## One Roll Theory

In June of 2005, a Blizzard representative made the following statement:

- "The way WoW calculates crit rate is over ALL attacks. Crit rate is not based on hits only. In other words, if you have a 5% crit rate, that 5% chance includes misses."

Based on the implications of this statement, coupled with extensive testing by dilligent players, it has become clear that the result of every melee or ranged attack is decided based on a **single** server-generated random number (a single "die roll" made internally on the server), checked against a server-side internal table for the attack.

From a computational perspective, this makes sense. Generating a random number requires several complex calculations that consume a lot of CPU time, relative to the time it takes to simply look up the chances for each different attack result. On a server with thousands of players fighting thousands of mobs, the result of each attack must be determined as quickly as possible. Generating one random number and comparing it against a table is a lot faster than generating a random number to see if an attack misses, then generating another random number to see if the attack is dodged, etc..

## Two Roll Theory

A theory posted on the Elitist Jerks forum by a user named Vulajin has been the source of some controversy recently as it proposes a "Two Roll Theory" for determining the outcome of special attacks (Backstab, namely). Below are two quotes from the original post.

- "Given this [one roll] table, it's straightforward enough to determine that, on 5924 Backstabs, I would expect to crit about 3428 of them. Of course, probability being what it is, it's certainly conceivable that I don't crit exactly 57.86% of my Backstabs all the time. I observed 3207 crits. How likely is that? This is where statistics comes in handy."

- "Under the assumption of a two-roll system, given our 5924 Backstabs, we'd expect 3256 to crit. Recall that I observed 3207 crits. The probability of experiencing this much of a deviation, if Backstab uses a two-roll system, is about 20% (z-statistic of -1.28). The observed crit rate is still slightly lower than expected, but 20% is magnitudes better than the infinitesimal probability of experiencing 3207 crits in the one-roll system."

The thread contains rather extensive testing and data to support this theory, however, concerns over its accuracy still exist. Experimentation using mobs with -hit debuffs is currently under way to further prove or disprove the theory.

It would not be entirely surprising if yellow-damage "special" attacks such as Backstab were resolved using more than one generated random number, at least when made against NPCs. Special attacks made against mobs from the front are known to be able to be blocked and crit at the same time, a result impossible under the mutually-exclusive attack results tables described below.

Original thread: http://forums.elitistjerks.com/viewtopic.php?id=9330

## The Table for Melee Attacks

The following tables are laid out in descending order of the **precedence** of one attack result over another. That is to say, the entries at the top of the table take precedence over the entries below them. (This precedence order is from Blizzard, and as such is accurate.)

Miss |

Dodge |

Parry |

Glancing Blow (only players and pets versus mobs) |

Block |

Critical |

Crushing Blow (mobs only) |

ordinary hit |

What this table means is this:

- Every melee attack has a chance to miss, to be dodged, to be parried, to be blocked, to be a glancing blow, to be a critical, and to be a crushing blow. Anything left over is an ordinary hit.
- The chances listed in your general spellbook tab (for you to Dodge, Parry, or Block) are absolute percentages. If you have a listed dodge chance of 4.5%, then on average 4.5% of
**all**melee attacks made against you by a mob of equal level will be dodged, not merely 4.5% of those melee attacks that didn't miss you. - Some melee attacks have a 0% chance for some of these attack results; e.g., an attack made by a player has a 0% chance of being a crushing blow, an attack made against a player without a shield has a 0% chance of being blocked, the warrior's Overpower attack has a 0% chance to be a block dodge or parry, etc..
- There is no such thing as a blocked crushing blow, a parried crit, a missed glancing blow, etc.. All of these possible attack results are mutually exclusive.
- If the total chances of all the entries above the bottom of the table reach or exceed 100%, the attack cannot be an ordinary hit.
- If the total combined chance of a miss, dodge, parry, or block is 100% or higher (as in the case of a well-geared warrior using Shield Block), not only can the attack not be an ordinary hit, the attack also cannot be a crit or a crushing blow.

### Example 1

Suppose a mob of equal level is attacking your warrior character in melee. Your Defense skill is maxed out for your level, but has no other bonuses. In the general tab of your spell book, you see that your listed Dodge chance is 4.5%, your listed Parry chance is 6.2%, and your listed Block chance (you have your shield equipped) is 5.1%. For the mob attacking you, its attack table will look like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 5.00% | 0.01 - 5.00 |

Dodge | 4.50% | 5.01 - 9.50 |

Parry | 6.20% | 9.51 - 15.70 |

Glancing Blow | 0% | — |

Block | 5.10% | 15.71 - 20.80 |

Critical | 5.00% | 20.81 - 25.80 |

Crushing Blow | 0% | — |

ordinary hit | 74.20% | 25.81 - 100.00 |

Now say that you elect to activate this warrior's Shield Block skill. Shield Block increases the warrior's Block chance by an additional 75%. For the next attack against your warrior, the mob's attack table now looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 5.00% | 0.01 - 5.00 |

Dodge | 4.50% | 5.01 - 9.50 |

Parry | 6.20% | 9.51 - 15.70 |

Glancing Blow | 0% | — |

Block | 80.10% | 15.71 - 95.80 |

Critical | 4.20% | 95.81 - 100.00 |

Crushing Blow | 0% | — |

ordinary hit | 0% | — |

Note that the chance of an ordinary hit has been removed from the possible attack results entirely, and the chance of a Critical hit has been reduced somewhat.

