A conceptual issue on admissions probability

Applying to College
1

<p>If you've taken any stats, help me think through this.</p>

<p>Prospective students want to know if they've covered their bases with an adequate assortment of targets, reaches and safeties in order to ensure that they aren't left empty-handed at the end of the process. If they can accurately estimate their odds of acceptance to at least one of their top choices, they can avoid paying $65 a pop for unnecessary applications which amount to overkill.</p>

<p>The likelhood of a series of events ALL coming true is equal to each of their odds multiplied together. So the odds of flipping heads four times in a row is .50 x .50 x .50 x .50 = 6.25%. Accordingly, if you look at the acceptance rate for each of the colleges in which you're interested, decide if you are above or below their mean, and estimate a percent likelihood of acceptance to that school, then you should be able to estimate the likelihood of acceptance to at least one of your chosen schools by multilying together the likelhoods of NON-acceptance at each. For example, if your estimated chances at your top five choices are 10%, 15%, 20%, 25%, and 30%, the odds of rejection resulting at ALL of them should be .90 x .85 x .80 x .75 x .70 = 32%, meaning that you have a 68% chance of getting into at least one of them (even though your chances at any one is no better than 30%). Unless . . .</p>

<p>Consider that the same individuals who apply to any one selective school also apply to several other selective schools. So the acceptance rates of your five schools above reflect numerous cases of the same individual being accepted to multiple schools. But does that really matter? After all, that individual can ultimately only attend a single institution, and since you just want a spot in an entering class, does your formula need to adjust for the schools at which that individual was admitted but didn't choose? And are there any other conceptual shortcomings of this way of estimating odds that occur to you?</p>

2

<p>I can understand where you're coming from but how can one reasonably arrive at the likelihood that THEY will be admitted to any single school?</p>

<p>Especially if you're talking the ultra selectives. Sure the overall admit rate is 8 or 9% but how would Joe Student know if his chances really were 50% or 1%? Given the holistic admissions policies of those schools, it'd be only a wild guess at best. Heck, the admissions rep himself or herself probably only has a vague, ball park guess at any given candidate -- and they're the ones going to be arguing for/against the decision!</p>

<p>And then you're multiplying 5 or 6 randomly generated numbers. Might as well flip a coin at that point. </p>

<p>Not trying to be a downer but your initial data generation is near impossible.</p>

3

<p>Once your application is completed and submitted the only variable is the adcom's mood. So your actual chance of admission to one certain college will usually either be (close to) 0 or (close to) 1 and not 0.2 or 0.75. Exceptions are places like Harvard that have to choose from an abundance of equally qualified applicants which inevitably involves some luck.</p>

<p>By the way, you can use the P(A^B)=P(A)*P(B) formula only if A and B are independent events but I doubt that that's generally true for college admissions.</p>

4

<p>Well, theoretically it's correct, but practically it doesn't work, because you can't estimate chances. Look at it this way, admission isn't TOTALLY random, usually it's some thing on your app that keeps you out. So if that keeps you out of one place, it will very likely keep you out of other places. It's not like "harvard admission office has a 30% chance to not spot your F junior year". So, since it's not a perfectly random event, i'm not sure if you can apply that reasoning at all.
Although, of course, you can use it roughly...but only like a wild approximation, which can very likely be 100% off. Because we are talking about actual reality, not a math problem. Statistics is only useful when applied on very big numbers. Tossing a coin gives a 50/50% chance. But if you throw it like 20 times, it's very possible to get something like 16/4. Now, taking into account that you only get one test with applying..statistics won't tell you much.
So in any case, use it for an approximation, but don't count on it, at all.</p>

5

<p>Granted, your approximated odds at any one school will be a guesstimate, and may even be wildly off. But as long as you're equally likely to guess below the theoetically "true" odds on one school as often as you guess above them on another, it probably wouldn't matter. The idea is to calculate the point at which you can stop adding schools to your list in order to be reasonably sure that you get into at least one with which you can be satisfied. I read a post from a young lady a month or two ago who had applied to 28 schools. I can guarantee you that the point of diminishing returns occurs WAY before that!</p>

