[QUOTE=elisa]
Ok, that’s the candidate I got:
The core skill rate curve is: s(x) = 100+1000EXP(-0.0006x), where x - current skill level.
When I say ‘core rate’ I mean that the real rate would be something like:
rr(x) = a*s(x)+b, where a and b - some coefficients.
As an example, I’ve tried to simulate a curve from Marco’s chart, and that’s a possible approximation:
s1(x) = 100+1000* EXP(-0.0006x)(0.7+0.3*COS((x+250)/80))
I’ve plotted this function on top of Marco’s chart and here’s the result:
https://www.planetcalypsoforum.com/gallery/files/9/2/0/CoreSkillRate_thumb.jpg[size=1][br]Click to enlarge[/br][/size]
The purple line is s(x) and the red curvy line is s1(x).
Don’t worry about the first 300 positions, they are taken from some different function to provide a desired effect.
It’s a close enough approximation, taking into account that both graphs are made in Excel and therefore aren’t guaranteed to me geometrically correct (as it can use datapoints, not real coordinates).
It would be a bit difficult to apply this function to GSI research case, trying to find the right coefficients, because it seems MA doesn’t caclulate the value of the skillrate function on the fly, but rather has a table of precalculated values of integral taken of s(x) for some levels. Therefore GSI research cannot give exact numbers.
I’d say the main result of this research is the coefficient -0.0006 and the fact the skillrate doesn’t seem to go down to 0, which proves the statement of unlimited skill levels possible. The rest is just mix and match.
So coming back to randomness factor, IMHO s(x) function is just a good representation of overall skill rate situation, but the real skill gain (for certain fixed weapon/mob/time/whatever other factor would be something like
SR(x, t, F) = R(t, F)*s(x)
where
x - current skill level
t - time
F - combination of equipment/mob/other factors present
and R is a random function, let’s say changing within [0.25, 1.75] interval (just guessing).
:laugh:
P.S. I’m actually mixing up the skillgain rate and GSI curve in this post, but you as gifted students surely know that the first derivative of the forementioned curve has the same shape as s(x), but with different coefficient, so it doesn’t really matter which one to study. :wise:
[/QUOTE]
U don’t really expect us to pay attention reading this … what u are trying to prove now :wise: :banghead: is that I should have paid more attention in my quantitative methods lectures from uni cos if I had, I would be able to understand PE skillgains better … . :rolleyes: omg …
