Every assumption, coefficient and limitation.
tl;dr (200 words)
We start from the published offer rate for your course. Then we shift it in log-odds space using factors that admissions data shows are predictive: grades, school type, TMUA score, STEP plan (Cambridge Maths), personal statement strength, interview prep, olympiad results, contextual flag, and college choice for Oxbridge. Each shift is small. None of them is fate. The largest single factor is the admissions test, which can move probability by up to 20pp. The smallest is interview prep at around 3pp. For Oxbridge we use a two-stage model: P(offer) = P(shortlist) x P(offer | shortlist). For Cambridge applicants we also surface the pool: ~700 applicants are pooled each year, ~22% of them get an offer from a different college. Around every estimate we display an 80% confidence band that reflects cycle-to-cycle variation, factors the public data does not capture, and small samples at niche courses. Source citations sit under each factor in the result card.
The model architecture
Uni Predictor is a logistic / Bayesian-style econometric model. All factors compose multiplicatively in log-odds space rather than as multiplicative percentages, which:
- Avoids the “stack to 100%” trap that breaks naive multiplicative models.
- Lets us compose adjustments cleanly without hard ceilings.
- Propagates uncertainty (variance on each adjustment sums in log-odds).
For Oxbridge we use a two-stage model: P(offer) = P(shortlist | application) × P(offer | shortlist). For non-interviewing universities (Imperial Maths and Computing, LSE, UCL) we use a one-stage model: P(offer | application) where the admissions test plus predicted grades carry the most weight.
The Cambridge pool
~700 Cambridge applicants are pooled each year. ~22% receive an offer from a different college. Our model computes P(combined) = P(direct) + P(rejected directly but pooled) × P(pool offer). Pool entry probability is calibrated to peak around the direct-offer rate; very strong and very weak applicants pool less. Cambridge Maths pools at ~25%, Computer Science at ~22%, Engineering at ~21%, Economics at ~18%. These are 2024-cycle averages.
The coefficients
- Grade effect: Conservative weights from a calibrated log-odds curve centred on the A*A*A baseline. Validates against Cambridge 2022-2024 profile data (94.7% of UK accepts achieved A*AA+).
- School type: Boliver odds ratio (2013) of 0.59 for state-vs-independent at equivalent grades, blended with each university's own grade-controlled gap (per OfS 2024). Cambridge grammar-school applicants accept at 24.4% in 2024, beating Independent at 21.6%. We bake this in.
- TMUA / ESAT score: Course-specific log-odds curves derived from typical successful applicant ranges. TMUA weights are calibrated slightly higher than published research alone supports. This reflects direct conversations with current Cambridge maths tutors and recent students who consistently rate TMUA as a heavyweight factor. As Cambridge Assessment publishes more TMUA-specific outcome data, we will recalibrate.
- STEP (Cambridge Maths): Massive binding constraint. About 48% of Cambridge Maths offer-holders convert to a place each cycle. STEP grade 1 carries a +0.26 log-odds shift; STEP S adds +0.79.
- Personal statement: Sutton Trust 2016 “Making a Statement” informs the per-course weight. Weight is low for Oxbridge maths (tutors openly downweight), medium for Cambridge Economics / Oxford Maths-Philosophy, high for no-interview LSE Economics.
- College choice (Oxbridge): Real per-subject offer-rate multipliers from Cambridge Admissions Statistics 2024 and Oxford's college-level data. Trinity Maths sits at 18.6% vs Robinson Maths at 33.9%, same profile.
- Contextual flag: OfS contextual offer programmes uplift 7-15pp on offer probability at high-tariff Russell Group. We use course-specific positive effects when available (Cambridge CS POLAR Q1 outperforms Q3-5) and the OfS generic uplift otherwise. Negative course-level effects are not applied (they reflect the STEP funnel, not a contextual penalty).
- Predicted-grade uncertainty: UCAS's 16% prediction-accuracy figure widens the confidence band by 1.4× when grades are predicted (not achieved). FE / sixth-form-college predictions are the least reliable.
The data we built on
- UCAS End-of-Cycle reports 2019-2025.
- 4 FOI returns (Cambridge Maths STEP, Imperial Maths, Oxford MAT, Cambridge applications-by-Apply-Centre).
- Cambridge Undergraduate Admissions Statistics 2022, 2023, 2024 cycles.
- Oxford Mathematical Institute Feedback PDFs 2020-2025; Oxford CS Feedback 2023-2025.
- Imperial College 5-year transparency workbook and per-department TMUA / ESAT dashboard.
