FSRS vs SM-2 for Language Learners

The short answer

FSRS (Free Spaced Repetition Scheduler) is a better scheduler than classic SM-2 for language learners because it predicts your chance of recalling each item, then places the next review near that forgetting point. SM-2 mostly multiplies intervals with an ease-factor heuristic. It works, but it does not model recall probability item by item.

In large Anki-collection benchmarks, FSRS-6 showed roughly 4.37% RMSE (bins) versus about 14.84% for Anki SM-2, and a 99.6% superiority rate (lower log loss for nearly every user). Treat those figures as dated snapshot evidence from the public Expertium benchmark, not eternal constants.¹ For vocabulary and grammar with wildly uneven difficulty, better predictions mean fewer wasted reviews on easy cognates and fewer late lapses on stubborn conjugations. For the broader memory model, see how spaced repetition works; for retention targets and tuning habits, see how to optimize spaced repetition.

SM-2: ease-factor heuristics

SM-2 (SuperMemo-2) is the decades-old algorithm behind classic Anki scheduling and many flashcard apps. After each review you pick a grade. The scheduler updates an ease factor and multiplies the previous interval to pick the next due date. "Good" stretches the gap; "Again" resets you to short intervals.

That design is simple and surprisingly effective. It is also a heuristic stack, not a calibrated memory model. SM-2 does not maintain an explicit probability of recall for each card. It assumes that multiplying intervals by ease will land somewhere near a useful spacing schedule for a typical learner. When material difficulty varies a lot, or when your grades are noisy, ease drifts. Cards can get stuck in short-interval "ease hell," or stretch too far and fail when you finally see them again.

The Expertium benchmark notes an important fairness caveat: SM-2 was not built to output probabilities. Benchmarks convert its intervals into predicted recall with extra assumptions so it can be scored against modern models.¹ Even with that conversion, SM-2 lags well-calibrated DSR schedulers on prediction error.

FSRS: the DSR memory model

FSRS tracks three state variables per item, often called the DSR model:

• Difficulty (D): how hard the item tends to be for you.
• Stability (S): how slowly recall probability decays (roughly, how many days until retrievability falls to a reference level).
• Retrievability (R): your estimated probability of recall right now.

When you review, FSRS updates those variables from your grade and schedules the next appearance when R is expected to hit your desired retention (often around 90%). Ye, Su, and Cao (2022) formalize spaced-repetition scheduling as optimizing review cost against a memory model trained on large learner logs, rather than relying on fixed multipliers alone.²

This post is the comparison for language learners, not a full FSRS walkthrough. For DSR definitions, machine-learning personalization, and why hard successful recalls grow stability more than easy ones, read how spaced repetition works. For choosing a retention target and avoiding common tuning mistakes, read how to optimize spaced repetition.

What the Expertium numbers actually mean

Expertium's public benchmark evaluates spaced-repetition algorithms on thousands of Anki collections and hundreds of millions of review events (on the order of ~350 million filtered reviews used for evaluation in the write-up).¹ Three ideas matter for learners:

1. RMSE (bins) measures calibration: how close predicted recall probability is to observed retention in binned reviews. Lower is better. Snapshot figures commonly cited for FSRS-6 versus Anki SM-2 are about 4.37% versus 14.84%.
2. Log loss scores how well each individual predicted probability matches the binary outcome (forgot vs remembered). Lower is better.
3. Superiority is the share of users for whom algorithm A has lower log loss than algorithm B. FSRS-6 (with recency weighting) shows 99.6% superiority over Anki SM-2 in that matrix.

Those numbers can move as datasets, filters, and algorithm versions change. Use them as evidence that modern DSR schedulers predict recall far more accurately than SM-2-style heuristics on real review histories, not as a guarantee that your personal deck will shrink by a fixed percentage tomorrow.

Why better predictions matter for language

Language decks are not uniform. A Spanish cognate like animal and an irregular past form like fue do not forget on the same curve. SM-2's shared ease logic often over-reviews the easy items and under-protects the hard ones. FSRS's per-item difficulty and stability let intervals diverge: solid words stretch out; fragile grammar stays closer.

That matters twice for production practice:

• Review load: Over-scheduling known material burns the minutes you need for writing full sentences. Under-scheduling hard forms creates surprise failures just when you are trying to compose.
• Honest signals: Spaced repetition only works if each grade reflects one memory unit. If a sentence packs several due words and you only store pass/fail for the whole string, any scheduler (FSRS or SM-2) gets corrupted labels. Per-concept grading is the missing half of the story; see word-by-word grading for language learning.

In short: FSRS improves when to ask. Granular attribution improves what the ask is about. Language apps that combine both can schedule vocabulary and grammar inside novel sentences without punishing known pieces for a single typo.

What FSRS does not replace

A better algorithm does not turn recognition quizzes into fluency. FSRS schedules retrieval events; it does not invent the right exercise format. Multiple-choice still tests recognition. Static sentence mining still binds memory to one string. Open prompts without a forcing function still let you avoid the exact concept that was due.

LinGoat uses FSRS for timing of words and grammar concepts, then generates native-to-target sentence translations that pack due items into novel natural sentences and grades each concept individually. That is written active production plus SRS, not a speaking replacement. The full loop is spelled out in LinGoat's full pedagogy.

See how LinGoat works or try the app.

References

1. Expertium. Benchmark of spaced repetition algorithms. https://expertium.github.io/Benchmark.html (RMSE and superiority figures cited as a dated public snapshot; values may change as the benchmark is updated).
2. Ye, J., Su, J., & Cao, Y. (2022). A Stochastic Shortest Path Algorithm for Optimizing Spaced Repetition Scheduling. Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 4381-4390. https://doi.org/10.1145/3534678.3539081