Quote:
Anyhow, what is the equation for the DA graph?
Sorry, was away~
y = 100n/(x+100)
is an effective equation of that graph;
y represents the percentage increase in damage caused by an increase in
n Double Attack effective on a base stat of
x.
Let's analyse the graph's features as further confirmation of the "decreasing returns" of Double Attack.
Differentiating the above function with respect to
x to obtain an expression for the change in
y relative to the change in x yields you the equation: (note
n is a constant as it is chosen independent to this graph - this may seem minor but it's a big deal that this is the case in calculus)
dy/dx =
- 100n/(x+100)^2
Notice the minus sign; this basically tells us that the function is decreasing. To further prove that this is the case, let us calculate the turning points of the function (dy/dx = 0)...
dy/dx equals 0 when either n or x = 0. If n is 0 then it should not be a surprise that there is a turning point, since there will in fact be no gradient to speak of since you are not adding anything (hence the initial equation simplifies to y=0)! x cannot be zero and produce a real result. Therefore, the rate of change of y relative to x is a decreasing trend with no turning points. This basically shows mathematically that this function is decreasing contrary to what some people may say!
Tl;dr: Yes, Double Attack does become less valuable as you add more of it.
Equation of graph: y = 100n/(x+100)
