# Critical strike

## Contents

- 1 Base chance to crit in Melee
- 2 Base chance to crit with Spells
- 3 Can Crits miss or not?
- 4 Chances to Crit, Hit and Miss
- 5 Modifier to Crit
- 6 Modifier to Hit
- 7 Defensive Reactions
- 8 Formulas for Melee combat
- 9 What's better: +Hit% or +Crit% with spells?
- 10 What's better: +Hit% or +Crit% with physical?
- 11 Examples
- 12 Further Input
- 13 Links

## Base chance to crit in Melee

For melee attacks with weapons, the chance to crit is based on agility, and critical strikes deal +100% normal damage (2.0 times your normal damage). To see your chance to crit, open your spellbook, and hover your mouse over the "attack" ability. The tooltip will show your percent chance to crit. The formula is generated as follows:

- [Base Crit] + Agility * AF + [Skill Modifier] + [Bonuses]

AF = agility factor, which is class-specific

The base chance to achieve a melee critical hit for each class (at level 60) is:

- Rogue 0%
- Druid 0.9%
- Hunter 0%
- Mage 3.2%
- Paladin 0.7%
- Priest 3%
- Shaman 1.7%
- Warlock 2%
- Warrior 0%

The agility bonus to base critical hit chance at level 60 is:

- Rogue [AGI / 29]
- Druid [AGI / 20]
- Hunter [AGI / 53]
- Mage [AGI / 19.44]
- Paladin [AGI / 19.77]
- Priest [AGI / 20]
- Shaman [AGI / 19.7]
- Warlock [AGI / 20]
- Warrior [AGI / 20]
- Mobs always have a 5% base melee critical chance.

This chance is further modified by the difference between your current Attack rating and the Defense rating of your target. The game tooltip assumes an even level opponent with a Defense rating equal to [Level * 5]. Normally, your Attack rating is equal to your skill rating with the type of weapon you are wielding. When the target is a mob you cannot apply more than [level * 5] points of weapon skill toward your chance to get a critial hit. This means at level 60 that level 61 and higher mobs are not critically hit more often even if you increase your weapon skill above 300.

When the target is a mob and attack rating minus defense is less than 0, the change is critical hit chance is 0.2% per point of difference. If the target is not a mob or the rating difference is above 0 then the critical hit chance is adjusted 0.04% per point of difference.

*Please note that the agility requirement for a crit percentage is lower at lower levels... so an AGI which grants you 10% to crit at level 30 will not grant you the same at level 60.*

Equipment which increases critical hit rate stacks together, so it is possible to achieve relatively high critical hit rates. A non-spell attack on a sitting target will always be a critical hit.

*Statistically speaking, every percent of chance to crit increases your average extra damage output from crits, over time, by 1%. If you have a 1% chance to crit, you have a 1% chance to deal 100% extra damage. For average damage calcutations you can easily turn those two numbers around, so you have a 100% chance to deal 101% (100%+1%) of your base damage. It's the same considering DPS instead of damage.*

Note however that this is not the same as increasing your actual damage output over time by 1%, as this depends on how much crit chance you had before the +1%. Consider actual damage versus what you'd do if all swings hit and only hit for normal damage:

Damage = BaseDamage * HitChanceNotIncCrit + BaseDamage * 2 * CritChance = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

Then with 100% Hit (enough +toHit to cancel default 5% miss), 5% dodge (can't be negated), 25% crit versus 26% crit:

Damage = BaseDamage * ((1.00 - 0.05 - 0.25) + 2 * 0.25) = BaseDamage * 1.20

Note that with 0% crit chance this would be 0.95, so the 25% is +25% damage, when stated this way.

Now, raise the crit chance by 1%

Damage = BaseDamage * ((1.00 - 0.05 - 0.26) + 2 * 0.26) = BaseDamage * 1.21

That is indeed an increase of 1%. But that is only an increase of 1% to the INCREASE in damage we get from crit. This is actually only:

1.21 / 1.20 = 1.00833

i.e. 0.833% extra damage overall from +1% crit.

Once you take crit-damage increasing talents, Parry, Block and Glancing Blows into account the situation is even more complex. But in general the more factors reducing the number of normal hits without decreasing the number of critical hits (i.e. if chance to hit becomes less than chance to crit your chance to crit is capped) then the more extra damage you will do for each extra 1% chance to crit. i.e.

- No base miss (+5% hit or more)
- 5% dodge
- 5% parry
- 5% block
- 25% crit

Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.25) + 2 * 0.25) = BaseDamage * 1.10

(With 0% crit we'd do 85% of BaseDamage)

Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.26) + 2 * 0.26) = BaseDamage * 1.11

1.10 / 1.11 = 1.00909

So actually 0.909% extra damage from +1% crit, i.e. the more you're not going to hit, the more +1% crit is worth. This does also mean that +1% crit is much more important for dual-wielding (base Hit% of 76%) than for 1h+shield, 2h or special attacks (base Hit% of 95%).

