Contents
- Why Students Choose Stanford Over Harvard (or Vice Versa)
- Overview
- Data Sources
- HYPSM Head-to-Head Win Rates
- Ivy+ vs. Ivy+ (Tier 2) Head-to-Head
- HYPSM vs. Tier 2 (Cross-Tier Matchups)
- Tier 2 vs. Tier 3 (Near-Ivy) Matchups
- LAC vs. University Matchups
- Public vs. Private Matchups
- NYU and Urban School Effects
- Factors Driving Cross-Admit Decisions
- Tier Dominance Patterns
- Yield Rate as Cross-Admit Proxy
- Sources
Why Students Choose Stanford Over Harvard (or Vice Versa)
cross_admit_dynamics.md · 2,768 words · 11 min read
Why Students Choose Stanford Over Harvard (or Vice Versa)
Overview
Every spring, a small number of high school seniors face a problem most families would envy: they get into both Harvard and Stanford. Or Princeton and MIT. Or Yale and all of the above. What they decide in those weeks tells us something acceptance rates and rankings cannot — which schools students actually prefer when the choice is real.
Researchers call this "cross-admit" data: among students admitted to two schools, what share picked each one? It is the closest thing college admissions has to a head-to-head record. Princeton sits atop the U.S. News list, but loses every one of its head-to-head matchups against the other HYPSM schools. MIT, ranked below Harvard on most lists, beats Harvard 63-37 when students hold both offers. Washington University in St. Louis ranks 11th nationally, but 62nd by where students actually choose to enroll.
The pages below pull together the major sources on these revealed preferences — Parchment's self-reported choice data, the Avery-Hoxby-Glickman-Metrick study published in the Quarterly Journal of Economics, Crimson Education's global rankings, and counselor analyses — and walk through what they say about which schools win, which lose, and why the answer depends on who you ask.
Data Sources
Parchment / College Results
Parchment's cross-admit comparison tool uses a "revealed preference" methodology. The denominator includes all students admitted to both schools; the numerator is those who chose a given school. Confidence intervals use Wilson's method at 95%. Sample sizes vary; elite-vs-elite matchups typically have medium-to-large samples (50-300+ students), while cross-tier matchups can be very large (1000+). Data is self-reported by students who use Parchment's transcript service.
Limitations: Geographic and demographic skew in Parchment's user base; students who use Parchment may not be representative of all cross-admits. Small samples for some LAC matchups.
Avery-Hoxby-Glickman-Metrick (NBER Working Paper 10803, QJE 2013)
Used hand-collected data on 3,240 high-achieving students to construct a revealed preference ranking of 105 U.S. colleges. Extended models from tournament rankings (Elo/chess-style). Top 5: Harvard, Yale, Stanford, Caltech, MIT. Key finding: Washington University in St. Louis ranked 11th in U.S. News but 62nd in revealed preference, demonstrating that traditional rankings diverge significantly from actual student choices.
Crimson Education Cross-Yield Rankings (2023/24)
Based on Crimson's global student network, using an Elo-based system. Their data shows a somewhat different ordering, with Stanford #1 and MIT #2 above Harvard #3, though this may reflect their international/STEM-heavy student base.
HYPSM Head-to-Head Win Rates
The five HYPSM schools (Harvard, Yale, Princeton, Stanford, MIT) form the apex of cross-admit competition. Data below is from Parchment unless otherwise noted.
Parchment Data (current)
| Matchup | Winner | Win % | Loser | Lose % | CI Range |
|---|---|---|---|---|---|
| Harvard vs. Yale | Harvard | 63% | Yale | 37% | H: 58.8-68.2% |
| Harvard vs. Princeton | Harvard | 73% | Princeton | 27% | H: 66.4-80.1% |
| Harvard vs. Stanford | Harvard | 65% | Stanford | 35% | H: 59.0-70.0% |
| Harvard vs. MIT | MIT | 63% | Harvard | 37% | M: 54.8-71.1% |
| Yale vs. Princeton | Yale | 59% | Princeton | 41% | Y: 51.5-66.0% |
| Yale vs. Stanford | Yale | 53% | Stanford | 47% | Y: 46.0-59.1% |
| Yale vs. MIT | MIT | 61% | Yale | 39% | M: 52.6-68.5% |
| Princeton vs. Stanford | Stanford | 73% | Princeton | 27% | S: 64.7-81.7% |
| Princeton vs. MIT | MIT | 58% | Princeton | 42% | M: 46.6-69.3% |
| Stanford vs. MIT | MIT | 61% | Stanford | 39% | M: 53.0-69.3% |
Aggregate HYPSM Rankings (Parchment-derived)
Based on total cross-admit points across all pairwise matchups:
- MIT -- Wins 3 of 4 HYPSM matchups (loses only to Harvard). Strongest STEM signal.
