As someone who primarily plays tanks, supports and the occasional bruiser, there are some massive flaws in your post. I'm not speaking about Bruisers here, just tanks in general. My post isn't about if Tanks are viable, just that the maths here and efficiencies here listed in the opening post kind of need a lot of tweaking. I'm not arguing that Tank Itemization is fine, just saying there's so many more factors needed to be added.
So base stat wise with no passives, yes, the value of each item for Tanks and Bruisers are generally cost inefficient. However in League of Legends, your ability to actually tank doesn't just come from being able to take damage, but the skill set you have as well as what the items actually bring to the table. Let's start adding some of the passives in and you'll find that the tank items, even if still cost inefficient, have far better uses.
Randuin's has inbuilt attack speed slow and movement speed slow. This affects multiple people. The price of that alone is insane. Yes, Randuin's has been nerfed so many times in the past BUT for your initiation, adding an extra slow on top of that is always useful. Plus like many tank items (not counting 'Bruiser' items), it's an AoE effect that affects multiple targets.
I'm only using Randuin's as an example because many people on GD I've noticed seems to agree that Randuin's right now is not up to par in the game. I'm not going to agree or disagree I'm afraid. Just that one of them items many people seem to dislike has functions that affect multiple enemies at once.
Righteous Glory on the other hand, my new favourite item of all time is INSANELY GOOD with both the passives. You're not only gaining Catalyst's effect, but you're also gaining the ability to speed up an entire team while able to slow down up to 5 players for 80%. Again, I'm not arguing about Randuin's Omen here being good or bad, I'm just saying that these items alone are probably worth more their weight in gold than a lot of the actives and passives you'll see later in the AP Itemization.
Even Ohmwrecker, who I'm sure no one actually uses, has inbuilt movement speed buff to your allies which maybe can prove invaluable. Even if it's no where near as useful as Talisman of Ascension or Righteous Glory, it really shows off the nature of tank items being more for team base play.
Many 'actual tank items' affect multiple targets whether it'd be an aura, passive or active while many AP Items are inherently selfish and affect only the user. The exception to those rules are Rylai's (which barely anyone builds) and Abyssal Scepter (Which quite a few AP Tanks like to build.)
Cost Efficiency with passives start becoming more of a thing which is why when you quote League of Legends Wiki on cost efficiency, you should probably quote the whole thing in turn. You also chose to cherry pick the items that would agree with your analysis as well. You didn't even include THESE two items which do have their cost efficiencies laid out.
Locket of the Iron Solari
Statistical Efficiency
The base stats are 87.62% gold efficient.
For the item to be considered 100% gold efficient, the aura and active would need to have a combined gold value of 345g.
The aura has a gold value of 670 for every allied champion it affects. If all allied champions are affected, the aura has a gold value of 2680, and the item becomes 183.39% gold efficient. This still does not consider the gold value of the active effect.[/quote]
The aura alone more than DOUBLES cost efficiency.
Frozen Heart
Statistical Efficiency
Frozen Heart is 140.1% gold efficient without the aura.
Now I did leave out one item in particular. Warmog's Armour. It's a far more selfish tank item than all the others that proceed it. But again, I'm not claiming to be an expert here. But I'm pretty sure aside from this item (if I'm wrong, correct me), most other tank items become as cost efficient as the AP items you've listed (with their passives/actives as well) when passives and actives are added to the mix.
In short: AP Itemization is more selfish in it's choices while Tank items are generally more team orientated. While both sets have selfish and team bases locked into them also, that's generally the case. If the cost of our tank items go down while leaving the stats they give the same, then the passives/actives will be nerfed to coincide with this.
The base stats are 109.4% gold efficient without the active.
is 102.8% gold efficient by itself.
is 147.2% gold efficient without the passive.
The base stats are 103.6% gold efficient, without the passive effects.
is 111.78% gold efficient, without the passive effects.
The base stats are 121.6% gold efficient, without the passive.
The item is 103.4% gold efficient without its aura.
The item is 159.9% gold efficient when fully stacked. it also stacks with roa and rabadon
The base stats are 95.9% gold efficient.
The base stats are 89.3% gold efficient.
The base stats are 85.3% gold efficient, without its passive.
The base stats are 92.5% gold efficient.
The base stats are 92.3% gold efficient.
Sunfire Cape is 80.7% efficient.
Ohmwrecker is 95.2% efficient.
The base stats are 91.7% gold efficient, without its passive.
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