April madness has occurred even as March madness continues. The selective colleges and universities have now sent out letters of admission. This will produce tears of joy for the chosen few, but salt tears for the large numbers of students who have failed — and failure is the construction most of them will place upon their thin letters of rejection (though most will of course have learned by going right to college admissions Web sites rather than waiting for snail mail).

The numbers are horrifying. I will use only my own institution, though I think that ours is only the third most selective process this year (following Harvard and Yale). Princeton has admitted only 9.25 percent of the 21,369 students who applied for admission to the class of 2012. This year was “the most selective in Princeton’s history,” according to our admirable dean of admissions, Jane Rapelye. Our applications increased by 12.8 percent this year, and their quality by the usual measure was staggering (to me, at least): More than 7,000 applicants had better than a 4.0 grade point average and more than 11,000 had a combined score of 2100 or higher on the three parts of the SAT examination. And they came from all over — from 7,436 U.S. high schools and 137 foreign countries. It is a strikingly diverse group along a number of parameters, including gender (50 percent each) and race/ethnicity (44.8 percent students of color). Students have been admitted from 61 different countries. If you are fortunate enough to teach in such an institution, these numbers are a boon. I happen to teach in the only selective major field (public policy) in a highly selective school, and my students are a joy to work with.

But of course the price of this selectivity is high. The elite colleges use alumni to interview high-school admissions applicants (Princeton “alumni volunteers had personal contact with an unprecedented 98.5 percent of applicants, or 21,052 students”), and those of us who participate have at least some sense of the pain out there. I have interviewed Harvard applicants for more than 35 years. I normally see four or five students each year, and speak to them for 30 to 45 minutes — enough for an experienced educator to form a superficial impression of quality — before writing an e-mail report for the admissions committee. But I cannot remember the last time one of the students I have interviewed has been admitted to Harvard.

This year I received a particularly painful e-mail message from one rejected applicant shortly after she had visited the Web site on Decision Day. She could not understand why her remarkable grades and test scores (and she was outstanding in other ways) had not qualified her for admission. The answer, of course, is that “many are called and few are chosen,” but only committed Calvinists will comprehend this response. Harvard, after all, admitted only a little over 7 percent of its applicants. My crude guess would be that, at a minimum, 20 percent of applicants to elite institutions are in fact fully qualified to do well in these colleges. Many of them, of course, will be admitted to other elite institutions, but not all, and many will harbor long-term feelings of rejection.

And the problem is exacerbated by the increasing asymmetry in the financial aid available to the best students — the more prestigious the institution, the greater the chance of the student (and her parents) emerging debt-free at the end of four years. So there is emotional pain and material consequence to the increasing selectivity of undergraduate education in these United States. I am grateful for the quality of students Janet Rapelye provides me with. But I worry a lot about those who did not have such fortunate lottery tickets — and I have absolutely no solution to propose.