### Example 2

Elliot the Rogue is level 60, and is attacking a boss mob along with the rest of his raid group. He has stocked up on all sorts of +crit gear, so his crit chance against the boss mob is a whopping 30%. Since he is dual-wielding, he incurs an additional +19% miss chance on every autoattack swing; and although his +5 weapon skill gear does counter a little bit of this, he did not bring any +hit gear with him, so his miss chance against a boss mob is 24.4%. (+Hit gear doesn't *directly* increase your chance of a hit; instead, it reduces your chance of a miss.) When he attacks the boss mob from the front, Elliot's attack table looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 24.40% | 0.01 - 24.40 |

Dodge | 5.40% | 24.41 - 29.80 |

Parry | 5.40% | 29.81 - 35.20 |

Glancing Blow | 40.00% | 35.21 - 75.20 |

Block | 5.40% | 75.21 - 80.60 |

Critical | 19.40% | 80.61 - 100.00 |

Crushing Blow | 0% | — |

ordinary hit | 0% | — |

Note that despite his nominal "crit chance" of 30%, his miss chance from dual-wielding and his glancing blow chance due to the boss's high level mean that only 19.4% of his attacks are going to be critical hits. This conundrum is sometimes referred to as the Crit Cap -- his chance to crit is capped at 19.4%, so 10.6% of his +crit bonus is wasted.

Realizing his stupidity, Elliot maneuvers around behind the boss mob to continue his attacks. From behind, a mob cannot parry or block, so Elliot's attack table now looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 24.40% | 0.01 - 24.40 |

Dodge | 5.40% | 24.41 - 29.80 |

Parry | 0% | — |

Glancing Blow | 40.00% | 29.81 - 69.80 |

Block | 0% | — |

Critical | 30.00% | 69.81 - 99.80 |

Crushing Blow | 0% | — |

ordinary hit | 0.20% | 99.81 - 100.00 |

Now that he's behind the boss mob, Elliot decides to Backstab it. A Backstab is an instant attack. Instant attacks do not incur the +19% miss penalty for dual-wielding, nor can they be Glancing Blows. For his Backstab, Elliot's attack table looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 5.40% | 0.01 - 5.40 |

Dodge | 5.40% | 5.41 - 10.80 |

Parry | 0% | — |

Glancing Blow | 0% | — |

Block | 0% | — |

Critical | 30.00% | 10.81 - 40.80 |

Crushing Blow | 0% | — |

ordinary hit | 59.20% | 40.81 - 100.00 |

### Example 3

Oh no! Elliot the Rogue has backstabbed the boss mob **too** hard, and has drawn aggro. The boss whirls around and raises his enourmous fist in the air, threatening to pound poor little leather-clad Elliot into paste. Elliot's Agility and Lightning Reflexes talent do give him a decent dodge chance, and his Deflection talent boosts his parry chance; but he has no gear that boosts his Defense skill beyond its unbuffed value of 300. On the whole, things look grim. The boss mob's attack table against Elliot looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 4.40% | 0.01 - 4.40 |

Dodge | 17.90% | 4.41 - 22.30 |

Parry | 9.40% | 22.31 - 31.70 |

Glancing Blow | 0% | — |

Block | 0% | — |

Critical | 5.60% | 31.71 - 37.30 |

Crushing Blow | 15.00% | 37.31 - 52.30 |

ordinary hit | 42.70% | 52.31 - 100.00 |

Thinking quickly, Elliot activates his Evasion skill. This gives a whopping +50% increase to his Dodge chance. The mob's attack table now looks like this:

Result | Chance | "Die Roll" |
---|---|---|

Miss | 4.40% | 0.01 - 4.40 |

Dodge | 67.90% | 4.41 - 72.30 |

Parry | 9.40% | 72.31 - 81.70 |

Glancing Blow | 0% | — |

Block | 0% | — |

Critical | 5.60% | 81.71-87.30 |

Crushing Blow | 12.70% | 87.31 - 100.00 |

ordinary hit | 0% | — |

## The Table for Ranged Attacks

A ranged attack cannot result in a dodge, parry, block, or glancing blow. (On their test realms at one point, Blizzard experimented with allowing a small dodge chance against ranged attacks, but this was considered too harmful to Hunters and the experiment was abandoned.) Thus, the attack result table for ranged attacks reduces to the following:

Miss |

Critical |

Crushing Blow (mobs only) |

ordinary hit |

**NOTE:** Some players have reported being able to block ranged attacks made by enemy Hunter players. It may be that ranged attacks made upon, or by, mobs, cannot be blocked, but ranged attacks in player-versus-player combat can. Empirical data is lacking on this point, however.

## Attack spells

Spells do not use the above tables. The result of casting a spell against a target are determined in an entirely different manner. See Formulas:Spell hit chance.