A stacking guide

[Iria-1342]

@dmkt-1267

Is there a mathematician out there who can dumb it down?

Yes, I’m one outside the game but there is a lot of garbage and a few good bits of math in this thread, so sifting through stuff will take me a while. I just got here!

Edit: ok here are some initial comments:

@dmkt-1267

The part about CC effect immunity is a good nugget. Can we simplify the math into an easy to understand rule so decision making doesn’t require multistep calculations/excel?

The formula the OP states has no context on where it was derived from. While I could speculate where some parts of the formula come from, this is not the way math should be presented!

@LindorMC-2584

5. Some maths for fun

There is the natural exponential function hidden in the stacking calculating formula.
Let’s assume you have a total sum of +x% damage evenly distributed over n items.
The Formula for the final multiplicator is (1+x/n)^n-1
As the limit of n goes to infinity, the multiplicator goes to e^x-1.
That being said, the final multiplicator might converge to e^x-1 but e^x is a terrible estimate for the multiplicator since the average error also grows exponential the bigger x is.

There isn’t anything in the game that stacks multiplicatively many times over to use the e^x approximation. Even Bane of the Stricken works by adding up all the stacks before multiplying by the modifier (e.g. 100 stacks of +1.2% is +120% which is a 2.20x damage multiplier).

Also, the “-1” in the formulas are wrong (if it was correct, then if x = 0 as in +0% damage, the multiplier in your formula would be 0 instead of 1).

@LindorMC-2584

The armor/reistance interaction is exactly one of the mechanics i talk about. resistances not only “scale” with themself giving diminishing returns but it also scales with armor in a 1:10 ratio.

This 1:10 ratio is a common misconception. To avoid confusion and over-complicating things, think of armor and resistances as providing a toughness multiplier [TM] instead of a damage reduction [DR] (they are related by TM = 1/(1-DR). Thus at level 70 (so the equations are simpler):

DR_armor = (Armor)/(Armor + 3500)
TM_armor = 1 + Armor/3500

DR_resist = (Resist)/(Resist + 350)
TM_resist = 1 + Resist/350

From these equations, it’s clear where the 1:10 ratio misconception comes from! If you could freely choose between adding armor OR resistances by adding Strength/Dexterity or Intelligence, then you would want a 1:10 ratio. However, each class can only add Armor OR Resistances through paragon! And furthermore, the +armor and +resistance affixes do not appear in the same quantity. Pants for example can get +750ish armor or +130 resistance.

In these situations, you want to optimize your toughness by “affix slot” not by “armor or resistance point”! Thus it will not quite be the 1:10 ratio! And in actual practice, you want all resist anywhere you can if you play a Str or Dex class and armor anywhere you can if you play an Int class since you get endless amounts of the other through paragon!

Finally, as you can see from the TM equations, there doesn’t reach a point when armor or resistance becomes irrelevant, the toughness boosts are almost linear!

@Hebalon-2718

That’s true, but it is mostly irrelevant, because you can never choose on a item between Skill and Elemental damage.

There is one relevant item: Holy Point Shot.

@Hebalon-2718

Set bonuses do not push us “a few” GR levels. They teleport us into completely different GR-spheres.

That’s a fancy analogy! Where’s your proof that GRs are spheres though? Could they be cubes, tetrahedra, or even flat planes (#FlatEarth)!