# Talk:Formulas:Magical resistance

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## Normal Distribution or Gaussian? Edit

Is the actual damage absorbed really a normal distribution around your average resistance? There are many distributions they might use such as triangular or approximately normal (or even flat) etc. Has data been compiled on this to verify that they truly apply a formula for Guassian distribution?

Sharpnova 19:01, 28 February 2006

## How do resist talents affect these?Edit

The page is general talking about how miss chance is "affected by any +spell hit% equipment or talents that the caster has" but it doesn't tell you how to tell whether or not a talent affects miss chance.

Do the mage talents that reduce arcane and frost spell resistance affect "miss chance" or "magical resistance" chance or both?

AFAIK, talents that "reduce enemies' chance to resist by X%" directly affect the first check - the chance to miss based on level difference. It doesn't fit in really well in the second check, the one checking the caster level vs. target resistance. I haven't had the chance to verify this by testing, but I'm pretty sure it's right.
Example: if a lvl 60 Shadow Priest with Shadow Focus 5/5 (-10% chance to resist) attempts to cast Mind Blast on a lvl 63 mob, the priest will have 7% chance (instead of 17%) to miss outright, before considering the target's resistances; the calculations around the target's Shadow resistance then doesn't take into account Shadow Focus (otherwise it would be used twice).
This is coherent with how miss chance and +hit are used in regard to melee combat. --Dorenthas 23:16, 15 October 2006 (EDT)

## Separate rollsEdit

This page states that resist is calculated in two separate rolls. I am somewhat surprised by this, since the rest of the combat system follows the same trend as most MMOGs, which is to have a table-based system in which all the possible eventualities are precomputed, so that the outcome is calculated with a single roll. Is there any evidence that this isn't the case with spellcasting? (Note that having a single "roll" for each spell cast rather than two means (roughly) half the calculations. If you factor this across the numbers of spells cast on a while server every second, that is a very meaningful optimization. I'd be VERY surprised that Blizzard would have it otherwise. EDIT: in spite of what's displayed on worldofwarcraft.com...)

From the example on that page, especially the part about Eyonix vs. Yeti of Doom, it looks like it's a single roll that's mathematically equivalent to the double roll described. Personally I think the double roll is a more intuitive way of describing it, and if it's equivalent to what's actually happening, the actual details are somewhat academic.
Yes, there is a single roll. This page links to Blizzard authority on it - Formulas:Spell hit chance - but I think that this Restiance page is still correct at the surface. It's just misleading because it implies two rolls take place. I'd tidy it up if I had more time. -Hammersmith 23:23, 17 November 2006 (EST)
I don't know how recent this information is (last response was dated November 2006, however I'm assuming your referring to both spell resist chance and spell miss chance, as they are now two separate events. Miss and resistance are in fact rolled separately (as of patch 3.3a). To further explain this, I will use an example which a level 71 player attacks a level 80 target (PvE), a level difference of 9 which means the player will have a 17% chance to hit his/her target (83% chance to miss). Additionally, the target has a 25% chance to resist all incoming spells. If the two stats (hit and resist) were rolled together on a single roll, the 83% chance to miss plus the 25% chance to resist would result in a 0% chance to hit (unless hit takes priority over resist, which is not the case, because if the player had a 75% chance to hit the target who had a 25% chance to resist spells, 25% of the spells would still result in a resist). When I tested this (I used a level 8 player and attacked the level 32-33 Yetis in the Alteric Mountains), the majority of the spells that landed on the target were successful while very few were resisted.

## miss chance Edit

you say "A level 10 Mage can very often land polymorph on a level 60 player."

i don't have data to back up an argument that this statement is untrue. however, it is not supported by the table you give. according to the table, a level 10 mage would suffer a 342% miss chance against a level 60 player... a figure that is purely mathematical but does not jive with succeeding "very often".

My answer to that would be that there is probably an upper cap on "spell miss" due to the level difference. I have no idea what that cap is, but it's at most 100% :) Indeed, it makes no sense to have "more than 100% chance of" doing anything. That cap might be approximated by series of tests, but I'm not going to do that just now. However, if the statement that "A level 10 Mage can very often land polymorph on a level 60 player." is true, it might be something like 75%, 80%, or 95%. Whatever it is, it should be indicated in the article.
I'd like to also point out that the lower cap of spell miss chance is 1%. According to Blizzard's website on Resistances: "If you are much higher level than the attacking caster, you will have a significant chance to resist the caster's spell, but if you are much lower level, you will have a minimal chance to resist the spell (minimum of 1%)." (Interestingly, this does not state that much higher level characters become immune to spell casting, but simply says that they have a significant chance to resist. We can deduce that there's indeed a cap, like I said, and that it is less than 100%.)
--Dorenthas 13:26, 13 September 2006 (EDT)
Quick experimentation made me think thhat the correct upper cap for miss chance (in PvP, not in PvE) would be around 75% or 80%. A level 21 mage cast 365 Polymorph (rank 1) on a level 60 mage with 18 Arcane Resist (10 talent, 8 Sorcerer's set bonus). The spell landed 73 times and was resisted 292 times, or 80% of the time. Considering that a small percentage of that came from the 18 Arcane Resist, I believe my initial assumption is correct. Larger samples are in order to confirm the exact value, however.
--Dorenthas 10:03, 14 September 2006 (EDT)

## When a spell misses ... Edit

... what gets reported in the Combat Log? Does it say "Your <spell name> misses", or does it say "Your <spell name> was resisted"? And does the word "Miss" or "Resist" appear in yellow above the target's head when this happens?

