Supply-Side Agent Modeling: Students & High Schools

supply-side.md

Supply-Side Agent Modeling: Students & High Schools

Research for the college admissions Agent-Based Model (ABM). Covers statistical distributions, feeder school effects, application strategy, student archetypes, and high school type distributions.

1. Correlated GPA/SAT Distributions

Real-World National Statistics

GPA by demographic group:

• Asian/Pacific Islander: 3.52

• White: ~3.09

• Hispanic: ~2.84

• Black: 2.68

• Affluent schools: ~3.0

• Less affluent schools: ~2.59

GPA in core subjects only: 2.79 (overall 3.0 boosted by non-core electives).

GPA-SAT Correlation

The correlation between high school GPA and SAT scores is approximately r = 0.5 to 0.65 depending on the population studied:

• College Board research found SAT sections correlate with first-year college GPA at r = 0.47-0.51 (adjusted for HS GPA).

• Combined SAT + HS GPA explains ~15% more variance than GPA alone.

• At Ivy-Plus schools (Opportunity Insights, 2024), SAT/ACT scores are more predictive of college GPA than high school grades.

For simulation, use r = 0.6 as the GPA-SAT correlation coefficient.

Competitiveness Thresholds

Algorithm: Generating Correlated GPA/SAT with Box-Muller + Cholesky

To generate correlated bivariate normal samples (GPA, SAT) in JavaScript:

Step 1: Box-Muller Transform (generate two independent standard normal variates)

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6Mjg2LCJhdHRycyI6eyJieSI6ImFpOmNsYXVkZSJ9fV0= function boxMuller() { let u1, u2; do { u1 = Math.random(); } while (u1 === 0); // avoid log(0) u2 = Math.random(); const z0 = Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2); const z1 = Math.sqrt(-2 * Math.log(u1)) * Math.sin(2 * Math.PI * u2); return [z0, z1]; }

**Step 2: Cholesky Decomposition for 2x2** (apply correlation)

For a 2x2 correlation matrix with correlation `rho`:

L = [[1, 0], [rho, sqrt(1 - rho^2)]]

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6MTk0LCJhdHRycyI6eyJieSI6ImFpOmNsYXVkZSJ9fV0=
function generateCorrelatedPair(rho) {
  const [z0, z1] = boxMuller();
  const x = z0;
  const y = rho * z0 + Math.sqrt(1 - rho * rho) * z1;
  return [x, y]; // two correlated standard normals
}

Step 3: Scale to GPA and SAT distributions

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6NTEzLCJhdHRycyI6eyJieSI6ImFpOmNsYXVkZSJ9fV0= function generateStudentStats(config) { const { gpaMean = 3.0, gpaSD = 0.65, satMean = 1050, satSD = 220, rho = 0.6 // GPA-SAT correlation } = config;

const [zGPA, zSAT] = generateCorrelatedPair(rho);

let gpa = gpaMean + gpaSD * zGPA; let sat = satMean + satSD * zSAT;

// Clamp to valid ranges gpa = Math.max(0.0, Math.min(4.0, gpa)); sat = Math.max(400, Math.min(1600, Math.round(sat / 10) * 10)); // round to nearest 10

return { gpa: Math.round(gpa * 100) / 100, sat }; }

**Step 4: Vary parameters by school type** (see Section 5)

Each high school type can have different `gpaMean`, `gpaSD`, `satMean`, `satSD`, and `rho` to reflect different student populations.

### Grade Inflation Adjustment

GPA inflation has been significant: in 2016, 47% of seniors graduated with an A average, up from 38% in 1998. AP/IB enrollment at affluent schools has expanded much faster, inflating weighted GPAs.

**Simulation approach:** Assign each school a `gpaInflation` factor (0.0 to 0.4) that gets added to raw GPA, then clamp at 4.0. Elite private schools may have grade deflation (negative adjustment) while some public schools have inflation.

***

## 2. Feeder School Multipliers

### What Are Feeder Schools?

Feeder schools are high schools that send a disproportionate number of graduates to elite universities. The Harvard Crimson (2024) found that **1 in 11 students** accepted to Harvard comes from just **21 high schools**. Of the top 100 feeder schools to Ivy League, **94 are private**.

### Key Feeder Schools and Their Rates

| School                   | Type             | Ivy+ Acceptance Rate                         | Notes                         |
| ------------------------------------------------------------------------------- | ----------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------ |
| Phillips Exeter Academy  | Private boarding | ~19% to HYPSM                                | ~40% to top-25 schools        |
| Phillips Academy Andover | Private boarding | ~11 students/year to Harvard from ~350 grads | ~3% of class to Harvard alone |
| Trinity School (NYC)     | Private day      | ~40% to Ivy League                           | Top NYC feeder                |
| The Dalton School (NYC)  | Private day      | ~31% to Ivy League                           | Strong Cornell/Brown/Columbia |
| Stuyvesant High School   | Public exam      | 40.9% Ivy League (Class of 2021)             | Top public feeder             |
| Boston Latin School      | Public exam      | 100+ students to Harvard 2009-2024           | Top public feeder             |

**Key insight:** 12 of the 21 top Harvard feeders are private, with tuition in the $50K-60K range. However, many feeder school admits are recruited athletes, so the "typical student" advantage may be less than aggregate numbers suggest.

