An SAT Story

The Math Inversion

How selective colleges quietly flip the country's section scores

Nationally, the average SAT-taker scores 14 points higher on Reading and Writing than on Math. At MIT, the median admit scores 30 points higher on Math. At Caltech, the gap reaches +45. Even at Williams and Pomona — places with no engineering school — Math beats Reading. We pulled the section data from every Common Data Set we could find and asked why.

−14 National Math − EBRW
+30 MIT median gap
+45 Caltech median gap
38% SAT lift over GPA, STEM majors
SCROLL TO BEGIN
Chapter I

The National Baseline

Two million high-school seniors take the SAT each year. Their average total is 1,024. Their average breaks into 519 on Reading and Writing and 505 on Math — a fourteen-point edge for verbal.

That is the country we live in. Reading and Writing comes a little easier, on average, than Math. The pattern shows up cleanly across nearly every demographic: women score higher than men on EBRW; the same students score lower on Math.

It is the natural starting line. To understand what selective admissions does to the SAT, you have to know what the SAT does on its own.

−14 pts Math minus EBRW for the national class of 2024 — a verbal advantage that quietly disappears the moment you walk onto a selective campus.

Because once you do — the picture flips.

Chapter II

The STEM Schools

Start with the obvious cases. At MIT, the median admitted student scores around 790 on Math and 760 on EBRW — a thirty-point gap. At Caltech, the median runs 795 to 750 — a 45-point gap. At Georgia Tech, where the applicant pool spans a much wider band, the gap at the median is 50 points.

Read against the country's −14 baseline, the actual reversal at these schools is closer to +44 to +64 points. That is not a small wobble. It is a different distribution.

Carnegie Mellon publishes section scores for the whole university but explicitly tells applicants to its School of Computer Science to submit the SAT "with an emphasis on the math section."

100% of MIT admits scored 700–800 on the Math section. The 25th-percentile Math (780) equals the 75th-percentile EBRW (780).

Engineering schools were the easy case. Now look at the comprehensive Ivies.

Chapter III

The HYPSM Pattern

Harvard is not a STEM school. Yale is not a STEM school. Princeton is not a STEM school. And yet at all three, admitted students show a clear Math advantage of +20 to +30 points at the median.

Stanford lands at +25. UChicago at +25. Northwestern, with its strong McCormick engineering program, runs an unusually large +45 — closer to Caltech than to Yale.

This is a finding that surprises people. Liberal arts requirements, humanities cores, creative writing seminars: these schools are nominally balanced. Their admits are not.

Math P25–P75
EBRW P25–P75

If the pattern holds at HYPSM, does it survive at the LACs — schools without a single engineer in the catalog?

Chapter IV

The Liberal Arts Surprise

Williams admits no engineering majors. Neither does Pomona, Swarthmore, Bowdoin, or Middlebury. And yet at all of them, the median Math score sits +10 to +25 above EBRW.

Amherst is the rare exception: its admitted class is roughly balanced, with EBRW slightly ahead at the 25th percentile. It is the only top LAC in our data that mirrors the country's verbal tilt.

Whatever is doing the work, it is not just engineering self-selection. Even at colleges built around a humanities core, Math scores are higher.

+10 to +25 Median Math − EBRW gap at top LACs. Smaller than MIT, but pointed in the same direction — and opposite to the national norm.

What explains the gap if it isn't STEM emphasis? The College Board has data on that.

Chapter V

The Predictive Edge

The College Board's 2023 Digital SAT Validity Study — sample size over 200,000 — shows the cleanest story. Math scores predict college math and STEM grades; EBRW scores predict humanities and social-science grades.

Mean STEM GPAs march upward in a stairstep with Math scores: 3.01 for the 400–490 band, 3.21 for 500–590, 3.42 for 600–690, 3.68 for 700–800. Non-math GPAs do the same with EBRW.

For STEM majors, the SAT adds 38% more predictive power beyond high-school GPA alone. SAT-Math beats SAT-EBRW as a predictor of retention. High Confidence

At the aggregate level, the section correlations with first-year GPA look almost identical — Math 0.47, EBRW 0.48, Writing 0.51. The differential validity only shows up when you break the data out by major.

If admissions offices know Math predicts STEM success, the question is what they do with that knowledge.

