Thread:ClariS/@comment-3017217-20141026134417/@comment-1330314-20141029082033

Your reasoning is confused, rambling and only marginally related to mathematics, Ntoulinho. You are also wrong, and would have stopped being wrong a long time ago had you listened to ClariS, who took great care in pointing out exactly where you were wrong.

A linear function takes the form ax + b, where a is the slope of the function and b is a constant. You've been trying to calculate the slope of a function while completely ignoring this constant, in this case the champion's base health. Here's how your reasoning should have gone:

Let's go with your Karthus example: Karth deals 45 damage per AA, you have 4500 health. At zero armor, you take 100% damage, and so will die in 100 hits. This is the constant in your function, since this is the amount of hits you can take when your armor is zero.

At 100 armor, you take 50% damage, which means each hit deals 22.5 damage and so would kill you in 200 hits. At 200 armor, you take 33% damage, and so would need 300 hits to die. You think this is proof for diminishing returns, since doubling armor doesn't double the damage you take, but you've been completely ignoring the base constant: 100 armor buys you 100 more hits compared to 0 armor, and 200 armor buys you 200 more hits compared to 0 armor. Each point of armor here buys you one extra hit, regardless of how much armor you have. You can then continue, with 300 armor letting you die in 400 hits, 400 armor letting you die in 500 hits, and so on. There are no diminishing returns.

The argument that the Damage multiplier/reduction curve is concave is also weak, and has been previously disproved: damage amplification/reduction is merely a function with an inverse relation to effective health, which is the true determiner for the returns brought by resistances.