Every chance, calculated step by step.

Each input contributes a number — a β coefficient— to a running sum of log-odds. The starting point is the school’s published acceptance rate converted to log-odds. The β values for stat band, rigor, EC tier, essay quality, legacy, first-generation, demonstrated interest, and application plan are added on. The final log-odds run through a sigmoid to produce a probability between 0 and 1.

All β values are locked by spec — re-litigation happens only when the spec is revised. Each is tagged below as either Research (anchored to a peer-reviewed source) or Estimated(rule-of-thumb pending recalibration). That distinction is shown on every chance result’s breakdown panel via the same badges.

Every contribution to the log-odds sum, with citation. Positive β raises the chance estimate; negative β lowers it. exp(β) is the multiplicative change in odds (e.g. β = +0.65 multiplies the odds of admission by ~1.92).

β_stat — academic-stat band Research

Source: Arcidiacono, Kinsler & Ransom (2019), Recruit to Reject? Harvard and African American Applicants (HCEO Working Paper). Top-decile non-ALDC admit rate at Harvard is 15.3% vs. 4.0% baseline (3.83×); top-quartile averages 2.7×. The β values above map to those empirical multipliers.

β_rigor — course rigor Research

Source: College Board AP/SAT predictive-validity studies; Geiser & Santelices (2007). Strong AP performance is the highest-correlation pre-college academic predictor of college success. When the school doesn’t offer AP/IB, the rigor signal is waived (no penalty, no boost).

β_ec — extracurricular tier Estimated

Anchored to AdmitEdge’s tier definitions (number of Tier-1/Tier-2 activities, depth, leadership). The empirical literature qualitatively confirms that stronger ECs correlate with admission at selective schools (Espenshade & Radford 2009) but doesn’t pin exact effect sizes. Values are conservative-side rule-of-thumb. Scaled by school selectivity (full β at sub-10% AR; compressed at higher AR).

β_essay — essay quality Estimated

Used only when essays are graded through our V-SPICE / admissions rubric tool. Self-reported essay quality is intentionally not trusted. Effect sizes are placeholder values pending direct empirical research on essay impact — published literature confirms essays matter at top schools but doesn’t quantify magnitude. Scaled by school selectivity, same brackets as β_ec.

β_legacy — legacy preference Research

Source: SFFA v. Harvard exhibits — legacy admit rate 33.6% vs ~6% non-legacy at Harvard (5.6× baseline). Compressed for stat-correlation (legacy applicants tend to have stronger stats too) and tiered down at less-selective schools. Gated on the school’s legacy-considered status — at legacy-blind schools (MIT, Caltech, Amherst, Tufts, Wesleyan, CMU, Pomona, Johns Hopkins; all UCs; UVA / Virginia Tech / William & Mary; Colorado, Maryland, and Illinois publics) β_legacy stays at 0.

β_firstGen — first-generation status Research

Source: Espenshade & Radford (2009), institutional-tier admit differentials by socioeconomic background. Effect size is largest at schools with explicit first-gen recruiting initiatives.

β_di — demonstrated interest Estimated

Anchored to admissions-reader anecdotes, not peer-reviewed literature. Gated: β_di fires only when the school’s acceptance rate is ≤ 40% AND the school self-reports applicant interest as considered/important/very important on its CDS Section C7. At schools that mark applicant interest as “Not Considered” (Stanford, HYP, USC, Caltech, Cornell, etc.) β_di stays at 0 regardless of how much interest the applicant has shown.

β_planAdjustment — early-decision plan adjustment Research

Source: CDS Section C21 ED/RD splits across Penn, Northeastern, and comparable ED-using schools. ED applicant pools are stronger than the published ED rate implies; β_planAdjustment compresses the ED bump for non-top-decile applicants accordingly. Top-decile applicants get the full published ED rate. RD / EA / Rolling plans take β = 0.

After Layer 1 sums the β contributions, the result is pulled toward the school’s published log-odds via a weight w ∈ [0.20, 0.85]:

logOddsFinal = w × logOddsLayer1 + (1 − w) × logOddsBase

wis high (0.85) when the applicant’s profile is rich (GPA + tests + rigor + ECs + essay + plan all present). It drops as signals go missing — for a profile with only GPA and a test score, w lands around 0.65. At sub-10% AR schools, w is capped at 0.75 to enforce extra shrinkage where holistic noise dominates outcomes regardless of stat strength.

The practical effect: estimates at the extremes are conservative. A top-decile profile applying to Stanford gets pulled meaningfully toward Stanford’s ~3.7% base rate, because at sub-10% AR schools, even maxed profiles face genuine uncertainty. A bottom-quartile profile at a 70%-AR public gets pulled toward that 70%, because schools at that selectivity admit broadly. The shrinkage prevents overconfident predictions at both ends of the AR spectrum.

Source: standard Bayesian conjugate-prior shrinkage. Mathematical framework follows the regression-to-the-mean construction in Gelman et al., Bayesian Data Analysis.