6

<p>wrong science guys...college admissions is politics not statistics</p>

7

<p>DONT DO THAT! it doesnt work. i tried to calculate my chances like that last year.
if u put together a phenominal application to a reach 10% school you might be admitted but if you write a crappy essay for the 60% match school you'll most likely get waitlisted/rejected. which is what happened to me.</p>

<p>just get together a list of schools you really like (w/matches safe, reach) and go for it.</p>

8

<p>
[quote]
For example, if your estimated chances at your top five choices are 10%, 15%, 20%, 25%, and 30%, the odds of rejection resulting at ALL of them should be .90 x .85 x .80 x .75 x .70 = 32%, meaning that you have a 68% chance of getting into at least one of them (even though your chances at any one is no better than 30%).

[/quote]
</p>

<p>That theory is playing with fire. Trust me, you do not want to approach college admissions in that way.</p>

<p>The bulk of your list should be schools that you like where you have a realistically good chance of being accepted, better than 50%/50%. Then, you want a school or two where you are all but guaranteed admissions. Finally, you might want to add a reach or two, but again, there is no point unless you can identify a realistic reason why they might accept you. An ideal reach would be a school where you have maybe 50%/50% odds.</p>

<p>To make odds predictions, you have to figure how you app stacks up against the other apps in your exact category. For example, a Native American applicant from a reservation in Montana is in a different stack with different odds than a white kid from an affluent New Jersey suburb.</p>

9

<p>interesteddad nails it above. The universe you are competing in is beyond your control and you have no idea how you compare in the pool. As for the coin toss analogy, if you toss a coin nine times and nine times it comes up heads, on the 10th toss, the chance of heads or tails is still 50/50.</p>

10

<p>There is nothing wrong with the basic premise that applying to more colleges increase your chances to be admitted to at least one of them. It is essentially the model used by med school applicants. You need to apply to a large number of schools to get at least one offer of admission. With med schools applications the process is more predictable than with colleges: med schools generally have similar admissions criteria mostly based on MCATs and GPA. </p>

<p>Imagining a simple world where 1) all the Ivies had a 10% admission rate, 2) had the same median SAT scores and GPAs and 3) the only factors used for admission were GPA and SAT scores then assuming 1) you applied to all eight and 2) your SAT and GPA were right at the median you have a 58% chance to be accepted to at least one of them. If having the Ivy label was all important and you did not care about which school you attended, that is obviously a lot better than 10% for any individual Ivy. If you wanted to attend a top 20 school and did not care which you would have close to a 90% chance to be admitted to at least one of them if you applied to all. </p>

<p>We clearly know that college admission is not that simple, that most top colleges use holistic approaches where GPA and SAT scores, while important are not the sole criteria for admission. Even worse the other metrics can be very vague, are seldom explicit and could vary from admissions officer to admissions officer. In addition, factors such as geography, economic background, gender, choice of major also play a role to the extent the schools are seeking to create a balanced student body. </p>

<p>Does that mean that a statistical approach is useless? I don't believe so. If that were true, high schools guidance departments would not be adopting tools such as Naviance. With enough research you can get a feel for the chances for a particular kid from a particular high school to get into a specific college. If your HS regularly sends 4-5 unhooked students per year to Harvard comparing an applicant's hard stats to the admitted and rejected students in prior years, will provide an estimate of chance of admission. It is obviously harder if nobody ever applied to a particular college from that HS, but again places like CC specifically gather useful admissions data. With such an approach you CAN develop a system to assemble a range of colleges with mostly reaches, a few matches and a safety with reasonable estimates of admission into each group. The more schools in each group the lower the variance from the original estimate. </p>

