"Chances" math

Prep School Admissions
1

<p>New to board and the BS search on behalf of my daughter. Can someone please help me out with the following "math" problem?</p>

<p>I'm trying to assess what the real acceptance rates are for the "top" schools. Reading many of these threads, it's clear that 1) this is an incredibly competitive process; 2) there are many factors in the admittance process. I take all that as read. However, being overly-analytical, one simple question nags me.</p>

<p>Take Deerfield. According to the website: 1,803 applications, 311 acceptances, 190 graduated. Assumption 1 (which may be way off, as are all these assumptions): they filled 190 spots to remain at 600 kids, meaning a 17.2% acceptance rate and 61% yield. Something like that. Moving on, it's clear from these posts that many students apply for 10th grade. </p>

<p>Question 1: What are freshman class sizes in proportion to senior class sizes at most schools? Can one generalize?</p>

<p>Moving on (to explain where I'm going with this), let's say that to fill the classes to get to 190 seniors, the ultimate admits look something like this by grade:</p>

<p>9: 110
10: 30 (140 total class size)
11: 30 (170)
12: 20 (190 grads)</p>

<p>If we assume an equal yield of 61% for each class, you have acceptances that look something like this:</p>

<p>9: 180
10: 49
11: 49
12: 33</p>

<p>Again, could be way off base (which is why I'm looking for clarification...)</p>

<p>Now here's a really wild assumption simply based off of threads on this board. Here's what applications look like in each year (as a guess).</p>

<p>9: 800
10: 600
11: 300
12: 300</p>

<p>I'm not concerned with much other than the number of 9th grade applicants for the sake of this undertaking. But here's what my "model" would say are actual chances were these numbers to be correct:</p>

<p>9: 23%
10: 8%
11: 16%
12: 11%</p>

<p>There is one more variable for Deerfield and that's day students. There are 80 in the school, so that's 20 admitted per year. Let's say, for the sake of community relations, 20% of day applicants get in. So that's 100 applicants for day spots, reducing the boarding acceptances to 160 (because day student yields are probably pretty close to 100%). This still gets you a 23% chance of getting in as a 9th-grader.</p>

<p>One last HUGE variable seems to be financial aid. From what I've read here, you either get it your first year, or you don't. Further, at least half of the applicants seem to want or need it (could be a wildly wrong guess.) But let's plug this in.</p>

<p>If 400 of 800 applicants need financial aid and only 55 get it (there are about 220 students at Deerfield who receive aid), that means two things:</p>

<p>1) your chances of being a non-local, financially aided 9th-grade student accepted to Deerfield are 13.75%, much less than the average acceptance rate.
2) your chances of being accepted without any aid are 35%, 2x the average acceptance rate!</p>

<p>Sorry for this long post. I know the "answer" to this question means absolutely nothing but it has been niggling me since I've begun reading posts on this board. And there are many people out there who have done much more work on this topic than I have, so why not give this angle on "chances" a try?</p>

<p>Thanks much for your help and good luck to every single one of you.</p>

2

<p>Not really sure what question you are trying to determine. Are you asking for us to estimate the % of kids needing financial aid and get accepted versus the % of kids who don't need financial aid and get accepted?</p>

<p>However, I know that I have called schools in the past and asked them specifically, how many kids do they admit for the freshman class compared to the sophomore class. I've never asked about Junior year and it has been my understanding that being accepted as a Senior is extremely rare. One thing your calculation doesn't appear to take into consideration are PG students. Deerfield accepts about 20-25 PG's every year.</p>

<p>I am sure that if you were to call the schools your daughter is interested in applying and pose the question "What are freshman class sizes in proportion to senior class sizes at your school?" you would receive an answer.</p>

3

<p>you are also leaving off quite a few other variables
--legacies and recruited athletes
--some schools like to pick up about half of the class size they are looking for in 9th grade and half the class size they are looking for in 10th grade (in other words, if they want a senior class of 200 -- they admit 100 in 9th, 100 in 10th) kids admitted in 11th are fill-ins for those who left. jennycraig is right -- few schools admit students in the senior year.
--many schools get a ton of day student applications and some get very few</p>

<p>and there are many, many other factors</p>

<p>What this means is that your "chances" for acceptance into a school will depend on the applicant, the rest of the applicant pool and the school the applicant is applying to. Their chances may be 80% at school one, and only 14% at school two.</p>

