Math/Statistics gurus...

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So, we were talking about this in my house, and for the purpose of the actual conversation, it applied to selective colleges, but I am just wondering about the math aspect.

I thought, to calculate the possibility of getting into the 5 selective schools that my son is still waiting on, it would be wise to calculate the averages of the acceptance rates of all 5.  (and I specifically tried to hunt down acceptance rates for computer science which these days is always significantly lower than most other majors, especially the schools we're talking about)

So let's say the averages of the acceptances rates is right around the 9% mark, I would say he has a statistical probability (assuming his application was within reach for the school and we weren't trying to send someone with a 900 SAT to stanford)...I would say his probability is 9%.

But my son (and I don't want to argue with him, he's 17 and holding out hope after all)...says that no, the fact that he applied to 5 increases his statistical probability to slightly more than the average of the acceptance rates.  

Now he's the one doing Calc 3 and all that and I never even took Calc or statistics....

But can someone explain this to me? Is he correct?  And, how?

[8filltheheart]

I am definitely not a mathematician and I am not responding with any sort of mathematical reasoning. My response is simply based on observing the admissions game over the yrs.

I disagree with your ds bc each school is really an isolated event and more applications does not increase his odds at any given school. The odds of admission at school 1 is X. Applying to school 2 does not increase his odds at 1. School 2's decisions are completely isolated and not related to 1's. (So, no, you can't add up the avg acceptance rate at various schools and find and avg % chance of admission based on that.)

Kids on CC argue all the time that applying to more increases their chances. Not really. Either they are really competitive and possibly even admitted to multiple bc the schools are seeking similar characteristics or they aren't competitive even thought they think they are and aren't accepted to any. Fwiw, I disagree with the contention that acceptances are random. If you watch the cycles closely enough, you can start to assess generalized stats/accomplishments/traits that are accepted.

[Arcadia]

Acceptance to any college is an independent event in probability. So applying to more does not increase the odds of getting into any.

https://mathbitsnotebook.com/Algebra2/Probability/PBIndependentDependent.html

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10 minutes ago, 8FillTheHeart said:

I am definitely not a mathematician and I am not responding with any sort of mathematical reasoning. My response is simply based on observing the admissions game over the yrs.

I disagree with your ds bc each school is really an isolated event and more applications does not increase his odds at any given school. The odds of admission at school 1 is X. Applying to school 2 does not increase his odds at 1. School 2's decisions are completely isolated and not related to 1's. (So, no, you can't add up the avg acceptance rate at various schools and find and avg % chance of admission based on that.)

Kids on CC argue all the time that applying to more increases their chances. Not really. Either they are really competitive and possibly even admitted to multiple bc the schools are seeking similar characteristics or they aren't competitive even thought they think they are and aren't accepted to any. Fwiw, I disagree with the contention that acceptances are random. If you watch the cycles closely enough, you can start to assess generalized stats/accomplishments/traits that are accepted.

 

This is 100% my thoughts.... 

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Whether applying to more than one school changes the probability of being accepted.

[daijobu]

Let's say you are only considering schools with a prob(acceptance) = 0.08.  Prob(rejection) = 0.92.  And we assume that each acceptance is independent of the others.  (Admissions committees from different schools aren't comparing notes.)  

If you apply to 1 school P(acceptance) = 0.08

If you apply to 2 schools P(acceptance) = 1 - P(rejected both schools) = 1 - (0.92)^2 = 0.15

if you apply to 3 schools P(acceptance) = 1 - P(rejected all 3 schools) = 1 - (0.92)^3 = 0.22

 

[daijobu]

Now it could be that 0.08 may apply to the entire applicant pool.  It could be that your own particular student is more impressive than average, so may actually have a higher probability of acceptance, say 0.25.  If you student is admitted to Harvard for example, I might argue that with this new information, his probability of acceptance at other competitive colleges is greater than 0.08.  

Actually getting in to Harvard doesn't make him a stronger candidate.  The fact that he did get in tells me that his probability is higher than my original estimate.  

[daijobu]

21 minutes ago, square_25 said:

Daijobu's calculation is correct, assuming independence of admission decisions (which is probably not quite correct, but not a bad model for sake of discussion.) 

 

Unless there is collusion or anti-trust violations happening, admissions decisions are independent.  Otherwise we'd be seeing a big scandal.  

I'm not familiar with Division I NCAA recruiting, so it could be that a player is "hot" and so the interest of one coach generates piques interest from other coaches.  But I'm assuming we aren't discussing athletes here.  

[daijobu]

Rereading, I think you are taking into account the different probability at different schools.

Prob(acceptance at a reach school) = 0.05  --> prob(rejection) = 0.95

Prob(acceptance at a safety school) = 0.80  --> prob(rejection) = 0.2

Prob(acceptance at an intermediate school) = 0.30  --> prob(rejection) = 0.7

If he applies to 2 reaches, 2 safeties and 2 intermediates, the probability he gets into at least one of these schools...

Prob(he's admitted somewhere) = 1 - Prob(he's rejected by all 6 schools) = 1 - (0.95^2)*(0.2^2)*(0.7^2) = 0.98   (good news!)

