There seems to be some confusion about what regression to the mean
means. Noone is penalized (or advantaged) because of regression to the
mean. You ALWAYS have RTM in a population whether everyone improves or
gets worse. It is a property of standardized scores only for a
population. The simplest explanation is in terms of the regression
equation for standardized scores
E(z2) = rz1
For positive r<1 if you select individuals with a given z1, their average
z2 will be smaller than z2 (in absolute value)
Thus Galton found that the offspring of his geniuses regressed towards
mediocrity. He apparently thought it was a law of nature rather than a
law of statistics. If he had studied the feeble-minded we would not have
a technique called regression analysis
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