FFT Growth formula : C is the number of levels needed to double the raw stat

[Singe Horizontal 1]

Hi everybody !
So last day I thought again about the growth formula, given on https://gamefaqs.gamespot.com/ps/197339-final-fantasy-tactics/faqs/3876
bonus = [current_RX / (C + Lv)]
I knew that the lower C is, since it's on the denominator, the best it is for the bonus growth.
But, something was bugging me and I had still not found the explanation of this :
"...it just so happens that the amount of raw stats you gain on a level up will be a constant."
I made my tests, and indeed the bonus was constant.
But how did they think about that ? And why is it constant ?
First I wrote the formula in sequence :
with u0 for starting_RX and un/(C+n) for bonus
un+1 = un + bonus
=> un+1 = un + un/(C + n)
Then I started simulating numbers with sheets, and I noticed that everytime the current_RX had doubled from its previous values, it was when the char had gained exactly C levels ! So,
When n = C, uC+1 = 2*u0

So, I thought maybe they designed the formula with having that in goal !

To verify it, I started from the definition of an arithmetic sequence :
un = u0 + nR (1)

And I applied the constraint :
When n = C, un = 2u0
2u0=u0 + CR
=>u0 = CR
=>R = u0/C

in (1) :

un = u0 + n.u0/C

un+1 = u0 + (n+1).u0/C
=> un+1 = u0 + n.u0/C + u0/C
=> un+1 = un + u0/C (2)

un = u0(1+n/C)
=> u0 = un/(1+n/C)
=> u0 = (un.C)/(C+n) (3)

Using (2) and (3)

un+1 = un + (un.C)/(C+n)/C
=> un+1 = un + un / (C+n)

Here we go !

Conclusion : The growth constant C for a stat is the number of levels needed to double the raw value of that stat :  for example in 1.3, knights have 35 PAC, that means for every 35 levels spent in knight, you double your PA.
With HPC = 8, every 8 levels, you double your base HP.
I think it’s a nice way to see it when planning characters.

 

Edited November 15, 2019 by Singe Horizontal