Pretty simple question here. Currently applying to college and am wondering if odds will increase when applying to more reaches. I have heard varying answers on this, as each college is an independent event. However, since each college looks at apps differently, do you think odds increase linearly as number of applications increase? Could someone explain the math behind this? Appreciate any insight, thank you!
No. Your odds for each school don’t change, and there’s nothing about applying to more reaches that will improve your odds for each reach. And if you overextend yourself with application supplements, extra essays, etc. (of which many reaches expect several), chances are you won’t do as well on any of them as you would if you concentrated your efforts on a few.
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Agree. Focus on the colleges you feel are the best options – spend the necessary time and energy on those supplements and let your interest/fit for those schools shine through.
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Well, it certainly is possible to get rejected by one reach while being accepted to a different reach.
Multiple applications from one student to multiple schools are not independent events. The various schools will on the most part be looking at the same grades, the same ECs, the same test scores, and the same recommendations. How much importance they put on each of these may vary from school to school. Some schools might for example not care about ECs (particularly outside the US) or not care about test scores. Some schools might not care about freshman year grades, and some others might not even ask for senior year grades (at least until after they made the admit decision). Also, each reach school is looking for students who are a good fit for them, and they might differ regarding what this means.
So I think that applying to a few reach schools is reasonable. Applying to every “top 20” school and every Ivy League school is IMHO probably usually a mistake – they are not all going to be a good fit for every student.
Which might be a slow way to say: “It depends”.
I think that this is the best approach.
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Let’s just say…if a college accepts on’y 10% of applicants….just because you apply to 20 top colleges doesn’t reduce that %of acceptance.
Each school should be viewed as a singlet.
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Whoever teaches AP Statistics can walk you through the math, but short answer is if you apply to 10 schools with a 5% acceptance rate, your odds at any one school is roughly 5%.
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Okay, I do have two degrees in math or a subfield of applied math.
First lets suppose statistical independence of each application. Suppose that 100 students, each with a chance of admissions of 5%, apply to 10 highly selective schools each. So, you might expect 50 acceptances in total. However, that does not mean that 50 different students will get accepted. Just randomly, one student might get 2 or 3 or 4 acceptances, while several other students get no acceptances. Even in this case, assuming statistical independence, for any one student the chance of getting in somewhere is less than 50%.
However, for any one student, the chances at each school is not independent from whether or not they get in somewhere else. Some reference might be “not sufficiently stellar”. Something might seem off about an essay. Everything might just hang together perfectly. When 80% of the applicants are academically well qualified and the school accepts something closer to 4% or 5% of applicants, it is hard to predict what will or will not get you accepted. This means that you might be slightly more likely that just pure randomness would predict to either be accepted to zero reach schools, or to multiple reach schools.
Then there is the issue that if you apply to too many schools, it will be difficult to do a good job on the many required essays.
Which means that applying to more than one reach school is likely to increase the odds of getting in somewhere, but the odds will not increase linearly as you apply to more schools.
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Deleted.
The probabilities observably are not, and really cannot be, independent.
I think reasonable models are going to suggest that if you do a good job identifying your best fits and apply to your best chances, as few as 3 reaches could practically exhaust your chances, meaning the chance you will get into your fourth-best reach opportunity conditional on being rejected at all three of your top three reach opportunities is getting negligibly small.
And I think beyond your best 5-6 reaches, it is getting implausible any reasonable model will show non-negligible conditional chances for additional colleges.
A couple caveats.
If there is some unusual circumstance which you are hoping will lead to unusual results, maybe a few extra reaches is warranted. Like, you had a bad semester of grades but have a reason for that and are asking for an accommodation. Advice I like is apply to some reaches assuming no accommodation, but then 2-3 more assuming there will be an accommodation.
Alternatively, if you are just not sure yet how to rank your reaches in terms of personal preference, that can also be a reason to do a few more. Like, sometimes people are not sure between universities and LACs. In cases like that, you might have more reaches due to having a decent number of university reaches and decent number of LAC reaches.
Because acceptance rates at certain schools are so low, some people say admission is like “a roll of the dice.” But in reality, rolling dice is not a good analogy when thinking about the statistics of admissions.
