How many new words am I actually learning? (Answer)

Hey guys. Q: How many words do I actually learn after doing x many official language courses?

When I do the official language courses in a particular language, even though it says I learnt so many words, there are MANY repeated words, both in itself and from previous ones, and I don’t actually know how many words I have truly learnt!

I HAVE FIXED THE PROBLEM! I calculated a formula to tell you exactly how many words you will actually be learning if you complete ‘x’ amount of OFFICIAL language courses (Sorry, the discussion tag is wrong, this is only for official courses).

I calculated this for the official German courses in this forum:

List of Unique German Words for Memrise?

Although I have estimated a system to work for every language.

Step 1: How ‘repeatable’ are the words of the language, out of 10
For this, German is about an 8. The words are generally repeated very often because they often come together to mean lots of different things.
Dutch and English = 7
Spanish and French = 5
Hebrew and Arabic = 3 or 4
Chinese and Japanese = 0 or 1

Note: I actually haven’t learnt these languages to know how repeatable they are (it is only an assumption, take it with a grain of salt), but you can determine this for yourself.

----> Note this number as R =___

Step 2: Note the total amount of words each course says it teaches.
Label this number T1,T2,T3…Tn


German 1 says it teaches 468 words —> (Therefore T1=468)
German 2 says it teaches 482 words —> (T2=482)
German 3: 640 words —> (T3 = 640)
T4 = 179
T5 = 405

Tn = ___

Now you are set, put all these values into this formula:
Words it actually teaches is:
= (T1 + T2 + T3 +T4 + … Tn) - 1/(11-R) * (T1ln(1) + T2ln(2) + T3ln(3) + T4ln(4) + … Tnln(n))

E.g. For German, R = 8 and T1,T2,T3,T4,T5 = (above)

Therefore, although it says after completing five German courses I have learnt 2174 words,
I have actually only learnt…
2174 - 1/(11-8)*( 468 ln1 + 482 ln2+ 640 ln3+ 179 ln4+ 405 ln5)
(put into online calculator)
= 1528 words

This calculator is only experimental and definitely not 100% accurate, but I personally think it is really good and only a little complicated. It only doesn’t work for comparing the first course against itself.

Hope it has been of some help to anyone!