Hello! Math time again. Some of you may know how attack tables work, but many of you, I'm sure, don't. This post in the European official forums contains the clearest explanation of attack tables I've seen, and I'd advise anybody interested in the mathier side of the game to go check it out. Some parts of it are copied into this post, because they are excellent and not everyone can access the official forums. I am also indebted to the ever-excellent WoWWiki.

"What is an attack table," you ask? Why, it's the method by which WoW decides what's going to happen when a mob or player attacks another mob or player. Is the attack going to miss, be parried, crit, or what? As it turns out, there are seven possible outcomes of a melee attack (six if there are no mobs involved). They are:

Miss
Dodge
Parry
Glancing Blow (players against mobs only)
Block
Critical Hit
Crushing Blow (mobs only)
Regular Hit

Each of these outcomes, besides "regular hit," has a certain chance to happen. If you're not dual-wielding, for instance, you have a base 5% chance to miss, which may be adjusted by agility weapon skill or hit rating. The other stats proceed similarly. When an attack occurs, the game performs a single check against the hit table (rolls a die, metaphorically speaking), and picks the corresponding outcome. It does not, as some people had hypothesized, perform one check to determine whether you hit at all, and another to determine whether that hit crits. Thus, if your character sheet reads 20% chance to crit, you will crit 20% of your attacks (less depending on your targets' Defense and Resilience), not just 20% of the attacks you land.

If the percentages on the hit table do not add up to at least 100%, "regular hit" fills in the rest. On the other hand, if the first N outcomes add up to at least 100%, everything over 100% falls off the table. For instance, let's say a mob has a 10% miss chance on a Warrior, and the Warrior uses Shield Wall Block, pushing his block chance up to 90%. He also has 15% to dodge and 20% to parry. Going down the table and adding up the percentages, you have 10% to miss, 30% when you incorporate parry, 45% adding in dodge, and we pass 100% partway through the 90% chance to block. Everything that is past 100% will not happen: the mob will not land any crits, crushing blows, or regular hits on the warrior while Shield Wall Block is up, and furthermore, you won't see 90% of attacks blocked, because miss, dodge, and parry get counted in first, leaving only 55% left to block.

So if you're a tank, what does this mean? It means, for one thing, that if you grab enough avoidance stats (dodge, block, parry), you'll never get crit or crushed. However, at first, as you start getting more avoidance, it will seem like you are getting crit more. This is because regular hits get pushed off the table first, since they're at the bottom; there's a point at which you will never get regular hit, only crit or crushed. You're not getting crit more than you were before, though, in terms of crit per attack; it's just that every attack that lands is a crit. Edit: Note that Defense does not work the same way as the other avoidance stats with respect to this phenomenon. That is, Defense directly reduces crit chance, as well as increasing your dodge, block, and parry, and your opponent's chance to miss you, by 0.04% per point of Defense (for an equal-level opponent). Therefore, it adjusts many parts of the hit table at the same time. The Defense "magic numbers" at level 70 are 475 defense against level 70 mobs, and 490 defense against level 73 mobs -- if you have this much Defense, you will not take any crits.

The mechanics of the attack table are also informative for DPSers, like Rogues. It tells us that getting more +hit doesn't affect your crit rate, for instance; it merely reduces miss chance. Conversely, +crit doesn't lower your miss chance, just your regular hit chance. In theory, if you hit your +hit cap and got enough +crit gear, you'd have a 100% crit chance on everything that didn't get dodged, blocked or parried (since you'd never miss); but if you didn't get any +hit and just stacked +crit, even enough to give you in theory a 100% crit chance, you'd still miss 24% of your hits (the base dual-wield miss chance). Of course, I'm pretty certain there's not that much crit gear in the game; it's also pretty dang hard (if possible at all) to collect the hit rating you'd need to cap out your hit chance. According to the formulae here, you'd need 379.2 hit rating at level 70 to max out your hit chance as a dual-wielder (less if you've got talents that improve your hit chance, like Precision or a Shaman's DW Spec).

