A 2019 paper in Nature Communications, by Robert Wilson, Amitai Shenhav, Mark Straccia and Jonathan Cohen, found that for a broad class of learning algorithms, training progresses fastest when the error rate is held around 15.87% โ€” roughly 85% accuracy. Get everything right and the learner is wasting attempts on things they've already mastered. Get too much wrong and the signal becomes noisy and unproductive. There's a sweet spot in between, and it's closer to "mostly right, sometimes wrong" than "always right."

What the paper actually studied

Wilson and colleagues were working in computational learning theory, modelling how gradient-descent-based learning systems โ€” a mathematical framework used both to train artificial neural networks and to model biologically plausible learning in animals โ€” improve fastest. They derived that for tasks involving a binary choice (correct vs incorrect, this vs that), the optimal training error rate that maximises the rate of improvement sits at roughly 15.87%, i.e. about 85% correct.

The intuition behind the maths: a task the learner already gets right 100% of the time provides essentially zero new information โ€” there's nothing left to correct, nothing left to learn from. A task the learner gets right only 50% of the time (chance level, for a binary choice) is so hard the errors become noisy and uninformative โ€” the learner can't tell what specifically is going wrong. Somewhere in between, the errors are frequent enough to carry real signal about where the gaps are, but rare enough that most of what's being practised is landing.

The honest caveat, stated plainly

It's worth being precise about what this paper does and doesn't claim, because "the 85% rule" gets repeated in education and edtech marketing more loosely than the original research supports. The derivation is specifically for two-choice classification-style tasks under a gradient-descent-like learning rule โ€” closer to a mouse learning to distinguish two visual patterns than to a Year 9 student writing an extended maths proof. The paper does not claim every classroom task should be tuned to exactly 85% accuracy. Treating "85%" as a literal universal target for KS3 homework is an extrapolation the paper itself doesn't make.

What the paper does support, more modestly, is the underlying shape of the idea: for tasks with a meaningful right/wrong structure, the fastest learning happens at moderate difficulty โ€” mostly succeeding, regularly failing โ€” not at either extreme.

Why this matters for reading a report card or a homework score

The practical implication, read cautiously, still cuts against a common instinct. Parents often treat a high score โ€” 95%, 100% โ€” as unambiguously good news. Per this research, a KS3 student consistently getting everything right on their practice work isn't necessarily thriving; they may simply be working below their actual level, where the task has stopped generating new information. A student getting a meaningful number wrong โ€” not overwhelmed, but genuinely challenged โ€” may be learning faster, even though the raw score looks worse on paper.

This connects directly to the flow zone: a near-100% accuracy rate is one concrete, measurable symptom of the boredom failure mode Csikszentmihalyi's model describes, rather than a sign everything is going well.

What "well-calibrated difficulty" looks like using this lens

Rather than chasing a specific percentage, the useful operational question for a parent or a tutor is directional: is the error rate closer to zero (task too easy, difficulty should rise) or is it closer to chance-level guessing (task too hard, difficulty should fall)? A tutor that tracks a student's real-time accuracy and nudges difficulty to keep genuine, productive mistakes in the mix โ€” not zero, not overwhelming โ€” is applying the spirit of this research even without literally targeting 15.87%.

FAQ

What is the Eighty Five Percent Rule?

A 2019 Nature Communications finding by Wilson, Shenhav, Straccia and Cohen that for a class of gradient-descent-based learning models, training proceeds fastest at an error rate around 15.87% โ€” roughly 85% accuracy.

Does the 85% rule mean my child should get exactly 85% right on every homework task?

No โ€” the paper derived this for specific two-choice learning tasks, not arbitrary classroom work. The useful takeaway is directional: near-100% accuracy usually means the task has stopped teaching anything new.

Why would getting everything right be a bad sign?

A task solved with zero errors provides little new information โ€” the learner has demonstrated something they could already do. Learning is driven by encountering and correcting genuine mistakes.

Duke Harewood ยท founder, aitutors.me ยท Updated 11 Jul 2026.