Common Error: "armor has diminishing returns, therefore it sucks as you get more of it".
Fact: "Each point of armor is just as valuable as the last point. Diminishing returns is a math trick with a bad name that makes it sound like it sucks".
Let's say you have 10% damage reduction (lets say, 10 armor), and you have the ability to purchase a new item that gives you +10% mitigation (lets say, 10 armor). Without diminishing returns, your armor would increase from 10 to 20, and your mitigation would increase from 10% to 20%.
If before your mitigation was 10%, that means your effective hp was 111% of your max hp (9/10 -> 10/9). Now, since it is 20%, that means your effective hp is 125% of your max hp. (4/5 -> 5/4). So the first 10% of mitigation increased your effective hp by 11%, your second 10% of mitigation increased your effective hp by 14%. What gives?
Now, let's say you have 80% damage reduction (let's say, 80 armor), and you have the ability to purchase a new item that gives you +10% mitigation. Without diminishing returns, your armor increases from 80 to 90, and your mitigation increases from 80% to 90%.
If before your mitigation was 80%, that means your effective hp was 500% of your max hp (1/5 -> 5/1). Now, since it is 90%, that means your effective hp is 1,000% of your max hp (1/10 -> 10/1). So the first 80% of mitigation increases your effective hp by 500%, your last 10% increased your effective hp by 500%. What gives?
Now, you're at 90%, and you get to increase your armor by 10 again. Now you have 100% mitigation. You win.
That is why diminishing returns exist. As you get more and more mitigation, your effective hp increases exponentially. What (most) "diminishing return" formulas do, is make it gradually harder and harder to increase your mitigation, because a 10% increase is more valueable at 90%, than it is at 80%, which in turn is more valueable at 70% and so on.
Without DR, the formula for the above example was:
Mitigation % = Armor/100.
With DR, the formula for the above example might be:
M = (1 - 100/(100+A))
So for 1 point of armor, you have 1 - 100/101 == .99% mitigation, which comes out to 101% effective hp.
For 2 points of armor, you have 1 - 100/102 == 1.96% mitigation, which comes out to 102% effective hp.
For 10 points of armor, you have 1 - 100/110 == 9.09% mitigation, which comes out to 110% effective hp.
For 100 points of armor, you have 1 - 100/200 == 50% mitigation, which comes out to 200% effective hp.
So, as you can see, you get exactly 1% more effective hp for each point of armor you add, with "diminishing returns". Each point of armor doesn't get worse and worse, as the name suggests. It stays exactly as valueable, in terms of abesolute % increase to effective hp.
The "correct" use of diminishing returns is that you get less out of things as you put more into it. For example, Inner Grace has diminishing returns because the first point gives 10 hps, but the second and third points only give 15/20 hps respectively.
This does somewhat kick in with the armor as well, but not in the same way as with Inner Grace where you actually get less abesolute gain. If you look at your relative % increases, armor does diminish.
Eg, from 101% to 102% effective hp, you only increase your effective hp "relatively" by .99%, whereas from 100% to 101% effective hp, you increased your effective hp "relatively" 1%. From 102% to 110%, you increase your effective hp "relatively" by .98% per point. The abesoulte increase stays the same, but the relative increase does not.
This is also true for health items. If you increase your max hp from 100 to 101, you increased your max hp by 1%. If you increase your max hp from 101 to 102, you increased your max hp by .99%. The abesolute value is the same, the relative value does diminish.