Even so, the rubric only shows that Michigan is willing to overlook academic shortcomings in their efforts to recruit athletic talent. Academic and athletic talent still might be correlated in the general population, while sampling bias from the university admissions process over-represents dumb jocks and under-represents dumb non-jocks.
For example, suppose the academic ability of jocks is normally distributed about 105 with a std dev of 15, whereas non-jocks are normally distributed about 100 with the same std dev. If the cutoff for admission is 110, but athletic talent gives you a 20 point bonus, then you're your comparing mean aptitude in a sample of non-jocks, given that every observation is >= 110, to the mean aptitude in a sample of jocks, given that every observation is >= 90. Under those conditions, you'll find a 10 point difference in favor of your sample of non-jocks, even though the population mean for jocks is higher.
I think you alluded to this point in an earlier reply, but it's worth spelling out.
For example, suppose the academic ability of jocks is normally distributed about 105 with a std dev of 15, whereas non-jocks are normally distributed about 100 with the same std dev. If the cutoff for admission is 110, but athletic talent gives you a 20 point bonus, then you're your comparing mean aptitude in a sample of non-jocks, given that every observation is >= 110, to the mean aptitude in a sample of jocks, given that every observation is >= 90. Under those conditions, you'll find a 10 point difference in favor of your sample of non-jocks, even though the population mean for jocks is higher.
I think you alluded to this point in an earlier reply, but it's worth spelling out.