Most colleges and universities in the US base their admissions on high school grades plus a standardized test (SAT or ACT). To decide whether a particular piece of data X is a good admissions criterion, people seem to focus on how well X correlates with college grades. (This may be freshman grades or total college GPA. Some people think success in getting a degree would be more appropriate. For the purposes of this question, I don't think these distinctions are relevant.)
Isn't this correlation a completely incorrect way of evaluating X as a tool for admissions?
It seems like an apples-to-oranges comparison. A student who has low X is admitted to a nonselective school, where standards are low and they compete with other low-X students. Grades at this school measure how well they did based on the low standards prevailing there. Students who have high X are admitted to a selective school. A "B" grade at Berkeley is not the same as a "B" grade at Cal State Dominguez Hills. A high-X student goes to Berkeley and gets a "B" in calculus. A low-X student goes to CSDH and gets a "B" in calculus. This shows up in the statistics as a lack of correlation between X and grades, since the students differed in X but got the same grade. But isn't that misleading, since the grades mean different things at the two schools?
Is there some more logically justifiable statistic to use in evaluating whether X is a good admissions criterion?