Lineage 2 Attribute Bonus Calculator:
https://lineage2ertheia.com/AttributeCalculator.php NEW Attribute System from Goddess Of Destruction
so, shortly, how does it work?
if attack > defense, damage increases, otherwise if it's lower damage is decreased, equals value make no damage difference
cap for the damage increase/decrease is between 20-30%
damage Bonus increases in stages.
The experiment went the following way: a clean hit with 0 attribute difference was used to establish a base value. Next, a difference of -280 attribute was set between the attacker and defender characters. The attribute of attacker was increased by 10 each step, and damage was noted down for each value. The raw data referred to the base value can be seen on the plot below:
Let x be the difference between attacker’s and defender’s attribute values, and f(x) the attribute formula. It can be immediately observed that f(x) is a discontinuous function. It can also be deduced that f(x) will take form of
where sat is a saturation function defined as
y(x) is an internal function, and lb and ub are the lower and upper bounds.
We should gather knowledge on y(x) before we find a suitable candidate.
It should be noted that the y(x) function has several properties similar to the signum function. An assumption was made that
where
and P(x) is a function that we will attempt to identify numerically.
Due to the shape of the results, it was assumed that P(x) is a polynomial function. Starting from the reasonably simplest polynomial of degree 2, an algorithm using least-squares criterion and Vandermonde matrix was coded to find the coefficients. It was also guessed that P(x) takes absolute value of X as an argument. The algorithm gave us the following function:
After plugging it into signum and sat functions, we have received the following fit:
The result is pretty much close to perfection, making it unreasonable to check higher degrees of polynomials. All that was left to do was simplification.
Observation: 0.0191 is related to a famous mathematical constant:
Result: the attribute system factor used in damage calculation (base damage is multiplied by the factor) is calculated using function:
where x is the attribute difference between attacker and defender. The function plot can be seen below:
