Estimating difficulty of anime from performance logs

Learning japanese is a long and arduous task, and over the years of practice it can feel like there is no real progress. To prevent myself from being too depressed about wasting hours every day in this task I’m clearly not suited for, it’s become pretty important to me to measure how well I’m doing to see if I’m progressing or not.

To that end, I use the same anime episode that I rewatch months appart and I measure how well I understand it (time for pauses, number of unknown words, etc…). From there I can deduce how much I’ve progressed, and infer a progress per day rate. Over the last few years, it looks like this:

But the progress rate is compound so to look at my actual level, starting at an arbitrary 1 and applying the interest rate the closest, I get something like:

Which immediately brings to mind exponential loads, so I modelled it to get the formula for japanese knowledge:

160 represents my japanese level at the beginning of this ordeal (I’ve been learning for more time than measuring), 500 represents my natural aptitude to learn japanese. Oh and d is the amount of days for which I’ve been studying.

So where does that leave me? It seems pretty clear that I’ve reached the “plateau” and all the progress I might make is going to be very slow. Yippy.

But with that data, I can solve a problem that has long troubled me: if I’m doing better with this anime than the previous one, is it because I’ve progressed or because I’ve picked an easier anime? By dividing the score by my modelized level, I can get some sort of normalized anime difficulty that can compare anime through time!

Well it seems that all this time, I’ve been too close to the plateau for it to make any real difference. It would appear that my progress is super neglectible compared to the difficulty difference between various series.

The positive view would be that hard series are just really hard and easy series are very easy, the negative view is that my progress is damn slow, the very negative view is that it’s slow and plateau-ing. I guess the next step would be to correlate this data with other learners. But at the very least I got a cute equation, so there’s that.

EDIT: To assess this hypothesis I’ve studied a full anime that I had already studied years ago (09/2020 to 11/2022). It would appear that I still made progress, from 27.3 mins per episode to 26.4 mins per episode. It does concur with my estimate of a fragment of a percent of progress per day. However, it did strike me as relatively hard, and on par with the other hard anime I’m currently studying. It would tend to confirm that progress is tiny compared to the difficulty difference between anime 😦

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