# Optimising lessons per day

Until now, I have done as many lessons as I could find time for. Maybe on a Sunday there is time to do 40 or even many more lessons. The problem is that then suddenly one gets a huge pile of reviews on specific days in future. If unlucky, more than one of these piles may come on the same busy work day.

Therefore I have taken a short break from lessons to let the reviews come under control.

The question is, how many lessons to do per day so that, even in a few tens of levels time, the number of reviews to do per day remains steady and manageable.

I believe that, if every review is answered correctly, each lesson has 8 reviews in total to burn. Therefore, every lesson adds 8 reviews to the total workload.

This means that, once enough time is spent to reach a steady state, one will be doing 8 times as many reviews as lessons each day.

Therefore, if I am comfortable with 80 reviews per day, I should rigidly do 10 lessons per day. Any more than that on a given day, and horrible pain will surely hit on a future day when the reviews crop up.

There are two assumptions in this argument. One is that all reviews are answered correctly. Letâs live with that for now and assume a low rate of incorrect answers.

The other assumption is that lessons go on forever, while in fact they stop after level 60.

My question: is the timescale of building up to the steady state long or short compared to the total 60 levels? In other words, will I quickly hit 80 reviews per day, or will I never get close? My guess is that, since the earliest burn time is 4 months, the steady state of 8 reviews per lesson will be reached mid way or late through the levels.

There would be a very useful script to be made here to caculate the number of reviews expected by future date for a given steady lesson rate.

Plus, any corrections to the formula appreciated!

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You wonât end up with 8x the number of daily reviews, because the higher-srs-level reviews are more spread out. If you take the time-spacing into account, about 80% of your daily workload will always be Apprentice items, because youâll do an itemâs first 4 reviews (to reach Guru) in the first 7 days.

[I canât remember the exact percentages, but thatâs reasonably close]

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Thank you @rfindley

I was surprised, but realised it wasnât too hard to put it all in a spreadsheet, and the result seems interesting. Here are plots of the number of reviews you will do per day if you start on 1st Jan 2018, and get all reviews correct

No matter how many lessons you choose (say 10 per day, or say 20 per day), by the 175th day you are getting 8x the number of lessons back as reviews.

After 55 days, you are at 7x number of lessons, which is around 90% of the max workload as @rfindley pointed out.

If anyone would like the spreadsheet to try out other lesson rates, please pm me (if thatâs possible) with your email

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YepâŠ look familiar

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Assuming 100% correct is a pretty strong assumptionâŠ

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The SRS penalty varies a little based on when an item is gotten wrong, but for the most part, Iâve observed a drop of 2 levels. That means the item will show up 3 more times for every mistake.

Because of that, the average number of reviews a day is adjusted by two factors:

1. Lessons per day; WaniKaniâs SRS system has 8 levels.
2. Number of items wrong per day. A worst-case -2 SRS penalty â 3 reappearances

Reviews/day = 8 * |lessons/day| + 3 * |penalty items/day|
R = 8 L + 3 P

Penalty items/day = (1 - Accuracy) * Reviews/day
P = (1 - A) * R

Plug the equation for P in, and weâll be able to solve for R.
R = 8 L + 3 (1 - A) * R
R (1 - 3 + 3A) = 8 L
R = 8 L / (3 A - 2)

This equation shows us that 1 / (3 A - 2) approximates a review multiplier based on accuracy.

I donât know how to make a table, so I guess Iâll use bullets. Weâll go with numbers for 10, 15, 20, and 25 lessons/day.

• For A = 100%, the multiplier is 1; 80, 120, 160, 200 reviews/day
• For A = 99%, the multiplier is 1.031; 82.5, 123.7, 164.9, 206.2 reviews/day
• For A = 98%, the multiplier is 1.064; 85.1, 127.7, 170.2, 212.8 reviews/day
• For A = 97%, the multiplier is 1.099; 87.9, 131.9, 175.8, 219.8 reviews/day
• For A = 95%, the multiplier is 1.176; 94.1, 141.2, 188.2, 235.3 reviews/day
• For A = 90%, the multiplier is 1.429; 114.3, 171.4, 228.6, 285.7 reviews/day
• For A = 85%, the multiplier is 1.818; 145.5, 218.2, 290.9, 363.6 reviews/day

With the multiplier being an inverse function â1 / (3 A - 2)â, review accuracy is very important. Lower average accuracy will lead to iterative penalties and consequently, many more reviews. This equation may just be an estimate, but it shows how imperative it is to maintain an average above 67% in order to finish WaniKani in a timely manner.

I hope this helps! (Also let me know if I made any embarrassing math mistakesâŠ :D)

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Nice math! Although I think it would be really good if we could use different formulas. I had a lot of stress trying to use WK throughout the past year. Balancing its gamification when Iâm already not that good at balancing time wasnât working out for me. And then when I did âslipâ, the whole âzillions of reviewsâ thing would happen.

So what I do now is log in one time each day, after I get off work. Now that I decided to get off the gamification schedule and treat this more like my nightly winding-down thing, itâs actually become a lot of fun to plow through the hundreds of reviews. I know it will take forever to complete the program. But now at the end of work, Iâm always looking forward to going through the reviews and learning five new words, rather than thinking about the program during work and trying to fit in reviews during lunch breaks and stuff like that.

One unfortunate side effect is the fact that I have to do the same items a bunch of times in a row, because Iâm skipping out on the <1d review intervals.

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Just what I wanted! It just goes to show how itâs better to maintain a constant steady rate of lessons to avoid review horrors in future.

I have changed my approach for now to do 10 lessons a day without fail. It is a shaame though to waste those weekend days when there would be time to do more. So I am considering the idea of doing as many lessons as possible by day, but using a reorder script so that all apprentice reviews get done on the day but advanced reviews can wait until the weekend if necessary

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