Geniuses tend to have ordinary children and genius can spring from ordinary parents. It’s also easy to see regression toward mean attractiveness in supermodels. Both the parents of supermodels and the children of supermodels rarely match them, let alone exceed them, in terms of attractiveness.

What kind of luck explains the fact that the children of high-IQ parents have lower IQs while they are reared in cognitive stimulating environments, when the children of low-IQ parents who were raised in chaotic environments still have higher IQs than their parents ? The IQs regress halfway (50%) to the population mean at both sides of the IQ distribution.

One would expect that children of high-IQ parents have higher IQ and children of low-IQ parents an IQ even lower. But the opposite happens.

So how does it work? The best way to think about it was a bivariate distribution, where the two random variables are additive genetic variation and environmental genetic variation. We each carry two sets of genes. You might have gotten lucky and gotten dominant genes that granted you a huge amount of some desirable trait. But your recessive genes are also a random selection from the average of your ancestors' genes, weighted by their closeness to you on the family tree. At the moment of your child's conception, you and your mates' four sets of genes are completely reshuffled. Thus, the children of the highly intelligent tend to have kids who aren't as bright as they are.

That's why elite families and royal dynasties are founded by usurpers with exceptional talents, but quickly recede to nothing-specialness.

In merciful contrast, the exceptionally dim tend to have children who are smarter than they are (progression toward the mean).

The genes you pass on to your kids aren't just the ones you display phenotypically, but also a weighted average of all your ancestors' genes. This is why in terms of many traits children often resemble some of their great uncles, cousins, great-grandparents, etc. more than any of their parents.

Steve Hsu in his presentation "Investigating the genetic basis for intelligence" calculated the speed of regression toward the mean for the trait of general intelligence. On slide 19 of the presentation, with the header "Your kids and regression" Steve writes "Assuming a parental midpoint of n standard deviations above the population average the kids' IQ will be normally distributed about a mean which is around +0.6n with residual standard deviation of about 12 points." He also gives a helpful example immediately below "So, e.g., for n=4 (parental midpoint of 160 - very smart parents!), the mean for the kids would be 136 with only a few percent chance of any kid to surpass 160 (requires +2 standard deviation fluctuation)."

Here are some implications:

1) The speed of the regression to the mean.

If one starts with two parents whose IQs are 160 and looks at the average IQs across generations the speed of the regression to the mean is quite fast.

Parents 160, 160
Children average 136 (assume these mate with a 136)
Grandchildren average 122 (assume these mate with a 122)
Greatgrandchildren average 113 (assume these mate with a 113)

There is already a huge drop between the grandparents and the grandchildren. So in just 4 generations the regression to the mean has brought down the Nobel-prize-level grandparents to the pretty much average intelligence. (all this is of course "on average")

This might be a reason why the intellectual elite might want to pay more attention to making America a country where those with IQs of 110-115 can still live satisfying lives with good middle class jobs and publicly funded services. Chances are that most of their descendants will need those jobs and services only century from now; after all “fool and his money are soon parted” – even if dimmer kids inherit billions chances are that they will not have what it takes to keep the wealth in the long run.

Imagine that with two parents with IQs of 160 set out to produce one child with the same IQ. How many kids we can expect them to have before they succeed? They would have to have 44 kids to have one kid whose IQ would be 160 or higher on average! This is clearly impossible. And if they set standard to IQ 170 - they would require 434 kids! Thus geniuses are really borne out of a people and not out of any two particular parents. Having smart parents helps, but even then, the chances that your little one is going to be the next Newton are small. Very, very small. On the other hand, according to historians none of Newton’s paternal kinsfolk were able to even sign their names.

2) Mating insights:

Many intelligent men bent on reproducing are troubled by the fact that most intelligent women want a career and likely do not want to have children (or want to adopt orphan baby at age 50, once they have “made it”). Women who are less intelligent may want to have families and even to have bigger families. Steve Hsu's calculations let one see the impact of say a man with an IQ of 140 marrying a woman with an IQ of 140 and having only one child (whose expected IQ would be 124) vs. that same man marrying a woman with an IQ of 120 and having three children. The second man's highest IQ child will have an expected mean IQ of 128, which is higher than the man who married the smarter woman but had only one child. Even if the smarter woman chooses to have two children the two smartest children out of the three children that the less intelligent woman had will have approximately the same expected IQ as the two children of the high IQ career woman.

Takeaway - twenty IQ points is a lot: 120 vs. 140 is a big difference and it will be by definition much harder to find a woman with an IQ of 140+ (one in 261) vs. one with an IQ of 120+ (one in 11) and it will be much more difficult to persuade your wife to give up IQ 140-career track (Fortune 500 CEO, Ivey League tenured professorship etc.) than IQ 120-career track (nurse, high school teacher etc.) for changing diapers in the middle of the night.

If one is concerned about having one or two competent kids to whom one can leave the family business to, one might consider finding a less intelligent woman who is willing to have more kids. Of course there are other factors. Having more children means giving each child less attention but spacing births helps mitigate this. Not to mention that having only one child can result in tragedy if God forbid something was to happen to it.