But this principle does come into play in real raid situations -- if you don't invest in any hit, you may have, say, only a 15% chance to hit a mob (everything else being avoided or missing). Any crit percentage above 15% is wasted, because Miss being at the top of the table, it gets counted in first. In order for more than 15% crit to be effective in this situation, you need to first get more hit. These numbers are slightly exaggerated, but the principle still applies. This phenomenon is sometimes referred to as a "crit cap." By the way, poison crit chance is based on your spell crit (which for most Rogues is based on your Int, unless you've got some +spell crit gear...).

What about Hunters? Well, ranged attacks use a similar table, although it is simplified. The ranged attack table looks like this:

Miss
Crit
Crushing Blow
Regular Hit

Simpler, eh? This basically just means ranged attacks can't be dodged, blocked, or parried; gear choices are not very much affected by this. Just thought y'all might like to know.

And finally, let's look at how spell damage is determined. Blizzard has stated that it works on a similar one-roll system to physical hit tables. However, there isn't any glancing or crushing blows, nor dodge, block, or parry. When a spell misses, the game says it has been "resisted," but it's analogous to a physical damage miss. The base miss chance for spells depends on your level, your target's level, and whether your target is a mob or a player:

Target's level, relative to yours	Chance to miss mob	Chance to miss player
Same	4%	4%
+1	5%	5%
+2	6%	6%
+3	17%	13%
+4	28%	20%
+5	39%	27%

Furthermore, some spells (specifically, spells that have a secondary effect on top of doing damage, like a snare or an interrupt) are "binary" spells. This means they never do partial damage: they either hit fully, or miss fully. Frostbolt is such a spell. If a mob has resistance to a particular school of magic, that resist rate is multiplied by your chance to hit the mob to determine if the spell hits. For instance:

Eyonix the Mage (level 60) fires a frost bolt at Yeti of Doom (level 63). Eyonix is also wearing a total of +6% spell hit gear. Yeti of Doom has frost resistance such that he takes 50% from level 60 frost attacks. So, here's the hit calculation:

0.83 (83% for +3 levels mob) + 0.06 (+6% spell hit) = 0.89

0.89*0.5 (50% damage from frost) = 0.445.

The game will roll a number between 0 and 1, and if it's less than 0.445, the frost bolt will hit for full damage. Otherwise, a resist message will appear.

These two checks for binary spells are why people will sometimes refer to two different types of resists (level-based and resistance-based). Non-binary spells do not function in this fashion. Since they can be partially resisted, the spell will check whether it lands or misses, and then, if it lands, check to see whether it's partially resisted. This partial resistance is somewhat randomized in terms of how much is mitigated on what hits, but will average out to be equal to a mob's resist rate for the relevant school of damage (a mob with 45% resistance to fire will resist 45% of the damage from your fireballs that don't miss). I imagine that wands act as non-binary spells, based on what I've seen.

I was unable to find out how spell crits are calculated, but given that Eyonix said spells were on a single roll system like physical attacks, I imagine spells have a similar table to physical attacks:

Miss
Crit
Regular Hit

(Keeping in mind targets' resistances, which may cause the appearance of more misses on binary spells than are actually being caused by your miss chance.) So, what does this all mean for gear choices? +Hit erodes your miss chance, like for physical DPS classes. If you're fighting mobs three levels above you, as is common in raid situations, a maximum of 17% spell hit will be useful. +Crit is more universally useful for casters than for melee fighters, since you're not likely to come up against a miss-based "crit cap;" on the other hand, unless you have talents to the contrary, spell crits only do 150% damage, as opposed to double damage for melee crits. Spell penetration, by the way, lowers your targets' resistances; any penetration that exceeds your targets' resistances has no effect. That is, if I have 20 spell penetration, and you only have 15 frost resistance, the last 5 points of my spell penetration have no effect; fighting you works as if you had 0 frost resistance, not -5.

A final word: there is some speculation that "yellow damage" attacks for physical classes (i.e. everything but auto-attack/autoshot) are calculated differently than white damage attacks, but this is as yet unclear, and there has been, as far as I am aware, no official comment on the situation. So...got any questions left?

Tags: attack table, attack tables, math, mathcraft, strategy, tables, theorycraft, warcraft, world of warcraft, wow

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