Thread:ClariS/@comment-3017217-20141026134417/@comment-1330314-20141028192739

The main reason behind the confusion on resistances and diminishing returns is that damaging returns is an inverse function: if x is a linear function, then 1/x is not. You are dividing the damage you take in the same way as cooldown reduction divides your cooldowns. As an example, 1% of damage reduction is not the same across the board: going from 0% damage reduction to 1% damage reduction makes you take a tiny bit less damage, but going from 99% damage reduction to 100% damage reduction makes you go from super-tanky to literally impossible to kill. Going from 98% damage reduction to 99% damage reduction means you take 1% damage instead of 2% damage, and so you're in fact twice as tanky as you used to be, something you clearly don't get by going from 0% to 1%. As a side note, this also means each percentage point of cooldown reduction has increasing returns.

ClariS is right: if you want to see exactly how much damage you can take with resistances, you need to take a look at effective health, which lists the exact amount of damage you can take of one type before keeling over. You can actually calculate it directly from the damage reduction formula and prove that it's linear:

Let's just take armor as an example here, since MR would work exactly the same. The formula for physical damage reduction is:

PDamage reduction = 1 - (100 / (100 + armor))

So 100 armor gives you 0.5 (50%) physical damage reduction, 200 armor gives you ~0.67 (~67%) damage reduction, etc. If you want to calculate exactly how much damage you can take (i.e. your effective health against physical damage), the formula for that is:

PEffective health = health / (1 - PDamage reduction)

So 50% damage reduction doubles your health into effective health, ~67% damage reduction triples it, etc. Plug in the first formula, and you get:

PEffective health = health / (1 - 1 + (100 / (100 + armor)))

<=>

PEffective health = health / (100 / (100 + armor))

<=>

PEffective health = health * (100 + armor) / 100

Which leads to the final formula:

PEffective health = health + health * armor / 100

Which clearly shows that, no matter how much armor you have, one point of armor will always increase your effective health against physical damage by exactly 1% of your health. It's a linear increase, and so does not have any diminishing returns.