"Finally, the last thing I’ll say to the people who don’t believe in cycling, the cynics and the skeptics: I’m sorry for you. I’m sorry that you can’t dream big. I’m sorry you don’t believe in miracles. But this is one hell of a race. This is the greatest sporting event and you should stand around and believe it. You should believe in these athletes, and you should believe in these people. I’ll be a fan of the Tour de France for as long as I live. And there are no secrets - this is a hard sporting event and hard work wins it. So Vive le Tour forever!"
Lance Armstrong (24 July 2005) - Farewell speech at the Champs-Elysees podium, after winning his 7th Tour de France, quoted in ”Paris salutes its American hero” by Caroline Wyatt in BBC News.
During the last few years we have seen a number of accomplished cyclists, such as Bjarne Riis and Jonathon Vaughters, claim that they used EPO, and/or other Performance Enhancing Drugs (PEDs) and/or blood transfusions (that I collectively denote as Illegal Performance Enhancing Technologies (IPETs)) in order to be more competitive in professional cycling races. Further, we have seen an array of cyclists banned from competing for a number of years through testing positive for banned substances found in their blood. Soon after these admissions or positive tests, the cycling governing bodies have typically moved to strip such cyclists of the titles that were acquired during that period, and have awarded these titles to the second-placed finishers. I find this to be a “double-edged sword” as these actions do punish those who have admitted using, or found to have used, IPETs, but these actions do assume that the second place finisher was not using IPETs. For those that have confessed to using IPETs, but who did not test positive, this is clearly an unreasonable assumption, as this scenario provides a clear demonstration of the limitations of the testing at that time. This somewhat logically flawed punishment (which, for any given event, could repeat itself until the title is awarded to the last placed finisher until he/she admits to using IPETs) provides strong motivation for other such cyclists to remain silent.
The most recent significant event, however, is that Lance Armstrong is no longer fighting charges that he used IPETs during his multiple appearances in the Tour De France. The discussions that I am reading and seeing in the press and in the editorial pages, such as those of the Seattle Times, suggest somewhat of a lack of understanding of the environment in which Armstrong was competing. However, it is important to realize that certain aspects of this environment can be deduced from the results of each stage of the TdF and from the records for various other events. I have assembled data from the TdF and other events and attempted to present them in a way that illustrates interesting trends that I attribute to the Natural Ability, Preparation, Recovery (NAPR) of the cyclists. While the ability of the cyclist is dictated entirely by biology and environment, both their preparation and recovery can be modified by IPETs.
I wish to stress that this is obviously not the first study of the performance of professional cyclists, or professional athletes in general. One recent study focusing on the use of EPO in professional cycling with a well-defined statistical analysis can be found in Ref. . Further, I am not claiming to use new techniques, and in fact, I have employed relatively unsophisticated statistical analyses throughout. Being a physicist and not a statistician, I am guided by the belief that if you can’t see it, it isn’t real, and as such have attempted to produce plots that exhibit, or do not exhibit, signatures of “interesting” behavior.
In this section, events that isolate individual performances are analyzed, i.e. that do not have potential contamination from contributions from other cyclists to the measured performances.
A quantity that has been discussed previously  is the all-time individual fastest ascents. The data given in Ref.  is shown in Fig. 1 along with further results from the Verbier climb in the 2009 tour. [In 2007, there were a number that set the fastest ascent speed, but only Soler’s time is shown. The peloton (Pereiro, Arroyo, Valverde, Schleck, Evans, Horner, Menchov, Boogard, Rasmussen, Zubeldia, Halgand, Leipheimer, Contador, Popovych, Cobo) went up the Marie-Blanque (not the climb on which Soler’s record was set) at the same ascent rate.] .
My observations are that
Information relevant to this data is:
A quantity that is related to the Fastest Ascent rates discussed in Section A, is the fastest average speed for the climb up the Alpe D’Huez during the TdF. The all-time fastest climbs  up Alpe D’Huez are shown in Fig. 2. While obvious, it is important to keep in mind that all other ascent rates are slower than these, but it becomes increasingly difficult to determine the slower speeds in each year from the available data.
There are a number of ways to consider this data in efforts to identify underlying trends. One way is to simply consider the average ascent rates as a function of year in which they were accomplished, from which one observes that
Information that is relevant to these observations:
Viewing the same data in decadel slices, while examining the performance as a function of the age of the cyclists, gives rise to the plots shown in Fig. 4.
