The formula for calculating damage reduction from armor in League of Legends is
Damage Reduction = Total Armor / (100 + Total Armor)
It seems clear to me that this formula dictates that adding more armor has diminishing returns.
For example, let’s say my champion has 50 armor, which gives damage reduction of 33.33% and I buy an item that gives 25 more armor; then my champion’s total armor would be 75 and damage reduction would be 42.86%. That means I saw a 28.6% increase in damage reduction (damage reduction was increased by 9.53%). Now let’s say I buy another of these items with 25 armor. Now my champion’s armor will be at 100 which gives damage reduction of 50%. That means I saw a 16.66% increase in damage reduction (damage reduction was increased by 7.14%).
Therefore, from the first 25 armor item I bought got me 9.53% damage reduction, while the second time I bought the item it only got me 7.14% damage reduction. It looks to me like it was 25.08% less effective the second time I bought it. That screams diminishing returns to me. Why would someone say otherwise? Would they say anything different about Magic Resistance?
Note: This question was inspired by a comment thread which started off of this question: What is the formula for armor/magic resist reduction?. I have heard similar insinuations made before, though, implying that magic resist and armor are somehow different in the department of diminishing returns (although I am not sure if that was implied in the comments on the related question).
As I mentioned in the comments, you’re looking at the wrong aspect of armor. You shouldn’t be looking at the percentage it reduces, but rather the amount of damage it actually prevents as a measure of how much longer that armor lets your survive.
Let’s consider an example for a champion with 0 armor. Say he has 1000 health, just ’cause that’s a nice round number. Now our champion gets caught in Garen’s judgement, and starts taking 100 physical damage each second (at one hit per second). Clearly, our protagonist can take ten hits before dying.
But now, imagine our champion has the 50 armor you mention, meaning the incoming physical damage is reduced. Now (still with 1000 health) it takes 15 seconds for that bastard Garen to claim our champion’s life. 50 armor extended our life by 5 seconds. (100 * (2/3) = 66.6 DPS; 1000 / 66.66… = 15 hits)
So our champion respawns, wises up, and buys 50 more armor. Now with 100 armor, we’re sitting at a flat 50% damage reduction. Again we run into Garen, who’s still dealing 100 base damage per second. It now takes him twice as long to kill us — 20 seconds. Once again the armor has extended our life, again by 5 seconds. (100 * .5 = 50 DPS; 1000 / 50 = 20 hits)
Back in base, we buy another 50 armor. We’re now at 150 armor, and 60% damage reduction. Enter Garen — spinspinspinspinspinspin and it takes 25 seconds before our champion dies. Again, adding 50 armor extended our life by 5 seconds. (100 * .4 = 40 DPS; 1000 / 40 = 25 hits)
So even while the amount of damage reduced per point of armor diminishes (as you observed), the amount of time armor extends your life (or effective health) remains distinctly linear.