With dice, the rolls really are independent events. Therefore the math is straightforward-- exactly what is taught in high school stats where you keep multiplying the fraction by itself as many times as you roll the dice. So if we call rolling a 6 to be a “win” then each time you roll a single die, you have a 1/6 chance of winning (or expressed otherwise, a 5/6 chance of NOT winning.) So if you really want to roll a 6, you should roll a lot. After the 1st roll, 5/6 have not won (83% have not won). But 2 rolls gives you 5/6 x 5/6 which is 25/36 or only 69% have not won. 3 rolls is 5/6 x 5/6 x 5/6 which is only 57% that have not won. After 20 rolls (which is 5/6 raised to the 20th power) less than 3% of people have not rolled a “win.”
But college admissions are NOT independent events like rolling dice. This does NOT mean that the colleges are colluding with each other or anything like that. It just means that they tend to all look at the same things (grades, class rigor, test scores etc.) So a few students with awesome grades, rigor and scores may get into multiple elite colleges, while other students will get into none.
Now, each college will look at your application slightly differently. So apply to a few reaches. But do not “shotgun” applications if it stresses you out to the point you start turning in crummy applications, or to the point where it stresses you out in general.
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The odds of you getting into 1 reach will increase with the number of applications you send to “reaches”. The odds of getting into a specific reach won’t change.
While technically this is true as long as the marginal conditional probability is above 0, it might only be an extremely little amount above 0, enough to be negligible.
Part of the problem here is college admissions is not really a stochastic process. In a variety of contexts, people will use a stochastic model for a non-stochastic process because in some notable way there is a practical benefit to doing that. But whenever you do that sort of thing, you have to be cautious about exceeding the practical limits of the model.
In this case, part of what is happening when an applicant gets actual admissions decisions is you are actually learning something about the applicant and their applications, things that were not necessarily easy to know prior to learning those decisions. And so if we imagine an applicant not getting admitted to their best-bet reach, and then not to their second-best-bet reach either, and then not to their third-best-bet reach either, well, unfortunately, we are learning something about this applicant and the applications they are submitting.
So when we apply that knowledge to their fourth-best-bet reach, including the knowledge this was only their fourth-best-bet among their reaches, well, our model should be adjusted to incorporate that knowledge, and the conditional probability at that point should plausibly be getting very low.
And then if they don’t beat those odds with their fourth-best-bet reach, nor their fifth-best-bet reach, well, the conditional probability for their sixth-best-bet reach is going to be even lower.
My two cents is at a certain point, imposing a stochastic model on this situation is doing more harm than good. That sixth-best-bet reach college is not pulling balls out of a sack, it is processing and evaluating your application. And we are getting to a very high level of confidence about how that process will turn out.
Still, technically anything is still possible. But assigning a probability to such things is not really meaningful, and for the purposes of decision making, not necessary either.
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In my opinion, the answer depends on nature of the reaches: are they high reaches or more “reasonable reaches.”
Take a student with a 3.75 UW GPA and a 1480 SAT score, with a reasonable mix of extracurriculars and accomplishments, but who has no spikes (no family member who donated a building, not an recruited athlete, no national awards in their extracurriculars, etc.). If that student applies to Yale, they are almost certain to be denied. If that student decided to “maximize their chances” and add in Harvard, Princeton, MIT, Duke, and Stanford, that student is still nearly certain to be denied by all of them, and the student hasn’t increased their odds at all. Adding in these particular reach schools will not increase that student’s chances because those reaches were all unattainable at the outset.
However, take the same student, but now they are applying to Bates College. That’s still a reach, and I’d guess that the student’s odds of admission (in regular decision) are on the low side. But, if the student adds in: Colby, Vassar, Middlebury, Colgate, Hamilton and Wesleyan, then I believe the student has increased their chances of getting into one of these reaches, at least somewhat, due to the nature of holistic admissions and the fact that these are all “attainable reaches.”
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I definitely think if you account for a little variability in what individual colleges are looking for, it explains why 2-3 reaches could sometimes be sufficient, but maybe not always. In particular, I think if you are interested in LACs, they are by nature a little more variable in terms of their preferences, and just have smaller applicant pools and smaller target enrollment classes more subject to quirky matching effects in general. So maybe an LAC-heavy reach list will naturally lend itself to a few more reaches.
That said, I do wonder–our college counselors would likely suggest a person interested in all those LACs should try to visit them, also carefully study their websites, possibly talk to students, and try to pick out the ones which they saw as the best fits. And in fact, based on our high school’s experience with admissions to those LACs, they might well nudge some kids in certain directions.
OK, so suppose you synthesized all that and then ranked those colleges by where you thought your were the best fit. You might not get into your best bet. Possibly not your second either. But that is seven colleges–how often really would people get into only their seventh-best bet, and none of their first six best bets?
