Is there something wrong with my logic?

<p>Why isn’t each admission decision an independent event, with a unique probability? It’s irrelevant that they’re driven by the same factors. It’s not as if acceptance into a school is conditional on the admissions decisions of any others.</p>

<p>Good question. </p>

<p>To say that two events are independent means that if you had some information about one of them, it would tell you nothing about the probability of the other. </p>

<p>Let’s take an example. I give you two students, Al and Bob. I tell you nothing about them except they are both applying to Harvard and to Yale. </p>

<p>Let’s assign your prior probabilities can be around 0.07 for either student to be admitted to either college. </p>

<p>Now I tell you that Al got into Yale SCEA. Do you think his probability of getting into Harvard is still 0.07, the same as Bob’s, or do you think it might be higher. I think it’s higher. </p>

<p>The reason they are not independent is because both school use similar criteria to choose their students. Sure the final decision may have some differentiating factors, but the factors that are the same are very significant. Knowing something about one decision tells you something about the probability of the other. Hence they are not independent.</p>

<p>Now consider Al and Bob again and you have no information about either of them other than the fact that Al had eggs for breakfast today. Are their probabilities of admission now different? I don’t think so. I don’t think Al’s choice of breakfast says anything about the admissions probabilities. </p>

<p>Does that help?</p>

<p>Oh, I see. However, that implies that the probability of getting into a specific top-tier school is roughly constant. If I assign myself a 5% probability of getting into any specific top 20 school, then i still have a 54% chance of getting into any one of them. Fingers crossed.</p>

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<p>It’s not in the common data set. A few colleges (including Brown and Princeton) publish it online; most don’t. </p>

<p>But you don’t need that much detail to follow my strategy (post #29). Just look up the 25th and 75th percentile SAT CR score for each school, and compare your score; if you’re above the 75th percentile score, you’re in the top quartile. If you’re above the mid-point between the 25th and 75th percentile, you can assume you’re in the 2nd quartile. Then do the same thing for SAT M. Then the same thing for (unweighted) GPA. If you’re in the top quartile for all three (CR, M, and GPA) and the school’s admit rate is 50% or higher, you can probably count it as a safety (though the higher the admit rate, the safer it is). If you’re in the top quartile for 2 of the 3 scores and in the second quartile for the third, and the school’s overall admit rate is in, say, the 35-50% range, you can count it as a match. Anything with an admit rate of 30% or less I’d count as a reach, no matter how you stack up relative to its 75th percentile scores.</p>

<p>You can also add a score for SAT W if you like, but many colleges still don’t use this, or weight it less heavily than CR and M, so I wouldn’t lean too heavily on a strong W score.</p>

<p>I’m not following the 54% thing yersini. :)</p>

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<p>The odds are 50-50: either he will get in or he won’t. However, he has his fingers crossed, so that improves his odds by 4%. ;)</p>

<p>^^^^ Hey, no fair asking BillyMc for the solution.</p>

<p>@MisterK</p>

<p>I am applying to 15 top tier schools. Assuming that the probability of acceptance to any single school is 5%, the probability of rejection from any one school is logically 95% (counting waitlistings as rejections, for simplicity). The probability of rejection by all of them (yikes!) is .95^15, or .46. Thus, the probability of getting accepted to at least 1 of them is 1-.46, or .54.</p>

<p>How many kids in the country have the qualifications that you have outlined? How many spots do the top 20 schools have? How many will they really have when you count the overlaps? You know that top certain students will be applying to a number of those schools and may get accepted to all of them. Most top students, the very top kids will be accepted to multiple schools on that list. Then you have the kids that those very schools will be accepting that don’t meet the criteria that you have outlined but have something else that the schools want such as development, legacy, URM, athletic, celebrity, special talent, first generation status. </p>

<p>So there may not be spots for all kids with those stats for those schools. So that means some of those kids are not going to get into any of those schools, if like the game of musical chairs, we start taking spaces away for various reasons. </p>

<p>The reason some kids are not accepted to some schools is not that they are not qualified but that there is only so much room and sometimes luck, chance plays a role in their not getting a spot. So that plays a role in some of those kids with the stats you outlined not getting a spot. They are not shoo ins, in fact have very little chance at the very top schools without some big hook, so a number of them are going to be flushed out right there. I know a number of such kids and to get into HPY, it’s not a good chance without some hook there. So when you start looking at those schools where such kids truly have a shot, it’s not the top 20 schools but maybe the 10 schools after the top 20, and as said before a lot of kids applying to the upper group will be in that batch too.</p>

<p>I know a lot of kids with 2200 SATs,3.7+ average UW going up past 4.0 weighted, with very good ECsbut no hooks. HPY without any other hook isn’t going to cut it for them except as a lottery ticket. Unless they are high tech kids, MIT and CIT are not good picks either. Stanford is also a lottery ticket school even for kid with even higher stats and Columbia’s selectivity this year was second only to Harvard which doesn’t make that a very likely school for this person without a hook. Brown and UPenn get enough kids from the NE applying to them that both schools say that, yes, all things equal, the geographics can matter. That’s nearly half the schools off the list. Anyone would have to say it is highly unlikely this student with those stats from the NE is going to get into the above mentioned schools. </p>

