<p>Apart from the factors mentioned by blossom and mathmom, I think there is a lot more refining you have to do.</p>
<p>For example, for a college with a 10% admission rate (HYPS), being at the 75% level in SATs and GPA does not mean anything like a 75% chance of admission. Maybe it means a 20% chance of admission, maybe not even that.</p>
<p>For most schools, even HYPS (although their yield is so high it doesn’t matter much), the stats on their admitted classes will be somewhat-to-significantly higher than the stats on their enrolled classes, since the higher-stats applicants are more likely to have other options and thus more likely to choose one of the others. So, as a rough matter, I generally assume the the 75% level on the enrolled class represents something like the average for the admitted group. That’s probably over-conservative, but you get the idea. Also, I think your function considerably misstates the difference between having stats at the 75% level and having stats at the 25% level. At colleges that accept less than 50% of their applicants, a 75% kid probably has more than three times the admissions likelihood of a 25% kid. But a kid with “above average” ECs probably doesn’t have twice the chance of a kid with “average” ECs (and how about below average?).</p>
<p>You also ought to account for some status factors – underrepresented minority status, legacy status, other strong connection to the college. Those can make a difference, although how much of a difference varies from college to college. Also, geographical issues. At a northeastern college, an applicant from Montana will always have the edge over an applicant from New Jersey with a comparable profile. Geography can be tricky, though. Here in Philadelphia, a very strong applicant probably has a much better than average chance at being accepted at Penn, but an average applicant may have no chance at all.</p>
<p>Basically, if you define a “match” as at least a 50% chance of admission, you probably have to exclude the most selective colleges categorically, or at least de-weight them more than you have. (Actually, you have probably de-weighted them enough to ensure that no one is ever a match there.) Sure, a Mexican-American Intel finalist/student body president with 1600 SATs and a 4.0 GPA with a challenging curriculum probably has better than a 50% chance of being accepted at Harvard. But I don’t know who else has.</p>
<p>I also think you need to account for some obvious things. An applicant whose resume does not scream math-science is not going to be a match for an engineering school, regardless of SATs, etc.</p>
<p>In the end, the whole “match” concept seems to have limited utility, especially for the strongest students. All of their “matches” are “reaches”, with some very limited exceptions, and some of those exceptions are widely believed to discriminate against applicants who look like they are probably headed to HYPS (see: “Tufts Syndrome”). In any event, it’s a pretty limited universe, and you don’t need an algorithm to identify it. Word of mouth does just fine.</p>