4

<p>Yeah, I definitely think those acceptance rates at all. I've emailed Exeter, Andover, Choate, and Milton and they all said that acceptance rates are about equal and vary only one or two percent for some grade levels.</p>

5

<p>i'm so confused. what's the question? this seems just the teeniest bit obsessive tho. :) LOL.</p>

6

<p>You're forgetting attrition, which can be a significant factor. NAIS has stats online about member schools: <a href="http://www.nais.org/files/PDFs/NAISMemFactsNoSalarie%5F200607.pdf%5B/url%5D"&gt;http://www.nais.org/files/PDFs/NAISMemFactsNoSalarie%5F200607.pdf&lt;/a&gt;.&lt;/p>

<p>2006-7 Average attrition rate for boarding schools: 11.9
Median attrition rate: 8.9</p>

<p>Also germane to your questions: Admissions Funnel Averages (inquiries : applications : acceptances : enrollment) : 1,594 402 193 109</p>

<p>These figures are based on the member schools who responded to a survey; each item is based on those schools who responded, and not all schools responded to each item. Thus, it's a picture of general conditions, and not a prediction for any school in particular.</p>

7

<p>In rereading the OP, I'd also venture that day students and boarding students aren't in competition. A day student spot won't be offered to a boarder. If a day student turns a school down, another day student will fill that spot. The ratio of day to boarding students is set by the number of beds available. I suppose a school could increase the number of day students much more easily than the number of boarding students, as day students don't require dorms.</p>

<p>Also, it isn't a lottery for admission. Different candidates have wildly different chances of admission at any one school. If you look over older threads for postings around March, it's striking how varied the admissions outcomes are.</p>

8

<p>Adding on to Periwinkle's observations regarding how boarding school admissions isn't a lottery, I don't see how getting a grasp of the math will help make better decisions or lead to greater success or more focused choices, etc. I assume the purpose of these questions is to gain information that has some practical application. And I fail to see how one gets from quantifying the admission process to developing some model or guide that will serve an individual applicant. </p>

<p>You can count cards and do better at blackjack. But your child's chances of being admitted cannot be altered by understanding historical data about admissions. If, however, there is some specific purpose behind these questions, then maybe we could help formulate better questions or provide insights that will better serve that purpose.</p>

9

<p>Sorry about the apparent "lottery" aspect of the question or the "obsessiveness." And this is exactly the sort of feedback I was looking for. Thanks, jennycraig, for the advice to call the schools: I will. And, J1, I think yours seems to be the most direct answer: variance is lower than I was guessing. And I agree with Periwinkle that day students and boarders probably don't compete, etc.</p>

<p>That said, there are "real" implications to this weak attempt at a model. First, there are many discussions on this board about the bias of many/most schools towards full-pay students. So, let's say you would love financial aid but are probably on the bubble financially. Should you apply for FA, hoping that you get lucky? Or not? This model would argue that you should not consider applying for FA because your chances of actually getting in versus agreeing to pay the full tuition are diminshed substantially (not marginally.) Trying to understand this quantification actually could serve an applicant and his/her parents.</p>

<p>As to the "lottery" implications of the question, there is much contradiction on the board about this aspect of the process. I would argue that's exactly why the results in March turn out to be so surprising. At some point, there is a lottery aspect to admissions in any given year. To hsmomstef's point, there are legacies and recruited talent admitted each year, the number of which either randomly increases or decreases chances at any time, as does the whole applicant pool, etc. Further, as an oft-cited example here, let's say my D is an amazing balalaika player (who meets the other criteria) and Daftover's theatre director has been foaming at the mouth to put on a production of Dr. Zhivago. Bingo! But there's no forecast for such a thing, therefore making that a random occurrence (the flip side of that is D gets pipped at the post by a stellar sprinter who fills a hole in the track team).</p>

<p>Further, as the primary criterion for anyone considering any of the schools should be "fit" and as the general criteria for admittance are widely known, applications in any given year for any given school are going to reflect a large degree of qualified "self-selection." Given that these are kids, not machines, there is going to be a natural distribution in the applicant pool of all the variables that a school feels are important (there's a list thread ranking the top six variables on this board) in any given year, which is going to leave a pool of "good, qualified fits" larger than the pile of acceptance letters to be sent out in any given year.</p>

