Armor is fairly important for tanks in league, as it lowers the physical damage they take from enemies.
Armor absorbs a certain percentage of incoming damage to the champion, it is not on a 1:1 scale. For example having 100 armor does not block 100% of incoming damage.
Armor also does not scale up at the same pace throughout the game, buying 15 armor at the beginning of the game when you have 40 armor has a greater impact than buying 15 armor at the end, when you already have over 100 armor.
Finally, different items have a different cost-effectiveness for armor values:
Cloth Armor costs 300 gold and gives 15 armor, that is 20 armor per gold
Chain Vest costs 720 gold and gives 40 armor, that is 18 armor per gold
So taking into account the way armor scales down with the amount of current armor your champion has, and the cost effectiveness of different items that give armor, I'd like to know when is it economically right to just stop buying armor. Or
What is the armor value at the point where buying X armor will only increase damage absorption by 1% (or less), and what is the minimal gold value to get there?
For example, I played Garen on Twisted Tree Line and started with 40 armor, which said gave me a 29% reduction to incoming damage.
I bought a Chain Vest right off, giving me 82 armor (40 + 2 additional from my masteries), with 45% damage reduction
I proceeded to record throughout the game:
127 armor = 56% reduction
170 armor = 63% reduction
198 armor = 66% reduction
As you can see, the difference of 30 armour in late game only bumped it from 63% to 66%, but adding 40 armour earlier bumped it from 29% to 45%