<p>I developed and used such a system with my D this past year, targeting 12 reaches (stats above the median of admitted students but below the 75% percentile), 5 matches (stats above the 75% percentile) and 1 safety (above the 90% percentile) among the schools that interested her and offered the specific program she wanted to study. She got into 5 reaches (42%), 3 matches (60%) and her one safety. She had visited every school except 2 and was willing to attend any one of them if that was her only choice. Although 8 admission offers may sound excessive, less than half of the colleges offered adequate financial aid packages, so it really came down to picking between two to three good choices in the end. Despite all the research and costs involved, I would do all over again.</p>

11

<p>cellar:</p>

<p>Note that your daughter's odds at any one of her colleges were radically better than the odds outlined in the original post. </p>

<p>With stats above the 50th percentile (I'm assuming you factored class rank and the whole shebang), then she was a legitimate applicant at her reach schools, confirmed by the fact that she got into 42% of them. Note my definition of a "reach" above as a school where you have roughly a 50/50 shot. You and I clearly view things the same way. Your definition of a match and a safety corresponds with mine, too -- again considering the totality of the app, not just the SAT scores.</p>

<p>That's a far cry from the 10% percentages cited in the original example. That math....applying to a whole bunch of schools where your individual app has a 10% chance and thinking you can make it up on volume....is dangerous as heck.</p>

<p>Basically, what I'm saying kids....don't count on Harvard unless you can come up with specific reasons why your app has a much better than 10% chance of acceptance.</p>

12

<p>Obviously, applying to a lot of schools stretches your apps thin, particularly if you apply last-minute. I applied to 13 schools and, while I got into Amherst and am very excited about it, I would not do that again. It is a crapshoot in a number of ways; for instance, between two schools which you like equally well and think you have an equal chance of getting into, you might be accepted at one and not the other - so if you're trying to minimize applications, what if you apply to the "wrong" one?</p>

<p>Of course, safeties are vital; I had 3 definite safeties and one more assumed. If I hadn't gotten into any of my top choices, any of those schools would have been great for me (though it still would have been hard to choose). But 1 or 2 safeties probably would have been enough, and I didn't need so many matches and reaches, either.</p>

13

<p>If an event is completely random and due to chance, then those probability rules apply. Admissions are far from random.</p>

14

<p>I actually did something like this. I think that I calculated a 90% chance of getting into at least one of my schools. It's obviously not a mathematically rigorous or statistically sound method of estimating chances, but I think that it could be useful as a rule of thumb. Assuming that your scores fall at least in the school's midrange, because that's the easiest method of estimating your competitiveness as an applicant, you should apply to enough schools that you feel comfortable with your estimated chance of not getting in anywhere.</p>

15

<p>idad:</p>

<p>Yes, we agree. A school where a student's stats is around the median will typically result in a 25 to 50% acceptance rate, therefore still a reach. Absent a major hook, a school where your stats are significantly below the median of admitted students is not a reach but a "hail Mary" in my book. Furthermore, if you intend to apply to a medical, law or business school after college, you generally need a reasonably high GPA in college. If you are well below the median coming in, it is not very likely you will be at the top coming out. With this type of definition of a reach school, one technically need not worry about having many matches or safeties. With enough schools in the reach pool, you are bound to get a hit at some point. With greater trust in the model, My D and I would have saved the time and expense of applying to matches and safeties. </p>

<p>With these caveats, the admissions process need not be completely random for a statistical approach to the admissions process to work well. You just need enough randomness or unpredictability. Beyond the anecdotal evidence of the kid with perfect stats rejected from all his top choices, we know that schools within a specific range of selectivity rank prospective candidates differently. If top schools all ranked applicants in the same order, you would have a much greater overlap in admissions that what actually is happening. Acceptance rates would increase quickly as you went down the list and yields would drop just as fast. But that is not true, at least among the top schools: they can all maintain low admission rates and high yields. Every student admitted to Harvard is not also admitted to Yale, Princeton, Stanford or MIT. If that were true, Yale, Stanford and MIT (all without a binding early decision program) would not have yields of 70%. Actually the vast majority are only accepted to one top school. Every student admitted to Williams is not also admitted to Amherst or Swarthmore. There are actually extremely few "supercandidates" virtually assured of admission at any top school. And the definition of a supercandidate differs radically at Harvard from MIT for instance. </p>

