Mathematically, the acceptance rate is obviously a function of the number of people who apply and the number of people who are accepted. But not every applicant applies to every college, indeed even the most popular colleges only get a fraction of the total pool applying to them.
So given that people choose which colleges to apply to, what does a relatively low acceptance rate actually mean? In some sense, it is going to be as much, if not more, about the choices (some) people are making when choosing which colleges they will apply to, rather than the colleges themselves.
With that thought in mind, this is a bit complicated, but:
If admissions were perfectly predictable, there should not be low acceptance rates anywhere. It wouldn’t matter whether it took very high qualifications to get admitted, you would know what it took, and you wouldn’t choose to apply if you didn’t have those qualifications.
Of course they often aren’t perfectly predictable, and sometimes in fact they are quite difficult to predict once you have competitive qualifications. That is an important qualification, because there are often lots of people who realistically do not have competitive qualifications for a given college. And usually they simply don’t apply.
OK, so when there is some uncertainty about which applicants with competitive qualifications will get accepted, it makes sense there would be less than a 100% acceptance rate. And the more unpredictability among that competitive group, plausibly the lower the acceptance rate might go.
OK, so pausing here, so far we have a case for acceptance rates essentially being a measure of unpredictability of admissions among well qualified applicants. And that is not in fact the same thing as a measure of which colleges have the highest standards, which are the best at educating people, or anything like that.
OK, then for complicated reasons I won’t elaborate on unless asked, I think the practical limit for this sort of effect is probably somewhere around a 15-20% acceptance rate. Meaning beyond that point, I think in practice it starts becoming implausible that lots more truly competitive people are applying, and instead the dominant effect is lots more non-competitive people applying.
So why would so many non-competitive people apply to some colleges rather than others? I think the most obvious answer is they essentially see it as a type of lottery ticket.
The basic model in question is that even though the odds are extremely low, you see the payoff as being extremely high, and that combination makes you see it as worth trying. As an aside, there is a well-known effect where once people are convinced it is worth going for something of this form, they can start persuading themselves maybe the odds are not so bad, or maybe they can somehow shade the odds in their favor. And sometimes that gets into something sometimes called “magical thinking”. But to be fair, sometimes lottery-type bets are rational, if the payout is high enough relative to the odds.
So, rational or not, I think usually an acceptance rate much below 15-20% is good evidence that a lot of non-competitive applicants are treating this application as a type of lottery bet. And that implies they see a very large difference in value between these colleges and whatever colleges they would actually be competitive for.
OK, so why might some people perceive such a large value gap? I think at that point, it is many different stories. In some cases it might involves peers, family, local culture, or so on. In some cases it might involve beliefs about possible career outcomes. In some cases it might involve beliefs about cost. In some cases, there could be a feedback loop where they believe lower acceptance rates mean higher value. And so on.
Personally, I think often people like this are making some form of mistake, not realizing there are in fact colleges where they could be competitive that are not as far away in terms of true value as they think. Not that they can’t value some colleges more than others. But when they see such a big gap between a few colleges and all others, then I get suspicious they are not seeing the full picture. Or maybe are just VERY influenced by peers/family/etc.
But that doesn’t really matter, what matters is they BELIEVE these particular colleges are lottery tickets, and so they toss in applications to these specific colleges, and not others, despite being non-competitive.
And there is no real lower bound to that effect in my view.
OK, so that’s my view. And all the colleges on that list are well below that 15-20% line, so I think there is very likely a large lottery effect in play (and to be clear, I think there could be some lottery effect above that, I am just very confident the lottery effect is strong below there).
Some last bits of commentary.
On the plus side, I think if you actually are competitive for those colleges, those numbers don’t really mean that much for you. To be sure, even if you are very well-qualified, you might not be in any better shape than 15-20%, and there is enough dependence you could get blanked by all such colleges even if you applied to a lot of them. But I am not sure it is really much worse than that–if you are actually competitive.
On the minus side, what it REALLY takes to be competitive for these colleges is probably misunderstood by a lot of the people applying. And in fact, if you sort of started with the view one or more of these was a lottery ticket school, and then convinced yourself you should apply, you might be one of those people who starts rationalizing that you are more competitive than you really are.
Meanwhile, I think there are lots and lots of great colleges that fall somewhere in that 15-20% range, or indeed quite a bit higher, that simply do not experience the same lottery effect because so far fewer people see them in the same way as the lottery ticket schools. Value them more? Yes. To lottery-like levels, no. Indeed, not to be snippy, but their target markets may mostly be too knowledgable about US colleges to buy into a lot of that lottery type thinking. Like, as in, maybe they went to one of those perceived lottery ticket colleges themselves, and didn’t experience a lottery effect, so know better.
Still, I guess you could see that as a wisdom of the crowds issue. But again personally, I don’t buy it, I think most of the people who see some particular set of colleges as unique lottery ticket opportunities are making a mistake of some sort.