Eddie Santos, a Fellow in the current session of Insight Data Science in Silicon Valley, is providing a day-by-day analysis of this year’s Tour De France. Below are two recent posts, originally appearing on the blog at Eddie’s website, VAMmer, that provide a data-driven perspective on whether Chris Froome of Team Sky was likely doping during Stage 10 of the race, which took place earlier this week.

July 20, 2015

Much has been made following the performance of Chris Froome of Team Sky during Stage 10 of this year’s Tour de France. Stage 10 was the first mountain day of the Tour, with the finish line at the top of the climb La Pierre-Saint-Martin, a 15.3 km stretch in the Pyrenees that averages 7.4%. Team Sky did what they’re known to do: they lined up their phenomenal cast of climbers and grinded out their opponents one-by-one until Froome, led by his Tasmanian lieutenant Riche Porte had dropped everyone by 6.5 km to go, save for the talented Colombian climber, Nairo Quintana. At this point, Froome dropped the hammer and attacked Quintana, leaving him and Porte behind for good, taking the victory in dominating fashion, and leaving no doubt that he is the favorite to win the general classification.

Coming off of one of the darkest ages in professional cycling that saw some of the freakiest climbing performances (see: Pantani, Marco. L’Alpe D’Huez, 1997) fueled by athletes doped out of their minds, any dominant performance is now met with a heavy dose of skepticism. So when Chris Froome blew the lid off of the peloton, anyone that has followed the professional circuit could not help by raise an eyebrow and ask if we’re seeing an authentic performance.

There has been rampant speculation as to the power-to-mass ratio that Froome achieved on La Pierre-Saint-Martin. Pierre Sallet, a French exercise physiologist, recently estimated Froome’s power-to-mass for the La Pierre-Saint-Martin climb to be an astounding 7.04 watts per kilogram (W/kg), a circa 2000 Armstrong-ian figure. Sallet, however, has not divulged the methodology of his calculation, and we’re only left to speculate that he used back-of-the-envelope calculations based on having precise knowledge of the road gradient, air density, cross-sectional area, and wind speed for all points on the climb. This is an extremely sensitive calculation, and minor misestimations of the highly variable parameters can and does lead to large errors.

The impact of his calculation, however, has been enormous. The French media have jumped all over Froome, all but claiming his performances have been artificially enhanced. Unruly spectators lining the side of the road have taken it upon themselves to protect the sport by taking direct action against Team Sky racers: during stage 14, a spectator threw urine on Froome’s face while yelling “doper!”. Also during the stage, Porte was punched in the ribs during the last 3 km of the final climb by another fan, further highlighting the volatility of the situation. Security around Team Sky has been beefed up, though only further conjuring up memories of the U.S. Postal team of Lance Armstrong and the large security detail he required.

I’ve taken it upon myself to analyze this climb and calculate the details of Froome’s performance. Let it be said I have no direct interest weighing on the outcome of the race nor do I have an allegiance to any rider. I’m a data scientist, a theoretical physicist, and an avid cyclist. I spent many years studying exercise physiology to gain an understanding of training and performance. I love watching professional cycling, and if I have to pick a favorite, I find myself pulling for Quintana. More than anything, however, I’m a quantitatively skilled and uninvolved observer. And so, without further ado, I have calculated the following:

Froome averaged 6.06 W/kg over the penultimate 14.4 km of La Pierre-Saint-Martin. At a recently reported mass of 68 kg, this amounts to 412 W over 38:15.

To determine this, for the La Pierre-Saint-Martin climb, I used the Strava segmentCol du Soudet D132, of which Robert Gesink is currently the leader, posting a time of 39:48 during stage 10. Gesink recording an average power of 409 W at a mass of 72 kg, for a power-to-mass ratio of 5.68 W/kg. Gesink attacked early, but he and Froome started the climb (and this segment) together. Froome eventually caught and dropped Gesink, and finished 1:33 ahead fo Gesink. This gives a time of 38:15 for Froome on the segment.

In the following plot, we can see the average power-to-mass from users with a power meter for this segment, and is clearly hyperbolic, as expected, since velocity is proportional to power-to-mass

Velocity∝PowermassVelocity∝Powermass

and velocity and time are inversely proportional,

Velocity∝1timeVelocity∝1time.

The subsequent fit is very strong, indicating strong predictive power of time to complete a climb given a rider’s average power-to-mass.

Plugging in Froome’s 38:15 to this fit provides the 6.06 W/kg figure quoted above. On the other hand, plugging in 7.04 W/kg provides a time estimate of 32:56. Pardon, Sallet, but that’s not even close.

I have no idea if Froome and his Sky teammates are indeed doping, but if I had to speculate based on the information I present here, I would say his values areconsistent with clean performances. History has taught us that we must question these dominant performances, but after careful scrutiny, the evidence shows his performance is not super-human. Thus, let’s give the man the benefit of the doubt and let him ride his race. He deserves that much.

July 21, 2015

As mentioned in yesterday’s post, Chris Froome’s performance on the final climb of stage 10 (La Pierre-Saint-Martin) of this year’s Tour de France, has sparked muchdebate as to the authenticity of his performance. Calculations performed by French exercise physiologist Pierre Sallet claimed Froome averaged 7.04 W/kg on La Pierre-Saint-Martin have sparked much fervor on the sides of roads amongst the spectators.

In response to public pressure, and perhaps more so to show how wrong Sallet was in his calculation, Team Sky today announced that Froome averaged 414 W on the final climb. They estimate his mass to be 67.5 kg, leading to a 6.13 W/kg. They also claim that their chain rings hamper the measurement of power by 6%, and give 5.78 W/kg to account for this.

As I demonstrated yesterday, fitting a simple model to actual power-to-mass data from the La-Pierre-Saint-Martin climb on Strava has shown that Froome averaged somewhere close to 6.06 W/kg for 38:15 for this particular segment. Using a reported mass of 68 kg leads to 412 W, which is a perfectly reasonable number to expect out of a clean grand tour champion. VAMmer nails this calculation.

Team Sky likely gave the 5.78 W/kg value to lower Froome’s number so that it makes him seem as pedestrian as possible, when in fact the 6.06 W/kg is more consistent with the values provided by other riders. For example, as I also showed yesterday, Robert Gesink uploaded a 409 W performance at roughly 72 kg, though his wikipedia page lists his mass at 68 kg. This puts his performance between 5.68–6.01 W/kg. Froome came in 1:33 ahead of Gesink, and thus Gesink’s values provide a lower bound for Froome’s power-to-mass.

With the Tour hitting the Alpine stages tomorrow, there will surely be more opportunities to scrutinize the performances of Froome and the rest of the peloton. Stay tuned!