pdf-quiz-generator/docs/study-recommendations.md

How the study recommendations and the adaptive session work

Two questions were asked and owed an answer: how do the study recommendations work? and how would an adaptive session work? Both are built; this is what the code actually does, including the parts that are weaker than they look.

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1. Study recommendations

GET /study-tools/recommendations — backend/app/routers/study_tools.py.

What goes in

Only the learner's completed, non-expired, non-course answers:

QuizAttempt.user_id == user.id,
QuizAttempt.completed_at.isnot(None),
or_(QuizAttempt.expired == 0, QuizAttempt.expired.is_(None)),
Quiz.course_id.is_(None),
*([exam_filter] if exam_filter is not None else []),

exam_filter is the learner's chosen study objective. Answers to questions linked to a different exam are excluded, and so is that material from the denominator — someone revising for a paediatrics board who happens to sit a step-exam plan does not have it steer their recommendations. Questions linked to no exam stay in: unlinked means unclassified, not excluded.

Membership: the same answers, three ways

Every answer is attributed to a set of group keys, and the grouping decides what a key is:

Tab	Key	How a question reaches it
Articles	article id	the question's categories → the published article filed under one
Disciplines	top-level category id	the question's categories, rolled up to the top of the tree
Systems	organ-system tag id	the question's symptom keyword → the system that keyword is filed under

A question counts towards every ancestor it has, not just its primary category, and question_category_links adds cross-filed categories on top. So one answer on Kawasaki disease raises the count for Kawasaki, for Cardiology, and for the Kawasaki article.

Systems is the odd one: no question is tagged with an organ system directly. It carries a symptom keyword (question_tags.type = 'keyword') and 726 of those keywords have a system as parent_id. That path reaches 1,502 of 2,948 questions, which is why that tab states its own coverage instead of implying it can see the whole bank.

The four numbers per row

accuracy  = 100 * correct / answered            # what you actually scored
coverage  = 100 * seen / available              # how much of it you have met
relevance = 100 * available / denominator       # how much of the bank it is
readiness = 100 * (c + 8 * overall) / (n + 8)   # accuracy, shrunk

Readiness is the only one that is not arithmetic on raw counts. It is a plain empirical-Bayes shrinkage: a category's accuracy is pulled toward the learner's own overall accuracy in proportion to how few answers it has. With READINESS_PRIOR_ANSWERS = 8, one lucky question in a category does not read as mastery and one unlucky one does not read as a gap — the category has to earn its distance from your average. It stays locked until READINESS_UNLOCK_ANSWERS = 40 answers exist at all, because before that the learner's own average is not a stable thing to shrink toward.

It is not a psychometric score and not a prediction of any exam. The basis string returned with every response says so, in those words, because a number on a dashboard acquires authority it has not earned unless something tells the reader what it is.

Relevance divides by bank_total normally, but by grouped_total for Systems — dividing by the whole bank when the grouping can only see half of it would make every system look half as relevant as it is.

Ranking

gap    = max(0, (baseline - score) / 100)       # how far below your own average
unseen = 1 - coverage / 100
priority = gap * relevance + 0.25 * unseen * relevance

baseline is the learner's overall accuracy (70% before there is one). So a topic rises when it is weak and a big part of the bank. Material never touched has no gap to measure, so it enters at gap = 0.5 and is carried by the unseen term at quarter weight — enough to surface, not enough to crowd out a topic you are demonstrably failing.

The top three rows with any answers are flagged is_focus_area.

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2. The adaptive session

adaptive_select() — backend/app/services/quiz_builder.py.

Four steps:

1. Candidates. The filtered bank for the chosen categories/state/difficulty.
2. Unanswered first, sorted by the accuracy of their category — so a question you have never seen, in the area you are worst at, comes first. A category you have never answered in scores 0.5, which puts it mid-pack.
3. Then recycle. If there are not enough unanswered, previously answered questions are pulled back in, weighted 1 - 0.85 if you got it right and 1 - 0.25 if you got it wrong — so a question you failed is roughly five times likelier to return than one you passed. Ties break toward the oldest incorrect answer.
4. Damping. Each time a category is picked, its weight is halved (damping[category] *= 0.5). Without this a single weak category would fill the whole session; with it, the session walks across your weak areas.

