute period.  In fact, over 20% of a match's goals are scored in the final 15 minutes, according to a study by Armatas et al.  This has been attributed to fatigue at the end of the match, since players certainly slow down as the game progresses.  I suspect there is more to it than this - concentration, the state of the game, the intent of players as the final whistle approaches are all factors, but certainly, the final 15 minutes produces more goals.
2. Altitude will have a greater effect on fatigue (and thus potentially concentration), and so if the trend is observed at sea-level, the theory might be that altitude exaggerates it even more.  That is, one might suggest that more goals will be scored in the latter part of matches at altitude than at sea-level.

This is of course quite easy to determine - you simply have to count the number of goals scored in each 15 minute period.  The tricky part is knowing whether it's just co-incidence, because it's very easy to read too much into it and come up with 'patterns' where there are none!

I've done this, counted all the goals scored, and I have this result.  However, it is for another post, because this one has given out enough numbers for one day, and besides, there's work to be done!

So next time, we'll look at when goals are scored, and whether there's a chance that altitude affects it!

Join us then!
Ross

Football - the world's most immoral sport

Football:  A sport where morals and ethics are irrelevant

Tomorrow is the start of the Tour de France.  For the next three weeks, media coverage will comprise a mix of adulation and condemnation.   Adulation for the efforts of men who propel themselves over 3,000km of mountains, cobbles and windy flat roads in the world's most demanding sporting event.  And condemnation because all the while, people will question the validity of their performances.  Are they doped? To what extent does success in cycling equate with success at avoiding doping controls?

And here on The Science of Sport, we've been as harsh as anyone on the sport of cycling.  And with reason.  Cycling has a problem of its own making, and its refusal to address its own problem eventually led to media and sponsors threatening withdrawal.  And only then, amid much kicking and screaming, did cycling begin to turn a corner.

Cycling is still burdened by its doping past, make no mistake, and the legacy of its "great" champions means it will forever be questioned - again, this is a deserved reputation.  But it has certainly improved - the efforts of the biological passport and the invasive testing and the sponsors have gradually begun to control the extent of doping in the peloton.  As we will see over the next few weeks, the power outputs produced by the winners are coming down.  They are now "physiologically believable".  And for this, anti-doping efforts deserve some credit.

However, today, I felt the need to comment on another sport, which is, without doubt, more corrupt, more fraudulent and more immoral than cycling.  That sport is football - a sport that is completely without morals and an ethical code. 

This is a post I've been meaning to write for some time.  Ever since the World Cup began, I've commented on the irritation I feel at the diving, the play-acting, the cheating and the open dishonesty of players.  The referees are part of a 'script' that rewards this cheating, and the game is poorer for it.  And then just the other day I was having a conversation with a good friend of mine, and he was sharing that he finds it impossible to enjoy watching football, because the fraud leaves such a bad taste in the mouth.  And as the tournament has progressed, I find myself more and more in agreement.

A rugby paradigm applied to football - it just doesn't work

My friend Colin comes from a rugby background, a sport which still has values.  And I think it's important for people reading this to appreciate that if you are from a rugby background, the notion that a player will charge up to a referee and insist on a yellow or red card is completely foreign.  In fact, the notion that players will even challenge a refereeing decision is unheard of in rugby.

A player who goes down and exaggerates the extent of an injury to gain an advantage would be ridiculed in rugby.  In football, he is celebrated.  In football, referees command absolutely no respect from players.  They are tools to be deceived rather than officials to be respected.  And before you point out that basketball shares this trait, do yourself a favour and watch 58 games of World Cup Football, and you will see the difference.

Football is a disgraceful fiasco which rewards cheating, even glorifying it. And I enjoy watching football, but I cannot bring myself to respect it.  The fervor of the fans, the passion, the colour and the celebration of skill make the sport worthy of watching.  However, the shenanigans around cheating, and the glorification of that cheating, destroy my respect for the sport and its players.

From the first whistle to the last, players in football will seek to gain any advantage, no matter what level of cheating it requires.  If two players are attempting to win the ball near the sideline, and it ricochets off one of them, then BOTH will appeal to the referee for a throw-in.  One of them is lying, and thus cheating.  Yet it happens 100% of the time.  If a player is tackled, he will go to ground.  Guaranteed.  And the referee will react, also guaranteed.   Today, in the Brazil v Netherlands match, Arjen Robben launched himself over the tackler with a clearance that the Olympic high-jump champion would be proud of.  The referee bought it, awarded the free-kick, and the game changed from that point.  This is not an isolated incident.  Penalties are won by dives, players are sent off thanks to play-acting (just ask the Ivory Coast for their diabolical cheat against Brazil), and generally, matches resemble the WWE more than they do a competitive sports event.

The other day, I completed a survey being done by researchers in the UK, looking at public perceptions of cheating in football.  The survey wanted to know my thoughts on whether the behaviour is cheating, and whether it is typical of the sport, or whether only certain teams do it.  The answer is that it's pervasive.  Every team, and most players, will seek to gain any advantage by cheating.

What is the difference between football and cycling?

And the tragedy is that the media glorifies it, the fans idolize it, and in general, it is praised rather than condemned.  Now, I can't see the distinction between this cheating and what happens in cycling.  I don't see how diving to win a free-kick or get an opponent sent off is any different to manipulating the system to get away with doping.  Yet it one sport - football - it is glorified, while in another, it dominates conversation.  Quite why this is is beyond me.

Cycling is a sport that, for all its faults, still has some code of behaviour that makes it almost noble.  If the race leaders crashes, the peloton waits, even if the Tour is at stake.  The group agrees to slow down for feeding stations and bathrooms breaks.  And sure, there are occasions where personalities affect the behaviour of the peloton (the Simeoni incident with Armstrong comes to mind as an ugly incident).  But in general, cycling is a peculiar mix of cheating through doping and honesty and sportsmanship.

In football, there is no redeeming value.   The most celebrated footballers of the current World Cup are its most celebrated primadonnas.  Ronaldo dived more two in three times that he ran with the ball.  Didier Drogba collapses like a matchstick man when he feels the breath of an opponent on him.  Arjen Robben exerted himself more rolling on the floor than he did running.  Yet these men are superstars.  They should be jeered off the field in disgrace.

If I were a footballer (and I played a little in my time), I would be so irate at the first opponent to tries to cheat by diving that I'd be liable to lash out at him and get myself sent off. Yet it happens all the time and collectively, the sport embraces it.  Referees must take much of the blame, but ultimately, FIFA are responsible for the decay of the sport into this realm of immorallity, cheating and dishonesty.

And frankly, it is shameful.  It devalues the sport and its athletes.  Yet FIFA is entirely complicit, because retroactive censure for these players could go a long way to stamping it out of the game.  Most footballer followers are equally complacent - they shrug their shoulders and accept it.  "It's part of the game".  Referees buy it, all the time.  FIFA does nothing to prevent it.  And players exploit the system.

Ultimately, football may be the "beautiful game", but given the degree of fraud and cheating that goes on in it, it is the immoral game.  There is no beauty in what we have seen in the first 58 games of this World Cup, only the sour taste that  remains when you've consumed something that should taste good, but for some reason, just tastes spoiled.

Ross

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!

Ross