Chapter VI

Three Forces

The Math-over-EBRW gap at selective colleges has three plausible drivers, and they are not equally important.

Self-selection is the largest. Students with strong math scores disproportionately apply to MIT, Caltech, and Georgia Tech in the first place. We estimate this accounts for 60–70% of the STEM-school gap.

Tail compression comes second. At the very top of the score distribution, Math scores compress more tightly toward 800 than EBRW scores do. The 99th-percentile Math is roughly 790; the 99th-percentile EBRW is roughly 770. Selective schools fish from a pool where this asymmetry is mechanical, not chosen — about 20–30% of the gap.

Institutional preference is the smallest. There is direct evidence that some colleges weight Math more heavily — but the size of that effect is modest: 10–20% at STEM schools, near zero at LACs. Moderate Confidence

There's one place we have explicit text: MIT.

Chapter VII

MIT Says It Plainly

Most colleges are coy about the section weighting. MIT is not. In its 2022 blog post announcing the reinstatement of the SAT/ACT requirement, the admissions office wrote:

"Our research shows considering performance on the SAT/ACT, particularly the math section, substantially improves the predictive validity of our admissions decisions with respect to student success at the Institute." — MIT Admissions, March 2022

Three claims in one paragraph. Math is particularly predictive of MIT outcomes. The effect persists after controlling for socioeconomic status. High-school grades alone are insufficient.

It explains the curriculum. Every MIT undergraduate, regardless of major, completes two semesters of calculus and two of calculus-based physics. There is no humanities track that escapes it.

+10–20% Estimated share of the gap at STEM schools attributable to direct institutional weighting. Outside MIT and CMU's CS school, the evidence is mostly inference.

For our simulation, the question is what to do with all of this.

Chapter VIII

Modeling the Inversion

The simulation currently uses a single composite SAT per student. Adding section scores would let us reproduce the observed gaps directly — but it would only change behavior if some colleges actually weight the sections differently.

The proposed weights mostly hover at 0.50 — equal weight. The exceptions are narrow and concentrated: MIT 0.60, Caltech 0.65, CMU 0.58, Georgia Tech 0.60, Purdue 0.55. Outside the top STEM schools, the math weight stays roughly balanced, with LACs nudged to 0.48.

The honest reading: most of the observed Math advantage at selective colleges is a property of who applies, not how applications are scored. A composite-only model that gets the applicant archetypes right will reproduce the section gaps as a side effect.

Section-level decomposition is most worth doing for STEM schools and as a calibration check — not as a behavior change for the bulk of the 192-college list.

7 Colleges in our list with materially asymmetric math weights (≥ 0.55). For the other 185, equal weight is a defensible default.
National SAT, Class of 2024
Mean section scores for ~2 million test-takers
Source: 2024 Total Group SAT Suite Annual Report; sat_section_data.json
STEM Schools — Math vs EBRW Section Ranges
P25 to P75 bars by section. Right column shows median Math − EBRW gap.
Source: research/sat_section_weighting.md (CDS 2024-25); sat_section_data.json
HYPSM and the Comprehensive Ivies
Math advantage persists at +20 to +30 even at non-STEM schools.
Source: Yale, Harvard, Princeton, Stanford, MIT CDS 2024-25; NextAdmit aggregations.
Top Liberal Arts Colleges
No engineering school. Smaller gap, but the direction holds.
Source: Williams, Amherst, Pomona, Swarthmore, Bowdoin, Middlebury, Wesleyan, Colby CDS & CollegeTuitionCompare.
SAT Math Predicts STEM GPA in a Stairstep
Mean first-year STEM GPA by Math score band (n > 200,000)
Source: College Board Digital SAT Validity Study, September 2023.
Why the Gap Exists — Decomposed
Estimated share of Math − EBRW gap by source, STEM schools vs LACs
Source: Inferred decomposition; research/sat_section_weighting.md §3.4. Confidence: moderate.
All Roads Lead to MIT
Math − EBRW gap by school type, on a single number line
Source: sat_section_data.json — section_gap_by_school_type.
Math Weight by College — Proposed
Where the simulation would deviate from equal weighting (0.50)
Source: sat_section_data.json — college_section_ranges; 0.50 = equal weight.