Talk:Armor/@comment-37658696-20181129044749

Whoever wrote the in-depth analysis on this article, you are a soul after my own heart. However, there's something of note within it:

> It is good to note that at the moment, this equation is currently unnecessary for most of the applications it has in-game since the preceding equation is pretty much always sufficient. At the moment, the game has no circumstances where the nominal health is a function of its armor and vice versa, this is more for mathematical rigor.

There is an important implication of the equation, and you can understand it if you put all the terms in plain English. The article uses the variable R = (A+300)/300 to simplify the EHP equation as E = HR, and dR = dA/300. In English, R is an "EHP multiplier": the real value of your hit points (e.g. R = 2 means, in English, "each of your hit points is really worth 2 hit points"). Keeping health constant (dH = 0), dE = HdR = H(dA/300). What this says in English is "keeping your health the same, every 300 points of armor is effectively adding another health bar" (e.g. H=500, "every 300 armor you add is effectively adding 500 health points"). Keeping armor constant (dA/300 = 0), dE = dHR. In English, this means "keeping your armor the same, every hit point you add is also effectively adding more from the damage reduction" (e.g. A = 300 -> R = 2, "every hit point you add is adding 2 hit points"). The point of the math above the in-depth analysis is to show that EHP is linearly proportional to armor and health. In practical advice, it means "when your health stays the same, stacking armor does not get any more or less efficient the more you do it, so don't try to find a sweetspot", and vice versa for health.

I know this seems redundant, but putting things in English explains why the in-depth analysis is very useful. It's useful because someone might be working from a base warframe and not have enough room to add Armor and Health: they might not have the mod capacity, or a new player might not have the Endo to upgrade Vitality and Steel Fiber to the levels they want. Thus they would ask the question:

Given my current health and armor values, would I get more EHP from increasing armor or health?

And here, the term (dH)(dA/300) is very useful. When either dH or dA is 0, dE is linearly propotional to the other nonzero term, but when neither of them has to be 0, dE is best maximized by maximizing the product of dH and dA/300. This is maximizing the product of two summands of a fixed number: if you have two numbers x and y which add up to 100, how do you maximize the product? Keep them as close as you can, i.e. x = y = 50, and the product is 50^2. The minimum is achieved by putting it all in one variable, e.g. x = 99 and y = 1, for 99. In English: "get the most you can by balancing them". dH + dA/300 isn't necessarily fixed, but the same principle applies: maximizing either dH or dA/300 at the expense of the other nets the minimum possible product and thus the smallest dE: spreading it maximizes the product and maximizes dE. In English:

'''If there must be a choice between the two, balance the gain in armor and health to maximize EHP. Putting it all in one gets you the least effective health.'''

That's the implication of the in-depth analysis. It's not just "mathematical rigor"; that implies the author did it for fun. The analysis demonstrates useful advice for a new player.