Adam Smith: "Take a step back and look at the big picture: take all elite distance runners and coaches as one group. I don't know how many people that may be, but let's say it's 1,000 people. If 3-10% of these people have hypothyroidism, that's 30-100 runners. It's not unlikely that these runners/coaches share the same group. In fact, it would be highly unlikely if no coach/runner pair shared this condition."
I disagree. Why does making it a group of distance runners change anything, if you still apply the same 3-10% formula? If you assume that thyroid problems are distributed at random, then picking any 3 individuals and having them all come up positive for thyroid conditions is very unlikely. Sure it's likely in large groups that train together that you will have multiple people with thyroid conditions, but if you consider Salazar/Farah/Rupp a separate group (debatable - should Salazar's whole "stable" be included?)then it would be anomalous for all 3 of them to have thyroid conditions.
Adam Smith wrote "Nevertheless, the math does not negate the occurrence of the event. I know that lottery winners are extremely rare (compared to contest entrants) yet I read stories about them every day. Should I presume these stories are false because I know that winning the lottery is rare?"
I don't understand your point. I'm not trying to prove that Rupp/Farah/Salazar don't exist because all 3 have thyroid conditions. I'm just pointing out that it is statistically anomalous if all 3 of them have "thyroid conditions" (and I should add, I'm not even sure if Farah has one).
The point of all this is, if all 3 of this dynamic trio have a relatively rare condition that requires medication, it is, if nothing else, surprising. Given that this whole thread is about them possibly looking for an unfair advantage, this shared need for thyroid meds seems like a fairly obvious avenue to investigate.