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<p>Could mean the GC is stupid.</p>
<p>Could it be that the guidance counselor was talking about a person who does not have the stats for Ivy? In a matter of speaking, 0.01% x 8 is 0.08 % if the probability is uncorrelated, practically zero no matter what.</p>
<p>@soccer92boy, #19: With regard to the student “challenging the thought from adults,” I’d advise treading somewhat carefully where the guidance counselor is concerned.</p>
<p>Challenging the thought from adults is excellent as a mind-set, if it means that one is not simply accepting what some adults say (and instead, reasoning for oneself).</p>
<p>However, confronting the adult with the challenge will receive variable responses. A reasoned argument presented to a professor in math or the natural sciences will generally receive an enthusiastic response (in my experience), whether the argument is right or wrong, because progress in those fields often depends on challenging the established ideas. </p>
<p>On the other hand, a GC may have to deal with time constraints, other students’ needs, non-college advising issues, . . ., and so may not welcome the challenge, and even view the student as troublesome. In this circumstance, I’d suggest picking a relatively small number of the Ivies, with well-considered reasons for applying to each.</p>
<p>As far as the independence of the decisions goes, I think the decisions are actually independent–except perhaps for the time when a Princeton admissions representative hacked the Yale site, to see who had been admitted to Yale. The decisions are made at each school without knowledge of the decisions of others. </p>
<p>bovertine raised some interesting issues, but I think those issues could be treated in a model where the student’s chances of admissions vary from school to school, and are often quite different from the raw odds. The student’s odds at the various Ivies are clearly correlated with each other, depending on the quality of the student’s applications. (Correlation of independent decisions would then reflect the correlation of the underlying, true, but unknown odds for a particular individual. I use the idea of odds because I think that there is still some randomness left in the decisions, even after the quality factors have been accounted for.) </p>
<p>In two scenarios, if the goal is to secure at least one Ivy admission, a student gains no advantage by applying to multiple schools:
a) If the probability of admission is actually 0 at each of the schools, and
b) If the probability of admission is 1 at one of the schools to which the applicant has applied. In this case, multiple applications could (obviously) yield more acceptances.</p>
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<p>It may not, but assuming you are applying for schools which are at least somewhere within your reach, there is no way it can make your chances worse, from a strictly mathematical formulation (unless, like I said, it affects the quality of your applications). I guess that’s what you’re trying to say in your second paragraph.</p>
<p>I’m assuming every student is applying to a grouping of schools they would like to attend and at which they at least have a reasonable chance. And I don’t think we are talking about just Ivy schools. Let’s say we’re talking about a group of forty extremely selective schools.</p>
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<p>In this sense, of course the decisions are independent. What I was trying to get across is that I believe similar criteria effect the chances of admissions in similar ways at various schools. I guess I should have said it isn’t a truly random variable. In other words, it is unlikely that a student who has a 80% chance of admittance at one school would have a 20% chance of admittance at another similar school.</p>
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<p>Yes, I suspect that scenario (a) may happen with some regularity, as umcp pointed out. I’m not sure about scenario (b).</p>
<p>Well, here’s my little anecdote to add to the statistical analysis: dd applied to three Ivies, among her other schools. She got one rejection, one waiting list, and one acceptance. </p>
<p>Her GPA and SAT were at the top of their range, no national honors or awards, no particular hook, but she did have a couple ECs that were somewhat unusual, and I realize now, those might have been appealing to the particular school where she got in.</p>
<p>I always feel bad when I read things about “fishing,” because it assumes we know what motivated a kid to apply to several Ivies. One thing I have learned over many years, is that we can see WHAT someone does, but we can not usually truly understand WHY they do it.</p>
<p>My dd, in CA, wanted to experience life on the east coast. She wanted a school with rigorous academics and a very low faculty:student ratio. She didn’t want to be a “stand-out,” she wanted to fit in intellectually and academically, and be inspired and challenged by her fellow students. We needed a school with generous financial aid.</p>
<p>She didn’t “love her safeties.” She would have gone and I have no doubt that she would have been very happy, because she is that kind of person, but they actually were fundamentally different than her reach schools.</p>