Anyway, I am raising this issue not to try to be dogmatic about the number of reaches, but more to suggest the real work to be done is in figuring out your best bets. And if you end up with seven reaches you really feel good about, OK. If it is only three, I think OK to that too. What I don’t think you need to do is indiscriminately keep adding more reaches until you run out of Common App slots. Whatever is your list of true best bet reaches, if you have taken the process seriously, is almost surely enough.
Not a simple question at all.
It depends on how “reachy” the reaches are based on the particular student’s situation.
For a 3.7GPA, 1350SAT, 3s and 4s on APs kid throwing apps into every one of the T10 schools won’t make their chances of getting into a single T10 school any better
For a 4.0, 1590, straight 5s on APs kid, the odds of getting into at least a single T10 are probably improved with applications to all.
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So if a school has a 7% acceptance rate, it may be a prestigious school that gets tons of applications from students who have grades/scores well below the threshold. The real metric is for kids who are in “range” of grades/scores and what % of those get offers. It goes to the point of how “reachy” is your “reach”.
I think the statistics work when you assume all the students applying are the same. But they are not. Numbers carry the same weight when picking lottery numbers. Students are variables and what universities will look at will be variable, what a particular reader on a particular day will consider attractive will be variable, and it goes on. There are students who get into multiple top 10s and there are similar students who won’t get into any of them. A URM student with excellent credentials may improve their chances by applying to more top 10 schools simply because there are a limited number of them. I think it’s beyond a numbers game and is different than just chance. That said if a school has a 5% acceptance rate then that means they reject 95% of their applicants. That’s important to keep in mind if attending a selective university is important to you. I think it’s important to apply to the best schools (for you) not just the “best” schools.
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Statistically, if your odds of getting into any given super reach are 5% and whether you apply to 1 or 10 your odds of acceptance to any of them don’t improve and remains 5% each. That would be true if admission were a pure lottery. It’s not. It’s not random. It’s a bunch of human AOs making subjective decisions. And there is not just one variable (a lottery ticket), but dozens or more variables that will all weight differently from school to school, student to student and AO to AO. One AO may be unmoved by your essay and it may be deeply reach another. So while average applicant X may have a 5% chance at 5 schools with a 5% admission rate, the reality is they may have a 0% chance at one, 5% chance at 3 and a 20% chance at another. Sure students/parents can do research and try and make an educated guess on which of those 5 colleges they have the 20% chance at, but its still a guess and they may guess wrong. So while the applicant pool as a whole has a 5% chance, individual applicants chances are all over the map, and they don’t know which schools its highest at.
As for the generally sound advise of focusing on a few and doing a really good job instead of diluting your energy by shotgunning at many, that too varies by the student and the circumstance. For one student focusing on 5 schools means they would put in the same energy and time they would in total if they had 20 schools. For another, they were going to do what they do and it they would not do better if they only did 5 instead of 20.
Here’s the reality. There are no shortage of kids who have shotgunned and said in hindsight that the school they ended up attending was not one that would have made their short list if they had been more selective in their they applied (and not because they coveted the school less than others on their list but more because they didn’t believe they would get in). There are also no shortage of kids who get completely shut out in shotguns and end up pretty devastated. And every possible nuance in-between – students who skipped ED to shotgun and ended up on a waitlist for the school they might have ED’ed to (and accepted to none), left wondering if it would have gone differently if they had ED’ed instead.
Part of what makes this process so stressful is both that the stakes can seem really high (though in reality in most cases we exaggerate this and students will end up just fine in whatever college they attend) and that there are so many “consequential” decisions – to ED or not and where, which to apply to, how many, who to get recs from, which essay idea to go the distance with, etc. For some, the decision of whether to shotgun is made for them by circumstance – they can’t afford to apply to that many places. For those that have the option, it’s like all those other decisions – there is no definitively right answer. You’re on the admissions battlefield with no ability to predict the outcome or the reactions of the enemy (the AO’s in this metaphor). For some shotgunning would be the right call, for others not. No way to know until the dust has settled.
So know yourself and go with your gut.
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The logic always holds. A % reach, A % target and a % safety. If a student is happy with their “safety list” then the rest is easy. The problem is some students/parents aim way too high and don’t have a nice soft landing.
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I’ve identified a certain approach I now think of as 19-reaches-and-1-safety.
Obviously that is not strictly defined, but it is characterized by the lack of a robust target/match list, which apparently they are trying to make up for by applying to as many reaches as possible.
If it is a true safety, then the kid is still going to go to college. But I think they could likely feel better about the outcome if they had more choices.
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