- Harvard -- Wins 3 of 4 (loses only to MIT). Dominant brand.
- Stanford -- Wins 2 of 4 (beats Princeton, loses to Harvard/MIT, near-tie with Yale).
- Yale -- Wins 1 of 4 (beats Princeton, near-tie with Stanford, loses to Harvard/MIT).
- Princeton -- Wins 0 of 4. Despite top U.S. News ranking, loses every HYPSM cross-admit battle.
Important Methodological Note
Different data sources yield different orderings. The Mathacle blog analysis of Classes of 2012-2014 (from a specific high school dataset) showed Harvard losing most HYPSM matchups, which contradicts Parchment data. Crimson Education's cross-yield ranking placed Stanford #1 and MIT #2. The Avery-Hoxby academic study had Harvard #1, Yale #2.
These discrepancies arise from: - Sample composition: STEM-heavy samples boost MIT/Stanford; humanities/policy-heavy samples boost Harvard/Yale - Geographic bias: West Coast respondents favor Stanford; East Coast respondents favor Harvard - Temporal shifts: MIT and Stanford have gained ground over the past decade - Self-selection: Parchment users skew toward students who actually make competitive choices
For simulation purposes: We use Parchment data as the primary source (largest sample, most current) while noting that individual student archetype should modulate these baseline rates.
Crimson Education Rankings vs. Parchment
Crimson's cross-yield data (from their own student network) shows different HYPSM ordering: - Harvard over Princeton: 70% - Harvard over Yale: 77% - Harvard over Stanford: 47% (Stanford wins) - Harvard over MIT: 36% (MIT wins)
This is broadly consistent with Parchment except for a stronger Harvard-over-Yale signal.
Ivy+ vs. Ivy+ (Tier 2) Head-to-Head
Parchment Data
| Matchup | Winner | Win % | Loser | Lose % |
|---|---|---|---|---|
| Columbia vs. UPenn | Columbia | 59% | UPenn | 41% |
| Columbia vs. Dartmouth | Columbia | 64% | Dartmouth | 36% |
| UPenn vs. Brown | UPenn | 53% | Brown | 47% |
| UPenn vs. Duke | UPenn | 53% | Duke | 47% |
| Brown vs. Dartmouth | Brown | 57% | Dartmouth | 43% |
| Dartmouth vs. Cornell | Dartmouth | 67% | Cornell | 33% |
| Duke vs. Dartmouth | Duke | 53% | Dartmouth | 47% |
| Duke vs. Cornell | Duke | 83% | Cornell | 17% |
| Brown vs. Cornell | Brown | 75% | Cornell | 25% |
| UChicago vs. Northwestern | UChicago | 62% | Northwestern | 38% |
Tier 2 Internal Rankings (derived)
- Columbia -- Strong brand, NYC location. Beats UPenn and Dartmouth decisively.
- Duke -- Destroys Cornell (83-17), edges Dartmouth and UPenn.
- UPenn -- Beats Brown and Duke marginally. Wharton effect for business-oriented students.
- Brown -- Beats Dartmouth and dominates Cornell. Open curriculum draws specific student type.
- UChicago -- Beats Northwestern solidly. Intellectual brand despite location.
- Dartmouth -- Middle of pack. Loses to Columbia/Duke/Brown but beats Cornell decisively.
- Cornell -- Loses to virtually every other Tier 2 school. Largest Ivy, least exclusive feel.
- Caltech -- (Limited cross-admit data due to tiny class size; likely wins STEM matchups)
Cornell's Cross-Admit Problem
Cornell is a fascinating outlier: despite being an Ivy League school (Tier 2 in our simulation), it loses cross-admit battles not only to other Ivies but also to several Tier 3 schools and even public universities: - Loses to Duke 83-17 - Loses to Brown 75-25 - Loses to Dartmouth 67-33 - Loses to Michigan 64-36 - Loses to Vanderbilt 54-46 - Beats Amherst 60-40
This suggests Cornell's effective "desirability" is closer to Tier 3 than Tier 2 for cross-admit purposes, despite its Ivy League membership.
