<p>It’s not going to be possible to answer the question you asked with any precision, and even if you could the precise answer wouldn’t really be useful for you. So content yourself with knowing that, absent a coach’s support, your son probably has a lousy chance of getting accepted at Yale.</p>
<p>The question you seem to be asking is “What percentage of unhooked, unexceptional domestic applicants are accepted?” You are probably not that far off in thinking that 40% or so of the class fits into that category, but good luck figuring out either the numerator (acceptances) or the denominator (applications) for that group.</p>
<p>There are a couple of groups of applicants whose acceptance rate – if you have identified the group correctly – is close to 100%. That’s key recruited athletes, a handful of developmental candidates, and what the admissions dean at Harvard calls “walk-on-water” (WOW) kids – applicants with truly extraordinary talents, academic or otherwise. (Grades and test scores don’t count. Really.) He says Harvard sees about 200 of the WOW applicants a year, and I doubt any other college sees meaningfully more of them. These groups, however, probably represent at most 15% of the acceptance letters.</p>
<p>Then there are some groups with much higher-than-baseline average chances of success, but nothing like 100%. Athletes with some but not total support, legacies, under-represented minorities. The categories overlap to some extent, but together they probably constitute 30% of the enrolled class. I don’t know what percentage of the accepted class they are, though – probably a little lower than 30%, since almost by definition they have a lower-than-average chance of getting in to an equivalent college. And we really don’t know what percentage of the applicant pool kids like this represent. So it’s really hard to back them out of the denominator for the regular-lkid average.</p>
<p>Then there are international students – about 10% of the class, far more than 10% of the applicant pool, probably a bit less than 10% of the accepted student pool. They have to be backed out of the denominator, too.</p>
<p>And when you have done all that, you should have an accurate calculation of the average admission chances of unhooked domestic students. The problem, however, is that no one really has an average chance. Based on his grades, scores, essays and letters of recommendation, your son would either be very competitive, with far better than average chances, or he would really have no chance at all. You can say that hoi polloi applicants have a 5% chance or a 4% chance, but really that’s the average of one group that may have a 30-60% chance each, and another group that has a 0% chance. And the border between those groups is next-to-impossible to discern. So you really can’t tell much of anything about your son’s chances in the general pool.</p>