Aggregate performance was either unaffected or improved in the presence of affirmative action. This fits with history: until 1972 almost no women were admitted to MIT, but it didn't make the men perform less well for all the affirmative action they received nor cheapen their accomplishments.
The issue is not that men perform less well because women are admitted into MIT. The issue is that women admitted due to AA might be lower quality than other candidates (men and women who would be admitted without AA), and therefore drag their group average down.
I'm arguing that men who were admitted might be lower quality than women who weren't admitted because their gender exclude them, but that didn't mean those men were unqualified or even necessarily dragged their group averages down.
None of our measurements are accurate enough to correctly distinguish 5,000 very good students from the next 5,000 nearly-identically-but-slightly-better students.
I'm arguing that men who were admitted might be lower quality than women who weren't admitted because their gender exclude them...
This is exactly what I'm saying - whichever group gets bonus points/preferences/etc will have lower quality. In the past, that group was women. Now it's usually men, though not always (some nursing schools give preference to men [1], some liberal arts colleges do also).
[1] Defining quality here is slightly trickier since nurses of both genders are needed for specific tasks (mostly related to bathing).
TL;DR: The Espenshade study found that African chromosomes (by the "one-drop rule") equaled 450 SAT points over Asian chromosomes as a college admissions factor.
(Not that actual genetic testing was used. It probably should be, though. Why encourage race fraud?)
Your link is to a study in which "affirmative action" is used in the sense it was originally implied, not the sense in which it is actually used:
Note that none of these constitute "reverse discrimination," an accusation affirmative action plans often face. In no case was a top-performing man denied a reward if he outperformed everyone else. The main effect the researchers found was an increase in the number of able women willing to participate.
Aggregate performance was either unaffected or improved in the presence of affirmative action. This fits with history: until 1972 almost no women were admitted to MIT, but it didn't make the men perform less well for all the affirmative action they received nor cheapen their accomplishments.