### Why Feeder Schools Have an Advantage

1. **Dedicated college counselors** with 30-40 student caseloads (vs. 400+ at public schools)
2. **Institutional relationships** with admissions offices
3. **Course rigor** recognized by admissions (AP/IB/honors curriculum well-known to AOs)
4. **Legacy/donor concentration** (wealthy alumni families)
5. **Recruited athletes** (especially in sports like rowing, lacrosse, fencing)

### How Colleges Assess School Rigor

* Admissions officers receive a **School Profile** with each transcript showing curriculum difficulty, grading scale, and course offerings.

* AP exam scores serve as a **standardized benchmark** that normalizes across schools.

* Schools are assessed in context: a 3.5 at a known grade-deflating school is valued differently from a 3.9 at a known inflating school.

## 3. Application Portfolio Strategy

### National Application Statistics (2024-2025)

| Metric                                        | Value         | Source                                  |
| ---------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------- |
| Average applications per student (Common App) | 6.80          | Common App End-of-Season Report 2024-25 |
| Total Common App applicants                   | ~1.5 million  | Common App                              |
| Total applications submitted                  | ~10.2 million | Common App                              |
| YoY increase in apps per student              | +2%           | Common App                              |
| YoY increase in applicant count               | +5%           | Common App                              |
| Common App school limit                       | 20 schools    | Common App policy                       |

### Application Counts by Student Tier

The national average of 6.8 masks huge variance by student ambition level:

| Student Type                 | Typical App Count | Safety | Target | Reach |
| ----------------------------------------------------------------------------------- | ------------------------------------------------------------------------ | ------------------------------------------------------------- | ------------------------------------------------------------- | ------------------------------------------------------------ |
| Low-ambition / local         | 2-4               | 1-2    | 1-2    | 0     |
| Average college-bound        | 5-8               | 1-2    | 2-4    | 1-2   |
| High-achiever (T20 aspirant) | 10-15             | 1-2    | 3-4    | 6-9   |
| Shotgunner                   | 16-20             | 1-2    | 2-3    | 12-15 |

**The "shotgun" approach** (applying to 16-20+ schools, mostly reaches) has become increasingly common among T20 aspirants. The Common App limit of 20 schools is the hard cap.

### The Portfolio Rule

The commonly cited "2-3-5" rule (2 safeties, 3 targets, 5 reaches) is a simplified heuristic. More accurate guidelines from College Board and counselors:

* **50% of list** should be target/match schools

* **2-3** safety schools (schools where your stats exceed the 75th percentile)

* **2-4** reach schools (schools where your stats are below the 25th percentile)

### How Students Classify Safety/Target/Reach

Based on the student's own GPA and SAT relative to the school's admitted student profile:

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6NTEyLCJhdHRycyI6eyJieSI6ImFpOmNsYXVkZSJ9fV0=
function classifySchool(student, college) {
  // Compare student stats to college's middle 50% range
  const satMid = (college.sat25 + college.sat75) / 2;
  const gpaMid = (college.gpa25 + college.gpa75) / 2;

  const satDelta = (student.sat - satMid) / (college.sat75 - college.sat25);
  const gpaDelta = (student.gpa - gpaMid) / (college.gpa75 - college.gpa25);
  const composite = (satDelta + gpaDelta) / 2;

  if (composite > 0.5) return 'safety';
  if (composite > -0.3) return 'target';
  return 'reach';
}

4. Student Archetypes

ALDC Composition at Elite Schools (Harvard Data)

ALDC = Athletes, Legacies, Dean's Interest List (donors), Children of faculty/staff.

Key stat: Among white admits to Harvard, over 43% are ALDC. Among non-white admits, ALDC share is less than 16%.

