Daniel E. Ho, a law professor at Stanford, also disputes the mismatch hypothesis. In a response to Mr. Sander’s 2005 law review article, Mr. Ho wrote in the Yale Law Journal that “black law students who are similarly qualified when applying to law school perform equally well on the bar irrespective of what tier school they attend.”

Political changes in the ’90s created another opportunity to study mismatch. In 1996, California voters passed Prop 209, a ban on affirmative action. Critics of Prop 209 expected black and Hispanic enrollment at top University of California schools, like U.C.L.A. and Berkeley, to plummet — and it did, for a while. But these schools eventually saw increases in minority enrollment, particularly among Hispanics, as sophisticated new outreach programs kicked in. Enrollment has not, however, gotten back to pre-Prop 209 levels.

Recently, economists from Duke studied the effects of Prop 209, comparing undergraduate graduation rates for blacks, Hispanics and American Indians before and after the ban. In a paper being considered for publication by The Quarterly Journal of Economics, the Duke economists conclude that mismatch effects are strongest for students in so-called STEM majors — science, technology, engineering and math. These subjects proceed in a more regimented way than the humanities, with each topic and class building on what came before. If you don’t properly learn one concept, it’s easier to get knocked off track.

The Duke economists say that lower-ranked schools in the University of California system are better at graduating minority students in STEM majors. For example, they conclude that had the bottom third of minority students at Berkeley who hoped to graduate with a STEM major gone to Santa Cruz instead, they would have been almost twice as likely to earn such a degree.

“Prior to California’s ban on affirmative action,” Peter Arcidiacono, one of the study’s authors, told me, “what Berkeley did well was switch relatively ill-prepared minority students out of the sciences and into majors where credentials are relatively less important.”

SOON the Supreme Court will decide Fisher v. University of Texas. The case is complex, but essentially boils down to a young woman’s claim that U.T. violated the Constitution’s equal protection clause by denying her admission because she is white. The justices, save perhaps Clarence Thomas, are unlikely to address mismatch in their opinions. But the court could force schools to be more transparent about the racial preferences they use in admissions, and even to track the consequences for their students. For now, social scientists debate what can be gleaned from flawed data sets. They continue to argue over whether mismatch even exists and the extent of the harm it causes if it does. This raises another question: Do some of the more concrete if intangible benefits of affirmative action, like prestige and the superior connections one makes attending a fancier school, outweigh the potential cost? If affirmative-action admits are less likely to pass the bar after going to a certain type of school, or less likely to follow through with their field of choice, then the cost is potentially considerable. But are we really going to tell a kid embarking on adult life that he’s better off attending a less prestigious school?

“The real question is what we want affirmative action to achieve,” says Richard Brooks, a law professor at Yale. “Are we trying to maximize diversity? Engagement in the classroom? Whatever it is, I don’t think the purpose of affirmative action is for everyone to have average grades.” Mr. Brooks believes that mismatch exists. But he rejects the idea that it’s as insidious as others claim and says that some mismatch might even be a good thing. Striving alongside people more capable than we are is a key ingredient for growth of all kinds.