What happens to your damage when you are giving your opponents negative magic resist / armour?

For example I am playing Fiddlesticks and I have:

  1. Passive (-10mres)
  2. Abyssal Scepter (-20 mres)
  3. Haunting Guise (20 mpen)
  4. Sorcerer's Shoes (20 mpen)

...and I am casting skill that does 100 damage on an Ashe with 30 base mres and no mres items?


3 Answers 3


I think you're really asking two separate questions here. The first is, "What order do the various MR reduction / penetration effects follow?"

The answer to that is relatively simple.

Armor/MR Reduction

% Based Armor/MR Reduction

% Based Armor/MR Penetration

Flat/Linear Armor/MR Penetration

So to answer the question as per the above, first Fiddlesticks' passive is applied to Ashe, reducing her Magic Resistance to 20. Next, the Abyssal Scepter effects is calculated, reducing Ashe's MR by 20, putting her at 0. Finally, the flat penetration from the Sorcerer's Shoes and the Haunting Guise are considered -- but Ashe is already at 0 MR, so there is no further MR to "penetrate".

Penetration can never bring a champion's defenses below zero.

So in the above scenario, spells would do 100% damage, so the full 100 damage in your example case.

To answer your second question, about the general case of negative magic resistances (possible on jungle creeps, and in some games featuring Karthas / Soraka / Kayle, etc), I bid you to look no further than this question.

The effects of negative defenses are exactly the same as the effects of positive defenses* - linear. In a nutshell, this means that an Abyssal Scepter will increase your spell DPS by the same amount regardless of whether the champion is starting with 100 MR or -100.

*the formula itself is different, because the armor calculation doesn't handle negative values well, but the end result is a continuation of Armor's linear scaling.

  • According to lol wiki (leagueoflegends.wikia.com/wiki/Armor), damage multiplier depending on armor / MR isn't a linear function. Could you give your source please ?
    – Dalshim
    Commented Sep 2, 2011 at 16:21
  • On the official LOL site : na.leagueoflegends.com/learn/gameplay/champion-statistics --- Armor: Reduces the damage a champion receives from physical attacks. Armor reduces the damage of incoming physical attacks by a percentage. This percentage is determined by the formula: Damage Reduction = Total Armor / (100 + Total Armor). For example, a champion with 150 points of armor would receive 60% reduced damage from physical attacks.
    – Dalshim
    Commented Sep 2, 2011 at 16:26
  • @Dalshim - As I cite in my answer, I've already written a fair amount on the subject, as mentioned here. The heart of the argument is that, while you're correct in the Damage Reduction % being decidedly non-linear, it is not the part of the formula that matters in actual gameplay. That would be one's "Effective Health", or, put another way, the Time-to-Kill (TTK) given constant damage at a given level of mitigation. Commented Sep 2, 2011 at 16:42
  • Didn't get the fact you were talking about effective health when I was talking about damage reduction. This makes it clearer indeed.
    – Dalshim
    Commented Sep 2, 2011 at 21:55
  • I didn't even take into consideration the order of mres/armour reduction. Fantastic answer, thanks.
    – theorise
    Commented Sep 5, 2011 at 9:16

As I had explained in a previous post, effective armor and effective MR are always calculated the following way :

  • Percentage armor / magic resist reduction
  • Flat armor / magic resist reduction
  • Flat armor / magic penetration
  • Percentage armor / magic penetration

The damage reduction depends on the effective armor / MR and follows the following equation : Damage Multiplier = 100 / (100 + Armor) when armor ≥ 0

enter image description here

However, in some cases, someone can end up with negative armor or MR, in these cases, this different equation applies : Damage Multiplier = 2 − 100 / (100 − Armor) when armor ≤ 0

enter image description here

Now, you have to know that penetration can't set effective armor below 0, only reductions can. Meaning if someone has 30 MR :

  • if you have 20 MR reduction + 20 magic penetration, his effective MR will be 0
  • if you have 40 MR reduction and whatever magic penetration his effective MR will be -10 (which is a big difference).

You will find all the information you need HERE and THERE ! They give plenty of examples for calculating effective armor / MR / Health in various different cases and all the formulas you will ever need.

  • 1
    Do note that those two graphs are terribly misleading, because the effectiveness of armor/MR is linear. Commented Sep 2, 2011 at 16:19
  • @Raven Dreamer : Damn, commented the same thing on your answer, we have to compare sources.
    – Dalshim
    Commented Sep 2, 2011 at 16:22
  • it's even mentioned on the page you cite: "Armor does not have diminishing returns from an effective health perspective; each point of armor increases the amount of physical damage required to kill the champion by 1 percent of the champion's health." Commented Sep 2, 2011 at 16:46

There is already a good answer for your question on penetration vs reduction.

To answer your question on negative resistances, the wiki page for Armor has all of the math included now.

Damage multiplier is 100 / (100 + Armor), if Armor >= 0. Otherwise, it's 2 - (100 / (100 - Armor))

Every point of armor requires a unit to take 1% more of its maximum health in physical damage to be killed. This is called effective health.

Example: A unit with 60 armor has 60% more of its maximum health in effective health, so if the unit has 1000 maximum health, it will take 1600 physical damage to kill it.

What this means: by definition, armor does not have diminishing returns in regard of effective hitpoints, because each point increases the unit's effective health against physical damage by 1% of its current actual health whether the unit has 10 armor or 1000 armor.

The fact that armor does not have diminishing returns is already covered in detail in a related question.

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