What a wrong answer costs you on WaniKani

The published rule

The API reference says only that the stage decreases "based on the number of times it was wrong". The exact formula lives in the knowledge base.

Two details are easy to miss. The floor at stage 1 means a miss at Apprentice I costs nothing. And the ceiling-of-half means missing the same item twice in one session costs the same as missing it once: the formula punishes bad sessions, not bad answers.

The two-thirds folklore

Two thirds is the number that circulates, in two forms. The weaker one calls 67% the break-even point for review load. The stronger one says that below it, demotions outnumber promotions and your queue moves backwards. On review load, two thirds is roughly right. On progress it is wrong, and the way it is wrong is worth seeing.

The reversal argument runs: a correct answer is worth +1 stage and a miss at Guru costs 2, so expected movement per review is $3a - 2$, which hits zero at an item accuracy of two thirds. The arithmetic is fine. The mistake is applying it to every stage, when below Guru a miss costs one stage and at Apprentice I nothing at all. At 60% item accuracy, stage by stage:

Only Guru and above drifts down. Everything below it drifts up. Items pool around the line where the sign flips, bounce off Guru, climb again, and every one of them still reaches Burned. You do not even need the simulation: Apprentice I to Burned is eight stages, every promotion is worth exactly +1 and every demotion costs at least 1, so any item that burns must log at least eight more promotions than demotions, at any accuracy. At 50% that works out to 89 promotions against 67 demotions: lopsided and slow, but still forward.

Eight reviews if you never miss

Eight consecutive correct reviews take an item from a fresh lesson to Burned. That floor is the same for everyone; accuracy decides how far above it you land.

The curve is gentle at the top and vicious at the bottom. Dropping from 90% to 85% item accuracy costs about two extra reviews per item. Dropping from 70% to 60% costs thirty.

The days column has a floor of its own: 174 days of interval waits that no accuracy can shorten. Everything above that number is time the misses added.

A three-point dip is a 230-review day

Reviews per item converts straight into reviews per day, because each item you start eventually generates its full review count.

At 15 lessons a day, held steady, that lands here:

This is not hypothetical. A June 2026 thread describes displayed accuracy sliding from 90-91% to 87-88% and the Apprentice pile ballooning until one 24-hour stretch delivered 230 reviews. The lessons never changed; each item just started costing more. That is the wall people hit somewhere in the level twenties.

Below roughly two-thirds item accuracy the pile also changes shape. Items reach Guru, fall back out, and feed Apprentice from above as well as from your lessons. The items doing the bouncing are a small, identifiable set: leeches. Attacking them one by one beats grinding the whole queue harder.

What the percentage actually counts

Everything above is stated in item accuracy: the share of reviews you clear without a single miss. The percentage WaniKani shows you counts something else. It counts questions, most items ask two, and every retry lands in your statistics because a missed question comes back in the same session until you answer it right.

Work the extreme case: a session of 100 items where every meaning is right and every reading is missed once, then corrected. That is 200 correct answers out of 300 attempts, displayed as 67%, on a session where not one item was cleared cleanly. Item accuracy: zero.

The gap has an exact shape, because a completed review always ends with one correct answer per question.

Because $m$ varies by person, the conversion is a range rather than a number. An item accuracy of two thirds displays as anywhere from 75% to 85% depending on how many wrong answers your misses generate. The tempting shortcut is to assume meaning and reading fail independently and take a square root, putting two thirds at $\sqrt{2/3} \approx 82\%$ displayed. It ignores retries, and misses cluster in the items you half-know rather than falling independently. Treat it as a curiosity.

What to aim for

Calibrate against reality rather than the forum, where reported figures range from 60% to 100% and the people who post their accuracy are mostly people pleased with it.

Reported accuracy in the high 80s is where the cost per item stops compounding. At 90% an item takes about 12 reviews to burn against the floor of eight, at 85% it is 17, at 80% it is 30. There is no cliff anywhere in that range, so treat a dip as a bill arriving rather than a failure state.

The lever is rarely accuracy itself. Accuracy is downstream of how many unfamiliar items you are holding in Apprentice at once, which is downstream of lesson pace. Cut lessons to 5 or 10 a day and the pile drains, accuracy recovers because each session holds fewer strangers, and the review cost per item falls with it. The lessons-per-day guide covers the pacing half.

Watch what your finished items cost rather than the percentage at the end of a session: burns averaging 12 reviews mean a 50% surcharge on every item you own, and 25 means triple. Wanilog measures exactly that from your review statistics, alongside which items keep bouncing off Guru.