On the usefulness of bad drug tests

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Say we've got some condition with a base rate of X% which has a really unpleasant treatment that nobody wants. Say you've got a test for the condition which has a sensitivity of 100% (the false negative rate is zero). Unfortunately, it's also got a specificity of 100-2X, so about 2/3 of the positives are actually false positives. I.e., even with a false positive test you're more likely to not have the condition than you are. Now, if you have some kind of better followup test, you can use this kind of test as a quick and dirty screen. But if this test is the last word then you generally can't use it to start treatment.

The case of drug testing in sports potentially represents an exception to this rule in a brutal utilitarian kind of way. In the medical case, people have some disease they presumably want to have fixed and so even though the treatment is unpleasant they want to get it if they need it. By contrast, athletes who are doping don't want their "disease" cured. They want to keep cheating without being detected. This means that unlike, say, lung cancer, people have no particular incentive to avoid behaviors that lead to the condition (like buying EPO and injecting it into your ass, say) unless there's some actual deterrent. The testing and the punishment is the deterrent.

In order for the deterrent to be effective, it doesn't have to be perfect. It merely has to significantly increase the chance that you'll suffer if you cheat. If there's (say) a 100% chance of getting caught if you do cheat but only a 5% chance of getting caught if you don't, then the incentive not to cheat is very strong. Now, it's true that there are a bunch of poor innocent suckers who get punished anyway, but of course since almost everyone, innocent or guilty, denies cheating, they're serving as a useful deterrent as well.

Please note: I'm not endorsing this reasoning, which is a little too utilitarian even for my taste but it's easy to imagine a slightly less blunt version (a few false positives are worth it for the goal of eliminating drugs from sports) fluorishing in the WADA.