IED stands for Ignore Enemy Defense.
Monsters have something called "PDR" or "Percent Damage Reduction". This reduces the damage you do to them, sometimes to the point where you cannot damage them at all. IED helps you counter this.
Say you have 30% IED. You might think that adding another source of IED, say another 30%, would put you at 60% IED. This is not the case, as IED is multiplicative. This means that each additional source of IED is less effective, and it is substantially harder to reach higher numbers of IED.
Calculating IED can be difficult, since you likely have many small sources of IED from things like links, legion, and skills that are hard to keep track of. In addition, IED from boost nodes does not show up on your stat sheet, so how exactly do you know how much damage you are ignoring when you use a skill that has an additional 20% IED? Well, fear not, since I have the solution for you. Here are two formulas, one for calculating total IED if you know every single source of it, and one for if you have your current IED and want to know what an additional source would do to it. I will also include a formula you can use to calculate your final damage multiplier versus a boss.
For \(n\) sources of IED, with values \( \{x_{0}, x_{1}, \cdots, x_{n} \} \): $$ \text{IED}_{\text{total}} = 1 - (\prod_{i=0}^n (1 - x_{i})) $$
With current IED \(x_{0}\) and additional source \(x_{1}\): $$ \text{IED}_{\text{total}} = x_{0} + (x_{1} * (1 - x_{0})) $$
For a boss with PDR \(p\), and IED \(x\): $$ \text{Damage Multiplier} = 1 - (p * (1 - x)) $$
Here are some examples of the above formulas in action you can use for reference
Lets say I have three sources of IED, with values of 15%, 30% and 40%. My total IED then be:
$$
\text{IED}_{\text{total}} = 1 - (\prod_{i=0}^n (1 - x_{i}))
$$
$$
\text{IED}_{\text{total}} = 1 - ((1 - x_{0}) * (1 - x_{1}) * (1 - x_{2}))
$$
$$
\text{IED}_{\text{total}} = 1 - ((1 - .15) * (1 - .3) * (1 - .4))
$$
$$
\text{IED}_{\text{total}} = 1 - ((.85) * (.7) * (.6))
$$
$$
\text{IED}_{\text{total}} = 1 - (.357)
$$
$$
\text{IED}_{\text{total}} = .643 \text{ or } 64.3\%
$$
Here is an in-game example.I have 79% IED, and I want to know what my IED will become after completing 4 set reinforced gollux for the 15% IED set effect. $$ \text{IED}_{\text{total}} = x_{0} + (x_{1} * (1 - x_{0})) $$ $$ \text{IED}_{\text{total}} = .79 + (.15 * (1 - .79)) $$ $$ \text{IED}_{\text{total}} = .79 + (.15 * .21) $$ $$ \text{IED}_{\text{total}} = .79 + .0315 $$ $$ \text{IED}_{\text{total}} = .8215 \text{ or } 82.15\% $$ Here is the in-game before and after, which match our calculations.
Lets say I wanted to kill Chaos Vellum, who has 200% PDR. With my 82% IED from above, how much damage would I do? $$ \text{Damage Multiplier} = 1 - (p * (1 - x)) $$ $$ \text{Damage Multiplier} = 1 - (2 * (1 - .83)) $$ $$ \text{Damage Multiplier} = 1 - (2 * (1 - .83)) $$ $$ \text{Damage Multiplier} = 1 - (2 * .17) $$ $$ \text{Damage Multiplier} = 1 - .34 $$ $$ \text{Damage Multiplier} = .66 \text{ or } 66\% $$ So, with 82% IED, I am dealing 66% damage to CVel. With the recommend 92% IED for CVel, you would be dealing 84% damage.
IED seems confusing, but in reality is quite easy to understand. Feel free ping me with questions, corrections, or anything else.
