Look, forecasters don't get the future inflation number or the USD-JPY rate correctly most of the time, but it doesn't stop them from using reason to arrive at a forecast , and they get the direction right most of the time even if not the exact number.

OP is similarly using reason. And the math is correct if you assume a set of qualified students whose stats put them in the range of these schools.

OP used 4% acceptance as an example. You can use Naviance to actually get a sense of probability of not being accepted to a school for your stats (calculate acceptance for that higher stat cluster). So let's say using the Naviance plot of GPA and SAT, your child has a 15% probability of admit at Cornell, and a 15% admit at Dartmouth, (that would be 85% probability of rejection at each). So the probability of rejection FROM BOTH is
0.85*0.85= 0.7225 , i.e. 72%.

If Harvard is a 8% admit probability for your stats, then the probability of reject from ALL THREE is
0.92*0.85*0.85= 0.6647 (66%).

The math is correct...and the correct interpretation is:
1. For those students whose stats put them within the range, applying to more elite schools lowers the likelihood of being rejected by all or put another way improves the probability of being accepted by at least one.
2. But that said , the resultant rejection probability is still high and for most of the best kids rarely gets better than a coin toss.

You don't get shattered when you lose a coin toss. Don't get shattered when your kid doesn't get into an elite.

Anonymous wrote:They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

In mathematical terms, related to game theory, they are totally independent events, in that the outcome of one does not affect the outcome of another.

https://mathematicalmysteries.org/independent-and-dependent-events/

But as noted, despite that you cannot use game theory because you can’t know the starting odds of your admission the way you can know that you have a 1 in 52 chance of drawing the 8 of hearts from a full deck of cards.

They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

Each college has its algorithms. They are proprietary trade secrets within the multi-billion-dollar enrollment management industry. Decisions are more data-driven than ever, but applicants are not able to access that.

Anonymous wrote:Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you apply to 10 colleges each with 4% admit rate.

If the students stats are in the top 25% for each school then, yes this would essentially be true. If not, the odds are 94% that the student would be accepted to none.

But as others have said you can’t win if you are not in the game, but if you don’t truly understand the math, are you really in the game.

Anonymous wrote: I guess I'll just shotgun the T20 with my 3.8 and 1480, since I've got a pretty shot at getting in somewhere, according to your math. There is no empirical evidence that this won't work.

cant hurt

I guess I'll just shotgun the T20 with my 3.8 and 1480, since I've got a pretty shot at getting in somewhere, according to your math. There is no empirical evidence that this won't work.

Anonymous wrote:But we do know the middle50% of their sat and gpa, so if someone falls into the top end of that or exceeds it , I think they will have at least that 4% or whatever chancd

Again, many factors are being ignored here.

But we do know the middle50% of their sat and gpa, so if someone falls into the top end of that or exceeds it , I think they will have at least that 4% or whatever chancd

So much wrong -on both sides.

Yes they are independent events, completely.

But NO, you CANNOT use game theory to determine this with any degree of accuracy.

Admissions rate is NOT the chance that any one individual applicant’s chances has at admission. You cannot know that number. Therefore you cannot use game theory formula with any accuracy whatsoever.

It is not like a deck of cards or a pair of dice.

If you don’t have accurate input to the formula, there can be no accurate output. Don’t fall into that trap.

Anonymous wrote:You miss 100% of the shots you dont take.

A stitch in time saves 9!

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Except that's not how it works, because each of those independent events is dependent on mostly the same factors.

This can't be true. JHU and Cornell are looking for different students, so are MIT and Yale.
Your reasoning reduces college admission to simple stats such as test score and gpa. However, that is not how it works!

OP's reasoning is falling into that trap, not this PP. Negative correlation is not zero correlation.

If Yale doesn't like what MIT likes, the student who might get into MIT, will gain almost nothing applying to Yale.

If Yale and Cornell like nearly the same thing, the student who applies to both is likely to get the same result from both applications.

A student is not one-dimensional, but they are multidimensional. A student could be a nerd, but at the same time artsy, or sporty.

Yale might like the artsy you, Dartmouth likes the sporty you, while MIt likes the nerdy you. Of course applying to multiple colleges enhances the overall chance of acceptance.

Unless you’re a one trick pony. In that case, yeah, applying to 10 is nearly the same as applying to 1.

I think my 3.0 student retains a 0% chance of getting into any school with a 4% acceptance rate even if he applies to 20 of them.

You miss 100% of the shots you dont take.

There are so many factors ignored here. It isn’t a simple math problem.