[daijobu]

This reminds me of the other thread about whether algebra should be required for high school graduation, which migrated into whether algebra--or any subject--should be required to have a life well lived.  I didn't have a good contribution to that thread because it is a question I struggle with.  But I think that in general if we are equipped with knowledge, our understanding of the world is enhanced.  We never know what knowledge will come in handy, and how much happiness it will bring us.  Does knowing the exact probability of acceptance enhance one's life?  (For me it does.)  Or would we be just as content to shrug and say "who knows?"  

Likewise, are we better off knowing that those twinkling lights in the night sky represent other suns in imaginably distant locations?  Or are we better off thinking they represent some Greek gods?  

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Thanks DAijobu!

i find this so fascinating!

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I just come here when I have a really good math problem!  Thank you so much ladies for being willing to puzzle through this.  We've decided his chances are somwhere between 8 and 22% because the things that one college rejects him for, are the things the other colleges are likely to as well.  Additionally his SAT was closer to the 30th percentile of admitted students, and he doesn't have amazing leadership stuff so I think it's a lot closer to 8 than 22 so maybe we will settle on about 12% LOL  I just totally made that up.

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Thank you!!

[daijobu]

24 minutes ago, Calming Tea said:

I just come here when I have a really good math problem!  Thank you so much ladies for being willing to puzzle through this.  We've decided his chances are somwhere between 8 and 22% because the things that one college rejects him for, are the things the other colleges are likely to as well.  Additionally his SAT was closer to the 30th percentile of admitted students, and he doesn't have amazing leadership stuff so I think it's a lot closer to 8 than 22 so maybe we will settle on about 12% LOL  I just totally made that up.

 

This is an excellent point.  While we can locate the probability of acceptance historically, among all applicants, this doesn't necessarily equal the probability of acceptance by any particular student.  A student with a less impressive application may have a lower probability than the historical average, or vice versa.  

This is one reason why I'm not as alarmed as others by the increasing number of applications.  While it does reduce the percentage of applicants that are admitted, that doesn't necessarily mean that any particular student's probability is reduced.  Suppose you are a super star student and a shoo-in for a tippy top school in 1987.  Now imagine 20 years later when there are many more applicants, but they are all comparatively weak and really not candidates for acceptance.  (Common App makes it easier to check another box.)  That shouldn't affect your chances of being admitted, because these are students who are unikely to be admitted.

Now, if the applicant pool is much stronger, that may reduce your chances.

[8filltheheart]

37 minutes ago, square_25 said:

 

Hah, that's the hard thing about all of this. All of the calculations are lovely, but we can't actually estimate his chances at one specific college all that well so then all the calculations are already based on unfounded assumptions and at the end, it's STILL all a guessing game. 

I just helped my (much younger) sister apply for colleges, so I know firsthand how stressful the waiting game is! I'll keep my fingers crossed for your son. 

Exactly. Isn't the assumption being made in those stats formulas that the probability of acceptance actually exists equally amg the applicant pool? The reality is that is not real. Certain applicants have a much higher probability of acceptance than others. 

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Exactly, which is why I would say that for my ds the stats are on the lower end, not the higher end.  However, he has a major hook in being a URM in COmputer Science.  Which also throws another curve ball.

Originally, this thread was more about the general math involved than the actual college applications for that reason.

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9 minutes ago, square_25 said:

Of course, since we pretty much made up the 2%, this isn't getting us a real handle on probabilities of getting in... just letting us think about whether applying to more colleges increases our chances (which is does significantly, especially for marginal students.) 

 

Right, it's just a thought experiment, but I wanted it to be based on some actual probability math which I've never studied....I think it's been really useful.

I mean it's not like I'm buying my College Mom Hoodie, based on this thread.  Don't worry! 🙂

[gstharr]

That is why many refer to highly selective universities as rolling the dice.

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It's an amazing subject that I have very little exposure to! I found a little online tutorial and am going through it right now.  It's very basic, but I'm really learning something this week!  Thanks square! and Dbaijou

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Just now, gstharr said:

That is why many refer to highly selective universities as rolling the dice.

Right, but that's only if you have the same stats as the 50th percentile (13 AP classes, 1500 and up SAT scores, clubs, leadership, community service or involvement, and some cool personal hobbies or achievements and you can write an interesting and not-boring essay, you can look at it as a random event.  

 

[8filltheheart]

51 minutes ago, Calming Tea said:

Right, but that's only if you have the same stats as the 50th percentile (13 AP classes, 1500 and up SAT scores, clubs, leadership, community service or involvement, and some cool personal hobbies or achievements and you can write an interesting and not-boring essay, you can look at it as a random event.  

 

No, it is not a random event. Schools are building a class. They have specific profiles they are seeking to fill. They avoid taking multiple students with the same profile (say tuba playing jugglers). A certain percentage of the slots are being filled by tagged applicants and unless you have that tag, your odds for those spots is 0%.

I disagree in general with the premise that applying to more statistically increases your odds of acceptance.