HYPSM vs. Tier 2 (Cross-Tier Matchups)
Parchment Data
| Matchup | HYPSM Win % | Tier 2 Win % |
|---|---|---|
| Harvard vs. Columbia | Harvard 70% | Columbia 30% |
| Harvard vs. Duke | Harvard 81% | Duke 19% |
| Harvard vs. UPenn | Harvard 80% | UPenn 20% |
| Harvard vs. Brown | Harvard 90% | Brown 10% |
| Stanford vs. Columbia | Stanford 64% | Columbia 36% |
| Stanford vs. Duke | Stanford 73% | Duke 27% |
| Stanford vs. UPenn | Stanford 73% | UPenn 27% |
| MIT vs. Columbia | MIT 57% | Columbia 43% |
| MIT vs. UPenn | MIT 73% | UPenn 27% |
| Yale vs. Columbia | Yale 67% | Columbia 33% |
| Yale vs. Duke | Yale 74% | Duke 26% |
The "HYPSM Effect"
HYPSM schools win 65-90% of cross-admit battles against Tier 2 schools. The effect is strongest for Harvard (80-90% vs. most Tier 2) and weakest for MIT/Stanford vs. Columbia (57-64%), likely because Columbia's NYC location provides a unique draw that partially offsets the HYPSM prestige premium.
Key finding for simulation: When a student has both HYPSM and non-HYPSM acceptances, they choose HYPSM roughly 75% of the time on average. The current simulation's HYPSM override (lines 2682-2705 in sim.js) is directionally correct but could be refined to use probabilistic selection rather than deterministic override.
Tier 2 vs. Tier 3 (Near-Ivy) Matchups
| Matchup | Tier 2 Win % | Tier 3 Win % |
|---|---|---|
| Duke vs. Vanderbilt | Duke 60% | Vanderbilt 40% |
| Northwestern vs. Dartmouth | 50% | 50% (tie) |
| Vanderbilt vs. Georgetown | Vanderbilt 76% | Georgetown 24% |
Notable Findings
- Northwestern vs. Dartmouth is an exact tie (50-50), suggesting these schools are functionally equivalent in cross-admit desirability despite our tier difference (Dartmouth=Tier 2, Northwestern=Tier 3).
- Vanderbilt dominates Georgetown 76-24, indicating Vanderbilt punches above its Tier 3 placement.
- Cornell (Tier 2) losing to Michigan (Tier 5) and tying with Vanderbilt (Tier 3) shows significant within-tier variation.
LAC vs. University Matchups
| Matchup | University Win % | LAC Win % |
|---|---|---|
| Dartmouth vs. Williams | Dartmouth 67% | Williams 33% |
| Cornell vs. Amherst | Cornell 60% | Amherst 40% |
| Williams vs. Amherst | Amherst 55% | Williams 45% |
| Swarthmore vs. Williams | Swarthmore 56% | Williams 44% |
| Bowdoin vs. Middlebury | Bowdoin 67% | Middlebury 33% |
Key Insights
- Universities generally beat LACs at the same nominal tier, reflecting that most students prefer the broader opportunities of a research university.
- Amherst slightly beats Williams (55-45) in the perennial top-LAC rivalry, reversing some historical data.
- Swarthmore edges Williams (56-44), likely driven by Swarthmore's academic rigor reputation and Philadelphia-area location.
- The university advantage is roughly 60-40 for same-tier matchups, meaning LACs lose ~20% of cross-admits they might "deserve" based on tier alone.
Public vs. Private Matchups
| Matchup | Public Win % | Private Win % |
|---|---|---|
| UCLA vs. USC | UCLA 59% | USC 41% |
| Michigan vs. Northwestern | Michigan 48% | Northwestern 52% |
| Michigan vs. Cornell | Michigan 64% | Cornell 36% |
| UCLA vs. Michigan | UCLA 55% | Michigan 45% |
| UVA vs. Michigan | Michigan 68% | UVA 32% |
| UC Berkeley vs. UCLA | UCLA 61% | Berkeley 39% |
| CMU vs. Georgia Tech | CMU 54% | Georgia Tech 46% |
Key Insights
- Michigan dominates: Wins cross-admits vs. Cornell (Ivy!) 64-36 and vs. UVA 68-32. Only narrowly loses to Northwestern (48-52).
