LMS Retention Landscape — 3D Spaced Repetition Field

Course Catalog

Days per second 2.0

Review threshold 80%

Avg. learner skill 0.7

Catalog size 36

Day

Avg. retention

–

Reviews / day

–

Mastered

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How it works

Every bar is one course module. Its height is that module's retention on the Ebbinghaus forgetting curve, decaying since its last review. There's no manual grading here — an autonomous simulated cohort reviews each module the instant it crosses the threshold, drawing a recall quality (0–5) from a distribution centred on "avg. learner skill" times the module's own difficulty. That quality feeds the SM-2 rule exactly as a real grade would: high quality both raises the ease factor and multiplies the memory-strength constant, so the bar's next decay is slower and it snaps back up to full height for longer next time.

R(t) = e^(−t / S)
q ~ N(5·skill·(1−difficulty), 1), clamped 0..5
q≥3: EF += 0.1−(5−q)(0.08+(5−q)·0.02); S = S·EF
q<3: reps=0, S = S·0.55   (lapse)

Days per second — simulated time advance rate for the whole catalog.
Review threshold — retention level at which a bar is auto-reviewed.
Avg. learner skill — shifts the recall-quality distribution up or down for every module in the field.
Catalog size — how many modules populate the grid; a larger catalog makes the review cadence visibly busier.

Real-world relevance: this is the view an LMS administrator's dashboard would show across an entire course — not one learner's single deck, but the aggregate health of every module's spaced-repetition schedule at once, which is what decides whether content stays "sticky" for a whole cohort.

New Learning Mastered Just reviewed

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