I posted this this morning in one of the other threads, it might help you get a better view into how outcomes are not random events:

http://www.manhassetsca.org/HighSchool/articles2010-11/DonBettertonpresentation2011.05.17.pdf

ETA: Equally, being a URM with high stats is likely to increase odds of acceptance (25-30% tagged based on the PP).

 

Edited March 12, 2019 by 8FillTheHeart

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1 hour ago, 8FillTheHeart said:

No, it is not a random event. Schools are building a class. They have specific profiles they are seeking to fill. They avoid taking multiple students with the same profile (say tuba playing jugglers). A certain percentage of the slots are being filled by tagged applicants and unless you have that tag, your odds for those spots is 0%.

I disagree in general with the premise that applying to more statistically increases your odds of acceptance.

I posted this this morning in one of the other threads, it might help you get a better view into how outcomes are not random events:

http://www.manhassetsca.org/HighSchool/articles2010-11/DonBettertonpresentation2011.05.17.pdf

ETA: Equally, being a URM with high stats is likely to increase odds of acceptance (25-30% tagged based on the PP).

 

 

No one is saying it's actually a random event. In that part of the thread, we are agreeing that for the sake of a student with all the same awesome stats as all the other incoming students, they could "look at it that way" aka, realize, that, in a way, it's like winning the lottery as far as their "chances" are concerned.  Of course it's not truly random. 

I think you're confusing the actual math part of this thread (what we were discussing with square and dbijou) and the fun, talkie-chatty part of this thread (where we just speculate how one feels about the chances)

Although I started on this thread agreeing with you, and my initial POV that applying to more (of the same type of schools) does not increase one's chances of admission, I think the math kind of sort of shows otherwise (I say kind of sort of because of course we also discussed that in this case there are so many reasons you can't perfectly use probability math on college acceptances- everyone agrees to that...since the colleges are looking for some things which are subjective and unique to each college) 

Edited March 12, 2019 by Calming Tea

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IN my son's case I doubt it's 25% wouldn't that be nice !

There's a ton of subjectivity involved, that no one can predict.  SO I guess that's random.

Edited March 12, 2019 by Calming Tea

[8filltheheart]

1 hour ago, Calming Tea said:

IN my son's case I doubt it's 25% wouldn't that be nice !

There's a ton of subjectivity involved, that no one can predict.  SO I guess that's random.

Sorry to be so non-compliant, but I don't think the "no one can predict" is completely accurate.

Know definitively? No one outside of admissions does know. But probability? There are certain students that you can say with a high probability will be accepted. So that is not really never predictable.

[Arcadia]

5 hours ago, square_25 said:

I wish they did more of it in school! It's so hands on, too :-). Like, I think people started thinking about probability when thinking about games of chance! That would be a fun intro. 

 

Grade 6 and grade 7 math Common Core. It prep my kids well enough for SAT and ACT. (ETA: the probability and statistics portion just to clarify)

http://www.corestandards.org/Math/Content/6/SP/

http://www.corestandards.org/Math/Content/7/SP/

Edited March 12, 2019 by Arcadia

[daijobu]

7 hours ago, Calming Tea said:

 

I mean it's not like I'm buying my College Mom Hoodie, based on this thread.  Don't worry! 🙂

 

Whatever you do, DO NOT BUY A COLLEGE HOODIE until after your student has been admitted.  Doing so will anger the college admissions gods with your audacity and jinx your student's probability.  Buy a college hoodie --> your chance of admission is cut in half. 

That's a scientific fact.  

[daijobu]

On the flip side, if your student doesn't play soccer, you can pretend he does, pay off a few people to claim he's in fact a soccer star, and get him in to college through the "side door."  

Who knew?  

https://www.stanforddaily.com/2019/03/12/head-sailing-coach-terminated-after-agreeing-to-plead-guilty-to-bribery-charges-in-admissions-scandal/

Edited March 12, 2019 by daijobu

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I know right! That thing ended up in the media at an interesting time 

[lewelma]

The waiting is so stressful! I remember it not so fondly. Hope you guys get at least one good option! 

[mathnerd]

On 3/12/2019 at 4:36 PM, daijobu said:

 

Whatever you do, DO NOT BUY A COLLEGE HOODIE until after your student has been admitted.  Doing so will anger the college admissions gods with your audacity and jinx your student's probability.  Buy a college hoodie --> your chance of admission is cut in half. 

That's a scientific fact.  

In that case, my son will never get admitted to Stanford, MIT or Caltech 😝 I bought him the hoodies when we were around those universities on vacation (and he was under 10 years old). Maybe the Admission Gods might look the other way if the child with the hoodie is an elementary school student? Stay tuned. I will post back on the outcome in about 7 years' time.

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On 3/13/2019 at 9:44 PM, mathnerd said:

In that case, my son will never get admitted to Stanford, MIT or Caltech 😝 I bought him the hoodies when we were around those universities on vacation (and he was under 10 years old). Maybe the Admission Gods might look the other way if the child with the hoodie is an elementary school student? Stay tuned. I will post back on the outcome in about 7 years' time.

 

You're ok.

It's the COLLEGE MOM HOODIE That will permanently curse you if you buy it before admission.  Bumper sticker is double curse.