<p>This is a classic example of the “gamblers fallacy.” The false belief that the length of a loosing streak has a posititve causal relationship to a win being right around the corner. Each school (Ivy or otherwise) is its own individual crap shoot.</p>
<p>bovertine, I definitely agree with you that the odds for a given student are strongly correlated, among the various schools; also, there will be some trends in the odds for a given type of applicant (higher or lower) at different Ivies.</p>
<p>I think there is still an element of “randomness” in the outcome, after all that has been taken into account. A particular student has some (unknown) odds at each college, rather than a definite 0 or 1, until the decision is actually made.</p>
<p>Suppose that an absolutely identical application (aside from name and SSN) could be submitted multiple times to a college, either in the same year or in different years with very similar circumstances (and barring recognition of the multiple copies, by the ad com). Do you think that the decision would be the same each time? </p>
<p>I think that the decisions would usually be the same. However, I think that there would be a number of applications that are “on the cusp,” so that these would receive some distribution of admissions/rejections.</p>
<p>Most likely, if the decisions did turn out to be different, the outcomes would reflect some underlying causal factors that are beyond the applicant’s control or knowledge. So this would not be truly random, I agree, yet it would be effectively random from the applicant’s point of view.</p>
<p>To give a couple of examples, suggested by stories told elsewhere on CC:</p>
<p>Suppose that a student with high scores, high GPA, and strong extra-curriculars is also an all-state oboist. The student checks the university symphony web site and discovers that all of the oboists are graduating! The application goes in. The general presumption on CC is that oboists are in luck! But the admissions director has suddenly grown tired of people playing the oboe in order to increase their admissions chances. The orchestra will have to recruit grad-student oboists for a year or two.</p>
<p>A Stanford admissions representative apparently commented to a student that the rep was looking for evidence of passion in an application, to assess intellectual vitality. The rep stated that it was fine if a student was passionate about shopping. So a student who is otherwise qualified applies, highlighting his/her knowledge of every Manolo Blahnik for sale anywhere in the U.S. But meanwhile, the director of admissions has been talking to the ad rep, and saying, “You know, a passion for shopping is not actually quite what we are looking for.”</p>
<p>Other possibilities: the application is read early/late in the cycle, or the ad rep knows someone from the student’s high school or area and likes/dislikes them, or shares/does not share an extra-curricular interest, or the ad rep is coming down with a cold, or is about to go on vacation . . . I know that there are many safeguards in the process to limit the influence of this sort of thing, but in the end, the applications are being read by human beings, and I don’t think the outcomes are 100% replicable.</p>
<p>historymom, the odds really do go up, for receiving at least one admission, if a student applies multiple places (with fixed odds at each one). </p>
<p>Agreed, if a coin is being tossed, the odds of heads are no better after a string of tails, tails, tails, tails, tails, . . . than after a string of heads, heads, tails, heads, tails. In fact, in the first case, the coin might not be fair, so the odds of heads would be lower.</p>
<p>But the issue of applying to multiple Ivies with the hopes of admission to at least one are more like tossing a coin twice vs. five vs. eight times, with the desirable outcome being at least one head. (Or maybe rolling 20-sided dice would be a better analogy, given the raw odds.)</p>
<p>If the guidance counselors at my kids hs didn’t limit the number of schools kids applied to then all of them would apply to all the Ivies and all the US News top schools - having visited none of them or even knowing the differences between them.</p>
<p>Quant Mech thanks for explaining. Are you saying then that the odds do not go up at an individual campus but for the Ivies as a group?</p>
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<p>I don’t believe this is a correct analysis. It assumes the probabilities are independent, and they clearly are not. Here’s a counterexample: Suppose your chance of getting into Yale was 10%. Suppose if you didn’t get into Yale, you had no chance whatsoever of getting into Harvard or Princeton, but if you were lucky and did get into Yale, you had a 50% chance of also getting into Princeton and an independent 40% chance of also getting into Harvard. Then your chance of getting into Yale would be 10%, your chance of getting into Princeton would be 5% and your chance of getting into Harvard would be 4%. But your total chance of getting into one of the three would remain 10%.</p>
<p>That’s a contrived example, but in general, a student’s chances of getting into Harvard are not independent of their chances of getting into Yale. The kind of student accepted from Harvard is similar to the kind of student accepted by Yale. The kind of student rejected out of hand by Yale is similar to the kind of student rejected out of hand by Harvard.</p>