SAT-Equivalent Advantage of Hooks

Research (Espenshade & Radford, 2009; Arcidiacono et al., 2019) estimated admission advantages equivalent to SAT point bonuses:

Income Distribution Context (Chetty/Opportunity Insights)

• 67% of Harvard undergrads come from the top 20% of the income distribution

• Only 4.5% come from the bottom 20%

• Children with parents in the top 1% are 77x more likely to attend an Ivy-Plus college than children from the bottom 20%

• Among Harvard recruited athletes (Class of 2025): 83% white, 46.3% from families earning $250K+

5. High School Type Distributions

National School Breakdown

Source: NCES, Pew Research Center (2024), MDR Education

Private school sub-types:

• Religious (Catholic, etc.): ~60% of private schools

• Independent/prep: ~25%

• Elite boarding (NAIS top-tier): ~50-100 schools nationally

School Type Effects on GPA and Rigor

Key insight on GPA inflation: AP/IB enrollment at affluent schools has expanded much faster, creating wider GPA inflation at those schools. A student from a rigorous private school may have 3.57 unweighted while peers at other schools show 3.8-4.4 for equivalent ability.

T20 Admit Source Distribution

Approximate breakdown of where T20 admits come from:

The "1 in 11" stat: 21 high schools account for ~9% of Harvard admits. These 21 schools represent less than 0.1% of all US high schools.

Most Ivy League schools admit roughly 25% from private schools and 60-70% from public schools, but this merely reflects application volume -- private school students are proportionally much more likely to apply to and attend elite schools.

6. Complete Student Generation Pipeline

Putting it all together, the simulation should generate students in this order:

Step 1: Generate High Schools

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6NDM5LCJhdHRycyI6eyJieSI6ImFpOmNsYXVkZSJ9fV0= function generateHighSchools(count) { const schools = []; for (let i = 0; i < count; i++) { // Weight by frequency const type = weightedRandomPick(HIGH_SCHOOL_TYPES); const config = HIGH_SCHOOL_TYPES[type]; schools.push({ id: i, type: type, name: generateSchoolName(type), ...config, studentCount: randomInt(config.studentCount.min, config.studentCount.max) }); } return schools; }

### Step 2: Generate Students per School

```javascript proof:W3sidHlwZSI6InByb29mQXV0aG9yZWQiLCJmcm9tIjowLCJ0byI6MTUwMywiYXR0cnMiOnsiYnkiOiJhaTpjbGF1ZGUifX1d
function generateStudentsForSchool(school) {
  const students = [];
  for (let i = 0; i < school.studentCount; i++) {
    // Pick archetype based on school's weights
    const archetype = weightedRandomPick(school.archetypeWeights);
    const archetypeConfig = STUDENT_ARCHETYPES[archetype];

    // Generate correlated GPA/SAT using school params + archetype boosts
    const adjustedGPAMean = school.gpaMean + archetypeConfig.gpaBoost + school.gpaInflation;
    const adjustedSATMean = school.satMean + archetypeConfig.satBoost;

    const { gpa, sat } = generateStudentStats({
      gpaMean: adjustedGPAMean,
      gpaSD: school.gpaSD,
      satMean: adjustedSATMean,
      satSD: school.satSD,
      rho: 0.6
    });

    // EC and essay strength with randomness
    const ecStrength = archetypeConfig.ecStrength + (Math.random() - 0.5) * 0.3;
    const essayStrength = archetypeConfig.essayStrength + (Math.random() - 0.5) * 0.3;

    // Application count
    const appCount = randomInt(
      archetypeConfig.appCount.min,
      archetypeConfig.appCount.max
    );

    students.push({
      id: `${school.id}-${i}`,
      schoolId: school.id,
      archetype,
      gpa,
      sat,
      ecStrength: clamp(ecStrength, 0, 1),
      essayStrength: clamp(essayStrength, 0, 1),
      hookMultiplier: archetypeConfig.hookMultiplier,
      appCount,
      ambition: archetypeConfig.ambition + (Math.random() - 0.5) * 0.2,
      feederMultiplier: school.feederMultiplier
    });
  }
  return students;
}

Step 3: Build Application Lists

Each student builds a portfolio of safety/target/reach schools based on their stats, archetype, and ambition level (see Section 3 algorithm).

Step 4: Submit to Admission Rounds

Students submit applications through the ED -> EA/REA -> EDII -> RD pipeline based on their strategy (determined by archetype and ambition).

Sources

• College Board, "2024 Total Group SAT Suite Annual Report" (2024)

• NCES, "America's High School Graduates" (2011) - GPA distribution data

• Arcidiacono, Kinsler, Ransom, "Legacy and Athlete Preferences at Harvard," Journal of Labor Economics (2022)

• Chetty et al., "Diversifying Society's Leaders?" Opportunity Insights (2023)

• The Harvard Crimson, "Most Schools Dream of Sending Students to Harvard. These 21 Expect To." (2024)

• Common App, "End-of-Season Report 2024-2025"

• Pew Research Center, "Facts about public, private and charter schools in the US" (2024)

• Espenshade & Radford, "No Longer Separate, Not Yet Equal" (2009) - SAT-equivalent hook bonuses

• NCES Fast Facts on Charter Schools (2024)

• PrepScholar, BestColleges, College Board counselor resources

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.