Lance Armstrong will be stripped of his seven Tour de France titles. Watching him win those races was exciting, and I had always hoped that the investigations regarding the doping allegations would come to a conclusion. Certainly, the allegations are still alleged, as there has never been a positive test and Lance has not confessed (in fact, he has merely refused to fight the allegations). But I digress.
There has been some discussion on how to award his Tour de France titles to other cyclists (more here). Here are my thoughts that are most definitely influenced by operations research.
1. An athlete’s strategy depends on the strategies of their opponents. If the doping cyclists did not compete, it would have been an entirely different race. The fastest non-doping cyclist would not necessarily win a race with only non-doping cyclists. Therefore, without Lance as an opponent, perhaps the sixth place finisher could have won with a more conservative cycling strategy. Lance won his races with different margins, and he had to come from behind in several of the Tours. However, many of the leading cyclists in the Tours were tainted with doping, so I suspect that widespread doping affected the non-doping cyclists’ strategies.
In diving, for example, one may change the selection of dives based on what they anticipate their opponents’ scores would be (see my blog post here). A diver may go big or go home, having a poor finish in an attempt to medal against super-human opponent. Without the superhuman opponent, they might make a more conservative strategy that would make a second place finish more likely.
2. Cycling is doubly challenging because cyclists are on a team, yet there is an individual winner. The team members (as part of the peloton) shield their team leader from wind, etc. That is, all of the teammates are sacrificed for the one member to have a chance at winning. What if the team leader is not doping but his teammates dope? That cyclist would have received an unfair advantage even if he did not personally engage in doping. This is a gray area.
3. In other competitions, second place athletes have refused a title/win after the first place athlete was stripped of their title. Reggie Bush being stripped of his Heisman trophy comes to mind. Vince Young, the second place athlete, was not offered the Heisman and publicly stated that he would not have accepted it. This is notable, since Vince Young almost certainly would not have competed any differently had Reggie Bush not been in the Heisman competition (concern #1), and therefore, Vince Young would have won if Reggie Bush had not competed. Yet Heisman Trust simply decided to vacate the award for 2005. In cycling, where the second place winner would not necessarily have won in a race without the alleged dopers, there is even more reason to vacate the Lance’s titles from 1999-2005.
4. My above arguments assume that we know the truth about who has doped and who hasn’t. This is a dubious assumption. If you are curious about unpacking the mystery, I recommend watching the 60 Minutes interview of Tyler Hamilton (one of Lance Armstrong’s teammates and accusers makes a compelling case against Lance) and Sally Jenkins’ latest Washington post article. Sally Jenkins does an excellent job of explaining why the alleged doping is just that: alleged. Alberto Contador was banned for two years after a substance was in his blood that was “too small to have been performance-enhancing and that its ingestion was almost certainly unintentional.” He was found guilty because “There is no reason to exonerate the athlete so the ban is two years.” Making decisions under uncertainly–naming new Tour winners from 1999-2005–is fraught with peril. There is no physical evidence of some of the accused, and there is so much that we do not know about who is innocent and guilty of their charges. Even if there was some reasonable way to address my concerns #1 and #2 about strategy in the presence of some dopers, I cannot imagine the newly named winners would be deserving.
Related blog posts:
Punk Rock Operations Research 
August 28th, 2012 at 1:32 pm
Jan Ullrich already said no when offered some of the titles :).
August 28th, 2012 at 2:34 pm
In more detail, Jan Ullrich “implicated” that he’s proud of his 2nd places b/c he believes he made them under “fair” conditions. In other words, no one who’s [ever] won the TdF, did it w/o doping – most simple solution: wipe all winners back to …well, ever.
August 28th, 2012 at 4:56 pm
I don’t recall the details of the Contador case, but ” too small to have been performance-enhancing” seems like a risky assessment to me. Other than blood packing and stimulants, doping is typically not intended to directly affect the athlete during the race; the point is to improve the athlete’s preparation. So most banned substances, particularly steroids, will likely be out of the athlete’s system (one reason testing is tricky) or working their way out by the time of the competition. Hence a small amount may just be the residue of an initial amount that was indeed large enough to enhance performance.
August 28th, 2012 at 5:10 pm
What about performance enhancing drugs in science?
Erdős was an amphetamine addict and credited the drug with his creativity. Should he have his Wolf Prize revoked? How about your Erdős number? If I am linked to Erdős by a paper he was on drugs to take does that mean the Erdős number is now 4* not 4?
Or how about Kary Mullis and PCR. He credits LSD with helping the insight. http://en.wikipedia.org/wiki/Kary_Mullis#Use_of_LSD Should is Nobel be given to someone else? Should we accept PCR based DNA evidence in court cases? I doubt many people would like murderers walking free because we suddenly get moral about performance enhancing drugs.
How about Grammies? Some of them have been won by people under the influence. As Bill Hicks pointed out the Beatles were so high they even let Ringo sing some tunes.
August 29th, 2012 at 12:54 am
There has been at least one positive test in France. See for instance http://en.wikipedia.org/wiki/Lance_Armstrong#1999_Tour_de_France_urine_tests
August 29th, 2012 at 4:57 am
I find this all rather interesting.
First of all, regarding an athletes participation changing the decisions of his competitors. This reminds of an example I use when I teach minimax regret as part of my decision analysis lectures.
Regarding how to redistribute the titles I suggest a look at a rather long post that demonstrates the problem with doing this.
As to “blame”, James Atherton recently posted about this and linked to one of his earlier pages on Shame culture. I think this shame culture occurs a fair amount in sports. Partly because people are willing to take sides and dispense with rationality, but also because some of the legal processes in question are only quasi-legal and do not offer the full set of recourse actions/appeals within a well functioning judicial system. Quasi-legal is all well and good for minor sporting issues but when it comes to major sporting decisions I think it poses a problem. I don’t know about cycling but association football has specific rules stating that you cannot appeal via the local legal system but have to go via CAS. Again, this makes sense for minor issues but for something more serious?
August 29th, 2012 at 7:26 am
Red Dave: Regarding your Erdős number, the answer depends. If you also take speed, your number stays 4. If you limit yourself to Irish whiskey, it’s 4.4. Nothing stronger than beer? 4.7.
Slightly more seriously, PEDs in science may not really be “performance enhancing”. Erdős might think speed made him more creative, but I doubt there’s empirical evidence of a general positive effect (or least nothing that cannot be accomplished by copious application of hot coffee) (which, by the way, did nothing to improve my mathematical prowess). Competitiveness in sports creates an incentive to use PEDs. I’m willing to believe that hallucinogens “improve” performance by some artists (meaning I’m hard pressed to come up with an alternative explanation for some paintings), but I don’t think there’s an explicit race for Nobel prizes, Turing awards etc. (meaning I don’t think people consciously “enter” themselves in the competition), and so I don’t see those creating a demand for drugs.
August 29th, 2012 at 11:03 am
Red Dave reminded me of “Getting an Edge“.
September 2nd, 2012 at 4:52 am
Maybe the more important question is whether an athlete really benifits from using drugs to enhance his/her performance. To my knowledge there is no scientific proof for this. See for example http://www.guardian.co.uk/commentisfree/2006/aug/04/sport.science
September 14th, 2012 at 4:04 pm
First timer to your blog. Thanks for the post and it is an interesting debate. Apropos comment #4, I see a key difference in that sports are played by a defined set of rules and performance enhancing drugs are not part of the rule book. When it comes to creativity, science, acting or music, nobody defines any such rules and the individual is free to use whatever that motivates them. It’s only the final result that is judged and not on the means.