The UCI should stand up and make a ban mean just that, caught and there's no way back.
Change the mind set to change the sport
We should be weary of drug tests as a cure-all to the sport:
Define:
P=Positive result of test
N=Negative result of test
C=Clean rider
D=Doped rider
Proportion of clean riders = Pr(C) = (1-a)
Proportion of doped riders = Pr(D) = a
Probability of testing positive while doped = Pr(P|D) = c (false positive)
Probability of testing positive while clean = Pr(P|C) = b (true positive)
We can conclude from the above that the number of false positives will exceed the number of true positives if and only if:
Condition X:= Pr(P&C)>Pr(P&D) <=> (1-a)b>ac <=> (b/c)>a/(1-a)
Which means for a sufficiently small proportion of dopers in comparison to clean riders, along with a sufficiently high inaccuracy of the test, you will have more false positives than true positives.
For an empirical example we have:
Pr(C)=.99
Pr(D)=.01
Pr(P|C) = .01, meaning 1% of clean riders test positive
Pr(P|D) = meaning 95% of doped riders test positive
Therefore the proportion of false positives = Pr(PC) = Pr(P|C)Pr(C) = (.01)(.99) = .0099
and the proportion of true positives = Pr(PD) = Pr(P|D)Pr(D) = (.95)(.01) = .0095
We therefore have the ratio b/c = (.01)/(.95) = .010526316, and a/(1-a) = .01010101, satisfying Condition X.
Indeed, .0099>.0095, so in this case we can conclude that out of all the positive tests, more of them are clean riders than doped riders, meaning we have a witch-hunt on our hands.
Of course these particular probabilities may not mirror the real world so Condition X may not be satisfied in reality.
However, we can conclude that the tests have to be
extremely accurate in order for A and B samples to be valid...
This is why I am NOT in favor of lifetime bans. In the case of the wrongly accused, I believe they should be offered a second chance at competition...
Feel free to play around with the numbers, we can also define:
Condition Y:= Pr(P&D)>Pr(P&C) <=> Pr(P|D)Pr(D)>Pr(P|C)Pr(C) <=> ac>(1-a)(b) <=> a/(1-a)>(b/c)
meaning, that given a sufficiently low ratio of dopers to clean riders, we can expect a reasonable number of true positives given a sufficiently low ratio of false positives to true positives.
Thus, we should set the threshold b/c = S, for some number S such that S is the acceptable level of effectiveness of the test when setting policy...
I'm a little too lazy to plug in the situation where most of the peloton is doped and the tests are mostly ineffective...I'll do that after lunch.