Overall chance of admission to at least one school?

[jon cocktoe]

So being as inept at math as I usually am, I was trying to figure out what my chances are of being accepted by at least one school, but the best I could figure out is my average chance of admission overall. Is there some way to figure out what the likelihood is of getting at least one acceptance based on the admission rates of all the schools that I applied to? For example, I applied to 5 schools with acceptance rates of 3%, 20%, 24%, 16%, and 22%. Is there are formula I can use? Is there a way to figure out the chance of getting into two schools? I've already been rejected by the school with the 16% admit rate, so does that change anything? I realize this is a somewhat pointless endeavor, but I'm hoping it might ease my nerves (assuming, of course that I have a pretty high chance of getting one admit). Thanks for your help!

[DJLamar]

Well, to calculate your chance of getting into at least one school, first we're going to just take the percentages and convert them to range from 0 to 1 (i.e. 3% = 0.03, 20% = 0.2). Now for each school, the chance of the average applicant not getting in is going to be 1 - x where x is the acceptance rate. So to calculate the chance of the average applicant getting in somewhere, we're going to first find the chance of the average applicant not getting in anywhere and subtract that from one. To get the chance of not getting in anywhere, we take the chance of rejection for each school and multiply them all together. So we get:

1 - (1 - 0.03)*(1 - 0.2)*(1 - 0.24)*(1 - 0.16)*(1 - 0.22)

=

1 - 0.97*0.8*0.76*0.84*0.78

=

1 - 0.386410752

=

0.613589248

So about a 61.3% chance of getting in somewhere.

This is pretty meaningless though since, among other things, the stats of the "average applicant to school x" are probably not constant across different schools.

[graddamn]

Lol, I was doing some similar calculations earlier. If you wanted to assume the chances of admission are independent probabilities , then yes, it's pretty easy. Your chances of not getting in anywhere noting that you didn't get into the one school, are roughly 40%. I did this calculation for my own app and made myself very, very depressed.

The problem is that your chances of admission are not independent for a few key reasons. First, your subfield may be more or less competitive than the department to which you are applying. Second the strength of your application means that you may not have the same chances (for better of worse) as the average candidate at that school. But as everyone here mentioned, grad apps are a crapshoot, so maybe the independence assumption isn't so bad after all. Good luck, waiting sucks!

[jon cocktoe]

So about a 61.3% chance of getting in somewhere.

I was hoping for a higher number , that's not much better than a coin toss. But, if I take out the school that I already got rejected from, and only use my top 3 choices, then I get 98%. I like those odds!

Re: independent variables. There are so many variables across the board, I think its just easier to treat it this way. The percentages I figured out were based on my subfield with only one exception, so I'm going to just pretend that these results reflect reality, even if it's only to get me by until March. I suppose once I get all my responses, I can come back here and check the accuracy of these%

Edited February 8, 2010 by shutterbug

[jon cocktoe]

Ok, I'm dumb. The 98% was really 54%. I have no idea how I got that number, but I got to be all happy for at least a few minutes!

[Ziz]

Imagine what a great GRE question this would be...

[glasses]

Imagine what a great GRE question this would be...

They'd have to make it "chance of eating a really amazing and rare apple," though. At the first sign of the phrase "chance of admission" I'd start whimpering, and I feel like I wouldn't be the only one.

[katalytik]

I think this sort of probability assessment is great math, but as others pointed out that the probability is not equal for each of your choices. Lots of variable are not being counted, and even if we took them into account, its still almost impossible to predict the outcome. Someone on the adcomm may simply not like something specific and then veto the candidate. So unfortunately, its just not even possible really.....

[The Pseudo grad student]

Well, to calculate your chance of getting into at least one school, first we're going to just take the percentages and convert them to range from 0 to 1 (i.e. 3% = 0.03, 20% = 0.2). Now for each school, the chance of the average applicant not getting in is going to be 1 - x where x is the acceptance rate. So to calculate the chance of the average applicant getting in somewhere, we're going to first find the chance of the average applicant not getting in anywhere and subtract that from one. To get the chance of not getting in anywhere, we take the chance of rejection for each school and multiply them all together. So we get:

1 - (1 - 0.03)*(1 - 0.2)*(1 - 0.24)*(1 - 0.16)*(1 - 0.22)

=

1 - 0.97*0.8*0.76*0.84*0.78

=

1 - 0.386410752

=

0.613589248

So about a 61.3% chance of getting in somewhere.

This is pretty meaningless though since, among other things, the stats of the "average applicant to school x" are probably not constant across different schools.

Just what I'd expect from a geeky CS major. JK, I'm an engineer so I totally get it, I love geeks

I have a less, well more stupid way of predicting the future of what grad schools to get into. As an extremely bored high school senior I played out the outcome of what undergraduate schools I got into by playing continuous card games and kept a tally of whether or not I'd get in to a certain school. And surprisingly it was accurate, because I got in automatically to UC Davis just as the cards had predicted. It was uncanny actually, I'm thinking of doing that all over again...

Anyone have a deck of cards I can borrow?

[luar de ouro]

Trying to figure this out mathematically gives the whole admission process a false sense of coherence, haha.

After we get past the stats and substantial credentials, the nitty-gritty of it is still madness.

[chocker]

P ( ... at least one acceptance ... | you are rejected by your safety school ) = 0

[jaxzwolf]

I wish these kinds of analyses actually worked. The problem is that each year there are new variables to contend with, so average acceptance rates from years past won't necessarily reflect acceptance rates this year. Along with the host of other factors (instant Ad Com rejections, personality conflicts, fit issues, etc.) this year we have to contend with a terrible economy and an impossible job market. Schools have been reporting increases as high as 50% in overall applicants... people who have been laid off and can't find work are thinking of returning to school, and undergraduate students are looking to avoid the job market as long as they possibly can. So just imagine: If last year, for a given program, there were 200 applicants for 10 available spots, that's a 5% acceptance rate. But if that school received 50% more applications than last year, then this year there will be 300 applicants for 10 available spots- 3.3% acceptance rate.

All conjecture, of course, but it's still depressing to think about.