ricky wrote:horizontal asymptote[...]
330 = 100%
3300 = 200%
33000 = 300%
330000 = 400%
sMartins wrote:P.S. Yeah with an asymptote i mean...is the current curve a logaritm with no asymptote at all?
I see the maths peanut gallery is out in force tonight. The logarithmic functions have no asymptote, horizontal or not.
LadyGoo wrote:The devs already implemented things so that with 200 ua you will have only 16% disadvantage to a player with 400 ua.
The fourth-root function for combat deltas was in fact implemented so that the actual effect of the combat deltas scale with the square-root of the character values, rather than linearly, as using the square-root for the effect would imply. By that I mean the following:
Consider character A with N points of UA, who fights B, with M points of UA. Let the function that determines the effect (the amount of opening created when hit) be f(r), where r is the ratio between the attack weight and the block weight, or N/M when A hits B, assuming their weights are their respective values in UA. The actually interesting effect, then, isn't actually f(r), but rather f(r) / f(1/r), because that is the proportional difference between A and B after each has hit the other once. Insert any polynomial (such as the fourth- or square-root) for f, and you will see that the effect is f²(r)*. In other words, if f(r) = √r, then the actual effect scales linearly. If it's ∜r, then the actual effect scales as the square root. In the latter case, if N = 2M, and A and B hit each other once, then the ratio between the openings they've got from that is ~1.41.
* Proving this is left as an exercise for the reader. ^^