<p>I see a lot of people have already replied, including some more mathematically astute than I. What do you think about my old FAQ on this subject? </p>
<p>APPLYING TO ALL EIGHT IVIES </p>
<p>Wrong extreme idea 1: </p>
<p>Some students “reason” that if an applicant applies to all eight Ivy League colleges, his chance of admission at any one of them is the same as the average base admission rate for all of them (which is wrong assumption a). Then the students “reason” that because the eight admission committees don’t all meet in the same room, that they select students “independently” in the STATISTICAL sense (which is wrong assumption b). The students then misapply a formula learned in high school that only applies to differing situations, to calculate that the chance of getting into some Ivy League college is almost a sure thing. </p>
<p>What’s wrong with wrong assumption a is that a weak applicant for admission at the least selective Ivy League college is a weak applicant at all the other colleges in the league, and that means that applicant’s chance of admission anywhere is well below the base rate of admission for any Ivy League college. </p>
<p>What’s wrong with assumption b is that usually colleges don’t have to actively collude to end up choosing similar kinds of applicants. ALL colleges prefer stronger applicants to weaker applicants. A teacher of statistics explained to me what “independence” means in the sense used by statisticians: “What is independence? It means that when you learn about the outcome of one event, it has no influence on your guess about the probability of success in another event. However, in this case, if a student gets rejected from 8 schools, that DOES influence my guess about how likely he is to get rejected from the 9th school. I’d say someone who gets rejected from 8 schools is more likely to get rejected from the 9th than someone who didn’t get rejected from 8 schools.” In other words, even if colleges act independently in the layman’s sense of the term, you can’t use the multiplicative rule of probability to figure out the joint probability of being admitted to one out of the eight Ivy League colleges. Plenty of students get rejected by all eight. </p>
<p>Other threads from time to time bring up </p>
<p>Wrong extreme idea 2: </p>
<p>Ivy League admission officers are thin-skinned and personally offended if you apply to their “competitors,” and will reject you if you apply to all eight Ivy League colleges. </p>
<p>Well, that’s just ridiculous. There are plenty of students each year who are admitted to more than one Ivy League college (of course, those are rather extraordinary students) and there are at least a few each year who apply to all eight and are admitted to all eight. Ivy League colleges do NOT collude in this manner when making admission decisions. They admit the students who they think will fit well into the next entering class and contribute to the campus community. The bottom-tier Ivy League colleges admit a lot of students who don’t enroll (that is, those colleges have rather low “yield,”) because they admit some students who prefer to enroll at one of the OTHER Ivy college colleges that admitted them. Each college has its own tricks, in five cases including binding early decision programs, to identify students who genuinely prefer that college, but in the regular action round, every college admits some students who are also admitted by some of the other Ivy League colleges, perhaps all of the Ivy League colleges. </p>
<p>Bottom line: don’t worry about either wrong, extreme idea. Apply well to all of the colleges that interest you. There is little point in applying to a college you wouldn’t possibly attend if admitted, but there is every reason to apply to a college you like, because you can’t get in if you don’t apply. </p>
<p>Good luck in your applications. Don’t use calculations that apply (well, maybe they do) to coin flips or dice tosses to guess what will happen to college applications.</p>
<p>CardinalFang, the effect of the student’s accomplishments and potential is included in the values of pH, pY, and pP. These numbers are not the raw odds for all applicants, but will be higher or lower, depending on the qualifications of the student (and the preferences of the colleges). However, if a given student actually has a 50% chance of getting into Harvard (so pH = 0.50), that student’s odds of getting into Yale (pY) are unaffected by whether they do get into Harvard or not–unless Yale and Harvard ad coms are conferring.</p>
<p>(For clarity: my analysis assumes that the decisions are made independently. It does not assume that the probabilities of admission to Harvard, Yale, and Princeton, namely pH, pY, and pP, are independent–indeed, they are most likely strongly correlated.)</p>
