Actually, there is a bigger problem with that. The notion of the standard deviation is tied to the normal or Gaussian distribution. There are certainly a lot of things that can be approximated by a Gaussian distribution or as a function to a Gaussian distribution (e.g. lognormal) in most of the population as long as their parameters are truly randomly distributed about a central mean, but almost nothing except in quantum mechanics is literally Gaussian. This means that the further you get away from the mean and into the tails, the less precise the approximation is going to be. Once you start estimating parameters outside of five or six standard deviations the estimates are essentially meaningless; it takes so little difference to change the “thickness” of the tails that they don’t provide any credible estimate of probability. As a practical example, buying two PowerBall tickets numerically doubles your probability of winning, but the odds are still so overwhelmingly against either ticket being the winning one that as a practical matter the likelihood that you will win has not substantially changed, as the likelihood estimate is lost in significant figures.

Speaking of a trait being “pushed 20-30 standard deviations” is not really a meaningful question to begin with. There is a level of natural variability in many traits, such as height, skin and hair color, et cetera, but these are not typically normally distributed and are often governed by more than one gene or expressed due to actions of other genes or epigenetic factors, so there is a complex interplay that defines how traits are distributed within a population. In many cases, there are physiological limitations as to how far a trait could be altered. The giraffe, for instance, is just about as tall as it could possibly be without having to rework the anatomy significantly; the Trumpeter Swan is about as large as waterfowl can get; a humanoid can’t grow to much more than 9 or 10 feet in height before bipedal plantigrade anatomy is not longer workable; no creature will every be able to see radiation above the ultraviolet levels because the radiation is inherently harmful to organic materials; et cetera, ad nauseam. Selective breeding by itself can only emphasize a few characteristics in their extreme, and if you notice, most highly breed domestic creatures such as dogs, cats, horses, et cetera, tend toward neotenic forms; in part because it makes them more emotionally appealing to us, but also because it is fairly easy to breed for characteristics that already appear during development rather than to advance those which appear only in adulthood.

Stranger