<p>If the admissions criteria were exactly the same, applying to more schools wouldn’t increase the odds of admission one iota. And because the criteria are closer to being the same than being different, the chances don’t increase much.</p>
<p>HOWEVER, what does happen is that while schools become more “competitive”, at some point they actually become less “selective”. It becomes less likely that a student who would benefit from what one specific school has (as opposed to the other) will actually be admitted to it (and choose to attend) rather than the other. One is more likely to see homogenization of admittees. (H and Y are poor examples because of high yield, and since so few students actually attend them, they don’t add much to the discussion.)</p>
<p>But it does increase your chance of winning one of them eventually, and the ratio is pretty close to double (and actually if you buy n tickets, it takes a fairly large n for the increase not to be close to a factor of n).</p>
<p>The odds of acceptance to very selective colleges can vary wildly depending on which adcoms read the applicants essays. An example of this may be that if a ciollege has 10 adcoms reading essays & each applicant’s essays are read by two adcoms. If an applicant uses a public figure in their essay & three of the ten adcoms have a favorable opinion of this figure, but 7 have a negative opinion, the applicants chances are influenced by which two adcoms happen to read their application.</p>
<p>This is an overconstrained problem. The colleges would need an acceptance rate of 100% to have a 50-50 chance (roughly) of yielding 1000 students. Unless you add wait lists (or something similar), there is no statistical way that each college will end up with exactly 1000 students.</p>
<p>There is no need for an IF when it comes to using waitlists. In the above theoretical case, based on standard practices, you could expect 1200 to 2000 admissions at each school, and probably around to 10,000 waitlists offers in total.</p>
<p>The reality of today’s admissions at top ten colleges is that the regular admission cycle is just one of the facets of the process. For many, it involves negotiated admissions for the very rich and very talented, likely letters, one or more rounds of early admissions, deferrals, waitlists, and more acceptances after the summer melt … all sandwiching the regular decision that gets the headlines in April and May. </p>
<p>What we see as a fickle and cacophonous process is in reality a well orchestrated symphony that runs all year in order to please the demands of the … school and its supporters.</p>
<p>"But it does increase your chance of winning one of them eventually, and the ratio is pretty close to double (and actually if you buy n tickets, it takes a fairly large n for the increase not to be close to a factor of n). "</p>
<p>no, it doesnt. not when you buy 1 ticket in one lottery, over and over again. Each time you start with the same odds. If you buy many tickets in one lottery, that will increase your chances of winning that particular lottery. But how many tickets you buy in one lottery has absolutely no bearing on you chances of winning future lotteries .</p>
<p>"The reality of today’s admissions at top ten colleges is that the regular admission cycle is just one of the facets of the process. For many, it involves negotiated admissions for the very rich and very talented, likely letters, one or more rounds of early admissions, deferrals, waitlists, and more acceptances after the summer melt … all sandwiching the regular decision that gets the headlines in April and May.</p>
<p>What we see as a fickle and cacophonous process is in reality a well orchestrated symphony that runs all year in order to please the demands of the … school and its supporters. "</p>
<p>well said. Admissions to selective colleges cannot be looked upon like a lottery. it is based on many factors- and when colleges have an oversupply of “qualified” applicants, they can pick and choose who to accept based on only the needs and goals of the college.</p>
<p>You are right that the number of tickets you buy across loteries, does not change the probability of winning one specific lottery. But it does increse the chance you win a lottery.</p>
<p>Taking this to the limit. Suppose you buy one ticket from a lottery every day. You keep buying this “until the end of times” (until t -> infinity). The probability you win at least one of the lotteries is 100%.</p>
<p>But buying tickets in future lotteries increases your chances of winning future lotteries. Let’s say that for each lottery and each ticket, there is a probability p that that ticket is the winning ticket. If you buy n different tickets for the same lottery, your probability of winning that lottery is now np. If you buy n tickets in n different lotteries, your probability of winning at least one lottery becomes 1 - (1-p)^n. Since 1-p < 1, it should be clear that as the number of lotteries entered increases, the odds of winning one of them also increase. </p>