<p>Every highly selective college recognizes that the number of qualified candidates is at least 2 to 3 times greater than what they can enroll. Even veteran college interviewers have given up predicting which student will be accepted. So, as long as the student is legitimately qualified, he can only improve his chances of getting into a reach school by increasing applications to other schools with similar selectivity profiles. With enough research and applications he can reach a certain level of confidence of being accepted to one of his top choices. </p>

<p>The much worse decision is for a student to actually apply to too few reach schools for which he is qualified and get accepted to none and then have to pick among matches or safeties where he is overqualified.</p>

16

<p>cellar:</p>

<p>I think that the distinction you and I are both making is that we are talking about "credible reaches" rather than just reaches. You have to look at the totality of the application (scores, class rank, curriculum, demographics, and "something interesting", or lack thereof) and evaluate whether you have a prayer.</p>

<p>Too many kids just look at the median SAT scores. At elite colleges, that's meaningless because the SAT scores of the applicant pool are often the same as the SAT scores of the enrolled class. In other words, the SAT scores won't get you accepted.</p>

<p>A classic failure is to not look at your specific grouping. For example, looking only at the SAT scores for UVa is a huge mistake if you are applying out-of-state. The actual SAT scores for out of state students is probably 100 points higher. So you have to evaluate based on your specific group.</p>

<p>The adcoms view applications differently. The same stuff that gets a Latino applicant from Little Havana Miami accepted might not get a white girl from Westchester County accepted.</p>

<p>It's also important to understand the cost of the multiple reach strategy. There are schools where you really want to put 100% effort into the application. Let's say, for example, that Swarthmore is a legitimate 50%/50% reach based on the totality of the application. If you apply early decision and put together an enthusiastic application that demonstrates considerable, specific knowledge and fit, your chances of admission go way up. If the same applicant dashes off the application as number six in the stack after five "wing and a prayer" applications, the odds of getting accepted go way down, simply because the application lacks the enthusiasm that makes a difference when the "acceptances" and "rejections" all have the same SAT scores.</p>

<p>The key is to look at your app and try to find a reason that a school would accept you. You can have all the stats in the world and still be a "no prayer" applicant at a place like Harvard. You simply can't "wow" them with stats. There has to be something about the application that stands out. Once you are applying to schools where you have a "stand out" application, then you get into the odds you are talking about, where you might get accepted at two equivalent schools and rejected at two others, simply because the adcom was in a different mood or you offered what the school was looking for that year.</p>

<p>I guess the point is, random odds alone won't turn a rejection into an acceptance. The caution about the theory that started this thread: if you are applying to reach schools where you have no prayer, it doesn't matter if you apply to a million of them. You probably aren't going to get accepted. You can't "make it up on volume" unless you are a legitimate applicant for the schools.</p>

17

<p>We cannot assume that all the outcomes are mutually exclusive, and beyond the statistical viewpoint, estimated probabilities usually are usually just issued on gut feeling or a ballpark estimate.</p>

<p>So perhaps its all just psychological?</p>

18

<p>idad:</p>

<p>I agree that an early decision strategy requires an entirely different system. With an "all the eggs in one basket" approach, you 'd better be certain about your choice and also about the trade-offs involved in not being able to apply to potentially more attractive schools. I was really more referring to a regular round approach which may be the only option if you are looking for financial aid options or some ultra-selective programs. I also indicated that you needed to look at your stats within the context of your own high school or at least very similar high schools if at all possible. </p>