While limited by statistics, there are some interesting trends, a summary of which is shown in Fig. 5):
To highlight the performances: If Armstrong, Pantani and Lemond had ridden Alpe D’Huez in
the same race, but at their respective fastest speeds, Armstrong and Pantani would have finished
approximately 11 minutes ahead of LeMond - or a distance of 3.3 km on the 13.8 km
I had not realized this until now, but the Alpe D’Huez stage that I saw on the
mountain in 1991, where Indurain, Bugno and one other cruised by me effortlessly it appeared,
with Indurain in yellow, was the first sub 40 minute climb in history !! Lemond and Fignon
appeared to be at their outer limits when the came by me. I was attending a Les Houches Summer
School that year, and took a day off with one other attendee to see this stage, after watching a
number of them on the TV there.
An aside: I had not realized this until now, but the Alpe D’Huez stage that I saw on the mountain in 1991, where Indurain, Bugno and one other cruised by me effortlessly it appeared, with Indurain in yellow, was the first sub 40 minute climb in history !! Lemond and Fignon appeared to be at their outer limits when the came by me. I was attending a Les Houches Summer School that year, and took a day off with one other attendee to see this stage, after watching a number of them on the TV there.
Performance in an individual time-trial (ITT) is good measure of particular capabilities of a cyclist that are distinct from their climbing abilities. The all-time 10 fastest winning ITTs in the TdF over distances greater than 20 km can be found in Ref. , and are shown in Fig. 6 as a function of year and distance.
Winning ITT means that it is the fastest performance in that given event, but these 10 fastest are not the all-time fastest ITT performances. It is also interesting to consider the performances as a function of age, as shown in Fig. 7.
One can observe from the data that:
Information that is relevant to these observations are:
Most TdF’s begin with a Prologue before starting the race proper. The Prologue is usually between 5 km and 10 km, although there have been a few number of longer and shorter ones which have been omitted from this analysis.
Figure 8 shows the winning speed in the Prologue as a function of year. The year that Lemond introduced aero-bars into the sport is shown by the vertical dashed line. While the winning speed is quite informative, a further interesting cut on the data is the number of riders exceeding a certain speed. To illustrate this point, Fig. 9 shows the number of riders producing an average Prologue speed exceeding vmin = 51.5 km∕hr.
What I observe in the data is:
An event that is not part of the TdF is the one-hour record (OHR), which has a long history. The data for the OHR can be found in Ref. , and is shown in Fig. 10.
This is quite a remarkable data set, going all the way back to 1893. After the initial turn-on during the early 1900’s, the record underwent essentially linear improvement until the mid-1990’s, at which point the record increased by ~ 10% within the space of two years, with the current record held by Boardman, with two remarkable performances. In the recent past, Moser set the record in 1984 (twice), breaking Merckx’s record which had stood since 1972. Then Obree took the record in 1993 with his distinct aero position, soon followed by Boardman and retaken by Obree in 1994. These performances were not inconsistent with the (approx) linear increase in average speed from previous decades. Then in 1994 things changed. The record was then shattered by Indurain, Rominger and Rominger in 1994, and finally retaken by Boardman in 1996 - setting a record that remains today. These last four records were truly outstanding and off the curve. Much was happening in cycling around this time period. Aerodynamics was being studied more scientifically, and aero-bars, disk-wheels, aero-helmets, skin-suits and so on were being introduced and used in the sport. The one-hour record is where these were being used very effectively.
Because of the aerodynamic improvements, the record was reset in 2000 to the 1972 Merckx record, and all future attempts at the OHR must be performed on equipment that is essentially that used by Merckx. This resetting removed all of the records set in the 1980’s and 1990’s.
It is important to attempt to quantify the technological advances. A study has attempted to do just this , in which they simulate the impact of wind-resistance as a function of rider position, the impact of altitude on the ride, and so on, and summarize with [ 7] (quote):
"In summary, by using field crank dynamometer measurements, the present study extended the mathematical modeling approach used in previous studies that compare hour record performances. After adjusting for differences in altitude and aerodynamic factors between cyclists, several conclusions can be drawn. The earlier record holders who used traditional round tube track bicycles (Bracke, Ritter and Merckx) averaged sea level powers of about 402 W. However, Merckx’s 1972 performance (429 W) stands out above the others. The next series of record holders, who all used various aerodynamic improvements (Moser, Boardman, Obree) averaged sea level powers of about 403 W, or about the same. The aerodynamic improvements during this era resulted in a record distance increase of about 10%. The last three challengers (Indurain, Rominger, and Boardman) averaged 446 W, a large increase in power compared with the previous record holders. During this period, the available bicycle aerodynamic improvements did not change as markedly. The increased power of these cyclists, resulted in a distance increase of about 7%. In other words, since Bracke’s era, about 60% of the improvement in the hour record distance has come from aerodynamic advances and about 40% from higher power outputs. The combination has produced the recent meteoric rise in the hour record. Finally, future hour records at altitude should be possible, especially if the current champions use indoor velodromes at higher elevations, where the conditions of the track are constant."
