Chancing Algorithm Question

Answered

No, that's incorrect. You do not have an 89% chance of getting into (1) 20% admission rate school if you apply to 10 of them.

The main reason this is incorrect is that getting into a college is not a roll of the dice or random. I would say it's the opposite of random selection. If college admissions were actually random then 5 people applying to Harvard from your high school with a 20% CV rate would yield exactly 1 person getting in. But in reality, most likely no one would get in because Havard admissions is based on 99 criteria on their scorecard rubric and most of your high school applicants would be missing key criteria like Legacy Status, being a recruited athlete, intellectual vitality, or something else. And if you attend a Private Boarding School like Deerfield or Exeter then, then 5 people applying might yield 2 or 3 admits because they are feeder schools.

If you applied 10 times to the same school with a 20% CV rate then you have an 89% chance of getting into that 1 college at least 1 out of 10 times you apply. That's the only scenario I can come up with where your math works.

But if you apply to 10 different elite colleges like Ivys or Stanford, UChicago, Duke, and NorthWestern, and your chancing rate is around 20% for all of them (give or take), then it's a new roll of the dice with each new college, its not cumulative or path-dependent rather it's path independent because applying to NW is not dependent on your roll of the dice with Duke or your roll of the dice with Columbia. There are 10 separate unrelated rolls of the dice.

And when I say a roll of the dice, it's not really a roll but a unique holistic evaluation of your academic and EC narrative, interviews, essays, short answers, recommendations, verifications, and institutional alignment. Each of the 10 colleges will have completely different scorecards and completely different institutional priorities to fill. So if you are 1st chair for Violin, that might matter to 2 out of 10 colleges, and if you are Team Captain of the Lacrosse team, that might matter to a different 4 out of 10 colleges, and if you are from a poor zip code in Arkansas, that might matter to 5 out 10 colleges and so forth and so on.

If the 10 colleges would pre-publish their institutional shopping list and post it on their website each admission cycle, then applicants would have a better idea of the symbiotic college fit but instead, it's a guessing game unless you have a very expensive college consultant who has friends in the admissions office that can do reconnaissance work on your behalf.

And this is why those high school students who only apply to reach colleges without safeties or targets, get the surprise of their lives when they get into zero schools and have to settle for taking a gap year or going to a state college with rolling admissions. At the same time someone who is say a US Presidential Scholar might get into 7-8 of the 10 top schools they apply to and might get rejected from Tufts and Emory but get into Harvard, Yale, Princeton, Stanford, and Columbia. But someone like that most likely has a CV chancing rate between 25-35% at the top 20 schools.

My recommendation is to apply to (10 ) 20% chancing schools but also apply to (5-6) 30-50% chancing target schools and (1-2) 70-85% chancing safety schools to make sure you land somewhere that you are perfectly happy to attend if you reach schools that don't pan out.

If you end up at Wake Forest, William and Mary, Kenyon, Macalester, Trinity, or St. Lawrence you are not going to have an inferior education or college experience to attending Colby, NYU, Tufts, Barnard, or Emory even though the acceptance rates are 22%-45% not 6-9%. It's a fallacy that low acceptance rate colleges offer sub-par educations or career paths.

Good luck.