<p>Hi, tokenadult. If you go back to my original post, I think you’ll see that we agree, although we are expressing things differently. I am not claiming that the process is like coin tosses or rolls of the dice, where each applicant has equal odds (the raw odds) of success. I have stated that the odds for a given applicant (which I called pH, pY, and pP, for HYP) depend on the applicant’s qualifications. However, I still think that there is an element of randomness in the process. That is why I think that probabilistic analysis is applicable, taking into account that the pH, pY, and pP values may be very close to 1 for some applicants, and very close to zero for others. Still, I’d guess that there are quite a few applicants whose true odds of admission are about 0.25 to 0.75.</p>
<p>And I emphatically agree that students should apply to colleges that specifically interest them, rather than casting a wide net for a category (such as Ivies).</p>
<p>This question keeps coming up on C.C and I am continually amazed by some outrageous and non-quantitative beliefs that are held with almost religious fervor by many. My thoughts on this issue:</p>
<p>Yes, the probability of admission to any one highly selective college (ivy or otherwise) goes up if you apply to more of them.</p>
<p>No, the probabilities are not additive, so applying to ten colleges with 10% admit rates does not give you a 100% probability of admission to at least one of them.</p>
<p>Yes, there is an element of pure randomness (exactly like a coin toss) in the process.</p>
<p>No, the process of admission is not a purely random process like a coin toss.</p>
<p>The extent to which the process is random determines how much you increase your chances by applying to multiple colleges. </p>
<p>And here comes the Heisenberg uncertainty principle of applying to multiple colleges:</p>
<p>The act of applying to a large number of colleges is likely to decrease the quality of each application, and hence, can decrease your chances of acceptance at any one college. In other words, you simply could not do a really good job of sending 50 applications. You are better off focusing on a well-constructed list of colleges that are fit you well and ones that you would actually like to attend.</p>
<p>^^agree with vicariousparent, and have to admire the variation on the Heisenberg uncertainty principle!</p>
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<p>I love this analogy. Not precise, I guess, but not totally off base.
Certainly very entertaining.</p>
<p>QuantMech, carefully read what tokenadult wrote. “‘What is independence? It means that when you learn about the outcome of one event, it has no influence on your guess about the probability of success in another event.’”</p>
<p>If I tell you that Applicant A has been admitted to Harvard, does that influence your view about whether he was also admitted to Yale? Of course it does. Harvard and Yale make their admissions decisions independently, in the sense that they don’t collude. But they both use roughly the same metrics, so their decisions are not at all statistically independent.</p>
<p>CardinalFang, I <em>always</em> read carefully what tokenadult writes! I know of tokenadult from the Art of Problem Solving (where I have not posted) as well as this forum.</p>
<p>I think that you are looking at an estimation of the odds of admission in retrospect–sort of like Bayesian probability analysis.</p>
<p>The correlation that you are considering is already contained in my probabilistic model, because pH, pY, and pP are not independent. Those who are admitted to Harvard will have higher values of pH on average than those who are not admitted. Those who have higher values of pH probably also have higher values of pY and pP (excluding the case of a Harvard-specific multi-generation legacy or offspring of a major Harvard donor.) </p>
<p>However, the decision processes are independent, in the following sense: if a student has some true, underlying set of probabilities pH, pY, and pP (which are not known and definitely are not the raw odds), then whether Harvard takes them or not, the value of pY is unaffected by the decision Harvard actually makes. </p>
<p>If we look at a positive Harvard decision in retrospect (which I think you are arguing), then we are justified in guessing that pY and pP are also pretty high, because those values would tend to be high among Harvard admits.</p>
<p>Another assumption that comes into my analysis, as stated above: I am assuming that there is an inherently probabilistic aspect to the admissions process, which is reflected in the fact that pH, pY, and pP may have values different from 0 and 1.</p>
<p>In a somewhat analogous situation, the National Science Foundation actually undertook an experiment to see how replicable their funding decisions were. In my field, they generally circulate a proposal to 5 separate reviewers for ratings. One year, they circulated a set of proposals to two different sets of 5 reviewers, to see whether it would affect the decision to fund or not fund the proposal. My recollection is that the different set of reviewers made a difference to the outcome in about 35% of the cases. (This was some years ago, and it was written up in Scientific American, as I recall.) HYP admissions can’t really run the same test, since they have admissions representatives with regional or subject area responsibilities.</p>
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<p>There is a limit at your school? I hear of school charging money for extra transcripts and recommendations, but I can’t see how they can get away with a hard limit on the number of schools a student can apply to.</p>