I have a quick question about this set’s full bonus, namely that your CDR = Extra damage. If I add up all my gear’s CDR including the set bonus of 20%, and the diamond in my helm, I have a CDR of 82.5%. In the game, my character screen says I have 62.6%. What damage gain do I actually get from the full set? Do I get the prorated CDR of 62.6% or the full CDR of 82.5%. Thank you in advance.
CDR and other defensive bonuses have diminishing returns. The higher you try to stack, the smaller the bonus is.
You get the 62.6% damage. You sheet cooldown is the bonus to damage you get.
Also, your sheet resource cost reduction is what defense you get as well, but resource reduction doesn’t have the “diminishing returns” problem, cooldown does.
CDR, RCR and DR are all multiplicative.
General formula is:
Total_R = (1 - product(1 - Ri))
e.g. You have 2 CDR, 20% and 50%.
The total CDR = 1-(1-0.2)*(1-0.5)
=1-0.8*0.5
=0.6=60% (not 70%)
CC set uses the numbers on the properties sheet for bonus. Ie the formula above.
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Exactly what I was going to point out. It’s not prorating, it’s just calculated multiplicatively.
But damage reduction DOES. You can’t get 100% DR to become immortal by stacking RCR.
I don’t know the formula, but Resource Cost Reduction and Cooldown Reduction are calculated differently.
For instance, using Captain Crimson and DH Set Unhallowed Essence with Yang’s Recurve it’s possible to reach 80-to close to 90% damage reduction just by stacking Resource Reduction. You’re right, you can’t reach 100%. But you get higher values by stacking Resource Reduction than you Cooldown values stacking Cooldown.
Hence, why I said it doesn’t have the “diminishing returns” problem. To be more accurate though, I should have said “same diminishing returns” problem.
They’re calculated differently. And it’s more than just Yang’s having 50% resource reduction on it’s own.
If you stack resource reduction and cooldown on equipment to the same amount, let’s say 8% on three pieces each. The sheet calculation won’t show the same the value for both stats. Resource Reduction will be higher.
At least, I’m pretty sure. Someone tried to explain it to me once and that’s what I got out of the explanation.
Nope. To illustrate the calculation of RCR, I took some screenshots from live data.
I have a build using gloves (6% RCR), Yang (49%), CC (20%) and paragon (10%).
The in game RCR is 65.48%:
Details shown in D3planner:
Use the formula:
total = 1 - (1-49%) * (1-20%) * (1-6%) * (1-10%)
= 1 - 0.51 * 0.80 * 0.94 * 0.9
= 1 - 0.3452
= 0.6548 = 65.48%
That matches the in-game number. Therefore, the formula works for both CDR and RCR, in fact DR as well.
(I rather hate to use the term “diminishing return”. Just focus on the value.)
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No, DR, RCR, and CDR are all calculated the same.
The only reason it seems different for RCR is because of Yang’s. As you’ve noted, because of the way CDR stacks, it’s hard to get a really big number, because a whole bunch of smaller values don’t multiply into as big of a value like you might expect.
However, CDR rolls don’t come as big as Yang’s. The RCR on Yang’s is colossal. A single 50% RCR roll is worth WAY more than individual CDR/RCR rolls that add up to 50%. This is a consequence of the way CDR/RCR are calculated.
It also means there’s a much bigger difference between a 40% and 50% Yang’s than you would expect. Going from a 40% Yang’s to a 50% Yang’s isn’t the same as adding a 10% RCR roll. It’s actually worth as much as a 17% additional RCR roll on another slot.
Same thing applies to damage reduction rolls. Especially for something like Band of Might or Karini. Going from a 60% Karini/Band of Might to an 80% is equivalent to adding an entire additional source of 50% DR. And you might think a 70% is halfway to 80%, but it’s not. 70% DR is only about 1/3 of the way between 60% DR and 80% DR. The last few % on a Karini/Band of Might are worth way more than the first few %. There’s a much bigger difference between a 77% and 80% Karini than between a 60% and 63% Karini.
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Just to clarify, calling it “multiplicative” because of how it is calculated is wrong.
Multiplicative implies exponential increase by multiplying each number on top of the result of previous multiplications.
With diminishing returns these multiplications are greatly reduced the more sources we add.
That is why we say “This stat has diminishing returns”, when the total result is less than what we expect the more sources we add.
We don’t say “You are getting less because it is multiplicative”.
As an example, something that is multiplicative is Focus and Restraint set bonus. It has no diminishing returns, and the bonuses multiply each other thus giving us a total of 125% bonus to damage.
So, we say “That bonus is multiplicative.”
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Let’s look at the two statements: “increased by N%” and “decreased by N%”
For “increased by N%”, the equation is:
Result_Damage = damage * ( 1 + N% )
For “decreased by N%”, the equation is:
Result_Damage = damage * ( 1 - N% )
The only different is the sign (increased/decreased). The two equations are the same mathematically speaking. If the damage buff is multiplicative, then it is correct to say that damage reduction is multiplicative.
“increased by -N%” is another way of saying "reduced by N%“.
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Think of it this way; you always get the notes Cooldown reduction displayed. If you have a skill with 100 seconds Cooldown and equip an item that reduced Cooldown by 10% it will do that meaning removing 10 seconds.
Putting on another item that reduces Cooldown by 10% it will do exactly that, however your current Cooldown is 90 seconds, so it takes of 9 seconds.
And so it continues.
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OK I do find this very interesting but in the end if I look at my sheet CDR/RCR I see the real effect?
DR is different though? Can’t just add them all up so will need to use all the maths you guys give here.