Question about "institutional priorities" and chances/acceptances

Applying to College
1

Something I’ve always wondered about: Regarding the ivy-type schools, conventional wisdom seems to be that applying to more top schools does not equate to better chances of getting into at least one.

Assuming a student has competitive stats for those schools (say, 2300 / 35 / 3.9 uw), don’t the schools then look at all of the other factors (extra-curriculars, LORs, etc.) to make the determination as to who gets in? If you happen to be an oboe player, one school may be looking for that, whereas the other 9 aren’t, but you don’t know ahead of time what their institutional priorities are.

So aren’t your chances of getting into at least one of the top schools increased if you apply to more, because of that unknown?

2

I am pretty lame with statistics and the like, but IMO, no. There’s no cumulative effect from applying to a bunch of top colleges. Every single time you apply, you start from scratch, as it is a complete unknown, because that college is unique and different from the next one, and has unique and different institutional needs. These colleges get so many applications from your dream student that they can assemble mutiple classes from all,the kids who don’t get in, who were equally qualified.

Yes, all the other factors you mentioned come into play. But let’s imagine Dream Student Barbie. She has great stats and she has a unique “spike” that makes her stand out: she has published a best-selling novel. She has applied to Harvard, Stanford, Vanderbilt, and Northwestern. They all offer her admission. Who wouldn’t want this prodigy at their college?

Now let’s imagine Dream Student Ken. Ken is an ORM. Great stats, president of the student body, 1000 volunteer hours, captain of the football team, great recs, great essay, etc… He applied to all those schools too, but was denied at all. Why? Who knows. Unless we were all sitting in the board room during decisions, we can’t ever know. It’s very possible that 500 applicants just like Ken were also turned down, but then along came Miguel. He did all that stuff too, except he wasn’t captain, he was just a player on the team, and he was accepted to Stanford and Vanderbilt. Miguel is a URM though, and those colleges really need a guy like Miguel. Plus, maybe they just liked him better. Maybe Ken’s essay made him sound a little arrogant to some people on the committee. At Stanford and Vanderbilt, the adcoms had a big tug of war between Ken and Miguel. They only had room for one of them though, and Miguel is the guy.

I think the issue is that you are really dealing with a bunch of humans. Humans aren’t computers, and we can’t make an algorithm that is going to accurately give the odds on humans doing something. Now I will wait for someone to destroy my theory :slight_smile:

3

"don’t the schools then look at all of the other factors (extra-curriculars, LORs, etc.) to make the determination as to who gets in?’
yes. thats how it works.

“So aren’t your chances of getting into at least one of the top schools increased if you apply to more, because of that unknown?”
No, that’s not how it works.
As Lindagaf correctly pointed out ,statistically, all admission decisions are independent events.

4

Admission decisions are not independent events, because many of the same criteria are considered by the various colleges.

5

Right, they are not independent events. For example, the LORS may be the same as well as some of the essays.

6

I would say the answer is yes. A stats professor once illustrated a similar question with an example that is sort of the other side of the coin. Say, for argument, that student independently had a 5% chance of getting into each of the Ivies. Now (professor’s example) imagine a deer in a field. Say a hunter in the tree line who had a 5% accuracy rate was aiming at it. Would the deer be in a more perilous position if eight total hunters with the same 5% accuracy rate were aiming at it at the same time, rather than just the one? Yes, it would. Similarly, though the reverse, the student who applied to all 8 Ivies would have a better chance at a positive outcome than applying to just one, if these are in fact independent events.

And you are right, you never know what in an application may strike an institutional chord, or a personal one.

But any student would still want to find less competitive schools that inspire them where they would apply. Even an outstanding student could hardly be surprised to ultimately fail to gain admission to any of them. The numbers at the most competitive schools are simply daunting for students who are not recruited athletes, legacies, etc. Good luck.

7

That is not what independent events means. A dependent event is an event that is affected by previous events
(This is why “counting cards” works, and is disallowed in casinos):

https://www.mathsisfun.com/definitions/dependent-event.html

Just because similar methods and criteria are used does not make them dependent. The result would be the same at one college if it were the only one applied to, or if 1,000 other colleges were also applied to.

Yes, individual elite college admissions are impossible to predict. That fact does not throw the laws of mathematics or game theory out the window. It does increase your odds – but if you odds are very close to 0%, so will be the cumulative effect of doing it 8 times.

