Do odds increase when applying to more reaches?

DadTwoGirls
Mon, 04 Dec 2023 01:54:53 +0000

skieurope:

short answer is if you apply to 10 schools with a 5% acceptance rate, your odds at any one school is roughly 5%

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.