There are a lot of people who are just spouting out what they’ve heard without ever doing the math. Let’s take Teemo at level 12 for example.
Teemo’s base stats at level with 12 with no items:
Health Points: 1307
Armor: 59
Magic Resistance: 30
EHP = 1307*1.59 = 2078
EHP = 1307*1.30 = 1699

Now let’s add Warmog’s Armor in there.
AD EHP = (1307+1370)*1.59 = 4256
AP EHP = (1307+1370)*1.30 = 3480

Now let’s try Guardian Angel.
AD EHP = 1307*(1.59+.67) = 2953
AP EHP = 1307*(1.59+38) = 2574

Hmm. That’s interesting… How about Banshee’s Veil.
AD EHP = (1307+350)*1.59 = 2634
AP EHP = (1307+350)*(1.30+.5) = 2982

I could go on but the point is, if EHP is what you are going for, Warmog’s Armor is better than many other choices.

You may be correct, but tanks (the people who would generally consider Warmogs) generally dont care much about MR and care much more about armor. Sources of AP damage tend to be bursty and not sustained**. Since a tank generally can't be bursted down, its not something they worry about, and sources of AP damage are rarely wasted on tanks anyway. The MR that a tank can get through sources like Treads and Aegis is generally more than enough. If its a really heavily AP stacked team, a tank might buy a Negatron Cloak, but thats about it.

What can kill tanks is sustained damage, which you generally counter with armor.

Thats why Warmogs is inefficient - tanks care about preventing physical damage a lot more than AP, so they can most effectively counter that with armor as opposed to HPs. As I'm sure your math will tell you, when you are primarily worrying about dps sources, warmogs is a terrible item to buy.

Rammus is a bit of an exception since he has low HP for a tank, but I'd much rather have a Sunfire over Warmogs. So I'd go Aegis, treads, Randuins, Sunfire generally against a generic lineup, so there is really no room for Warmogs.

** The major exception to AP being bursty is a lot of AS + Madreds. But obviously you wouldnt want Warmogs against that anyway, so its hardly a relevant exception. Really, Madred's is a huge problem for Warmog's advocates since its such a common item that really does a number of Warmogs users.

This is a really contrived situation because:

1) You are assuming a fully charged Warmogs at level 12. So they not only got Warmogs, but they also had 100 CS since they got Warmogs...all by level 12. Just not realistic.

2) Its a bit silly to choose a really low HP champ for the comparison. Warmogs becomes less and less effective the more HP you have (while armor and MR become more and more effective since they are multiplicative instead of additive effects). If you were to compare these things on tanks with more HP (the much more likely champs to get warmogs anyway) or even level 18 champs (also more likely since you are assuming a fully charged 3k item) the math would be very different since both those scenarios have much larger HP pools to skew things toward armor/MR.

3) The other items have EXTREMELY beneficial effects while Warmogs health regen is pretty crappy. Realistically, GA would look more like:

AD EHP = 1307*(1.59+.67) + 750*(1.59+.67) = 4648
AP EHP = 1307*(1.59+.38) + 750*(1.59+.38) = 4052

which makes GA a much better buy even given the first a second objections I have above which unrealistically skew things toward Warmogs.

Math is fun and all, but unless applied realistically, its pretty meaningless.

Please, run the calculation with anyone you like then. I chose level 12 because that's about the level when you can complete it at on average with decent last hitting. Please go ahead and run the calculation with any champ at any level and let me know if you come up with one where the items do better.

Building to counter whatever happens to be killing you usually works better. With a little armor or magic resist, your health becomes a lot harder to take away, even if there is slightly less of it. Also, going warmogs costs you the utility of items like banshee's veil, randuin's omen, or guardian angel.

Oh and bloodrazer. If I see a warmogs in the game my next item tends to be bloodrazer.

It has nothing to do with the stats on a warmogs. It has to do with the fact that a Randuins AoE actively and passively snares so as a tank you can just walk away from anything that could possibly kill you.

'Impossible to kill' stats on a Randuins is under budget.

Here is the really bad thing about Warmogs.

Lets do your level 12 Teemo. But lets say that he is facing a level 12 Trist with Madreds.

Trist has a base damage of 81 at that level. Against Warmogs, she will do 218 damage (30+81+.04*2677) a shot. Against GA, she does 163 damage (30+81+.04*1307) - both these are done before mitigation from armor/MR. Thats a 33% increase in damage (BEFORE EVEN CONSIDERING RESISTS) just because you chose to use Warmogs. Ouch.

So yeah, Warmogs has a counter item which is common and very powerful anyway, while GA and the like dont really. Thats in addition to all the other objections above.

Sure, but if you built Warmogs AND a source of MR like FoH...well, thats a hell of a lot of gold and you still dont have any armor. This is really the problem - you want armor to take care of the DPSs (which are the main threats to tanks anyway as I argued above), but now you build two VERY expensive items that dont get you to that goal at all. But yeah, Warmogs really forces you to build stuff like FoH, which forces you into a bad situation where you probably are going to be hardpressed for armor for games of reasonable lengths.

Most tanks would rather just not worry about MR much and go with armor and all the really strong other effects on items like Randuins, Sunfires, Aegis, GA etc.

I find Warmog's to be a nice second or third item. Say you start with a Doran's shield, then boots, then item 1, then Warmog's.