Where it is weaker than it looks

• .limit(2000) on the candidate query. The bank is 2,948 questions, so adaptive selection cannot currently see about a third of it, and which third depends on database order. This is a real cap, not a tuning choice.
• accuracy() is computed per category from a linear scan — next((r[1] for r in rows if r[0] == qid), None) inside a loop over every answer. That is O(answers × candidates); at 2,000 candidates and a few thousand answers it is the slowest part of building a session.
• Difficulty is not used in the ordering, only as a filter. A genuine adaptive scheme would move up and down the difficulty range as you do well or badly; this one does not.
• Step 2 sorts by raw category accuracy, not readiness. The shrinkage that the recommendations page applies precisely so small samples do not mislead is not applied here, so a category with one wrong answer can sort first.

The first two are defects and are worth fixing. The last two are honest limitations of the current design and would be the substance of a better one.

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3. What the adaptive session should be

Written 2026-09-11, after the exam blueprint landed. The design below is not built; this is the argument for it, so the decision is on paper before the code is.

The thing that was missing

Every version of this so far has ranked questions by how badly you are doing and nothing else. That is half a question. The other half is how much it matters, and until today there was nothing in the database that could answer it — so the code guessed, by treating every category as equally worth an hour.

exam_blueprints.weight answers it now. The ABP publishes that preventive care is 12% of a general paediatrics paper and rheumatology is 2%. Six points of weakness in preventive care costs six times what the same weakness costs in rheumatology, and a session that does not know this will spend your evening in the wrong place while looking perfectly reasonable.

The score

For each topic, one number — the marks you would expect to gain by studying it:

expected_gain  =  relevance  ×  headroom  ×  confidence

• relevance — the domain's published weight, divided among the topics under it. From the blueprint. This is the part that is a fact rather than a model.
• headroom — 1 − readiness. How much of that share you are currently losing. Readiness is the shrunk accuracy the recommendations page already computes, not raw accuracy: one wrong answer out of one must not read as "you know nothing about neonatology".
• confidence — how much the estimate can be trusted, n / (n + k). A topic you have answered twice cannot outrank one you have answered forty times on the strength of a bad afternoon. This is what stops the session chasing noise.

Sort topics by expected gain; fill the session from the top, damped as now so one topic cannot take the whole session.

Then, within a topic: difficulty that moves

The current session filters by difficulty and then ignores it. It should walk: start near the learner's demonstrated level for that topic, step up after two right, step down after one wrong. The point is not to be hard, it is to sit where the information is — a question you would get right nine times in ten teaches nothing, and neither does one you would get right once in ten.

And a floor on coverage

A pure gain ranking will never show you a topic you are already good at, which is how people arrive at an exam having forgotten something they knew in March. Reserve a share of every session — a fifth, say — for spaced return: topics you were right about, longest ago first. This is the one part that should not be optimised, because its whole purpose is to be unwelcome.

What has to be fixed first

The two defects named in §2 are load-bearing here, not tidying:

• .limit(2000) means a third of the bank is invisible to selection. A scheme that reasons carefully about which question matters most, over an arbitrary two-thirds of the questions, is a scheme that reasons carefully about the wrong set.
• The O(answers × candidates) accuracy scan is already the slowest part of building a session. This design asks for per-topic readiness and per-topic difficulty, which makes it worse. It needs to become one grouped query.

What this deliberately does not do

No item-response theory, no per-question difficulty estimated from other learners' answers. Both would be better with enough data and worse without it, and a bank this size with a handful of learners does not have it. The weights are published, the readiness is measured, and the arithmetic above can be explained to a learner in two sentences — which is the point, because a session that cannot say why it chose a question is asking to be trusted rather than earning it.