"Crits can Miss" vs. "Three Outcomes"
 

Has anyone been able to confirm exactly which of these mechanics is correct?

http://www.wowwiki.com/Formulas:Crit...miss_or_not.3F

I've operated on the "Three Outcomes" assumption, but there's a debate about it in the mage forums right now, and I realize I have no actual proof that it works this way.

One person has suggested that it could be disproven by taking a level 65 Frost mage with some tank and healer support, attacking a level 70 target, getting Winter's Chill fully stacked, landing a Frost Nova on the target, and seeing if every hit is a crit (since the resulting crit chance, plus the base miss chance, would leave no room for normal hits). Any obvious flaws in this test? Or has something like this already been performed?

Your attacks will either hit, miss, or be avoided (dodge/parry). Crits are a subset of the hits result.

Let me elaborate. It sounds like you see it as working this way:

1) Roll is made for hit, miss or avoidance.
2) If it hits, roll is made to see if it crits.

The "Three Outcomes" method would work this way:

10% miss
80% hit
10% crit

Add +1% hit and +2% crit via gear:

9% miss
79% hit
12% crit


Reading the original blue post on the subject, it seems to me it has to work in the latter manner:

http://forums.wow-europe.com/thread....14551513&sid=1

Presumably "avoidance" would modify the miss chance before the roll is made, or simply be part of the table:

10% miss
5% parry
5% dodge
70% hit
10% crit

Add 1% hit and 2% crit and it would change to:

9% miss
5% parry
5% dodge
69% hit
12% crit

There's a thread on this applying to rogue specials and 1-roll vs 2-roll. Net was that while normal melee's on a 1-roll as described, specials appear to be on a 2-roll. I don't remember, unfortunately, if that extended to more than rogues, though I don't think we're unique snowflakes to that extent.

It'd be fairly important to have a final word on this for my spreadsheet. That makes a pretty huge difference in calculation.

I'm confused when you bring dodge and parry into caster mechanics.

The only outcomes I know of for a spell cast:
Miss
Resist (0%/25%/50%/100%)
Crit
*immune*

I unsure how comparing a melee system to a caster system will bring you closer to a solution.

Glossary of terms:
Miss: This is the chance you have to miss a target. It is ONLY based on the difference in level of you and your target. (also if the target is a player or mob)
Solution: Spell hit rating (formerly +to hit) and buffs/talents to the same effect

Resist: This is the chance you have to resist on a target. It is only based on the built in values for mobs. For players, it is the resistance to the school you are casting. (See Resistance page)
You can have your direct damage spell resisted by 0% (no resist/full damage) 25%/50% or 100% (full resist). Binary spells by name are either on or off, 100% resist (no damage) or 0% resist (full damage)
Solution: Spell penatration gear and buffs/talents or mob debuffs for the same effect. (Gonna leave out talking about caps for resistance on boss mobs)

Note: A full resist and a miss are not the same thing; although they do have the same result.

The only blue post we really have (at least on the american forums) is Tserics old post:
First of all, the binary example can confuse people. (Should never use 50%)

Take the frost example (binary)
50% resist
.89 * .5 = .445
Roll 0 - 1
if < .445 full damage
if >= .445 no damage

80% resist
.89 * .2

[top] .178
Roll 0 - 1
if < .178 full damage
if >

.178 no damage

The second problem is that he never mentions if the +hit is floored for binary spells in the resistance calculation.

e.g.
Fighting a 70 vs 70
You have +7% to hit
You have a 1% chance to miss (floor) (.96 chance to hit for equal level mob/player .96+.7=.99)

Does the resist calculation look like this though?
.96+.07=1.03
Target has 8% resistance to school
1.03*.92=.948
Roll 0-1
if < .948 full hit
if >= .947 full miss

or is the cap in the resistance check

Target has 8% resistance to school
.99 * .92 = .911
Roll 0-1
if < .911 full hit
if >= .911 full miss

This is the whole "breaking the +to hit max on mobs equals a better resist rate" for binary argument.

Anyway, this leads me to the conclusion that it is a two roll system.