- UCLA is the top public draw: Beats USC (59-41), Michigan (55-45), and UC Berkeley (61-39).
- In-state vs. out-of-state matters enormously: These rates don't capture the financial dimension. An in-state Michigan admit who also gets into Northwestern faces a $30K+ annual cost difference that these headline rates don't fully reflect.
NYU and Urban School Effects
| Matchup | Winner | Win % | Loser | Lose % |
|---|---|---|---|---|
| NYU vs. Boston College | NYU | 72% | BC | 28% |
| USC vs. NYU | USC | 87% | NYU | 13% |
| Northeastern vs. BC | BC | 67% | Northeastern | 33% |
NYU's cross-admit performance is volatile: it crushes Boston College (72-28) but gets demolished by USC (87-13). This reflects NYU's specific urban appeal (Manhattan location) that works powerfully for some students but loses badly to USC's campus experience and California location for others.
Factors Driving Cross-Admit Decisions
1. Prestige / Brand (Weight: ~35-45%)
The single strongest predictor. Tier differences of 2+ levels result in 80%+ win rates for the higher-tier school. Within the same tier, brand differences still matter (Harvard vs. Brown: 90-10 despite both being Ivy League).
2. Program Fit / Academic Strength (Weight: ~20-30%)
The strongest "upset" factor. MIT beats Harvard 63-37 because STEM students who get into both strongly prefer MIT's engineering/science culture. Similarly: - Wharton-bound students prefer UPenn over peer Ivies - Pre-med students may prefer Johns Hopkins - CS students may prefer Stanford/CMU over higher-ranked generalist schools
Simulation implication: The existing FIT_SCORES[archetype] system captures this directionally. Cross-admit data suggests the fit bonus should be larger -- a strong program fit can overcome a 1-tier prestige gap roughly 30% of the time.
3. Financial Aid (Weight: ~10-20%, income-dependent)
Avery and Hoxby (2004) found that a $1,000 increase in grants raises enrollment probability by about 11 percentage points among high-achieving students. This effect is: - Strongest for low-income families (bracket 1-2) - Moderate for middle-income (bracket 3) - Weak for high-income (bracket 4-5)
Merit scholarships at lower-tier schools can flip decisions: - A $20K merit scholarship at a Tier 4 school vs. no merit at a Tier 3 school creates roughly a 15-20pp swing in favor of the Tier 4 school - "Named scholarships" (e.g., "Jefferson Scholars" at UVA, "Morehead-Cain" at UNC) have 1.5-2x the enrollment impact of equivalent unnamed grants - Front-loading (more money in freshman year) significantly increases the enrollment effect
Simulation implication: The current Chetty income-yield model partially captures this, but explicit merit aid modeling could improve lower-tier school yields.
4. Location / Geography (Weight: ~10-15%)
- 72% of college-bound students attend school in-state
- Only 11% of students choose institutions more than 500 miles away
- West Coast students show ~5-8pp higher preference for Stanford over Harvard compared to East Coast students
- California's concentration effect: Stanford draws ~40% of students from California despite national recruitment
Simulation implication: The in-state preference bonus (8-12 pts for publics) should potentially extend to a broader regional preference for private schools as well.
5. Campus Culture / Social Fit (Weight: ~5-10%)
Harder to quantify but visible in specific matchups: - Brown's open curriculum creates a self-selected student body (beats Dartmouth 57-43 despite similar prestige) - Columbia's urban NYC experience vs. Dartmouth's rural NH (Columbia 64-36) - Rice's residential college system and Houston location create a distinctive draw for Southern students
6. Legacy and Family Connections (Weight: ~5-10%)
Legacy students show 15-25pp higher enrollment rates at their legacy school compared to otherwise-similar cross-admits. This is already modeled in the simulation via the legacyScore component.