8

Regarding more discussion of independent events, see this post, especially the comments of Math Goodies.

http://talk.collegeconfidential.com/college-admissions/1891502-college-admissions-are-not-independent-events-p1.html

9

“Just because similar methods and criteria are used does not make them dependent”
EXACTLY!
The decision that ONE admissions committee makes is COMPLETELY independent of any decision ANOTHER admissions committee makes.

for them to be DEPENDENT would mean that there had been some sort of relationship or communication between the 2 committees.

GAWD, every SINGLE YEAR kids, or sometimes parents, think there is a mathematical "IF> THEN relationship correlation between college admissions decisions. There isnt.

10

If admissions decisions to the 8 ivies are independent from a probability standpoint, then the more schools you apply to the higher your chance to get accepted to at least one. That’s simple math.

And there’s no reason to think that admissions decisions to the ivies are anything but independent.

Now, let’s say you increase your SAT scores by 100 points. Your probability of getting into each ivy increases. But the probability that you get into one ivy is still independent of getting into a second ivy, so it again makes sense to apply to many (not considering, of course, that these are very different schools - we’re just talking math here).

Now let’s consider the oboe player example. This year, Harvard needs and oboe player, so your probability of getting into Harvard is a whopping 0.15. Princeton does not need one, so your probability of getting into Princeton this year is 0.05. You should still apply to both if you’d be happy at both, even though you have a “hook” at Harvard and even though your chances of getting into Harvard are 3x greater. Of course, if you know which school is looking for the oboe player, then apply to that one SCEA!

11

I think @mjrube94 might have a valid point.

Consider the cases of four applicants, Bob, Carol, Ted, and Alice. Bob and Carol are athletes; Ted and Alice are musicians. All are excellent students and clearly qualified for any college they might choose.

Princeton needs a pole vaulter but Harvard doesn’t, so pole vaulter Bob gets recruited by Princeton. Similar story for long distance swimmer Carol, whose talents are coveted by Yale but not Stanford. We all accept that this is how athletic recruiting works and that these are realistic outcomes.

But what about Ted and Alice? Since music departments don’t recruit, neither knows that Columbia’s orchestra desperately needs Ted’s oboe abilities and that this year Harvard is looking for a harpist such as Alice.

Assuming there’s any validity to the “school X needs an oboist” mantra, it makes sense that for Ted and Alice to cast wide nets is not statistically insignificant.

12

No need for communication across schools - they just need to be affected by the same characteristics. Say a student applies to both H and Y and writes what she thinks is a quirky essay about her dreams of being a murderer. The student’s stats are well in the range of acceptance of both schools. Does the rejection from H predict a rejection from Y? In this case, yes.
In practice students seem to take the actual acceptance rate (e.g. 5%) and use that as their own predicted probability instead of what they really need which is the information about the specific probabilities of acceptances for students with high stats and unfortunate essay topics

13

I agree with @sherpa. What is of interest to one may not be to another and if you don’t have the information to know which is which, casting a wider net helps. And it could be of interest to all or none. That’s why they are INSTITUTIONAL priorities, they are unique to the institution.

14

Assuming you are a strong/viable candidate then then applying to more top tier colleges can improve your odds somewhat as you get more “at bats”. However, you do have to weigh the number of applications against spending enough time and energy on each application and the supplement to make it stand out. In other words, a lot of hastily put together applications will not be as good as fewer thoughtful well constructed applications.

A second point is that even among the top tier of colleges, there is a wide variety of types of schools. Unless someone is in it for prestige alone, a person who is attracted to say Dartmouth may not be as interested in a larger/urban school like Penn. It is important to choose schools that are good fits for an applicant.

15

Some of the information posted above is not correct, it’s based on using everyday senses of terms like “independent” rather than the specific mathematical/probabilistic meanings, or using definitions from websites that aren’t completely accurate (or just plain misunderstanding the concepts).

In fact, this is correct:

Yes, as @menloparkmom says, the decisions are made independently (i.e., separately) by different committees – but that does not make them independent in the probabilistic sense.

Here’s a thought experiment that may help clarify things. Person A applied to a bunch of schools; they got accepted to Stanford; do you think they got accepted to any of the other schools they applied to? Any person not being obtuse would say yes, they probably got accepted to most if not all of the other schools. But if all those admissions events were independent, you couldn’t say that, the fact that they got into Stanford would say absolutely nothing about those other schools.

Maybe a better way to think about it is to use correlation. One way to think of correlation mathematically is that it’s a value between 0 and 1, relating two events/sets of data; if the value is 0, then they’re totally unrelated – independent; if it’s 1, then they’re perfectly correlated. Any non-0 value means they’re dependent – in particular, they don’t have to be perfectly correlated to be dependent.