Roll 1 (Using the mechanics Tseric mentioned)
Hit (Binary Spell: Include resitance check here)
Miss

Roll 2
If hit, roll crit
(Direct damage spell: Include resistance check here)

From the comment It seems safe to assume partial resists for direct damage spells is factored in at time of impact, where binary spells get the resitance included in on roll 1.*

*This leads to the whole +to hit for frost mages is better argument. If there is no cap in roll 1 resistance check and the player beats the hit cap than a frost mage could actually beat the "innate" resistance of boss mobs that neither spell pen or CoE and the likes can break. (Although beating the 16% hit cap seems rather hard)

I'm assuming the basic mechanics of both are the same. Namely that both physical and spell damage use either a two-roll system (hit or miss, then if hit, regular hit or critical hit), or use a one-roll system (table of possible results, roll once to find result).

I realize that for casters, using non-binary spells, there is then a subsequent roll after a hit or crit to determine if some of the damage was resisted, but that's not the roll I'm concerned with at present.

The source of the debate is this: in a two-roll system, increasing your chance to hit also increases your chance to crit (since you can't crit if you don't hit). This increases the value of 1% hit relative to that of 1% crit. In a Three Outcomes system, increasing your chance to hit has no effect on your chance to crit.

The simplest example is a Frost mage or a Warlock with Ruin. In a Three Outcomes system, 1% crit has the same value for these specs as 1% hit (until you hit the cap). In a two-roll system, 1% hit is worth more than 1% crit (again, until you hit the cap).

Melee uses two different systems; autoattacks (and mob melee) use a single roll system, while special attacks use a two roll system.

There's no reason to assume the mechanics are the same between the two, given that melee uses different mechanics on different types of attacks.

I fail to see how improving your hit increases your crit. The more hits you get the more likely you are to see your crit rate approach expected values.

Now a significant miss rate will decrease your visible crit rate.

20% crit and 16% chance to miss

Roll 1
Hit 84% chance
Miss 16% chance

Roll 2
If it is a hit roll crit 20%

So my expected crit rate is 84*.2=16.8%

Same stats 16% to miss 20% crit
Lets say I get some huge +to hit gear like 30%
84% + 30% = 99% (floor)

Roll 1
Hit 99% chance
Miss 1% chance

Roll 2
If hit roll crit
Effective crit rate 99*.20 = 19.8%

So hit gear does not increase your crit rate, it just gives you a better chance at achieving your expected crit.

At least that is how I understood it to work.

This is only true if it's a two-roll system and not a Three Outcomes system -- which is the central question of this thread. Which is it, actually? The blue post I quoted above implies that it's a Three Outcomes system -- but has anyone been able to confirm this through testing?

All spells are special attacks (yellow damage) and use a two-roll system.

http://elitistjerks.com/showpost.php...8&postcount=17

That thread had pretty much the same subject as this one. And while there were several posters who claimed it was a single-roll system, all tests done supported a two-roll system.

Also, if you have parsed your combat stats, your expected crit rate (from character sheet) will tend to be equal to the % of hits that crit, not the % of casts that crit.

On a side note, I do wonder when the partial resist roll is done because as you may have noticed, on a partial resisted crit, the resisted damage is a pre-crit value. e.g. your fireball would normally crit for 1500, but you get a 25% resist, the combat log will say "your fireball crits for 1125 (250 resisted)"

And the blue post I quoted, and has to do with caster mechanics, implies it is a two roll system.

Using the same numbers I used what does a 3 roll system generate?

If you want experimental testing, we would have to know if we saw a 3 roll outcome.

Thanks, that helps a lot. And means I need to adjust my theorycrafting script.

For what it's worth, I got combustion up to 10 charges last night (increases your chance to crit with a fire spell by 100%), and got a resist on the next fireball.

Back when I had recap that is not what I found. Over the course of a raid my crits as a percent of casts were exactly as predicted by the 1-roll model.

I don't find border-case tests (e.g. level 1 characters with Rallying Cry) particularly compelling. All they really prove is that things don't work the same at extreme margins, which doesn't help for the actual application of the math which is weighing different stats at realistic margins. That may mean our model doesn't perfectly represent the underlying math but it doesn't negate its predictive power in relevant scenarios.