Thread:Deshiba/@comment-6016076-20140527061534

Hi Deshiba, I noticed there's been a long discussion on diminishing returns on the item page. I wanted to prove that there are indeed no diminishing returns without resorting to effective HP, but it requires derivatives, if you are familiar with those.

Conceptually, the main idea is this: Although the % mitigation loses value per point of resist (as you said), the %Damage taken (%DT) is actually gaining value per point of %DT. A 1% difference between 0% to 1% DT is worth a lot less than a 1% difference between 98% and 99% DT. It turns out that these two competing changes exactly balance each other out.

Unfortunately, I don't know a simpler way to prove this without resorting to EHP. Here is the math avoiding using EHP, if it helps:


 * Since % mitigation and % Damage taken (%DT) are dependent on each other, we need to find out how %mitigation and %DT change together.  We cannot analyze this by only looking at one or the other individually without entering the territory of EHP.  One way we can express the two together is by the ratio of % mitigation to %DT.


 * We take the formula for %mitigation


 * x / (x + 100)


 * and divide it by the formula for %DT


 * 1 - x / (x +100)


 * The result is : 0.01 * x


 * This is their ratio.  Naturally, the ratio widens the higher the resist: You are approaching 100 % mitigation, but dividing this by %DT, which is approaching 0%.  The key point here is whether the increase in %mitigation is going up faster or slower than the simultaneous decrease in %DT.


 * To find out, we take the derivative to see the rate of change of this ratio--and it is a constant 0.01.


 * This means that % mitigation is increasing at relatively the same rate as the %DT is decreasing.   In other words, there are no diminishing or increasing returns; there are only static returns.


 * To provide an example of a diminishing return, let's say the formula for % mitigation were:


 * x / (2x + 100)


 * Then %DT will be given by:


 * 1 - x / (2x + 100)


 * Dividing % mitigation by %DT, we end up with:


 * x / (x + 100)


 * Taking the derivative of the ratio like before, we have the final result of:


 * 100 / (100 + x)^2


 * This is not a constant, and it indicates that the higher the resist value, the smaller and smaller our ratio continually becomes.  We are getting per point of resist, a comparably smaller amount of %DT in return. This is a diminishing return.


 * I don't know if this helps, but I hope it did!  It's really a lot easier if you make the conceptual transition to EHP.  It's worth investing a little time to see how EHP works because it's a simple concept that makes all of this a lot easier to understand, which will improve your understanding of the game as a whole. 