<p>So s/he applies to Cornell, Duke, Dartmouth, UCh, NW, Vandy, WUSL, RIce, JHU, ND and whatever the heck #20 is these days. I think I would tell such a kid that s/he better have some safeties. I wouldn’t bet anything that s/he would get into one of those reaches. My son has a number of friends with those stats that didn’t get into those schools. Would they have gotten into the ones that they did not apply to, had they also been on the list just out of sheer probabilities? And would adding HPYCS up their probability of getting into one of the ten? I don’t think so.</p>

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<p>I don’t know where you got the 5% from, but it doesn’t sound right. I’d be surprised if you can find 15 schools where you have a probability of .05 of getting into. I think if you looked on Naviance, you’d find that for some of them, you have a probability of 0.00, and for some you have probabilities considerably higher than 0.05. </p>

<p>For example, if you are male, your probability of getting into Wellesley is zero barring a clerical error, but if your female, it’s probably considerably higher :-)</p>

<p>If we use this illogical 54% number, everyone who applies all 20 top 20 schools stand a very good chance irrespective of their CV.</p>

<p>Well, we’re applying the 5% probability to people with specific, rather subaverage stats (3.7 GPA/4.5 WGPA, 2200 SATs, respectable EC’s).</p>

<p>5% is the general number used for anyone’s chance next year when Harvard’s applications hit 40,000.</p>

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<p>You can’t use that formula because the admissions decisions at each of those schools are not independent events. </p>

<p>If two events are independent, then knowing how one event turned out would not change your probability estimates for what will happen with the second. For example: two coin flips are independent events. Suppose I hear that the first coin landed heads. My estimation of the probability of the second coming up heads will not change due to this new piece of information. It is still 50%. </p>

<p>However, two college admissions decisions are not independent events. Suppose a kid applies to both Harvard and Yale. I know nothing else about her, so my baseline estimate of her chance of getting in to each is 6-8%. But then I hear that she got into Harvard. Due to this new piece of information, my estimation of her probability of getting into Yale has now changed. It is higher. Therefore, these two events are not independent. The formula you used only applies to independent events.</p>

<p>yersiniapestis, </p>

<p>I still don’t think you get it. You have no basis for choosing 5%, and you have not removed the dependencies. </p>

<p>I’ll look up your stats on our Naviance just to demonstrate what I’m trying to get across. I’ll round to the nearest 5%. The data includes 2007-2011. YMMV</p>

<p>Harvard: 0
Princeton: 0
Yale: 0
Columbia: 0
Stanford: 0
Penn: 0.2
CalTech: 0
MIT: 0
Dartmouth: 0
Duke: 0.15
Chicago: 0.5
Northwestern: 0.5
Johns Hopkins:0.3
Washington U: 0.3
Brown: 0.1
Cornell: 0.25</p>

<p>Now after looking at this, we’ve removed the dependence on stats from your school, things are much closer to independent. Maybe close enough to treat that way. You’d have to be a fool to put the effort into applying to all 8 schools where you have an infinitesimal probability of admissions. I would pick one just because studies show that your future earnings correlate more with the highest ranking of the school that rejected you than the ranking of the school that you actually go to, LOL! Let’s pick Harvard. </p>

<p>The remaining 8 schools (there were 16 top 15 schools) paint a much brighter picture: </p>

<p>Harvard:0
Penn: 0.2
Duke: 0.15
Chicago: 0.5
Northwestern: 0.5
Johns Hopkins:0.3
Washington U: 0.3
Brown: 0.1
Cornell: 0.25</p>

<p>If this was your ranking in terms of preference, you would have the following probabilities of attending, which is the probability of getting accepted times the probability of getting rejected by all of your choices with higher preference:</p>

<p>Penn: 0.20
Duke: 0.12= 0.15<em>(1-0.2)
Chicago: 0.34=0.5</em>(1-0.2)*(1-0.15)
Northwestern: 0.17
Johns Hopkins:0.05
Washington U: 0.04
Brown: 0.01
Cornell: 0.02</p>

<p>You’d still have a 0.06 probability of not getting in anywhere. An intelligent application strategy might be to set a threshold on probability of attendance at 0.05. In that case you’d eliminate Brown, Cornell, and WashU. Would it be worth your time and effort to still apply to Brown in this scenario where it is your 8th choice - obviously no. At that point, you still have a 12% chance of having no school, so I’d add another match (40-90%) and a safety (or two). Suppose I added a match like Notre Dame with a 0.5 probability, and a safety like UMASS. </p>

<p>So you’d have the following probability of attending
Harvard 0
Penn: 0.20
Duke: 0.12= 0.15<em>(1-0.2)
Chicago: 0.34=0.5</em>(1-0.2)*(1-0.15)
Northwestern: 0.17
Johns Hopkins:0.05
Notre Dame: 0.06
UMASS:0.06</p>