When you upload a SCOIR CSV from your high school’s counselor and mark the relevance setting, AdmitEdge blends the empirical (admits, applicants) sample for each school into Layer 2’s shrinkage anchor using a Beta-Binomial conjugate prior:

blended_prior =
  (n_scoir × p_scoir + n_prior × p_cds) /
  (n_scoir + n_prior)

Three relevance states:

• Matched (n_prior = 50): the SCOIR sample is broadly similar to your profile. The empirical rate dominates when the sample is large.
• Unmatched(n_prior = 200): the sample exists but doesn’t represent your profile well. The CDS rate dominates; SCOIR data only nudges the prior.
• Disabled (default): SCOIR data is ignored entirely, even if uploaded.

Hard floor: when fewer than 5 applicants from the school are reported for a given (school, plan) pair, SCOIR data is dropped — too noisy to blend even at high n_prior. Layer 1’s log-odds always anchor on the school’s published base rate; SCOIR only modifies the shrinkage direction.

High, Moderate, and Low describe input completeness, not output certainty. The label maps directly to the shrinkage weight w:

High confidence does notmean “we’re confident you’ll get in.” It means we have the data to compute a stable estimate; the estimate itself can still be a 4% reach or a 92% safety.

Honest disclosure. Each item below is something AdmitEdge knows it can’t see, and explains a class of cases where the displayed chance will be off.

Yield-protective behavior is separate from CDS C7 demonstrated interest

Yield-protective advisory fires when a school’s documented admissions behavior favors applicants who’ve shown interest. CDS C7 demonstrated-interest weight (β_di) fires only when the school self-reports applicant interest as a meaningful factor on its published Common Data Set. These are two different things — a school can be yield-protective without weighting interest in its CDS, and vice versa. USC, for example, marks DI as Not Considered on its CDS (so β_di stays at 0) but is still flagged yield-protective (so the advisory shows on top-quartile RD applicants without DI).

Public universities without published residency-split admit rates

For some public universities (Florida system: UF, FSU, UCF, FAU, UNF; and several others), residency-specific admit rates are not published. AdmitEdge uses the overall acceptance rate as a conservative estimate. Florida residents applying to UF, FSU, etc., should expect their actual chance to be meaningfully higher than the estimate shown; out-of-state applicants should expect their chance to be meaningfully lower.

Hooks not modeled

• Recruited athlete: admit rate is dominated by coach-contact decisions (~80–90% admit at top schools per SFFA exhibits). The model surfaces a static advisory; it doesn’t factor athletic recruitment into the chance number.
• URM / race-conscious admissions: post-SFFA the legal framework is in flux. Race is not a model input.
• Development case: applicants connected to a major donor or trustee are not modeled.
• Faculty / staff child: at schools where this preference exists, it isn’t in the model.
• Geographic preferences: state of residence beyond the in-state / out-of-state split is not modeled. Schools that recruit from underrepresented states (Caltech in Mississippi, e.g.) will produce conservative estimates for those applicants.

Major-specific rates: covered for highest-impact programs only

Penn (Wharton, SEAS), UC Berkeley (EECS, CoE), Cornell (CoE, CALS, ILR), CMU (SCS, CIT, Tepper), Georgia Tech (Computing, Engineering), USC (Viterbi, Marshall), NYU (Stern), and Michigan (Ross, CoE, CSE) have program-specific admit rates wired in. When the user’s intended major matches one of these programs, the chance model uses the program-specific rate as the base. All other schools fall through to the school overall, even when published per-major data exists. Coverage grows as primary sources are confirmed at audit cycles.

Year-over-year drift, interaction effects, unobserved factors

• Drift: admit rates and stat distributions shift cycle-over-cycle. AdmitEdge updates from each school’s most recent CDS; older CDS data ages out within ~2 cycles.
• Interactions: the log-odds model assumes the β contributions are additive. Real admissions decisions can have non-linear interactions (e.g. a maxed-stat applicant with weak essays at HYP is treated worse than the additive model predicts).
• Unobserved factors: recommendation strength, high-school context, application narrative, interview impressions, and admissions-officer judgment are not in the model. They’re real and they matter — they show up in the residual variance the shrinkage step accounts for, but the model can’t predict them.

• Arcidiacono, Kinsler & Ransom (2019) — Recruit to Reject? Harvard and African American Applicants (β_stat anchor)
• SFFA v. Harvard (2019) trial exhibits — legacy admit-rate disclosures (β_legacy anchor)
• Espenshade & Radford (2009), No Longer Separate, Not Yet Equal, Princeton University Press — institutional-tier admit differentials (β_firstGen anchor)
• Geiser & Santelices (2007) — AP performance and college success (β_rigor anchor)
• CDS Section C21 reports across Penn, Northeastern, and other ED-using schools (β_planAdjustment anchor)
• Gelman, Carlin, Stern, Dunson, Vehtari, Rubin — Bayesian Data Analysis (3rd ed.) — Layer 2 shrinkage framework
• Friedman, Sacerdote, Vegelius, Yagan (2025) — Test Scores at Ivy-Plus Colleges (NBER 33570) (sub-10% AR shrinkage cap rationale)