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.
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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