-- Tracer 13:02, 25 August 2006 (EDT)

I don't remember having seen "Your <spell name> missed." I would be enclined to think that any spell that "misses" is displayed as being "resisted". In fact, if my previous comment regarding a table-based system is just, you wouldn't have two rolls to determine 1) spell miss/hit and 2) spell resist, but instead just one determining spell miss/hit(resist). Let's have an example of this.
Player A is fighting Monster X. Both are level 60, so Player A has 96% chance to land a spell. If Monster X has 180 fire resist (resulting in an average of (180/300) * 75% = 45% effective damage or spell resistance), then if Player A casts a fire spell, the following logic is applied. (That table is calculated for direct-damage fire spells only; another table is used for non-fire spells (different resist score means different resistance values) or non-direct-damage spells (no partial resistance possible).)
(Using values from WoW website on Resistances, adapted to fit a level 60 target.)
- Fully resisted: 4% (due to "first check") + 96% * 1% (due to "second check") = 4.96%
- 75% resisted: 96% * 18% = 17.28%
- 50% resisted: 96% * 48% = 46.08%
- 25% resisted: 96% * 26% = 24.96%
- Hit (full effect): 96% * 7% = 6.72%
So if this table is correct, the game displays no difference about whether your spell "missed" or was "100% resisted". For the player, the spell was "resisted" either way. Now a question that remains is how talents like "Targets have 10% less chance of resisting your Shadow Spells" affect that table.
--Dorenthas 12:32, 13 September 2006 (EDT)
I answered this last question in response to someone else's post in the beginning of the discussion. --Dorenthas 23:16, 15 October 2006 (EDT)

## Damage Absorbed Edit

The section of damage absorbed is absolutely awful. The second section on the formulae for magical resistance is ok.

The idea of desribing the amount resisted - as based on the amount of health you have is really not a clever way of going about it. A "%" would be fine.

The equations in that last section are not balanced properly with the brackets and cannot be followed. That is if you follow the equations - mathematically (I'm not sure how else you can do it) then you get a wrong answer.

I'm not suggesting the publisher did not know his stuff but it has been described awfully.

That would be me who wrote that. There's already a section that describes how the %resist chance is calculated - it's the second section, titled "Magical Resistances". The relationship between resistance and max health is useful for two reasons: one, it shows how long you can expect to live while taking a fixed amout of magical DPS. Two, the same relationship of damage absorbed / incoming damage, or time to live, is linear in the case of armor and physical damage (and is why the page about AC is linked). Since it's decidedly non-linear here, the comparison is warranted. I'd be interested in hearing why you think this is "really not a clever way of going about it".
I'm not sure what you mean by the brackets not being properly balanced. The three lines of math in that section have, respectively, no brackets at all, one each of open and close brackets, and three each of open and close brackets. As for it not being followable, yes, I left out some lines for conciseness. If you want the full thing, it looks like this:
```Damage absorbed = Total incoming damage * damage reduction  [1]

Total incoming damage = Damage absorbed + Actual damage taken
Substituting into [1]:
Damage absorbed = (Damage absorbed + Actual damage taken) * damage reduction
Damage absorbed = Damage absorbed * damage reduction + Actual damage taken * damage reduction
Damage absorbed - Damage absorbed * damage reduction = Actual damage taken * damage reduction
Factoring:
Damage absorbed * (1 - damage reduction) = Actual damage taken * damage reduction
Damage absorbed * (1 - damage reduction) / Actual damage taken = Damage reduction

Left hand side of all future equations no longer changes, and so is omitted after this line.
Damage absorbed / Actual damage taken = Damage reduction / (1 - damage reduction)
= 1 / (1 - damage reduction) - 1  [2]

Average resistance = (1 - damage reduction), and also
Average resistance = (Target's Resistance / (Caster's Level * 5)) * 0.75 from the earlier section.
Substituting into [2]:
= 1 / (1 - (resistance / (5 * caster level)) * 0.75) - 1
```
Like many other formula pages, doing the full derivation on the page itself would take up a lot of space for not much benefit. I put the result and one extra line to suggest how the derivation was done, and figured that anyone who was interested in the derivation would be able to do it themself if it came to that.
Esselte 23:58, 4 November 2006 (EST)

## "Level-based resistance" paragraph Edit

The last paragraph in the "Miss Chance" section mentions "Note: Level-based resistance (not to be confused with level-based miss) that can play a factor in total resists". Disregarding for a moment the grammar, this entire paragraph is extrememly confusing, and should be rewritten or moved.

It has nothing to do with spell miss chance, as this paragraph deals with an additional level-based resistance. Additionally, it seems to be contradicted in the very next section ("Magical Resistances"), which states that resistances are not based on a level differences.

I'm not enough of an authority on spell mechanics to change this. Would someone be willing to tackle this?

Adonran 17:24, 1 August 2007 (UTC)