Final damage from ignore enemy defense
Definitions- Percent damage reduction is a property intrinsic to monsters that reduces damage output. It is henceforth referred to as PDR.
- Ignore enemy defense is a stat that mitigates percent damage reduction. It is henceforth referred to as IED.
Formula for calculating IED
Let $\text{IED}_1, \ldots, \text{IED}_n$ be individual sources of IED. Then the total IED contributed by each of these sources is given by $$ \text{IED} = 1 - (1 - \text{IED}_1) * \cdots * (1 - \text{IED}_n). $$ A calculator which does exactly this is available here.
Comments:
- enemy defense debuffs like Nether Strike can be treated as IED
- 1 large source of IED is more effective than 2 medium sources (e.g. 30% vs two 15%'s)
Warning: The stat screen is not a reliable way to calculate IED because it rounds up to the nearest integer and because it does not display some sources of IED. For instance, IED bonuses which apply to only to certain skills are not displayed.
Some PDR values
- 100%: Chaos Von Bon
- 300%: Chaos Vellum, Lotus, Damien, Lucid
A bowmaster with 80% IED picks up a 30% IED line through his codex. What is his IED now? $$\text{IED}= 1 - (1 - 0.8) * (1 - 0.3) = 86\%.$$ A shade with 93% IED picks up a 40% IED line through his emblem. What is his IED now? $$\text{IED}= 1 - (1 - 0.93) * (1 - 0.4) = 95.8\%.$$ An angelic buster with 95% IED now receives a 20% IED to his main bossing skills after maxing his nodes. What is the total IED applied to his main bossing skills? $$\text{IED} = 1 - (1 - 0.95) * (1 - 0.2) = 96\%.$$ Example final damage calculations
The bowmaster in the previous example is wondering how much more damage he now deals to Chaos Von Bon. This is given by $$ \frac{1 - 1 * (1-0.86)}{1 - 1 * (1 - 0.8)} = 1.075 $$ The shade above has been practicing for a Chaos Vellum solo. His final damage increase in this setting is $$ \frac{1 - 3 * (1 - 0.958)}{1 - 3 * (1 - 0.93)} \sim 1.106 $$ The AB's final damage increase in Hard Lucid is $$ \frac{1 - 3 * (1 - 0.96)}{1 - 3 * (1 - 0.95)} \sim 1.035 $$ Justification of comment (1)
There's the view that enemy defense reduction debuffs should be (a) applied directly to the monster and the view that (b) it should be treated as IED. We'll show that these are the same.
Let IED be the base IED and let I be the additional IED gained. The damage reduction in case (a) is given by $$ (\text{PDR} * (1 - \text{I})) * (1 - \text{IED}) $$ and the damage reduction in case (b) is given by $$ \text{PDR} * ((1 - \text{IED}) * (1 - \text{I}) ). $$ Justification of comment (2)
Let $\text{I}_1$ and $\text{I}_2$ be nonzero sources of IED. Then $$ 1 - (1-\text{I}_1)(1-\text{I}_2) = \text{I}_1 + \text{I}_2 - \text{I}_1 \text{I}_2 < \text{I}_1 + \text{I}_2. $$ The left-hand side of the inequality is the IED given by multiplying two medium sources of IED together and the right-hand side of the inequality is the IED given by adding the two medium sources together.