## Base chance to crit with Spells

For spells, the chance to crit is based on intellect. Critical damage spells deal +50% (+100% with appropriate Mage/Shaman/Warlock/Druid talents) more damage. Critical heals will heal +50% their normal amount (=150%). There is currently no way to see your chance to crit with spells.

The base chance for a spell critical hit for each class is :

- Druid [INT/39]%
- Mage [INT/59.5]%
- Priest [INT/50]%
- Warlock [INT/40]%
- Paladin [?INT/29.5?]%
- Shaman [INT/32]%

I just read this:

Class | Expected Int at 60 | Int per 1% crit chance |
---|---|---|

Warlock | 200 | 60.6 |

Druid | 192 | 60.0 |

Shaman | 259 | 59.5 |

Mage | 286 | 59.5 |

Priest | 160 | 59.2 |

So it makes no sence that it should be different on base crit. why not just base int / int/1% crit chance for ur class? (note that it is not 60int for all lvl 60s) interested? see more here: http://wowwiki.com/Talshuler%27s_Int_Research

## Can Crits miss or not?

The only real source for answer of this question is this Blizzard post. There exist two ways to interprete it.

One school ("Crits can miss") claims that the half-sentence "if you have a 5% crit rate, that 5% chance includes misses" means that a crit can be a miss, so if you have a 10% crit chance, and 5% miss chance, only 8 swings out of 100 will crit in the average. This means that each swing can be either a hit or a miss, and crits are calculated completely independently.

The other school ("Three outcomes") claims that the mathematical formulas given later in the post make clear that crits may never miss, and that a swing can have exactly one of three outcomes - crit, hit or miss. The probability for each of these three is calculated separate, the only restriction is that their sum has to be 100%.

### Argument for Crits may miss

There are many crit modifying spells within the game which can miss (such as [Cold Blood]).

A way to confirm or deny this, would be to let a rogue with 300 dagger skill, no +% talents or effects, use only auto-attack on a (preferrably healing-class) player with no +def for about an hour or longer. Record his crit per swing, and compare that to the crit chance displayed in his tooltip. It is however crucial that the mod/program/whatever which is recording, only recordes crit per swing and not crit per hit. So it would have to count swings, and count crits, and then divide the first by the later. Then redo the entire thing with, respectively, more %hit and more %crit.

### Argument for three outcomes

The counter-argument to the "cold blood may miss" argument is that you may never increase your crit chance at the cost of your miss chance, i.e. if you have a 5% miss chance, you crit chance cannot increase beyond 95%. Using cold blood only guarntees that you will never see a normal hit, it does nothing to your miss chance.

Interpreting the blizzard post with the following steps:

- "The crit rate includes misses" is a contradiction to the assumption that crits, hits and misses are the three possible, separate outcomes of a swing.
- Replacing "misses" by "swings that do not hit" yields: "The crit rate includes swings that do not hit".
- This version of the sentence matches the formulas

This rather formal way of interpretation assumes a little slip in the natural language used by Blizzard. If there are three different outcomes, replacing "miss" with "not a hit" is mathematically a severe error. In natual language though it's only a slight imprecision. In other words, Blizzard uses the term "miss" a little loose, they mean it to include all swings which are not normal hits.

## Chances to Crit, Hit and Miss

Thus we assume that melee attack can have exactly one of the following results:

- Critical Hit
- Normal Hit
- Miss

The probabilities for these three results are independent of each other, except for the requirement that the sum must be 100%. If the game's tooltip says a character's critical hit rate is 5%, they will crit 5% of all attacks (vs. an opponent with the same defense skill as the attacker's weapon skill).

## Modifier to Crit

Plusses to Crit simply affect the probability to acheive a critical hit. They do nothing to the miss rate, thus they decrease the Hit rate. This seems to be strange at first, but it's WoW's way to express the concept that critical hits must also be normal hits. The difference between opponents defense skill and attackers weapon skill will modify the critical hit chance by 0.04% per point of difference. So, for example, if a Rogue with 300 dagger skill is attacking a Mob with 325 defense skill, the rogue's crit rate will be decreased by 1%.

Be aware though that +Defense in this context does not apply to PvP. It will not reduce a critical hit chance between players, only vs. PvE mobs.

Items with the "**Improves your chance to get a critical strike by X%**" modifier effect only melee and ranged attacks.

## Modifier to Hit

Plusses to Hit, increase the probability to get a non-critical hit. They do nothing to your chance to Crit and they decrease your chance to Miss. In fact, one might argue that "+hit%" is a misnomer, and that such bonuses really ought to be called "-miss%".