Most likely the correlation between admissions decisions at schools is fairly strong, especially if the schools are similar (like top schools are). Not independent, not perfectly correlated, but still related, and hence dependent.

Getting back to the OP’s original question, i.e., will one’s chances of getting into at least one top school be greater if they apply to more?, the answer is basically yes. Think of it this way, basically dividing applicants into three groups: some have basically no shot to get into any of the top schools; some are likely to get into more than one of them; others have a shot at some of them. For people in this latter group, applying to more than one of the top schools would increase their chances of getting into at least one of them.

But should you do it? That depends. You should first evaluate other considerations, like fit and affordability. You should also make sure to include sufficient match/safety schools on your list. And you don’t want to apply to too many schools, so you have sufficient time and energy to do a good job on all of them.

After that, if you still want to shoot for some top schools, you should try to assess your chances at such schools, you might be able to get some idea where you’d have a better shot. Maybe you can find some where your chances are increased, based on “institutional priorities”, or whatever. But remember that any increased chances of getting into these top schools will be marginal, so you need to make sure you’re taking these other steps, to have a good list of schools to apply to.

16

Respectfully, it is not. The fact the the same criteria are considered and likely to produce the same result does make them dependent events. Some 3rd party definitions of dependent/independent events:

An event that is affected by previous events. Example: removing colored marbles from a bag. Each time you remove a marble the chances of drawing out a certain color will change.

https://www.mathsisfun.com/definitions/dependent-event.html

or

In probability, a dependent event is an event that relies on another event to happen first.

http://www.statisticshowto.com/dependent-event/

Another batch of examples:

http://www.mathgoodies.com/lessons/vol6/dependent_events.html

What happens at Stanford does not affect what happens at other schools in any way. They are two bags of marbles.

Of course, some of the circumstances may be similar – the red marble is larger and courser in both bags - or the same bad essay and transcripts went to both colleges, so the result is the same. This does not make them dependent events, so they are by definition independent events.

17

^^Thank you Postmodern for explaining it so clearly!
EACH college application is looked at by INDEPENDENT admission committees.
What ONE committee decides does NOT effect the decision of ANY OTHER committee.
Therefore they are INDEPENDENT events.
Look at it this way folks- a very weak student who decides to apply to highly selective colleges does NOT increase his chances of acceptance at any one of those colleges, simply because he applied to other similar colleges.
That’s not how it works folks.
8-| :open_mouth:

18

^The original assumption is that it is not a very weak student, it’s a student who is statistically well-qualified at all of the schools, and is looking to increase chances through the institutional priorities of at least one of the schools.

19

Actually, respectfully, it is. You’re too hung up on these imprecise definitions you’re finding. The fact is, it’s hard to define precisely. You have to state it just so, and cover all the qualifications, and if you’re not very careful and precise, it’s easy to get wrong. Better would be to refer to a textbook on probability, where it will be defined precisely (i.e., mathematically).

Let’s try looking at this wikipedia page:
https://en.wikipedia.org/wiki/Independence_(probability_theory)
It starts out by stating:

That’s a little imprecise, because “does not affect” is ambiguous, and makes you think of causing or preceding or some such. But let’s ignore that, and look at the mathematical definition of independence, which they have a bit later on the page. That, after all, is the precise definition.

I’ll write this here as: P(A.B) = P(A) * P(B)

First, notice that definition says nothing about one event preceding or causing or affecting the other. It’s simply not relevant, and only comes up in imprecise definitions.

Now consider someone applying to a top school, with an admissions percentage of 10%, and some lesser school, with an admissions percentage of 50%. If those events were independent, then according to that definition, the probability of the two events both happening would be .10 * .50 = .05. But in fact, anyone who gets into the top school is almost assuredly going to get into the other school, so that probability is actually just about .10. So, by the precise mathematical definition, they are not independent.

Experience tells me that this won’t convince you. So be it. But I assume you will accept that someone who gets into a top school is very likely to get into a lesser school. Maybe you can realize that that is not possible if the events are independent.

20

@menloparkmom
Oh boy. I guess I don’t have the emojis or ALLCAPS necessary to get you to understand this. My only suggestion is to try to realize that you can’t use everyday meanings of words to understand/explain things that have precise mathematical definitions. That and maybe you should try to appreciate the Dunning-Kruger effect.

Except that is not what the OP was talking about. They asked if the chances of getting into at least one top school would be increased by applying to a number of them. And the answer to that is clearly yes – but perhaps not significantly so.