<p>And intuitively this should be clear too. If you roll one die, you’re probably going to get something other than a 6 (~83%). If you roll 50 dice, it would be very surprising if none of them turned out to be a 6 (~0.011%). Entering a separate lottery is just like rolling a separate die for a 6, except that the odds are astronomically longer.</p>
<p>Using the formula you posted to explain my argument, by taking n-> infinity, (1-p)^infinty = 0. Therefore probability = 1-0 = 1 = 100%.</p>
<p>The key is the “at least” versus the “specific” word. Using your dice example, the probability of getting a 6 in a specific dice is always 1/6. The probability of gettin at least 1 is .99 (as you posted).</p>
<p>Going back to the subject of college admissions, I do believe that probabilities increase with the number of applications. Observing what happened with me and a few of my friends, the accepts, waitlists, and rejects were unpredictable and all over the map. Those people who sent more applications had more acceptances (and also more fin aid packages to compare ).</p>
<p>Munequita and Wildwood have it right. The underlying assumptions of independence and randomness are not satisfied, so the calculations are not valid.</p>
<p>^
True. You can’t calculate out a specific formula with the data available. The process certainly isn’t transparent by my reckoning. But it’s entirely possible that the fact that the admissions process is neither entirely random nor entirely uniform across various universities increases the justification for applying to several schools. If you start with the assumption that you are generally in the ballpark for admission to a group of schools, and that the adcoms at different schools are composed of people with different prejudices tasked with meeting institutional goals as they build a class out of a distinct group of applicants, you have a better chance if you put your application in front of as many varied “eyes” as possible.</p>
<p>If you’re looking to find a spouse I don’t see why you would limit yourself to one date, or one method of seeking the spouse out. Your chances are better if you use your network of friends, go to a few clubs, museums, or whatever, hit a few bars, and get on more than one dating site.</p>
<p>The spouse analogy is a good one. But those who just apply to every Ivy are like those casting a net, advertising, “I don’t care who I marry, as long as they’re famous!”</p>
The evidence that this is true is readily available in results threads here on CC. College admissions decision are not random, but they occur in a black box that includes elements that make them appear somewhat random to the outside observer. Why does a non-legacy kid get admitted to Amherst, but not Williams, while another kid gets admitted to Williams, but not Amherst? It’s possible that if you could see inside the black box, it would be clear. We know it’s not entirely random, and we can make some conclusions about the criteria used, because the kid with a D average and lousy SATs never gets into Williams or Amherst. If you’re a student who likes both Williams and Amherst, and has the stats to be a credible applicant to those schools, isn’t it obvious that the sensible strategy is to apply to both? In terms of your behavior, I would argue that there is no difference between a random factor and a factor that isn’t random but that is unknowable by you.</p>
<p>Let me give an example. Let’s say you’re the most qualified kid in Idaho, and you apply to both Williams and Amherst. What you don’t know is that there is another kid from Idaho whose qualifications are almost as good as yours who happens to be a double legacy at Amherst. He applies to both Williams and Amherst as well. If you could see in the black box, you might see the adcoms at Amherst deciding to reject you on sensible, non-random grounds: we like to take at least one kid from each state, and between these two kids, we’re going to take the legacy if the qualifications are close. But you won’t get that explanation–you’ll only get a rejection letter. At Williams, you might get accepted, and he might be rejected.</p>
<p>Occasionally a post compels me to say, “I wish I had written that.” Hunt’s is one of those posts. What appears random from the outside may be completely determinstic to someone on the inside. In tennis, you do not know whether your opponent will serve to your forehand or backhand, but he knows. In soccer, you do not know whether the shooter taking a penalty kick will shoot to your left or right, but he knows, etc. In both cases, you implicitly put probabilities on the different strategies. To say that you do not know the true probabilities is to miss the point. As bovertine sugested, you can still draw useful lessons. </p>
<p>Many years ago, Paul Krugman made a related point: </p>
<p>I love the spouse analogy. To make it a little more realistic and attainable, it could be “applied” to inviting the 10 most popular girls in the Senior Class, or the most “beautiful” , to the prom. </p>
<p>Ask all 10 of the girls to the prom. Let’s say you’re a good looking guy, can talk to girls, are respectful and popular – but you’re not the next Matt Damon (or whoever you want as your ideal.) </p>