The base miss chance vs. an even level opponent is 5%. It is modified by the level difference. It rises quickly for mobs in PvE, but it rises much more slowly for other characters in PvP. The minimum miss chance is 0% on instant attacks. For each increased weapon skill you get 0.04% less miss chance, but for each defence point the target has, your miss chance is increased by 0.04%. So against a level 63 mob, you would at most want +5.6% hit, and for dual wielders you would at most want +24.6% hit. The cap for the miss chance is 60% (this cap is not confirmed. Can anyone add a link or elaborate?).

If due to large negative modifiers, your chance to Hit becomes negative, the negative amount is deducted from your chance to Crit. (If your chance to Crit would also become negative, the remaining negative amount is deducted from your chance to score a Glancing Blow, if any. See the Attack table article.)

## Defensive Reactions

WoW, like many other games, makes use of a table based combat scheme (where one roll determines the outcome of a swing), so percentages are absolute.

Refer to the separate section for details on each defensive reaction:

You will not get terribly wrong results by simply adding the targets chances to parry and dodge to the attackers miss chance.

## Formulas for Melee combat

If adding some crit or hit modifier, the following formulas can be used:

- New crit rate = (Original crit%) + (change to crit %)
- New miss rate = (Original miss%) - (change to hit%)
- New hit rate = (Original hit%) - (change to crit %) + (change to hit)

## What's better: +Hit% or +Crit% with spells?

Spell crits do +50% spell damage unless you talent to increase this effect. Spell hits do +100% spell damage. So in terms of total damage output the +hit with spells will be more efficient until you have reduced your chance to miss that mob to the minimum.

If you have talents such as [Ruin] or ice shards that increase crit damage then the total added damage is almost the same and +crit and +hit are equivalent in terms of damage added.

That being said, keep in mind the situation. If you want burst damage such as PvP encounters it may be better to have +crit, and in PvE encounters where aggro must be avoided it would be better to have +hit.

Unlike melee, there is a 99% hit cap on spells. Spell casts against a same level mob or player have a 96% hit (no resist) chance, so +hit equipped past 3% in this case is wasted. Level 63 mobs have an 83% hit chance, so +hit equipped past 16% would be wasted. The only limit to crit is 100%, but bear in mind that the spell cast system does not combine hit and crit calculations into a single roll. A spell must hit in order for it to have a chance to crit.

However, some spells and schools have talents which proc additional effects on crit. For example, mages can put talent points in ignite, which grants an addition 40% damage over time on crit. Warlocks can put talent points in Improved Shadow Bolt, which grants an additional 20% damage to the next 4 sources of shadow damage. The effect of these procs are to increase the damage bonus of a crit beyond 100% over time, which means that in some cases additional +crit yields a greater average increase in damage than +hit.

The decision between equipping +crit and +hit is further complicated when procs can be resisted, and also depend on the currently equipped +crit and +hit. It is known that Improved Shadow Bolt can be resisted, and it is thought that this is based on standard Binary Spell resistance, which is mitigated by +hit. The same is probably true for other procs. In the case of vulnerability procs which require refreshing and have limited duration/charges, +hit comes back into favour as it allows the proc to stay active on the target for a greater proportion of time. It is also worth noting that in a raid, keeping these procs active will also increase the damage of all other casters using that spell school.

In general, if you do not have a talent to increase spell crit bonus to 100%, then +hit is far better than +crit (until you run into the hit cap). If you have talents to increase spell crit bonus and/or proc additional effects, then +hit is of roughly equal value to +crit.

It should be noted, however, that benificial spells cast on friendly targets (such as heals and buffs) **always** hit, regardless of +hit gear. If your role in groups is primarily healing (i.e. if you are a holy priest or paladin, or a restoration druid or shaman) then you will gain much more benefit from gear that increases your spell crit chance. Although it is not advisable to *rely* on the extra healing granted by critical effects from healing spells, a lucky critical heal may mean the difference between life and death for a group member. Additionally, there are talents available to Priests and Shamans which grant a temporary armor bonus to the recipient of a critical heal, which in essence increases the effect of a healing spell even further by reducing the physical damage taken by that party member. When given the choice between +hit and +crit, a primary healer will always benefit from more +crit.

Just to be clear, if an item says "Improves your chance to get a critical **strike** with spells by X%", it will also improve the critical effect chance of healing spells.

## What's better: +Hit% or +Crit% with physical?

If you're only going to be attacking mobs of the same level from behind, and you don't dual wield, your attack tables will look like this:

base | +5% crit | +5% hit | |

to miss | 5% | 5% | 0% |

to hit | 90% | 85% | 95% |

to crit | 5% | 10% | 5% |

Now assume your weapon does 100 points of base damage, before modification, you will do (5 * 200 + 80 * 100) = 9000 damage over 100 swings. With +5% to crit, the result is (10 * 200 + 75* 100) = 9500 damage over 100 swings. With 5% to hit, the damage figure is (5 * 200 + 85 * 100) = 9500 damage over 100 swings.

