Gas station without pumps

2014 May 3

College lottery

Filed under: Uncategorized — gasstationwithoutpumps @ 11:58
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On one mailing list I subscribe to, a parent remarked

For über-selective schools, I have come to believe in “lottery” because I think the chance of any given (non-recruited) student having his/her application selected from the enormous pile of  similarly “qualified” applicants—due to where s/he lives, or a specific extracurricular interest, or something about his/her demographics, or a passage of an essay or recommendation that tickled an ad com’s fancy, or whatever—is akin to having a lottery ticket chosen.

I believe that from the students’ perspective, admission at highly selective schools is best modeled as a lottery. Although each individual admissions officer is trying to put together an “optimal” class, they have different ideas of what is good (far too often looking for students like themselves, for example). Which admissions officer first reviews a student’s file may make a huge​ difference, but is not under control of the student (or even of the institution).  Having a student who is a perfect fit for a highly selective institution is no guarantee of their getting in—in fact, being a perfect fit may change their odds of getting in insignificantly.

All the things we do to maximize our kids’ chances (grades/no grades, detailed transcripts/one-page transcripts, accredited courses/customized instruction, extensive testing/minimal testing, Mommy grades/external grades/no grades, normal curriculum/esoteric subjects, SAT prep/no prep, college visits, letters of recommendation, college courses in high school, …) are probably just magical thinking, giving us the illusion of having some influence over a process that is really completely out of our control.

Of course, there are a lot of exceptions to normal admissions: there are scandals every year about the extremely low academic performance of student athletes in high-money sports, and a lot of private schools give big boosts to children of donors and smaller boosts to children of alumni.  Stanford claims that the children of alumni have about a 3-fold greater chance of admission, but how much of this is due to their being “legacies”, how much to exceptions for big donors who happen to be alumni, and how much due to the children of Stanford grads having higher academic performance than the average applicant to Stanford is kept secret.  (I do find it telling that alumni trying  to get their children into Stanford are directed to talk with administrator in charge of getting donations not to the admissions office.)

Luckily, there are many decent-fit institutions, and college selection is more a matter of finding a good enough fit and making it work than of looking for a perfect match.  That idea applies to both students and colleges.

Students have to decide how many lottery tickets to buy (the main cost is the time to write the essays). By looking at the admissions probability for each college they apply to, they  can buy enough tickets to have a reasonably high probability of at least one acceptance.  The standard advice to apply to “safety” schools is primarily to raise the expected number of acceptances, which is just the sum of the probability of acceptance over all schools applied to. Students need to determine which colleges are a decent fit (academically, socially, and financially) and apply to enough of them to get into one or more.  As the admissions odds continue to get worse even at large state schools, each year students need to apply to more schools, which creates a feedback cycle of lowering admissions odds and increasing the number of applications needed.  The testing agencies, who charge ridiculously large fees for each test report and financial aid report, get rich, but everyone else loses from this cycle.

The colleges could save themselves a lot of money by eliminating most admissions officers and using a real lottery (probably with weighted probabilities to shape the class they want). This would probably result in better balanced incoming classes, as the biases of the admissions officers would be substantially reduced.  A lot of state schools are already effectively lottery entry, though there are some questions about whether the weighting schemes they use are really in the best long-term interests of the state or the school, and they still hire more admissions officers than are really needed to manage the lottery.

One hard part for students and parents is trying to estimate the probability of acceptance in order to figure out how many applications are needed. The raw figures from the Common Data Set for each school can be misleading—gender is the only predictive factor from which probabilities can be derived. Students and parents have no access to how the probability of admissions changes with score level or other characteristics, just the overall level for males and for females. There are some numbers reported about the admitted cohort in terms of class rank and standardized test scores, but without similar statistics about the applicant pool, these statistics don’t provide much predictive power.  Being at the 25%ile or the 75th%ile for the admitted class does not tell a student what the probability of acceptance is for students at that level—even being well above the 75%ile does not raise one’s probability much above the baseline at the highly selective schools.  In fact, some schools may have a higher probability of acceptance for lower scores (admissions officers unconsciously want students like themselves, and the brightest students rarely go on to become admissions officers).

The only school I’ve seen that provides more detailed statistics on score ranges is MIT, and even then they only report on those admitted, not those applying.  One can gather that applicants with low math scores have little chance of acceptance, but assigning probabilities is hard—what fraction of the pool had each of these score levels?

MIT 2013 admissions statistics

SAT Critical Reading SAT Math SAT Writing
700-800 67.1% 93.8% 69.9%
600-699 27.3% 6.1% 26.5%
500-599 5.4% 0.1% 3.6%
400-499 0.2% 0.0% 0.0%
300-399 0.0% 0.0% 0.0%
200-299 0.0% 0.0% 0.0%
100% 100% 100%

Of course, the jobs of admissions officers rely on their pretending that the admission process is not a lottery, and that they possess some magical skill at selecting just the right students to admit. So the colleges will not release data that assigns probabilities or allows others to do so. And all the admissions web sites and blogs will say things like

But, as we say here over and over and over again, the numbers are probably the least important part of an application to MIT.

Not that numbers don’t matter. If your grades and scores suggest that you are not prepared to do the work at MIT, you will not be admitted, because we don’t want to admit people just to have them fail out.

But once students have demonstrated academic preparedness—as the majority of MIT applicants can and do—then the additional returns accrued by marginal increases in academic performance diminish markedly. When comparing two applicants who have scored in the latter band, we’re not sitting there saying “well this person has a 750, and this person has a 780”, we’re saying “both of these applicants are academically qualified for MIT, so which one would contribute more to the community here?”


Since, from a student perspective, admissions to college is a lottery, it would probably benefit almost everyone to implement it more directly as a lottery.


1 Comment »

  1. I agree that from the point of view of the student, treating the experience as a lottery is the right way to think of it in general, with the caveat that there are some characteristics that might skew probabilities, like being an underrepresented major, gender, minority, geography) significantly enough that they should be considered when making lists of schools to maximize probabilities that you’ll get in somewhere. Most of those characteristics are fixed, though, so they influence application choice, rather than personal choices and so I think treating the process as a lottery (i.e. stop worrying about whether you should play soccer or baseball if you want to go to a particular or other choices people make in their lives) is the right option. Even if you do become a recruitable soccer player or a baseball player, you could find that in your year, there was a better 1st baseman who wanted to go to Harvard or goalie who wanted to go to Stanford. The comparative rankings make the admissions probability nearly impossible to predict, even if they weren’t also susceptible to bias in the form of individual admissions officers biases (which if not random are unpredictable to the point of randomness).

    Now, the question of whether this randomness from the applicant point of view really should translate into random choices on the part of the school. It would eliminate unproductive admissions officer bias (i.e. being attracted to candidates seem like themselves on paper, say liking flautists better than violinists). But, to the extent that they really do balance the class, say, including people with different strengths, at least as well as you can tell from paper, they might be gaining value, even if the applicant can’t predict whether their type is needed in a class.

    Comment by zb — 2014 May 3 @ 16:19 | Reply

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