- LSE Planning Division Tableau dashboard plus 2020 / 2021/22 entry XLSX FOI returns.
- UCL Apps-per-Place 2024-25 and 2025-26 PDFs.
- OfS contextual admissions framework plus 2019 “Promoting Fairness and Rethinking Merit”.
- Sutton Trust “Making a Statement” (2016), “Access to Advantage” (2018).
- Boliver (2013) British Journal of Sociology paper on Russell Group access.
- OCR STEP Explanation of Results 2024 and 2025 plus STEP Support Programme.
- UKMT BMO1 / BMO2 awards data and UK IMO squad results.
- Cambridge college-level data: real per-subject offer rates from 2022-2024 cycles.
Known limitations
- TMUA-specific predictive validity has not been independently peer-reviewed. Cambridge actively refuses to publish a TMUA-to-offer threshold. Our weighting blends published cohort ranges with current-student / current-tutor knowledge and is recalibrated whenever new data emerges.
- Predicted-grade inflation. Only 16% of UCAS predictions are exactly accurate (Wyness 2016). Predicted grades are systematically over-predicted, especially at FE / sixth-form colleges. The confidence band widens to compensate.
- Personal statement weight is qualitative. Sutton Trust's effect estimates inform our weights but we cannot directly observe how an individual PS scores.
- Per-college, per-course data is partial for Oxford. Cambridge publishes college-level subject offer rates; Oxford only publishes college-level all-subject rates. Our Oxford college multipliers blend the all-subject signal with the small number of college-level subject feedback PDFs.
- Oxford 2026 TMUA cycle is the first ever. Oxford's TMUA thresholds are extrapolated from MAT-era data and Cambridge TMUA cohorts. High uncertainty. The confidence band reflects this.
Frequently asked questions
What model architecture does the Uni Predictor use?
A logistic, Bayesian-style econometric model. All factors compose multiplicatively in log-odds space rather than as multiplicative percentages, which avoids the “stack to 100%” trap, lets us compose adjustments cleanly without hard ceilings, and propagates uncertainty so variance on each adjustment sums in log-odds.
How does the Oxbridge two-stage model work?
For Oxbridge we decompose P(offer) into P(shortlist | application) × P(offer | shortlist). For non-interviewing universities (Imperial Maths and Computing, LSE, UCL) we use a one-stage model where admissions test plus predicted grades carry most of the weight.
How is the TMUA coefficient calibrated?
Course-specific log-odds curves derived from typical successful applicant ranges. TMUA weights are calibrated slightly higher than published research alone supports, reflecting direct conversations with current Cambridge maths tutors and recent students. We recalibrate when Cambridge Assessment publishes new TMUA outcome data.
How does the Cambridge pool factor into the prediction?
Around 700 Cambridge applicants are pooled each cycle. Around 22% of them receive an offer from a different college. The model computes P(combined) = P(direct) + P(rejected directly but pooled) × P(pool offer). Pool entry probability peaks around the direct-offer rate. Cambridge Maths pools at around 25%, CS at 22%, Engineering at 21%, Economics at 18% (2024 averages).
What does the confidence band represent?
An 80% confidence interval that captures cycle-to-cycle variation, factors the public data does not measure (interview performance, personal statement quality), and small-sample noise at niche courses. Predicted grades widen the band by 1.4× compared to achieved grades, reflecting the 16% UCAS prediction-accuracy figure from Wyness (2016).
Why does state vs independent school matter?
We use the Boliver (2013) odds ratio of 0.59 for state vs independent at equivalent grades, blended with each university's own grade-controlled gap (per OfS 2024). Cambridge grammar-school applicants actually accepted at 24.4% in 2024, ahead of independent at 21.6%, so we bake the real direction in rather than the headline assumption.
How are Oxford college multipliers derived?
Oxford only publishes college-level all-subject rates, not per-subject. Our Oxford college multipliers blend the all-subject signal with the small number of college-level subject feedback PDFs the Mathematical Institute and CS Department do publish. Confidence bands widen for Oxford colleges where per-subject data is thin.
What are the known limitations of the model?
TMUA-specific predictive validity has not been peer-reviewed. Predicted-grade inflation is systematic (only 16% accurate per Wyness 2016). Personal statement weight is qualitative. Oxford per-college, per-course data is partial. Oxford 2026 TMUA cycle is the first ever, so thresholds are extrapolated from MAT-era data and Cambridge cohorts.
Version
v2.0 (Uni Predictor) calibrated 2026-05-19. The model recalibrates whenever new End-of-Cycle data or FOI returns arrive.