Damage Over Time

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Let us say you instead have ailments deal damage 10% faster, 30% DoT multiplier, and 200% increased damage.

An additional 10% of each would give you 9.1% more dps, 7.7% more dps and total damage, and 3.3% more dps and total damage.

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DER_PSYCHOPATH wrote:

Let us say you inflict an ailment that deals 100 damage per second. To make it a little more tangible, let us say that ailment is ignite and thus has a duration of 4 seconds.

Ailments deal damage 10% faster will cause it to deal 110 damage per second over 3.63 seconds for a total of 400 damage. If you apply a second ignite dealing the same amount of damage before this expires, your dps from the ignite will be 110%.

+10% damage over time multiplier will cause the ignite to deal 110 damage per seconds over 4 seconds for a total of 440 damage.

10% increased damage will cause the ignite to deal 110 damage per second over 4 seconds for a total of 440 damage.

Assuming that every single of your ignites has a base damage per second of 100, the final dps for all three of these stats remains the same.

Now for the second example:

The damage per second is
100 * (100% + 10%) * (100% + 30%) * (100% + 200%) = 429

It has a duration of 3.63 seconds.

Now, we add ailments deal damage 10% faster. It becomes
100 * (100% + 20%) * (100% + 30%) * (100% + 200%) = 468

468 / 429 = 109.1%

10% of this stat cause us to deal ~9.1% more damage than before. Incidentally, the duration of the ignite is
4 / (100% + 20%) = 3.33 seconds

If we instead use damage over time multiplier, it becomes
100 * (100% + 10%) * (100% + 40%) * (100% + 200%) = 462

462 / 429 = 107.7%
With this, we deal ~7.7% more damage than before, even though the stat is still 10%.

And if we take increased damage, it is
100 * (100% + 10%) * (100% + 30%) * (100% + 210%) = 443.3

443.3 / 429 = 103.3%
10% increased damage only causes us to deal ~3.3% more damage than before.

I have not accounted for the ailment duration in this example, which does make a difference for non-stackable ailments because only the instances with the highest damage rolls deal damage, so a longer duration means additional chances of inflicting an ailment with a higher damage roll, but the math for that is really complicated, and you will not constantly inflict ailments at the same rate either (unless you play Blade Vortex which has a fixed maximum hit rate, but BV is usually played with poison or as a hit build rather than ignite).

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adghar wrote:

IMO it's easier to understand DER_PSYCHOPATH by taking a conceptual point of view rather than a deep dive example like that.

The core concept here is that multipliers that stack additively with others of their type, multiplied against multipliers of other types, scales proportionately. Classic example is attack damage and attack speed; the more of one you have, the more powerful the other gets, because they multiply; since the relationship is x*y aka length times width, as the rectangle that represents your total DPS gets super long, a little bit of widening then goes a long way, and vice versa.

Or, imagine a factory that can produce 100 units per day. You build another factory, and another factory, and another factory. You soon end up with 500 units per day. Adding another +100 units brings your total unit production up to 600. That's still a 100% increase (in POE terms) from your day one production. But if you could suddenly upgrade all your machines in your factories to produce 100% faster (twice the speed; 100% increased machine speed in POE terms), suddenly you can build 1000 units per day instead of 500, which is obviously much more than a 100% increase to base factory quantity. That's what we call 100% more; in order to get 100% more production from factory quantity, you'd need 500% increased base factory quantity. That is, in order to get the same end output you'd need to have your "x% increase" be from the existing multiplier amount, which in POE terms would be x% more; that is how, in this case, 500% increased = 100% more (in POE terms).

Same thing with the example he made:

"

Let us say you instead have ailments deal damage 10% faster, 30% DoT multiplier, and 200% increased damage.

An additional 10% of each would give you 9.1% more dps, 7.7% more dps and total damage, and 3.3% more dps and total damage.

The fact that these are all separate multipliers makes it self-evident that you need proportional comparison.

(1.1 + 0.1) / (1.1) = 1.0909090909, or "9.1% more DPS"
(1.3 + 0.1) / (1.3) = 1.0769, or "7.7% more DPS"
(3.0 + 0.1) / (3.0) = 1.0333333 or "3.3% more DPS"

This is exactly analogous to attack damage/attack speed, or length/width of a rectangle, or increasing base number of factories you have vs. increasing the per-machine production power at all factories.

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DRBrown994 wrote:

Does the second ignite stack cause a second 110% increase on top of the original if the original doesn't expire?

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DER_PSYCHOPATH wrote:

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DRBrown994 wrote:

Does the second ignite stack cause a second 110% increase on top of the original if the original doesn't expire?

No, it does not. By default only one ignite can be active at any point in time.

If you inflict two ignites on the same target, the stronger one will deal damage. On average, the stronger out of two will be around 30% higher within the rolling range, which is already not exactly a simple proportion, and it gets even more complicated with more than two ignites.

To keep the examples simple and understandable, I have deliberately omitted these mechanics.

In general, the number of ignites you inflict over a 4 second period will not differ significantly from a 3.63 second period, so the lowered duration from the ignite dealing damage faster isn't quite as significant in practice. Even more than that, you will actually not even end up spamming your skill to ignite in the first place. DoT builds typically inflict their debuff and then dodge or move to the next pack.

You might effectively have 2-3 ignites on an enemy (again, with only the highest dealing damage), but the "ailments deal damage X% faster" stat is so rare that it won't significantly impact the duration to the point that it would be a noticable dps loss compared to regular multiplicative scaling.

Even for Burning Arrow, which has a debuff that stacks up to 5 times and deals damage based on the damage of the ignite, you will only attack roughly 5-8 times per ignite duration, regardless of how many attacks you can actually fit in, because the damage gain beyond the first few is marginal.

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DRBrown994 wrote:

Interesting.

I have a question that's just come up from my Caustic Arrow build, I have wither that does "6% increased chaos damage taken", is that 6% of the current chaos damage I do (10k) and adds it to 10k?