Not 100% true Spikywarkitten.
The amount less damage you take, per point of armor, DOES suffer from diminishing returns.
However, the effective hp it grants still goes up equally fast.

IE, two champions, both with 2000 health.
ChampA has 50 armor.
ChampB has 250 armor.

If they both buy 10 armor, ChampA will see a larger change in how much less damage he takes. HOWEVER, because ChampB is already seeing a lower amount, his smaller improvement will still net him the same +200 eHP.

200 eHP *is* a bigger improvement for the guy at 3000 eHP than the guy at 6900 eHP. That is where the additional, illusory, diminishing returns shows up, and the actual reason you balance health and resist items.

Now I want cookies ):

Oh come on now, you claim armor is becoming less effective when it clearly isn't. Health is becoming more effective; armor is clearly staying the same. Of course health will look better if its effectiveness increases while armor stays the same, which is all the 'cookies' conversion shows. It says nothing about armor. And I don't think anyone has argued against the rising effectiveness of HP, only that armor itself does not diminish, so it's an easy argument to shrug off.

I think maybe a better argument for armor falling off is this:

Say a champ has 2000 HP and 0 armor. They buy an item that gives them 100 armor. Their effective HP is now doubled, giving them 4000 Hp against physical damage.

So say they buy another 100 armor. They gain the same flat 2000 EHP, bringing them up to 6000; but that's now a 150% increase in EHP, as opposed to doubling it.

And then they buy another 100 armor. Another flat 2000 EHP, they're up to 8000, but it's only a 133% increase in EHP. And so on.

As you buy armor, you get the same flat amount of EHP, but the relative chunk that your increasing your TEH by diminishes. 2000 extra HP at 10000 effective health is not as compelling as 2000 extra HP at 2000 effective health. Thus armor is 'better' at lower values as it makes a more noticeable impact on your TEH.

There, just using effective HP and armor, you can show that each point of armor falls off as you get more of it. But I'm not sure it's technically correct to call it 'diminishing returns', since what it's giving you only diminishes in a relative sense. Not sure of the strict definition for diminishing returns, but it seems like armor would have to have exponential growth in order to not have this sort of 'diminishing' returns, and it seems like there should be some middle ground that's neither exponential or diminishing (i.e., flat).

I had a long wall of text here about how armor and HP doesn't give diminishing returns....

But come to think of it, it doesn't matter.

As long as you realize that ALL stats in game (except CDR and maybe dodge) have the same kind of returns, it doesn't matter whether you call it diminishing returns or flat returns. :P

All arguments lead to the same conclusion - get mixed stats.

I'm pretty sure that given a fixed amount of gold to itemize from, and the exact situation that the tank should expect, both of the ideas shown here will lead to the exact same itemization.

TL;DR - Why so serious?

The only problem here between rick and others is one of communication.

When most people say Armor doesn't have diminishing returns, they mean that each point of armor will give you the same EHP the last point did. This is 100% true.

Do those same people think that, for instance, for a 1000 hp champ--having 100 armor and +1000 health is worse than having 200 armor and +0 health? No.

When rick says armor does have diminishing returns, I think(?) he means in regards to what you "buy next"; Buying armor may not be as optimal as buying armor and health.

Neither side is wrong, and both would be able to tell you which armor + hp value would be optimal for a shared pool of both. They just mean different things when they say "diminishing returns". It's silly.

Armor does suffer from diminishing returns in terms of how long it takes someone's DPS to KILL YOU.

Let's say you have 2000 HP and the enemy performs 500 Damage Per Second. With no armor and an effective health of 2000, you die in 4 seconds.

With 100 Armor, you mitigate 50% of the damage. Now your effective health is 4000, and you die in 8 seconds. From 0 to 100 Armor you have improved your durability by 100%.

With 200 Armor, you mitigate 66.7% of the damage. Now your effective health is 6000, and you die in 12 seconds. Now this is the tricky part most people don't realize. From 0 Armor there doesn't appear to be any diminishing returns. Your effective health has changed from 2000 to 4000 to 6000. Which is a durability increase of 200%. But from 100 Armor to 200 Armor your durability has only increased 50%. The same 100 armor that gave you a 100% increase in survival time only gave you a 50% increase in survival time. That's where Armor suffers from diminishing returns and you utilize extra HP to create a multiplier effect so you can match all of the multiplier effects that incoming damage can have. So it depends on perspective.

If you pretend you have always started with 0 Armor, then Armor does not suffer from diminishing returns. It can be graphed as such via Armor and Effective HP. If you are looking at how much of an effect Armor will have by starting from differing frames of reference such as 50 and 100, then you are getting different numbers of % increase in durabilty. That can also be graphed and you can see the curve.

The key is though as our Riot has been mentioning, EHP isn't the only thing a tank needs to worry about. Value of the item at the time is quite important in addition to the other attributes on him.

You should not use the term '% armor reduction' to talk about armor damage mitigation as % reduction refers to a different stat that debuffs the target's armor by a % value.

There was way to much time in this thread spent explaining the same thing different ways

Everyone agrees that stacking one type of defense (health, armor, magic resistance), is not optimal, and that you need to balance them out to obtain the maximum defensive benefit.

Case closed.

Instead of talking about how you arrive at your conclusion from multiple different angles (because there is more than one way to 'skin the cat'), it would be much more valuable to discuss what numbers achieve the maximum EHP + utility for the least amount of gold. You know, something actually relevant to the game .

Discuss.

So...
0 to 100 Armor gave me 4 seconds to live
100 to 200 Armor gave me 4 seconds more to live

I can't say I see the deminishing returns here. Or do you want to say that 4 is more % from 8 than from 12? Yep, that's right. But it doesn't matter to me.

What does matter to me is that I've got another 4 freaking seconds to last in a teamfight and do my job before being dead.

Of course HP becomes better with more mitigation, but that is out of the question of "diminishing returns on stacking armor" =)