How the
number works
The estimate is a Bayesian shrinkage toward the national FAR pass rate. Here is the entire arithmetic, the constants, and — the part that matters — the list of things it has not been validated against.
beta · not yet validated against real exam outcomes
1 · Mastery per Blueprint group
Every question and every simulation cell is attached to one group of the AICPA FAR Blueprint — 22 groups across three areas. Each group holds an ability estimate θ, updated on each answer:
b = −0.8 / 0.0 / +0.8 for difficulty 1 / 2 / 3
p_expect = σ(θ − b)
K = 1.6 / (1 + 0.25 × evidence)
θ ← θ + K × (observed − p_expect)
The learning rate K decays with evidence, so early answers move the estimate a lot and later ones move it less. A group with no answers in it is held at θ = 0 and marked untested — which is displayed differently from tested and weak. Treating those two as the same thing is the most common lie in adaptive study products.
2 · Rolling up to a section estimate
Groups roll up to areas by evidence weight, and areas roll up to the section by Blueprint weight. Untested groups are still counted — at 0.5, with their weight discounted to 0.35 — rather than being quietly excluded. Excluding them would let a candidate who has only practised their strongest area look finished.
w_group = 0.35 if untested, else 1 + ln(1 + evidence)
area_mastery = Σ(mastery × w_group) / Σ(w_group)
content_mastery = Σ(area_mastery × area_weight_normalised)
3 · The two halves
Multiple choice and simulations each carry about half the FAR score, so the predicted score is built from two halves. The simulation half is not inferred from the multiple-choice half:
tbs_component = 0.5 if you have done no cells
otherwise shrink(correct/cells) toward 0.5 with prior strength 6
blended = 0.5 × content_mastery + 0.5 × tbs_component
One consequence is deliberate and worth stating plainly, because it looks like a bug: a single simulation cell updates both halves — the Blueprint group it belongs to, and the simulation component. It therefore moves the estimate about twice as much as one multiple-choice question. This is not double-counting the same evidence; answering a cell correctly demonstrates two different things — that you know the topic, and that you can produce it under multi-cell time pressure. A design that separated them cleanly would also be defensible, but it would be a different calibration.
4 · Score, uncertainty, and the prior
predicted_score = 50 + 45 × blended
σ = 4 + 12 / √(1 + n)
p_model = σ((predicted_score − 75) / σ)
w = n / (n + 10)
p_pass = w × p_model + (1 − w) × 0.4212
n is the total count of questions and cells. With n = 0 the estimate is exactly the national rate. At n = 10 it is half the national rate and half the model. At n = 200 the prior is contributing about 5%. The interval widens as w falls, and widens by a further 8 points when no simulation cells have been recorded.
Why shrink to the national rate at all? Because the alternative is what the market already does: report a number derived only from your own recent practice, which for most candidates is both small and non-representative. A readiness figure that reads 85% after a strong week is describing the week, not the exam.
5 · What is not calibrated
This is the section other methodology pages do not have, and it is the reason to trust the rest of this one.
- The score mapping is a placeholder. 50 + 45 × blended was fitted by hand to three extreme cases — everything right, everything wrong, half right — anchored on the idea that a median candidate sits just below the pass line because the national rate is about 42%. It is not a regression on real “predicted score vs. actual outcome” data, because we have none.
- Nothing here has been validated against exam outcomes. Not one. The first real calibration sample will come from candidates who record an estimate before sitting and tell us the result afterwards.
- Two conservative mechanisms stack. Widening σ at low evidence and shrinking toward the prior both push low-evidence estimates toward the middle. That is intentional — we would rather understate than flatter — but it means the low-evidence range is more conservative than any data requires.
- Difficulty is coarse. Three levels, hand-assigned. Real item response theory would estimate difficulty from candidate data. We do not have the data yet.
- Self-reported input is unaudited. On the public calculator you supply your own counts, so the estimate inherits their errors.
Quote the number as an estimate that shows its uncertainty. It is not a prediction, and we do not describe it as accurate, calibrated, or validated, because it is none of those yet.
6 · Where the tutoring fits
When you miss a question, it opens by asking you one thing about the specific wrong choice you made, rather than pasting the explanation. You get the full walkthrough within a few exchanges either way — and if you would rather just have it, ask three times and it is yours.
Two things about that are worth stating precisely, because they are easy to overstate. First, the sequence is a rate limit, not a mastery gate: answering well gets you to the full walkthrough in three or four exchanges, and answering badly still gets you there — our own tests put the worst case at eight. Nobody is held at a wall. Second, the correct answer is not sent to your browser before the walkthrough stage; the front end does not have it to leak. That is a transport-layer fact about how the product is built, not a claim that a language model can never say too much.
Where the inputs come from
Two numbers in the arithmetic above are not ours and are worth being able to check. The prior is the 42.12% cumulative FAR pass rate for 2025, read off the AICPA’s own pass-rate page on 2026-09-05 and reproduced with its quarterly detail on our pass-rate page. The structural weights the group estimates are built on — three content areas and the split of the score between multiple-choice questions and simulations — come from the published Blueprint and the AICPA’s exam pages, and are laid out group by group on the Blueprint hub.
Everything else on this page is ours, including the shrinkage constant and the mastery-to-score mapping, and neither has been checked against exam outcomes.
Source: AICPA, “Learn more about CPA Exam scoring and pass rates” · checked 2026-08-15 · the 42.12% national FAR pass rate used as the prior
Source: NASBA, “CPA Examination” · checked 2026-08-15 · exam sections and administration