Anonymous
Post 04/06/2025 06:04     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote: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.
You can only do this math if the events are independent, which is obviously not the case.


No, you have it backwards.

These events ARE independent, as illustrated by the definitions in the link and card draw example above.

You can only do this math if you know the odds of an event happening. Since you can’t possibly know the odds of any individual being accepted you don’t have the numbers for the formula.

Want more proof? Do the math for one student - specifically, the OP. Show your work.
Anonymous
Post 04/06/2025 06:00     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote:
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.
The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.


You did not read the link nor do you understand the mathematical concept of independent events.

Dependent Events: one that affects the outcome of another. Picking a card from a deck (1:52), then picking a second card from that deck changes the oddds (1:51)

Independent events: One that does not affect the outcome of another. Picking a card from a deck (1:52) then picking another card from a SECOND deck (1:52).

Whether you are accepted to MIT does not affect the likelihood of whether or not you are accepted to Harvard. Independent events.

This is not debatable.
Anonymous
Post 04/06/2025 03:24     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote: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.
You can only do this math if the events are independent, which is obviously not the case.


DP.
It's semi-independent.
You can mentally adjust the result, knowing that it's not completely independent.
Anonymous
Post 04/06/2025 01:48     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote: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.
You can only do this math if the events are independent, which is obviously not the case.
Anonymous
Post 04/06/2025 01:44     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
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.
The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.
Anonymous
Post 04/06/2025 01:41     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
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.
All the mentioned colleges are mostly looking for the same students -- highly accomplished with impressive ECs and an interesting story.
Anonymous
Post 04/06/2025 01:40     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:Except that's not how it works, because each of those independent events is dependent on mostly the same factors.
Then they're not independent
Anonymous
Post 04/05/2025 23:38     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote:
You can’t do the math without knowing the factors, and you have no idea what the factors are for an individual applicant.

Weather forecasts don’t wait to measure every gust of wind to predict rain—they model with temperature and pressure alone. Admission odds can be modeled with GPA and SAT, even if extracurriculars and essays aren’t known.




You can keep claiming that, but it does not make it so. You need to know the odds one one thing happening to know the odds of it happening in multiple tries.

Your weather example, you admit, uses actual data. You have no comparable data for an individual applicant. You don’t. You can’t.

Game theory is a terrible - make that useless - way to develop an application strategy.
Anonymous
Post 04/05/2025 23:34     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
You can’t do the math without knowing the factors, and you have no idea what the factors are for an individual applicant.

Weather forecasts don’t wait to measure every gust of wind to predict rain—they model with temperature and pressure alone. Admission odds can be modeled with GPA and SAT, even if extracurriculars and essays aren’t known.


Anonymous
Post 04/05/2025 23:18     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote:
WRT an individual applicant, whose likelihood could be 0% or 100% at any one college.

There is a 100% likelihood of an applicant being between 0% to 100%, so that is quite a meaningless understanding of probability.

Probability is about trying to quantify uncertainty. The more complete the model, the lower the error range/standard deviation. So sure, if someone had a line of sight on acceptances based on SAT+GPA+ ECs they would have a better model than someone with just a line of sight on SAT+GPA.

But the only public data that can be modelled comes from Naviance (school level SAT+GPA) and CDS (overall acceptances accurate, SAT+GPA based on those reporting). For those who are so inclined, they can calculate their probabilities of rejection from each and multiply them.

I think the third interpretation from the math for me is very clear, if applying to reaches, apply to a whole bunch of them , it will improve your chances of acceptance to at least one. Applying only to say Harvard is quite meaningless.



No, I am sorry, everything you are saying is wrong. In fact your first sentence makes exactly my point. You cannot use game theory to get any useful knowledge of whether applying to more highly selective colleges will have a substantive increase in your odds. It is not a reasonable way to develop an application strategy.

You can’t do the math without knowing the factors, and you have no idea what the factors are for an individual applicant.
Anonymous
Post 04/05/2025 22:15     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
WRT an individual applicant, whose likelihood could be 0% or 100% at any one college.

There is a 100% likelihood of an applicant being between 0% to 100%, so that is quite a meaningless understanding of probability.

Probability is about trying to quantify uncertainty. The more complete the model, the lower the error range/standard deviation. So sure, if someone had a line of sight on acceptances based on SAT+GPA+ ECs they would have a better model than someone with just a line of sight on SAT+GPA.

But the only public data that can be modelled comes from Naviance (school level SAT+GPA) and CDS (overall acceptances accurate, SAT+GPA based on those reporting). For those who are so inclined, they can calculate their probabilities of rejection from each and multiply them.

I think the third interpretation from the math for me is very clear, if applying to reaches, apply to a whole bunch of them , it will improve your chances of acceptance to at least one. Applying only to say Harvard is quite meaningless.

Anonymous
Post 04/05/2025 21:29     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote:
Anonymous wrote: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.





WRT an individual applicant, whose likelihood could be 0% or 100% at any one college.


Dead wrong.
Anonymous
Post 04/05/2025 21:19     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
Anonymous wrote: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.





Your point is accurate and well taken, but the flaw in your logic is it does not work WRT an individual applicant, whose likelihood could be 0% or 100% at any one college. So yes it obviously increases your odds (assuming you can do all applications of equal quality) but you cannot say to any individual applicant what the odds are and whether the increase is statistically significant. They could all be 0%.

You’re trying to handicap the odds of pulling the 8 of hearts from a deck that is anywhere from 52 cards to infinity -1 cards. Can’t be done. Don’t use this logic when choosing an application strategy.
Anonymous
Post 04/05/2025 21:12     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
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.


Misleading. They are not independent separate events, which is why the math above fails to represent reality. Each decision depends on roughly the same inputs in reality.
Anonymous
Post 04/05/2025 21:07     Subject: Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap
PP here - in my comment above , important to note that the "resultant rejection probability is still high" refers to the rejection from ALL being still high. That is what applicants need to understand.