I came across this article:
http://news.harvard.edu/gazette/story/2015/04/harvard-college-admits-1990/
and I was struck by the specificity of the following excerpt.
(apologies for the lack of HTML skills)
“About 13,500 students scored 700 or above on the SAT critical reading test; 16,100 scored 700 or above on the SAT math test; 13,900 scored 700 or higher on the SAT writing test”
Hmmm, says I, I wonder if you can use those numbers to estimate the number of applicants who scored a 2100 overall SAT? That would be an interesting thing to know, because overall, we know very little about the applicant pool at Harvard (or any other top school.)
So, using the data from here:
http://research.collegeboard.org/content/sat-data-tables
I came up with an estimate of about 11,000 applicants with at least a 2100 SAT. (Not going to bore you with the details here, but if anyone is actually interested, I can post the details of the two methods I used to develop the estimate.)
Now, coincidentally, 2100 also happens to be pretty close to dead on the 25th percentile number for Harvard (not exactly, but close enough for a back of the envelope type estimate of this type) - so that let us calculate an admit rate for applicants with SATs of 2100 and over:
3/4 of the Harvard admits is 1500 students. If there are 11,000 applicants in that range, that puts the admit rate for those students at roughly 14%. Of course, that number doesn’t really apply equally to the whole group (I think we can all agree that chances of admission rise with higher test scores, right?), so the applicable score is the population midpoint of that group, and that is right around a 2200 score.
There is one caveat here - so far, I’ve completely ignoring the ACT. True enough, but only 15% of Harvard applicants in the last few years submitted ONLY the ACT, so we can ballpark that by inflating the 11,000 by 15%, and that drops the admit rate to 12%. Also, it ends up meaning this high scoring group is almost dead-on 1/3 of the total applications.
I think that is fairly reasonable to assume that’s probably not too far off - if you’ve got a 2200 SAT, your estimated admit rate to Harvard is probably pretty close to 12%. We can also turn the whole thing around, and say with at least the same amount of confidence that if your test scores are below 2100 (or the equivalent ACT score of 32), you have less than 2% admit rate.
Anyway, I thought it was kind of interesting, because it is a topic people speculate about this all the time - how many applications to the top schools are “no-hopers” and I think this kind of analysis provides a framework for estimating that kind of thing.