<p>My point is: when you have an increasingly large set of random variables (including, on top of all the others, the mood of the interviewer/ee on any given day, how articulate your teacher rec-writer was, etc.) in the process of admitting a class and a pool of generally qualified people, the outcome does approximate the outcome of a lottery over time, whether we like that characterization or not.</p>

<p>So what's the practical implication of that? Schools publish "Admissions Funnel Averages" (or pieces of it) for a reason: to manage expectations and image. Just reading this board, we know that AEDS, etc. are super selective, other schools less so. Assuming that she's qualified (generically), if there's a 1 in 6 chance of getting into a school, I would hope that my D could find 6 schools at which she feels comfortable or (better yet) about which she is sincerely excited. (Can she still get rejected at all 6? Sure!) If she has a 1 in 3 chance of getting into any given school, finding 3 schools to apply to would be equal to 6 in the above example. Understanding this helps one manage expectations and assists in determining "how much work" one should do upfront to discover an appropriate pool of schools to which one eventually applies. (I think everyone on this board agrees that only applying to Exeter, for example, is an exercise in futility.)</p>

<p>Before you jump all over me, let me make one last point. The concept of a "safety school" (much discussed and sometimes applauded or maligned) is a derivation of the question I'm trying to ask here. If a family likes a school that has "average" acceptance of 50% (vs 17%) and the child is qualified on average for more selective schools, the less selective may be applied to as a "safety school." In short, perceived odds actually do influence decision-making. I'm trying to understand the "real" odds, which may or may not be possible to calculate. Aside from the FA question, will this have any real impact on our decisions? Perhaps, perhaps not. But it would be neat to know a little more about this opaque process.</p>

<p>Thanks to all for their patience and understanding of a dad very new to this board and the BS process.</p>

10

<p>OP -- I appreciate your attempts to quantify a process that is difficult to quantify. One variable that is not understood by many is the competitiveness of an applicant. A big fish in a small pond does not necessarily equate to a big fish in the ocean. This is hard for applicants and parents of applicants to understand. How could they know when they have only been competing in a small arena? </p>

<p>Good luck to you! I'm glad you realize that applying to a range of schools that are all good fits should increase chances of a happy result in March.</p>

11

<p>Thanks, Burb Parent. I'm unclear on the etiquette of thanking people for replies and advice or encouragement. As each reply "bumps" the thread, I'll issue a blanket thanks to all and only reply if I need some clarification. (If I'm wrong, please explain how it works.)</p>

12

<p>a blanket thanks works great -- no need to acknowledge every post, that can get tiring!</p>

<p>I think you are getting a good understanding of how the chances work -- and the number of variables that go into it. It is good to understand the odds, even if you can't really quantify it. You can certainly tell if one school is less selective than another, if it doesn't give any FA, if it is a good fit, etc -- which is how you pick your schools. some reaches, some matches and a safety or two is always recommended -- depending on your choices at home.</p>

<p>Welcome to the board!</p>

13

<p>If you were advising dozens of students, then I suppose the statistical approach would be useful. But while it appears like a lottery on a macro-level, it just isn't one. You're trying to take large numbers and boil them down into something meaningful that you can rely upon for an individual and somewhat unique applicant. Pools of applicants can be fungible, but a single applicant from that pool just can't be quantified that way. So, I will agree that it's an interesting exercise but I remain blind to how this sort of analysis can be of use to an individual applicant.</p>

14

<p>Good response, D'yer Maker, or, should I say, D'yer Ma'ker, but I'm also one of those obsessed parents who is trying to figure out the real stats, too.</p>

15

<p>Understand that I was not immune to being psychotic during this process:</p>

<p><a href="http://talk.collegeconfidential.com/prep-school-admissions/328976-keep-open-mind.html#post3953127%5B/url%5D"&gt;http://talk.collegeconfidential.com/prep-school-admissions/328976-keep-open-mind.html#post3953127&lt;/a&gt;&lt;/p>

<p>But the stats don't tell half the story. And the admission stats are just a small, arguably immaterial, part of the statistical story. After you look at how bad I was about the process, scroll up to read liv&learn's original message in that thread.</p>

<p>About the name...yeah, yeah. I crunge every time I type it out. I still contend I entered it correctly when I signed up and there was some sort of communication breakdown.</p>