User:Double Slap/Sandbox

There isn't a diminishing function with resistances, i.e. amror and magic resistance. It may very well seem like it, but there isn't. The reason there isn't a diminishing function is because the result of the function of armor is a percentage of damage taken--damage reduction.

Fortunately, we have a formula for the function of armor that results in the multiplier of all physical damage. That formula is:

$${\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it Armor}}, & {\rm if\ }{\it Armor} \geq 0\\ 2 - {100 \over 100 - {\it Armor}}, & {\rm otherwise} \end{cases}$$

To obtain the % of damage decreased, all that needs to be done is: 100%(1-f(armor)). Now, looking at this function alone there is, in fact, diminishing returns. f'(armor) indeed does rapidly approach 0 as it reaches higher values of armor. Though, f'(armor) is not a constant value in itself. The % of damage reduced is dependant on the damage taken. If there is no damage at all, then there is no damage to reduce. So this introduces another formula, calculating the amount of damage taken with armor. That formula is fairly simple.

$${\rm Initial\ damage}x{f'(armor)}={Damage\ taken}