The red highlighted sentences in this summary are interesting. I conclude that:
Further information relevant to this record:
In this section, events that depend at some level upon the collective performance of more than one cyclist are analyzed. Performances in this category cannot be uniquely assigned to a given cyclist, and are more suggestive of the average NAPR of a team, or of the peloton as a whole.
The most obvious quantity to examine is the overall average winning speed of the TdF as a function of year and age. A complete set of data for the TdF overall classifications and details of the stages can be found in Ref. , from which the winning speeds can be extracted, as shown in Fig. 11.
In addition to exploring the changes in average speed with time, it is also interesting to explore the age dependence of the data as a function of decade, the distributions for which are shown in Fig. 12.
Taking the averages of the results shown in Fig. 12, an estimate of the evolution of the average speed as a function of age can be determined, and is shown in Fig. 13.
There are number of interesting trends in the average winning speed data:
Let us focus on the greatest cyclists of the modern era - those who have won 5 or more TdF’s. Given the hunting accident which deprived LeMond the chance to win 5, and given his other accomplishments, LeMond has been added to this elite group of cyclists for further consideration. The average winning speed data for these multi-tour champions are shown in Fig. 14.
My observations are:
The team time-trial (TTT) is a clean measure of the performance of the capability of each team in the TdF (ignoring crashes). It is well known that a strong team is currently a requirement for winning the TdF, and has been for decades. The fastest winning TTTs in the TdF can be found in Ref.  (he does seem to have overlooked the US Postal performance in 2004 as the fourth fastest TTT), and are shown in Fig. 15 as a function of year and distance. Winning speed means that it is the fastest time to win the TTT, and this data does not represent the all time fastest TTT’s.
In Fig. 16 we show the first several teams in each of the fastest years.
One observes that
A survey of the internet shows some relevant information regarding doping at the team level, which would certainly be somewhat isolated by the performance in the TTT. The following information is available:
The results of a number of individual and collective performances in the Tour de France, and other events, have been examined in an effort to put Lance Armstrong’s performances and accomplishments into context. Fig. 17 is a combination of plots that summarizes aspects of individual performances as a function of year for a selection of events,
while Fig. 18 summarizes collective performances as a function of year.
Looking at the data shown in Fig. 17, there is the clear trend that cyclists NAPR exhibited a peaking between the years of 1990 and 2005, with peaks occurring in the vicinity of 1996. Given that humans do not change biologically on such short time-scales, and one expects that superior training and dietary techniques are not deliberately discarded, one is led to deduce that IPETs were being extensively used during this period. Such manipulations to cyclists NAPR were peaking when Armstrong returned to professional cycling in 1999. Armstrong’s individual performances did not exceed those of the record-setting cyclists in the previous 9 years, such as Pantani, Riis, and Boardman. In fact, it is in the collective events, such as the average winning speed of the TdF and the team time-trial, that Armstrong’s performances were exceptional compared to the previous years. His final TdF was the fastest of all time, and the Discovery Channel team time-trial performance was truly outstanding. In each year that Armstrong won the TdF, he was clearly dominant, but it is clear from the data, that this might not have been the case if he had competed with the same NAPR just 5 years earlier (due to NAPR-modifications of competitors).
It appears that a new generation of IPETs were being explored in the late 1980’s, and fully exploited in the 1990’s. Of course, EPO is the prime candidate for this IPET, but this cannot be extracted from the data we have analyzed. The substantial reduction in performance variability that was already complete by ~ 1991, and has been in place since, suggest that variables dictating performance are being manipulated to an approximately standard set of values, significantly reducing the impact of natural-ability on performance (see Ref. ).
So what can one conclude from all of this information?
Finally, it is worth mentioning that the data analyzed in this work is but a small fraction of what could potentially be analyzed. One of the interesting features that was touched upon only in the analysis of the TdF prologue data, is the complete distribution of riders speeds in each event. If, in fact, IPETs that minimize the impact of natural ability in performance are being used, this trend should be clearly evident in the distribution of speeds in any given single event.
To close, the data that has been analyzed in this work points to the combined natural ability, race preparation and recovery of post-1999 Armstrong being consistent with, but slightly better than, other elite cyclists competing at that time. The strength of Armstrong’s performances in the collective events suggests that his preparation and recovery methods were shared with his team-mates.
This was written as a result of many interesting discussions, arguments and email-exchanges about doping in sport among John Costello, Jon Gates, Chance Reschke, Mike Taxay, Charlie Varela and I, along with others, throughout the last several years. I would like to thank them for their help in shaping this article.
 http://en.wikipedia.org/wiki/Alpe_d’Huez, which is claimed to have been adjusted to the 13.8 km distance, http://autobus.cyclingnews.com/road/2004/tour04/?id=results/stage16 , http://le-grimpeur.net/blog/archives/52