There's probably more than one way to solve it.

I set gold=constant and maximized EHP. The formula I got at the end was the solution, or the simplest consequence of the solution along the lines of how your guide was set up. I used Lagrange multipliers, but I think if you do a substitution somewhere, you can probably use single-variable (Calc 1) methods.

It agrees with your tables, so I think you got the same thing.

Actually, to calculate it all i used local maximum of 3D function.

where x is armor
y is health
and z is result of ehp divided by total cost

so function looks like this:

F(x,y,) = z = <y * [1+(x/100)]>/[x+(y*6,5)]

And now you find maximum z for given y with variable x.

It's kind of advanced math, but I should describe the method and pattern i used =)

By the magic of calculus,

R = (H-650)/6.5

H = health, R = armor + MR. This assumes the cost ratio for MR vs health is 6.5, as given.

If it were 6.473 instead, it would be R = (H-647.3)/6.473, etc., or if you call the ratio Y, it's (H-100Y)/Y. I think you just divide by .6 if there's 40% penetration, so Y=6.5 --> Y=10 or 11, roughly. 10 for nice rounding.

I tend to undershoot on the resists given by the gold efficiency standard... With a full build, 6000 health and 320 resists is about the same effective health as 4500 health and 425 resists, but this falls wildly over the "sweet spot" of the formula. Guardian Angel costs 400g less than Warmog's Armor, I guess is what's going on there. But then you're comparing HP5 with a resurrection aura, and it's apples and oranges. Anyway, that health you need for Northern Winds is probably why it's so hard for Sejuani to be tanky and do damage at the same time, but then again, building AP is even harder for any would-be tank.

Health is a bit more flexible... you can take more magic damage than expected, and you get forgiven for it somewhat, or you can not take magic damage and you still use the extra bit of health that goes over the sweet spot almost as efficiently as planned.

Of course, then there's always Bloodrazor, so it's all over the place.

Is this using the magic of Calculus, or did you consult spreadsheets? It would be interesting to have a formula with a parameter for armor/MR ratio.

I thought you still didn't turn it on lol

This is somewhat a discussion for pure tanking...
It's important to take some damage/resist or damage/health items into consideration.

Nevertheless, it's a very informative reading. Thanks for putting it up.

@Pelikins
Thx for your effords on that comment, let's reply:

I already mentioned that armor/m.res. increases efficency of health regeneration in my other guides as I'm totally aware of that. Although I should mention it here too, that's good point.

The fact about true damage is also well known to me. I didn't mention many thing because I wanted this guide to be as short as possible for valuable informations I'd contain. It's my guide's very big disadvantage that I usually produce huge wall of text, informative, but still huge. I'm trying to avoid that.

I'm a big anti-fan of metagame as it's simply very easily to be exploit by off-tanks. Very easily. To be honest current meta works usually for low-mid skilled teams, but high-skilled almost never blindly follow it. And you are VERY wrong with statement "I think it's pretty obvious that any non-carry needs to have a magic resist source, an armor source, and a hp source." as I understand you also meant that "carry" is that squishy glasscannon not building defense. And through my experience from LoL, DotA, HoN, and thatlike games, which is around 6 years (so pretty much from the moment they exist) I can honestly say that it's tankier team that wins the games, and usually game is carried by offtanks, not squishy glasscannons.



This guide is about cost efficent defense, not about health regeneration efficency, nor about metagame. I just wanted to help people understand when to start buyng resistances and when to health in order to get as much for its cost as possible. This guide was meant to be as informatic in this topic as possible while also as short as possible for informations it contains.

Anyways +Rep for you, for very informating comment, I'll add several extra infos according to your call.

Thank you for feedback,
-glizdka

Needs some more information. It's a good start, but over simplified and rushed it seems.

Factors such as percent based damage Despair Blaze Bio-Arcane Barrage were not discussed. Neither were factors such as life steal, spell vamp, healing skills, or health regeneration. All of these appreciate the value of resists.

Additionally, spell vamp and life steal convert your offensive stats and abilities into a hp source. So even your offensive stats can be secondary defensive stats and effect the optimal defensive kit for your champion.

True Damage such as Feast Icathian Surprise and Ignite appreciate the value of base hp on the other hand. ( Ignite and similar effects depreciate the value of life steal, spell vamp, healing skills, and health regeneration as health sources in addition.)

The chore of building your defensive kit isn't just a simple formula of what gives the most static effective hp per gold. It's a much more complicated problem than that.

In fact, the "meta golem" build that currently is abused by AD bruisers in the meta game has nothing to do with your effective health and everything to do with build synergy/getting stats for free. I'm of course referring to grabbing Warmog's Armor followed by Atma's Impaler to meet your armor needs while gaining a ton of free attack damage, followed by a Force of Nature to meet your magic resist needs while gaining a ton off free health regeneration.

I think it's pretty obvious that any non-carry needs to have a magic resist source, an armor source, and a hp source. But where those stats come from and how much of each you need (ideally) is completely situational on the champion's kit, team, and opponents.

i JUST FINISHED it, forgot to turn on comment-to-vote

and for god's sake forgot to reserve 1st comment as I do in each of my guides...


...you... you... you...nice guy ^^
thx for warm words and comment =D

This guide is very nice! and i like all ur guides they are very usefull.

Just a little tip toggle (Comment to vote) on becasue of trollers (:

Well very nice guide 1+ from Acoil!!

Im first (: