Put simply they don't, nothing has diminishing returns in D3. I shouldn't say nothing I think stuns/immobilizes become less effective the more you use them on a monster. But the common things that get talked about, armor, all res, %damage, resource cost/cooldown reduction, none of that stuff suffers from diminishing returns.
First we should define what we mean by diminishing returns. Diminishing returns is the idea that the more you put into something the less you get out of it.
In D3 if a stat increases a number it is additive with itself i.e. 30% meteor damage on one source and 25% on a second source gives you 55%. A stat that makes a number smaller is multiplicative with itself i.e. having 50% damage reduction from armor and 50% damage reduction from a resistance gives you 75% damage reduction overall.
Let's go back to that meteor damage. We'll say our meteor does 100 damage for simplicities sake. With that 30% increase and that 25% increase it now does 155 damage. What makes people say "there's diminishing returns on that" is the relative increase between the two. After we apply that 30% our meteor goes up to 130 damage if we then add on the 25 it's only a 19.23% relative increase to get to that 155 damage. The problem here is that isn't diminishing returns the 25% is still worth one of itself. If you look at it from a real life scenario it should clear things up. Let's replace meteor with bank account and damage with account balance. Now you have 100 dollars in your bank account and you add 30 giving you 130 dollars a 30% increase, nice. Now if you add 25 more dollars that's a 19.23% increase of your 130 dollar balance but your 25 dollars is still worth 25 dollars. If there were diminishing returns here that 25 wouldn't have added 25. Looking at the relative increase is good for optimisation but it doesn't make any of the individual parts worth less.
The same goes for armor/resistances, every single point in those stats is exactly equal to the next. The reason why people will cry diminishing returns is that as you add more into these stats you notice you get less %damage reduction. But each percentage point of damage reduction is actually worth more that the previous. At 50% damage reduction you are effectively doubling your max health, at 75% damage reduction you have quadruple effective health which means that 25% more is worth exactly as much as the 50% that came before it meaning each of those percentage points are twice as effective.
You shouldn't think of armor/resistances as damage reduction but rather as effective health. Every 1000 armor is 28.57% effective health and every 100 resistance is 28.57% effective health.
So 1000 armor is 22.22% damage reduction. Let's say we have a character with 100 health that is hit with a 100 damage attack. That 100 damage is reduced to 77.78.
77.78/100=1.2857 or 128.57 effective health giving us that 28.57% increase. Now if there were indeed diminishing returns if we add another 1000 armor on we'll have a lower increase in effective health.
That gives us 36.36% damage reduction turning that 100 damage into 63.64 damage
100/63.64=1.5713 or 157.13 effective health a 57.13% increase.
57.13-28.57=28.56 off by .01% thanks to rounding errors.
You can see that each new point of armor has the same exact effect on your effective maximum health as the previous ones. Your resource cost reduction and cool down reduction both have and effective increase as well. RCR increases your effective maximum resource and CDR increases your effective uptime/casts per base cooldown period.
TL;DR Every 1000 armor/100 resistance increases your effective health by 28.57% no matter how much of it you have. You should look at the effect on the base number additive percentages have rather than relative to each other. A stat that is multiplicative with itself is worth more the more you have of it not less. There are no diminishing returns.
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