Thread:ClariS/@comment-3017217-20141026134417/@comment-1330314-20141029230058

While that is also an issue, I don't think Ntoulinho entirely wants to admit the above, since he would otherwise not be trying to prove that H2(2a) =/= 2H2(a), which would be an obvious fact had he understood the formula properly. If we really do want to talk about the definition of diminishing returns, how about this:

The Wikipedia definition for diminishing returns (in economics) is: In economics, diminishing returns is the decrease in the marginal output of a production process as the amount of a single factor of production is incrementally increased, while the amounts of all other factors of production stay constant." In layman's terms, this means that each additional unit being measured has an objectively lesser value when compared to any preceding unit, all else being equal (or ceteris paribus, if you want to be pedantic). From this, constant returns would imply that each unit has exactly the same value, regardless of how many you already have.

Applying this to resistances, one point of armor gives you exactly 1% of your raw health against physical damage, and this is true regardless of how much armor you have (the same applies for MR and magic damage, obviously). Since the measure of value for armor here is its capacity to make a champion tankier, every point of armor offers an equal amount of tankiness, and so has constant returns rather than diminishing returns. It makes little sense to use any other measure, particularly percent damage reduction, as they are not a direct or complete indicator of tankiness and only follow from effective health.