What’s interesting here, and might be driving your intuition about clones being a disappointment, is that if you select high enough and the heritability is high enough, then even as you drive the average of the clones very high compared to the population, they may have an increasingly low probability of matching or exceeding the original.
So to work it out: what percentage of clones, because of regression to the mean, would be expected to surpass the original on some quantitative trait?
Using again von Neumann at an arbitrary +5SD (roughly 80 such individuals in the USA), then clones are expected to regress back to 4.47SD, because IQ 80% heritable, leaving 20% leftover (most of it non-sharedenvironment).
20% variance is another way of saying a SD of 0.44 around the new mean of +4.47SD. How much luck does one need for ±0.44 to reach up from 4.47 to 5?
(5 − 4.47) / 0.44 = +1.2SD
≤1.2SD is 88% of the population (pnorm(1.2))
So only 100% − 88% = ~12% of the clones would match the original (ie 1 in 10 vs a base-rate of 1 in >4 million, a multiplier of >400,000×, as opposed to a measly 100× or something—that’s tail effects for you, always larger than you think).
You could also run this with my dog cloning code. I considered a scenario where there’s two thresholds: one for picking the elite donor, and then a more ordinary pragmatic threshold. (In that case, ‘best military dog anywhere’ and ‘acceptable military dog after training’.) But you can simply set the two thresholds equal and now it calculates the probability of a clone passing the original selection threshold (ie matching or exceeding the original—at least as far as you can tell by comparing!):
Because of thin tails, it’s unsurprising that the more extreme you get, the lower the probability gets: it just gets wildly harder and harder the more SDs out you go. (Similar to bivariate double-maxima.) But the reduced variation + higher mean also benefits from the tail effect in that it gets ever more effective compared to the baseline of random screening/larger samples; the further out you go, the lower your probability may be, but the more effective it is relative to the alternatives which get worse faster. It’s worth noting that a probability like ‘0.05’ is astonishingly huge compared to the base rate (that “5% probability of matching the original” is for pnorm(-8), which has a base rate of 6.22096057e-16, ie. there is not a single person in the world 8SDs out—should you have such a person and you want another such outlier, better get busy with the cloning research, otherwise, you’ll be waiting a while):
So to work it out: what percentage of clones, because of regression to the mean, would be expected to surpass the original on some quantitative trait? Using again von Neumann at an arbitrary +5SD (roughly 80 such individuals in the USA), then clones are expected to regress back to 4.47SD, because IQ 80% heritable, leaving 20% leftover (most of it non-sharedenvironment).
20% variance is another way of saying a SD of 0.44 around the new mean of +4.47SD. How much luck does one need for ±0.44 to reach up from 4.47 to 5?
(5 − 4.47) / 0.44 = +1.2SD
≤1.2SD is 88% of the population (
pnorm(1.2))So only 100% − 88% = ~12% of the clones would match the original (ie 1 in 10 vs a base-rate of 1 in >4 million, a multiplier of >400,000×, as opposed to a measly 100× or something—that’s tail effects for you, always larger than you think).
You could also run this with my dog cloning code. I considered a scenario where there’s two thresholds: one for picking the elite donor, and then a more ordinary pragmatic threshold. (In that case, ‘best military dog anywhere’ and ‘acceptable military dog after training’.) But you can simply set the two thresholds equal and now it calculates the probability of a clone passing the original selection threshold (ie matching or exceeding the original—at least as far as you can tell by comparing!):
Because of thin tails, it’s unsurprising that the more extreme you get, the lower the probability gets: it just gets wildly harder and harder the more SDs out you go. (Similar to bivariate double-maxima.) But the reduced variation + higher mean also benefits from the tail effect in that it gets ever more effective compared to the baseline of random screening/larger samples; the further out you go, the lower your probability may be, but the more effective it is relative to the alternatives which get worse faster. It’s worth noting that a probability like ‘0.05’ is astonishingly huge compared to the base rate (that “5% probability of matching the original” is for
pnorm(-8), which has a base rate of 6.22096057e-16, ie. there is not a single person in the world 8SDs out—should you have such a person and you want another such outlier, better get busy with the cloning research, otherwise, you’ll be waiting a while):