I agree with nearly everything you said there and think it’s good advice, so I upvoted your comment. However, I care about statistics and you made a common error here:
If you’ve had horrible luck so far, does that mean that regression to the mean will be working in your favor as long as you keep trying?
Regression to the mean doesn’t work that way. The fact that a random event came out one way several times in a row doesn’t make it more likely that it will come out the other way the next time. For instance, if you flip a fair coin and it comes up heads ten times in a row, the probability that it will come up tails on the next flip is still no greater than 50%. The only way that having found multiple bad psychiatrists will improve mixednuts’ chances of finding a good one next time appreciably is if he starts crossing off an appreciably large proportion of the bad psychiatrists in his area, leaving the good ones dominating the remaining population. This effect isn’t regression to the mean. The error you made is known as the Gambler’s Fallacy.
I’m familiar with the gambler’s fallacy. I wasn’t being very clear about what I had in mind when I referenced regression to the mean, so here’s my model. If someone has been to a few good therapists (better than the typical therapist) and they haven’t been able to help, then “find a better therapist” would be tough advice to follow. But if they’ve been to a few lousy therapists (worse than the typical therapist) then finding a better therapist should be doable, since they’ll have a good shot at doing that even if they just pick a new one at random.
Alternatively, if they’ve been to a few good therapists but haven’t found the right one, that’s evidence that “the right therapist for me” is a small category, but if they’ve been to a few bad therapists and haven’t found the right one, “the right therapist for me” could still include a fairly large subset of therapists.
Edit: The more general point is that being unlucky is a reason for optimism, since it means that things are likely to get better just from your luck returning to normal.
I agree with nearly everything you said there and think it’s good advice, so I upvoted your comment. However, I care about statistics and you made a common error here:
Regression to the mean doesn’t work that way. The fact that a random event came out one way several times in a row doesn’t make it more likely that it will come out the other way the next time. For instance, if you flip a fair coin and it comes up heads ten times in a row, the probability that it will come up tails on the next flip is still no greater than 50%. The only way that having found multiple bad psychiatrists will improve mixednuts’ chances of finding a good one next time appreciably is if he starts crossing off an appreciably large proportion of the bad psychiatrists in his area, leaving the good ones dominating the remaining population. This effect isn’t regression to the mean. The error you made is known as the Gambler’s Fallacy.
I’m familiar with the gambler’s fallacy. I wasn’t being very clear about what I had in mind when I referenced regression to the mean, so here’s my model. If someone has been to a few good therapists (better than the typical therapist) and they haven’t been able to help, then “find a better therapist” would be tough advice to follow. But if they’ve been to a few lousy therapists (worse than the typical therapist) then finding a better therapist should be doable, since they’ll have a good shot at doing that even if they just pick a new one at random.
Alternatively, if they’ve been to a few good therapists but haven’t found the right one, that’s evidence that “the right therapist for me” is a small category, but if they’ve been to a few bad therapists and haven’t found the right one, “the right therapist for me” could still include a fairly large subset of therapists.
Edit: The more general point is that being unlucky is a reason for optimism, since it means that things are likely to get better just from your luck returning to normal.
That makes sense. Thanks for clearing it up.