So all other things being equal, in this case, increasing your probabilities to hit or to crit increase your average damage output by exactly the same amount. Useful differences would only arise from effects which require hits or crits (like some abilities or procs).

However, real combat is rarely done against equal-level mobs from behind without dual wielding. Consider the following table, which represents a melee attack made against a boss mob (effectively level 63) by a level 60 dual-wielder from the front:

base | +5% crit | +5% hit | |

miss | 24.6% | 24.6% | 19.6% |

dodge | 5.6% | 5.6% | 5.6% |

parry | 5.6% | 5.6% | 5.6% |

block | 5.6% | 5.6% | 5.6% |

glancing | 40.0% | 40.0% | 40.0% |

normal hit | 14.2% | 9.2% | 19.2% |

crit | 4.4% | 9.4% | 4.4% |

While it's true here that +5% crit adds as much average melee damage as +5% hit, adding more +crit% gear will soon result in a kind of "crit cap". With no +hit% bonus, adding +crit% bonuses beyond a total of 14.2% will not increase the attacker's actual chance to crit against that target. If this attacker had more than +14.2% of total +crit bonuses, adding +hit% gear would actually increase his crit chance!

This makes more sense when you realize that so-called "+hit" gear doesn't so much increase your hit chance as *decrease your miss chance.*

If you are not dual-wielding, or if you are using an instant attack or "special" attack such as Sinister Strike or Heroic Strike, your base chance to miss an equal-level target is only 5%, and your chance to miss a boss mob (if you're level 60) will be, at most, 5.6%. The common consensus is that +6% is the desirable maximum for +hit% unless you are a dual-wielder.

See Formulas:Weapon_Skill and Attack table.

## Examples

Let's say a dual-wielding rogue with 300 weapon skill attacks an opponent with 310 defense skill. The rogue has a base 20% crit chance, a 25% miss chance and then the rogue equips items that give an additional +5% toHit and +5% crit. The victim has a 10% chance to dodge, a 10% chance to parry, but doesn't have a sheild. This will result in the following:

- Crit: 20% + (-0.4%) + 5% = 24.6%
- Miss/Dodge/Parry: 25% - 5% + 10% + 10% = 40%
- Hit: 55% - (-0.4%) + 5% - 5% - 10% - 10% = 35.4%

If the victim was rogue who activated [Evasion], his dodge chance would jump by +50%. If the attacker was also a rogue, and activated Improved Backstab so that his crit rate would jump by +30%, the numbers would become:

- Crit: 24.6% + 30% = 54.6%
- Miss/Dodge/Parry: 40% + 50% = 90%
- Hit: 35.4% - 30% - 50% = -44.6%

Obviously the new numbers make no sense. That's because the chances to miss, dodge, and parry take *precedence* over both normal hits and critical hits; when there is no chance to score a regular hit, the miss/dodge/parry rate will consume crit chances. So in the above case, the numbers get modified to:

- New crit chance: 10%
- New miss/dodge/parry chance: 90%
- New hit chance: 0%

This example doesn't actually work, because backstab must be performed from behind the target and characters can't dodge, parry, or block attacks from behind (but note a mob/creature can dodge with you behind it, c.f. 1.3 Patch Notes).

## Further Input

Kitsunei, lvl 60 Rogue found the following: In endgame PvE (Molten Core and beyond), +hit and +crit are not equal. +Weapon Skill also becomes more useful at this stage. The reason for this are the "glancing blows". White-damage attacks made against Lvl 63+ mobs (including all Boss mobs) have a 40% chance of being a Glancing Blow, which do less damage than normal hits. This is most upsetting for rogue builds concentrating on white damage.

There are two aspects with glancing blows: Their frequency, and their amount of damage reduction. +10 weapon skill will suffice to cancel all damage reduction from glancing blows, but Weapon skill beyond the normal untrained max for your level will not reduce their frequency. See Formulas:Weapon Skill.

The real problem is that glancing blows are a fourth possible outcome, and that they take precedence over crits and normal hits in the player's Attack table. Assume a Rogue has a 40% glancing blows, 30% miss/dodge/parry, 5% block, and 30% Crit. This rogue will never produce a normal hit. The actual numbers resulting will be 30% miss/dodge/parry, 5% block, 40% glancing, and only 25% Crit; 5% of his crit rate is wasted. It would be much smarter to use more +hit gear (which reduces miss chance), since there is no way to reduce the probability of a glancing blow.

## Links

This Blizzard post is the base of all our knowledge.

Slant's To-Hit FAQ can be found in the Ultimate Rogue FAQ.

Mizzajl's Critical_hit_table.