<p>There you have it, 8 schools, 4 reaches, 3 matches and 1 safety. </p>

<p>Suppose instead, your preferences were in order of admissions probability. That will make your list longer. Then your probability of attendance would be </p>

<p>Harvard 0
Brown 0.1
Duke 0.14
Penn 0.15
Cornell 0.15
Johns Hopkins 0.14
WUSTL 0.10
Chicago 0.11
Northwestern 0.06
UMASS 0.06</p>

<p>So you’d have 10 schools to apply to, 7 reaches, 2 matches and 1 safety. </p>

<p>Of course, you’d also be a fool to base your preferences totally on ranking in a magazine or on admissions probabilities, but I hope this hypothetical scenario demonstrates how you can use conditional probabilities from Naviance in an intelligent manner to figure out how many schools to apply to and which schools are worth the effort.</p>

<p>Yeah, there is something wrong with your logic. Suppose we have two events A and B. </p>

<p>P(A and B) = P(A | B) * P(B)</p>

<p>The probability that A and B will happen is the probability that B will happen times the probability that A will happen knowing that B has happened. By multiplying the rejection percentages together, you are assuming that P(A and B) = P(A) * P(B), which carries the assumption that P(A | B) = P(A). You are assuming that knowing B does not affect the probability of A. That is not true. </p>

<p>Suppose you applied to Stanford, Caltech, and Berkeley. Not knowing any of your acceptances, you can assert that you have a 10% chance at Stanford/Caltech, and a 20% chance at Berkeley. Let’s say you first get accepted by Stanford and Caltech. Now your probability of getting accepted at Berkeley is much higher, because most applicants who get into Stanford get into Berkeley.</p>

<p>IMO there is a random element to it, but it isn’t completely random either. There are “squishy” elements to one’s application that are not quantified in US News, but are very important in the context of the holistic admissions processes of the most selective colleges. So for example if you have a teacher’s rec letter that says you’re basically a tool who contributes nothing, that will be looked at as a less favorable aspect by readers at all the schools,not just some of them.</p>

<p>There is some degree of commonality (though incomplete) in what they are looking for, beyond mere published stats, so their review process while appearing random to a decent extent should not be completely random either IMO.</p>

<p>So each college’s decision is not really completely independent of each other college’s, since they are all seeing the same (mostly) application, which includes essays, rec letters, extracurriculars, and they are not completely random, between each other, in how they view and evaluate all this data.</p>

<p>You don’t need a pure statistical model to see this situation… Most 2200 SAT, 3.7 uw kids don’t have a shot at HPY. Adding those schools to their college lists isn’t going to increase their chances of getting into Emory, Cornell or JHU. Also those kids who get into HPY are very likely to be accepted to any of the schools on the lower end of the top 20 spectrum. </p>

<p>I think things loosen up quite a bit after you eliminate the 10 most selective universities from ones’ lists. That is when the odds of such a student getting into one or a number of such schools on such a list become quite good. </p>

<p>A young man with near perfect SATs, and grades that were also very high in difficult course at a “good” school that only gets a few kids to the most selective colleges each year, applied to all of the ivies, Amherst, Williams, Swarthmore, Bowdoin,…some other highly selective LACs. The parents were absolutely demoralized at the results. Didn’t get into any of them. Was waitlisted at several of the “next tier” in selectivity of schools and did end up at one of them after an excrutiatingly painful time. </p>

<p>When you are looking at schools with such low accept rates and tally up how many acceptances go out in total and how many applicants there are, you can see how tough this is going to be, especially considering the fact that the top picks are going to take up a lot of those acceptance spots. You also have to take into account that there are kids with stats lower that are going to get those spots due to hooks and the wants/needs of these schools.</p>

<p>OP said: “What about the stats I just outlined? What group do they fall in, Ivy-wise?”</p>

<p>The stats fit well with applicants who are accepted and those who are rejected.</p>

<p>1) For the HYed schools, most applicants are highly qualifed and most are denied admissions. For example, Brown denies ~80% of valedictorians, ~70% of those with a perfect 36 on the ACT, ~ 75% of those with an 800 SAT Math and ~80% of those with an 800 SAT CR. </p>

<p>2) Since the schools you are concentrating on are quite different from each other, the same applicant will “fit” with one and not with others. For example, Columbia has a defined Core curriculum that all student must follow, while Brown has no breadth requirements. A brilliant student who needs curricular structure will have a much more difficult time being accepted into Brown, all else being equal.</p>

<p>3) What matters most to the schools - and that should matter most to you - is fit. Concentraing on the HYPed schools and prestige has little to do with you as an applicant; it just means you’re chasing Collegiate American Idol. Kids who do only that run the risk of not being accepted anywhere.</p>

<p>Bottom line: whether you apply to 1 school ED, 4 schools (the national average) or 8-10 schools (a cultural norm here at CC?), make sure that these schools are a good “fit” for you , whether reaches (like all the schools you are concentrating on), matches, safeties, or “financial aid safety schools.” </p>

<p>So, go for it . . . and LOVE THY SAFETIES . . . you have a greater chance of needing them than being accepted into those HYPed schools.</p>