How does negative armour / magic resistance work?

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?

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.

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

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

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.