<p>The comment that the applicant pool overall has similar stats to the admitted pool is somewhat misleading. That may be true overall counting legacies, athletes, URMs and other hooked candidates. Among students applying RD without a major hook, however, those with a higher SAT and Rank combination will be admitted in much greater numbers than those lower ranked. Even at Harvard less than 25% of applicants are in the top 1% of high school candidates in terms of SAT scores and rank but over 75% of admitted candidates fit that profile. While it is also true that some admitted students have extraordinary achievements not captured by SAT and rank, these WOW (walk-on-water) students constitute typically less than 15% of the entering class at places like Harvard or MIT. The vast majority of admitted students are just very bright with very similar profiles. And you simply can't predict that anybody's ECs are going to stand out more than somebody else's. So, while a high academic ranking alone does not guarantee entry at a top school, it certainly offers a major statistical advantage.</p>

19

<p>Harvard's kind of an outlier because there's no group of schools that it loses yield battles to and because it gets a significant number of "no prayer" applications (regardless of stats). I see hundreds examples here on CC every year, where I read the "what are my chances?" post and wonder why in the world the student would waste $60 applying to Harvard...whether it's class rank, or just nothing that stands out on the application besides high SAT scores.</p>

<p>At any normal highly selective college, the stats of the accepted students are slightly higher than the enrolled students, which are slightly higher than the applicant pool. But, we are talking fairly small differences...surprisingly small.</p>

<p>The problem is that just having median stats isn't enough for an unhooked white applicant. A white applicant from a popular region really needs to be at or near the 75th percentile stats to have decent chances. At super selective schools, you would need that PLUS something interesting about the application.</p>

<p>You can't always predict what a given college will consider "interesting", but you can separate out a lot of "interesting" applications from cookie-cutter applications. A lot of it has to do with how a special interest is communicated and highlighted. The key is to really think about, "what would make me stand out from the other applicants?"</p>

<p>BTW, an "interesting" application doesn't have to mean national awards. It can be something on a local level; it just has to be something that makes an adcom say, "wow, I'd really like to have lunch with this kid; he/she sounds like in interesting young adult". They just get so many cookie-cutter apps that they go numb. For example, I know a kid whose "interesting" thing was that she refused to take the mandatory state high school testing in the 10th grade, organized a protest of the testing at the state legislature, and was denied a high school diploma for her refusal. That's not the kind of thing many CCers would envision as a "standout EC", but it demonstrated a degree of spunk that colleges might find interesting.</p>

20

<p>Actually every highly selective college shows a very strong preference for high academic achievers and the preference gets stronger as you go down to less and less selective colleges. Many second tier colleges will seek to skew the process by essentially bribing with merit aid the high achievers who may not enroll otherwise. This is in part driven by the need for many colleges to hold on to their USNWR rankings. Harvard can actually afford to pick some students with lower stats and not affect the median because they have so many strong applicants as well. Outside of HYPSM not a single college has a yield in the regular decision round greater than 50%. That means that they loose a substantial number of their top admits to higher ranked schools. The top LACs lose around 75% of their admits in the regular round. That also means they need to admit large number of high academic achievers to hold on to some of them and meet their SAT and rank targets. I have found as a rule of thumb that with stats in the median of enrolled students (not of the admitted students) an applicant has about a 25% chance of admission to a highly selective college. That percentage then rises to about 50% if he is in the 75th percentile. It is precisely because of these low rates that a student needs to apply to a substantial numbers of reach schools if he is to be accepted to at least one. </p>

<p>It is also true that even a strong applicant needs to dress up his application with decent ECs, strong recs, polish his essays and show some passion. In my experience most top academic achievers also have these qualities. In the same way many have been prepped to get good test scores and tutored if necessary to get good grades, they also have counselors help them package their application. The level of sophistication among applicants to top colleges is quite high, not least because of sites such as CC.</p>