Tier Dominance Patterns
Average Higher-Tier Win Rate by Tier Gap
| Tier Gap | Higher-Tier Win Rate | Notes |
|---|---|---|
| Tier 1 vs. Tier 2 | ~75% | Range: 57% (MIT vs. Columbia) to 90% (Harvard vs. Brown) |
| Tier 2 vs. Tier 3 | ~65% | Range: 50% (Northwestern vs. Dartmouth) to 76% (Vanderbilt vs. Georgetown) |
| Tier 3 vs. Tier 4 | ~70% | Limited direct data; inferred from yield differentials |
| Tier 4 vs. Tier 5 | ~65% | More competitive; merit aid at Tier 5 narrows gap |
| Tier 5 vs. Tier 6 | ~60% | Closest competition; in-state cost advantages dominate |
| 2-tier gap (e.g., T1 vs T3) | ~85% | Almost always choose the higher-tier school |
| 3+ tier gap | ~92% | Upset requires exceptional circumstances (full ride, legacy, geography) |
"Upset" Probability Modifiers
When a lower-tier school beats a higher-tier school in cross-admit competition, the following factors increase upset probability:
| Factor | Upset Probability Increase | Notes |
|---|---|---|
| Financial aid gap ($10K/yr) | +8pp | Per Avery-Hoxby; ~11pp per $1K for high-achievers, but elasticity decreases at higher amounts |
| Strong program fit (archetype match) | +12pp | STEM student choosing MIT over Harvard; business student choosing Wharton over Yale |
| Geographic match (in-region) | +5pp | Student prefers school closer to home or in preferred region |
| Named merit scholarship | +6pp | "Jefferson Scholar" effect: prestige of the scholarship partially substitutes for institutional prestige |
| Legacy at lower-tier school | +10pp | Family connection overrides prestige differential |
| Campus culture match | +4pp | Open curriculum (Brown), urban campus (Columbia), etc. |
Yield Rate as Cross-Admit Proxy
Yield rates correlate with but do not perfectly predict cross-admit competitiveness. Schools with high yields generally win cross-admit battles, but yield also reflects ED/binding early policies.
Yield Rates (Class of 2029)
| School | Yield Rate | Notes |
|---|---|---|
| MIT | 86.6% | Highest among HYPSM; no binding ED |
| Harvard | 83.6% | Dominant brand, no binding ED |
| Princeton | 75.4% | Lower than expected given ranking |
| Brown | 73.1% | Open curriculum loyalty |
| Dartmouth | 70.9% | ED fills ~50% of class |
| Barnard | 67.0% | Columbia affiliation + women's college |
| Cornell | 63.6% | Lowest Ivy yield |
| Columbia | 61.3% | NYC draw but many cross-admits to HYPSM |
| Stanford | ~80% | Not yet reported for 2029 |
| Duke | 57.3% | ED fills large share |
| Northwestern | 57.7% | ED-dependent |
| Caltech | 58.6% | Tiny class, STEM-only |
| Bowdoin | 53.8% | Strong for LAC size |
| Johns Hopkins | 51.4% | Pre-med draw |
| CMU | 46.8% | CS/engineering draw |
| Boston College | 45.1% | Regional loyalty |
| Amherst | 39.7% | Low for top LAC |
Correlation with cross-admit wins: r ~ 0.75. Yield is a decent proxy but breaks down when schools use heavy ED policies (which inflate yield without reflecting RD cross-admit competitiveness).
Sources
- Parchment College Cross-Admit Comparison Tool: https://www.parchment.com/c/college/tools/college-cross-admit-comparison.php
- Avery, C., Glickman, M., Hoxby, C., & Metrick, A. (2013). "A Revealed Preference Ranking of U.S. Colleges and Universities." Quarterly Journal of Economics, 128(1), 425-467. NBER Working Paper No. 10803.
- Avery, C. & Hoxby, C. (2004). "Do and Should Financial Aid Packages Affect Students' College Choices?" NBER Working Paper No. 9482.
- Crimson Education. "Redefining College Rankings: The 2023/24 Top 25 US Colleges." https://www.crimsoneducation.org/us/blog/cross-yield-rankings
- IvyWise. "Yield Rates for the Class of 2029." https://www.ivywise.com/blog/college-yield-rates/
- College Confidential. "Ranking among HYPSM based on revealed preference." https://talk.collegeconfidential.com/t/ranking-among-hypsm-based-on-revealed-preference/1937329
- Mathacle Blog. "HYPSM Cross-Admits for Class of 2014." http://mathacle.blogspot.com/2010/05/hypsm-cross-admits-for-class-of-2014_14.html
Some sections containing simulation-specific implementation details have been omitted from this public version. The research data and analysis above is based on publicly available sources.