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PSA: regression to the mean/mean reversion is a statistical artifact, not a causal mechanism.
So mean regression says that children of tall parents are likely to be shorter than their parents, but it also says parents of tall children are likely to be shorter than their children.
Put in a different way, mean regression goes in both directions.
This is well-understood enough here in principle, but imo enough people get this wrong in practice that the PSA is worthwhile nonetheless.
The analogy here: If what happened was that the ball happened to land near the right of the plinko board, then putting the ball through the same board isn't going to make it on average go to the right again. Since some component of height is not determined by the genes passed on, that component is like our little ball.
If a family has consistently tall members though, this suggests that the cause is basically genetic enough that they'll have tall kids again.
As tailcalled says in another comment:
their children will exhibit some regression to the mean ... b... (read more)
Let me check: you mean the grandchildren have the same ex ante expected height as the ex ante expected height of the children. Of course! (Just as the children have the same ex ante expected height as the parents' ex ante expected height, which is now screened off by knowing their actual height.) But if you reset your expectations based on the observed children's heights, you'll still witness (on average) regression to the mean.
(If not this, I'd appreciate an explainer!)
4tailcalled
Yes, but in this case because you know the parents' heights, the children's ex ante expected height differs from the population mean.
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Though not towards the population mean but rather towards the ex ante expected height of the children.