<p>One of the girls might say yes, a couple might say yes, or all might say no. Some may put you off to see if someone they asked says “yes” or not. All of them would probably say “yes” to Matt Damon…or maybe Zac Effron. You think you have a good idea of what kind of person you need to be to get all 10 girls to say yes…but you can’t be exactly sure. </p>
<p>And, you could be not very good looking at all, a little awkward in social situations and not popular, but there’s something about you that 1 or 2 of those girls find appealing, and they would say “yes.”</p>
<p>But maybe the Matt Damon clone isn’t attracted to the 10 most popular girls in the class. Maybe he likes Plain Jane who not only finds him attractive, but shows interest in the things he likes and bakes him brownies once a week and adores his parents.</p>
<p>Forget statistics. This is one of the best and realistic analogies I’ve seen to the Elite school admissions process.</p>
<p>(And…the 2 highly qualified kids from Idaho will BOTH get into Williams and Amherst - especially if neither went to an elite Eastern prep school. Both schools would be happy to take 2 highly qualified kids from Idaho! Both kids will have a positive affect on geographic diversity!)</p>
<p>I strongly disagree. You are being harmful to students. There is a random compontent, trying to ignore it is just disingenuous. </p>
<p>Here is the advice from someone who just went through the process: If applicants are interested in selective colleges, it is better for them to apply to as many schools as they can manage. More applications equal higher chances of acceptances. A school such as Williams only takes 500 students per year. If (say) you are interested in Williams, you would do yourself a favor by applying to other selective NESCAC schools.</p>
<p>The fact that the soccer player already know where he/she is going to kick, does not change your optimal strategy because there are many soccer players kicking the ball.</p>
<p>So even if you cannot know which specific soccer player will keet to the left or the right (and they may already decided). Your best strategy is to send many applications (= try to defend many penalty kicks). The more penaly kicks you try to defend, the higher is the chance that you will catch at least one ball (= get one acceptance).</p>
<p>In fact, the fact that all kickers are not perfectly equal (schools are not perfectly equal) makes it even more likely that one of them will accept you (provided you are a competitive student).</p>
<p>By competitive I do not mean “shoe in”. I mean, have the stats to be among the average admitted student.</p>
<p>How is 2boys being “harmful to students”? It apears to me that s/he is suggesting the same thing as you are- apply to many schools to help your chances. S/he is just giving another rationale (and a better rationale IMO) for doing so.</p>
<p>Whether you think the process involves diligent adcoms scrutinizing every application for tiny nuances, or a machine that makes an initial cut then shuffles and sorts the aps into accept and reject piles, it generally makes sense to apply to a number of schools. At least up until the point of diminishing returns for your labor, where filling out more applications has an adverse effect on the quality of other applications.</p>
<p>Of course if you really think the process is inherently random, you won’t reach that point as long as you can fill out all the required boxes on the application.</p>
<p>To me, it seems like the third stage has a lot of randomness to it. Thinking about unhooked candidates and ignoring binding early admission and wait lists and other yield management tricks:</p>
<p>The first stage would be, does this student have the grades and test scores and rigor of course work we are looking for? </p>
<p>The second stage would be, does this student have additional factors that we like? Special talents or experiences? What’s in his resume? Did he write a good essay or two? Do his references say he’s great? Does he seem like someone who would be a good addition to our campus?</p>
<p>The third stage is where it seems random. The admissions committee looks at what the students put in their essays and and looks at their experiences - debated on a national level, played concert violin, saved the whales, fed the children in Appalachia/the inner city, juggled on a unicycle, published a novel, patented an invention, raised younger siblings while working two jobs, was elected mayor, didgeridoo’ed, programmed a great app, a combination of these - every top school says they could fill their freshman class several times over with highly qualified applicants. What makes an admissions committee choose the editor over the ballerina? There are differences between the admissions committees/students applying/students accepted at different colleges of course - think Dartmouth vs Brown - but I see randomness here, and because of this randomness, a student’s odds of admission to a top school of his choice are higher if he applies to eight top schools of his choice than if he applies to 2 top schools of his choice.</p>
).</p>