College Admissions
Academic Index
"[A]cademics make up 75% or so of the admissions decision" Understanding the Academic Index.
TODO: Give background
Footnote 29 (pg 22) from Document 415-8 lays out the basics of how the Academic Index is calculated:
- (Highest Math SAT Score + Highest Verbal SAT Score) / 20
- (Sum of Two Highest SAT Subject Test Scores) / 20
- "Class rank or, less preferable, high school grade point average are converted to a 20-80 scale to mirror that of SAT scores"
This results in the "Academic Index" scale from 60 to 240.
This is pretty clear-cut, but how is class rank converted to a number from 20 to 80? Other sources around the internet refer to this as "Class Rank Calculation" or "Converted Rank Score". As far as I can tell, the actual method used to compute this was revealed by A Is for Admission: The Insider's Guide to Getting into the Ivy League and Other Top Colleges, who published a table. It seems to match extremely well with simply converting the class rank to a z-score and then linearly transforming it so it has mean 50 and standard deviation 10.
Ultimately, then, all three terms in the sum are roughly normal variables with standard deviation of ~10, and the Academic Index is simply the sum of the three, centered around 150 and with a standard deviation in the mid-to-high 20s.
In addition to the Academic Index, Harvard tags applications with an Academic Rating (assigned by a human via these guidelines Document 419-1) and Standardized Academic Index (assigned by a confidential algorithm) - there is "probably significantly correlation between the" two Nagai, and there is a r~0.85 correlation between the Academic Index and the Academic Rating (pg 15 from Document 421-145).
Non-Meritocratic Factors
Table 3 from Legacy and athlete preferences at Harvard helps elucidate how important legacy, athletic, and racial factors are in admission to Harvard. If we look at the author's preferred model (logistic regression, column 5), we find the following coefficients for applicants:
| Variable | Coefficient |
| Faculty or Staff | +2.5 |
| Dean's Interest | +3.3 |
| Black | +3.6 |
| Hispanic | +2.0 |
| Asian | -0.4 |
| Legacy (white) | +2.1 |
| Legacy (black) | +1.3 |
| Legacy (hispanic) | +1.4 |
| Legacy (asian) | +2.8 |
| Disadvantaged (white) | +1.6 |
| Disadvantaged (black) | +0.1 |
| Disadvantaged (hispanic) | +1.0 |
| Disadvantaged (asian) | +1.8 |
Table 5 from Asian American discrimination in Harvard admissions is similarly informative, generally agreeing with the above coefficients and adding that early action generally adds about 1.4 points. Table D4 from Legacy and athlete preferences at Harvard suggests the coefficient for being a recruited athlete is large than any of the above: around 8.
These are obviously large effect sizes! As an example, being a white legacy boosts your admission probability from 5% to 31%. Moreover, since roughly 30% of students are legacy or athletic and roughly 30% of students are races with affirmative action (compared to whites), these large effects are applied to huge swaths of the class. Large effects on large portions of the population imply these factors are no longer just important for individual students, they actually start to explain significant proportions of overall population variance. How strong is the effect?
Well, a study Espenshade used data of applicants to elite colleges in the 1980s and 1990s also applied a logistic model (Table 2, column 7), finding
| Variable | Coefficient |
| SAT (< 1000) | -3.0 |
| SAT (1000 - 1099) | -1.7 |
| SAT (1100 - 1199) | -0.7 |
| SAT (1200 - 1299) | - |
| SAT (1300 - 1399) | +0.6 |
| SAT (1400 - 1499) | +1.4 |
| SAT (1500 - 1600) | +2.3 |
| White | - |
| Black | +1.7 |
| Hispanic | +1.3 |
| Asian | -0.3 |
| Athlete | +1.4 |
| Legacy | +1.1 |
| I applied the natural log function to each coefficient from Table 2 to convert from odds ratios to coefficients. | |
This suggests that, by prioritizing an athlete over a non-athlete, elite schools are sacrificing about 200 SAT points. For legacy admits that's about 160 points. For black and Hispanic students, that's about 210 points. Roughly half of Harvard students fall into one of those categories, so the overall effect on Harvard is likely that the student body's average SAT score is about 100 points lower (~0.5 SD), with a corresponding negative effect on other traits (e.g. interview scores are likely lower on average).
Note that the more recent data (from Legacy and athlete preferences at Harvard and Asian American discrimination in Harvard admissions) suggests that legacy and athlete status are now 2-6 times more important today than they were in the 1980s and 1990s, so one would naively expect the deleterious effect on SAT scores might be even worse today. However, Harvard's median SAT score is 1530, which means the maximum negative effect is 70 points. So, the more likely explanation is that both SAT score and athlete/legacy status have become more important, both from the simple fact that admissions has become more competitive.
TODO https://doi.org/10.1016/j.econedurev.2022.102255 (working paper: https://doi.org/doi.org/10.3386/w26456)