A racial-discrimination lawsuit filed against Harvard by Students for Fair Admissions has pitted expert witnesses David Card and Peter Arcidiacono against each other in a battle of statistical wit. Both were given a trove of previously private admissions data and tasked with determining whether Harvard University discriminates against Asian Americans. The two economists took a similar approach, using statistics to uncover Harvard’s admissions formula and assessing if and to what degree it took race into account. Arcidiacono, paid $450 an hour by SFFA, concluded that Harvard’s formula penalizes Asians. Card, paid $750 an hour by Harvard, found race didn’t play an important factor. But tabling the fraught question of racial discrimination, the debate has generated buzz among Harvard hopefuls, higher education watchers, and statisticians alike: What is the Harvard admission formula—or does one even exist?
The lawsuit has pulled back the curtain on what exactly happens after a student presses “submit.” Upon arrival, each of the 30,000–40,000 applications to Harvard University is sent to one of 20 dockets, groups of four to five individuals responsible for reading each application from a particular geographical region. Within the dockets, applications are assigned scores in a process that’s both quantitative and highly subjective. Each applicant is ranked on a 1–4 scale—with 1 being the best and 4 the worst—in four categories: academics, athletics, extracurriculars, and personal. Each of these four profile scores are subjectively defined, as is the applicant’s overall score. The overall score, which is not simply the average of the four profile scores, also includes substantial wiggle room for a reader’s discretion—for example, an applicant’s race can directly influence his or her overall score. The overall score is extremely predictive of admissions decisions: For example, the probability of admissions increases by more than 50 percent when an applicant’s overall score moves from a 3 to a 2.
These rankings are added to a summary sheet, an important reference for admissions-committee officers as the applicant passes through successive rounds of reviews. Arcidiacono provides substantial detail as to what goes into the summary sheets: profile scores, test scores, demographics (including gender and race), information about the applicant’s parents, information about extracurriculars (including how much time is spent on each activity), scores reflecting the overall strength (as judged by the admissions officer) of teacher and guidance-counselor recommendations, personal and overall scores provided by an alumnus interviewer, and additional comments from the docket reader. The reader may also highlight particular points of interest.
Most applications don’t make it out of the docket round, but some will advance to a final round, which takes place during a two-week period in March. Here, docket members advocate for each of their top applicants in front of the full committee, which comprises all admissions officers along with senior members of the admissions office. According to director of recruitment Roger Banks, the entire admissions committee will often discuss a single applicant for up to half an hour. An applicant’s artwork might be broadcast on a big screen, or a recording of an applicant’s Beethoven piano sonata performance could be played. The full committee votes on each applicant, and students with majority support are accepted. The panel tallies class demographics (including race) along the way.
All applications pass through the docket and full committee meetings. But not all applications are treated equally. For one, there are “interest lists”—specific applicants flagged by the dean of Harvard University or director of recruitment who are given special consideration. According to Card, the lists may include “applicants that the Dean or Director have encountered at recruiting events, as well as applicants related to donors to Harvard or lineage applicants.” Arcidiacono reports that 42 percent of the 2,501 applicants on this list were admitted between 2014 and 2019—highly favorable odds when compared with the 6 percent overall acceptance rate. The applicant is also flagged if he or she is the child of either an alumnus or a faculty or staff member. Applicants who are “legacies” (4,644 between 2014 and 2019) are admitted 34 percent of the time, and children of faculty and staff (321 between 2014 and 2019) are admitted 47 percent of the time.
For the rest of the applicants, the best strategy is to be well-rounded in the four profile areas. Getting four 2s in the profile scores, for instance, gives you a 68 percent chance of admissions. Three 2s combined with a poor fourth score (a 3 or 4) gives you a 43 percent chance of admission; this was the winning recipe for nearly 700 admitted students each year.
It’s also possible to get in with a single excellent profile score. Card looked at applicants who received a 1 in only one of the four categories and found that acceptance rates for these unidimensional stars were high, but they were exceedingly rare. Applicants with a single academic 1 were admitted 68 percent of the time, but there were only about 100 such applicants in each of the last six admissions cycles. (In comparison, 361 applicants to the class of 2019 had perfect SAT scores.) During the same years, only about seven applicants per cycle got a single 1 in the personal-profile area, and these students were admitted 66 percent of the time. For the 80 or so applicants excelling only in extracurriculars annually, 48 percent were admitted. Numbering more than 200 per year, athletes were the largest group of unidimensional admits and have a whopping 88 percent acceptance rate.
Peeking behind the admissions curtain shows that there’s certainly no machine that eats an application and flashes “Yes” or “No,” but that Harvard admissions decisions do have a degree of predictability. While Harvard maintains that there are many intangible factors that go into any admissions decision, the reports give us an idea of exactly how important the tangible factors are. Card boasts that his formula, which takes into account more than 50 academic and demographic variables, correctly predicts 74 percent of the admitted class. Arcidiacono’s formula, as pointed out by Card, predicts 68 percent of the class.
But their formulas aren’t particularly useful to an aspiring Harvardian for several reasons. First, whether it’s 74 percent or 68 percent, there’s still a sizable portion of the admitted class that neither expert can explain. There’s also good reason to suspect that the models are less accurate than the experts think—they had to use the same data to create their models and to estimate their accuracy, which means they are likely guilty of statistical “double dipping.” As is, it’s difficult to assess the degree to which they are predicting admissions decisions versus simply memorizing the decisions that have already been made. Third, and perhaps most importantly, neither expert is releasing the entirety of their model fit, making them harder to assess.
Had Card’s or Arcidiacono’s models predicted Harvard’s admissions decisions perfectly, one might argue that Harvard had a formula. Even so, it would be a complex and comprehensive one, taking into account many disparate facets of an applicant’s life. So for now, Harvard hopefuls will have to keep guessing—and keep practicing piano, like their mother told them to.