SM-2 Calculator

Overview

Fluent uses SM-2 (SuperMemo 2) to decide when the learner next sees an item. This skill is the single source of truth for the algorithm. Every practice skill updates <data_dir>/spaced-repetition.json (where <data_dir> is resolved by fluent_paths.data_dir()) through these rules after each answered question.

When to Use

Load this skill whenever the tutor:

• Grades a review-queue item and must compute its next due date.
• Maps a 0-10 score to an SM-2 quality.
• Updates easiness_factor, interval_days, repetitions, or mastery_level on a spaced-repetition item.
• Decides which queue (today / tomorrow / this_week / later) to place an item in.

Skip this skill when the fluent-db-updater skill is already being used — the update-db.py script runs SM-2 internally.

Instructions

1. Convert score to quality

Score	Quality	Meaning
10/10	5	Perfect, instant recall
8-9	4	Correct after hesitation
6-7	3	Correct with difficulty
4-5	2	Incorrect but remembered when shown
2-3	1	Incorrect, familiar
0-1	0	Complete blackout

Rule: quality = floor(score / 2).

2. Update interval

if quality >= 3:   # correct
    if repetitions == 0:
        interval = 1
    elif repetitions == 1:
        interval = 6
    else:
        interval = round(previous_interval * easiness_factor)
    repetitions += 1
else:              # incorrect
    interval = 1
    repetitions = 0

3. Update easiness factor

Apply after every answer:

EF_new = EF + (0.1 - (5 - quality) * (0.08 + (5 - quality) * 0.02))
EF_new = max(1.3, EF_new)

4. Update mastery level

Track consecutive_correct and consecutive_incorrect per item:

if consecutive_correct >= 5:
    mastery_level = min(5, mastery_level + 1)
    consecutive_correct = 0
elif consecutive_incorrect >= 3:
    mastery_level = max(0, mastery_level - 1)
    consecutive_incorrect = 0

5. Update per-item fields

After each answer, the item in spaced-repetition.json must have:

• easiness_factor — updated via formula
• interval_days — new interval
• repetitions — incremented or reset
• consecutive_correct / consecutive_incorrect — one incremented, the other reset
• total_reviews — incremented
• mastery_level — possibly changed
• due_date — today + interval_days (YYYY-MM-DD)
• last_reviewed — today

6. Route to correct queue

After updating:

• interval_days == 1 → review_queue.tomorrow
• interval_days <= 7 → review_queue.this_week
• interval_days > 7 → review_queue.later

If the learner got it wrong (quality < 3), keep the item in review_queue.today so it reappears in the same session.

7. Preferred implementation

Do not hand-edit spaced-repetition.json. Call .claude/hooks/update-db.py with a review_results array — the script runs SM-2 atomically and rebuilds the queue. Only do manual math when the script is unavailable. See the fluent-db-updater skill for the payload schema.

python3 "${CLAUDE_PLUGIN_ROOT:-${CLAUDE_PROJECT_DIR:-.}}/.claude/hooks/update-db.py" <<'EOF'
{
  "session_id": "session-NNN",
  "date": "YYYY-MM-DD",
  "review_results": [
    { "item_id": "vocab_huis", "quality": 4 }
  ]
}
EOF

Examples

See .claude/references/sm2-worked-examples.md for 4 worked examples covering: correct answer (regular case), wrong answer (reset + EF drop), 5th consecutive correct (mastery bump), 3rd consecutive wrong (mastery drop). Each example shows the full before/after state.

Quick version:

• Correct, q=4: interval = round(prev * EF), repetitions += 1, EF barely moves.
• Wrong, q<3: interval = 1, repetitions = 0, EF drops sharply, item stays in today's queue.

Critical Rules

• Floor EF at 1.3. Never let the easiness factor drop lower — rounds to infinite daily reviews.
• Reset repetitions on wrong answer. The item returns to the start of the learning sequence.
• Do not hand-tune intervals. Trust the algorithm. Shortcuts break long-term retention.
• Prefer update-db.py. Only reimplement this math when the script is unavailable.

Why This Matters

SM-2 reviews items just before the learner forgets them, maximizing long-term retention per minute of practice. Wrong scheduling means wasted reviews (too early) or forgotten items (too late). The whole Fluent system rests on these numbers being correct.