People say that the offspring of high IQ individuals will regress to the mean (average) of their 'population' - and they calculate this as if it were a mathematical law...
But intelligence is a measure of a biological variable, and 'regression towards the mean' happens, if-and-when it does, for biological reasons - it is not a mathematical law.
When a high IQ individual is a descendant of high IQ parents, grandparents etc - there is no regression to the mean.
(Except for the trivial reason that test-takers who score highly because they 'have a good day' will re-test at lower scores. This can be somewhat dealt with by having several measurements of IQ - although this also increases the chance of 'having a bad day' maybe
from non-random illness, and falsely dragging down the average. In practice there is no substitute for high quality data and increased numbers/ averageing does not help. This means excluding from the data any people who are suffering from acute, test-score suppressing illness or any other systematic cause for false measurement. In biology; smaller higher quality studies are always better than larger, poorer quality studies.)
In other words, to the extent that a high IQ individual comes from a genetically-relatively-intelligence-inbreeding caste or class; there is no regression to the mean.
And, in fact this is a very common situation - at least to the extent that regression to the mean is insignificant in amongst other factors.
The point to hold in mind is that no variation/ distribution is really random; randomness is just an assumption, a model, which may be expedient for specific purposes - but is not a general truth; indeed randomness is usually a false model when it comes to biology.
In sum, human behaviour and ability cannot be explained by mathematical rules - at most such rules summarise a specific data set - which must then be evaluated in terms of scientific quality. We cannot explain unless or until we know something of causes.
https://charltonteaching.blogspot.co.uk/2010/10/scope-and-nature-of-epidemiology.html
https://charltonteaching.blogspot.co.uk/2008/05/social-class-iq-differences-and.html
