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TheoryCraft 101: The melee hit table, page 2


The single roll system and the crit cap

With all of the numerical bits out of the way, let's take a quick look at how the attack table actually works in real terms. For these examples, we'll use Mutter, the level 80 frost death knight (seriously, it's a real character!). Now, Mutter has chosen to run into ICC without a single clue as to what he's doing. He doesn't have any hit rating on his gear, he has no expertise and he didn't take key talents such as Nerves of Cold Steel nor Tundra Stalker. (Yes, he is exceptionally fail.) Mutter wants to feel like a berserking warrior of death and is wildly swinging at the boss from the front instead of being behind it, like a sensible player. One saving grace that Mutter does have is that his chance to crit is up to 40% by this point. Due to dual-wielding, Mutter has a base chance of 27% to miss with every swing. The boss has a 14% chance to parry every attack and a 6.5% chance to either dodge or block it. There is also a baseline 24% chance that all of the death knight's attacks will land a glancing blow.

Result Chance Roll
Miss 27% 0.01 - 27
Dodge 6.5% 27.01 - 33.5
Parry 14% 33.51 - 47.5
Glancing Blow 24% 47.51 - 71.5
Block 6.5% 71.51 - 78
Critical Hit 22% 78.01 - 100
Hit N/A N/A
As you can see from the table to the right, things are not looking too good for our death knight champion. In total, there is a 47.5% chance that Mutter's attack is going to fail to connect to the boss for one reason or another. After that, there is a 30.5% chance the each attack will deal reduced damage, leaving only a 22% chance that Mutter will land a critical blow against the mob. Notice that it is currently not possible for Mutter to land a normal hit using this attack table. This is because the roll caps out at 100% with all following resultants being "lost" or pushed off the table. This is an example of the crit cap. The crit cap occurs when a character has enough combined total results so that a normal hit can never land, and thus every attack that does land is either going to be a glancing blow or a critical hit.

One of the most interesting aspects of the single roll system, the crit cap wasn't a concept that had much theoretical application until Wrath of the Lich King. Up until this point in the game, it wasn't really possible for melee attacks to reach the crit cap outside of extreme circumstances. The thing about the crit cap is that it is a bit awkward in practice. First and foremost, hit and expertise rating do not have any impact on your chance to crit until you reach the crit cap. In the above example, Mutter's crit chance is artificially deflated because he has stacked crit at the expense of everything else. If he were to get 18% chance to hit, then he would end up with a 9% chance to miss and a 40% chance to crit. However, any additional hit or expertise he gained beyond that point would merely convert all of the remaining attacks into hits. Since everything things except glancing blows can be removed from the table, the crit cap is effectively 80.8%. If at any point you end up having a higher chance to crit than can fit on the table, then increasing your crit chance will have no net effect on your actual crit rate; you will have to gain additional hit or expertise instead.

For dual-wielding classes, the formula for determining your current crit cap is:
104.8% - (24% + (27% - Hit Chance) + (6.5% - Dodge Reduction))

For classes that use a two-handed weapon or a single weapon, the formula for determining your current crit cap is:
104.8% - (24% + (8% - Hit Chance) + (6.5 - Dodge Reduction))

A final note about the crit crap is on a different phenomenon known of "crit depression." Crit depression is an occurrence that happens against raid-level mobs wherein your actual crit chance is statistically lower than expected beyond the elements of RNG. It was determined through various parsing and testing methods that all melee attacks suffered a 4.8% crit depression, where the actual chance to crit against a raid boss was going to be a RNG variable closer to a value that was 4.8% less than the crit chance displayed on your character sheet. Due to the lowered chance to crit against these mobs, a player's crit cap is always going to be set against a constant of 104.8% instead of merely 100% since the additional loss of crit needs to be made up as well in order to push regular hits off the table.

Special attacks and the two-roll system

Everything explained thus far has been in relation to "white" or auto-attacks. "Yellow" or special attacks follow a different roll system than auto-attacks do. Special attacks are any attacks which are a result of a player's actively using an ability. This can be an instant swing ability such as Shred or Lava Lash or it can be an on-next-swing attack such as Heroic Strike or Rune Strike. All of these attacks follow a two-roll system instead of the one-roll system that standard attacks utilize. Beyond the difference in roll systems, there are two differences in the way that special attacks functions as opposed to normal attacks. First, all special attacks follow the same base miss chance rules as a two-handed or single weapon even when dual-wielding. Second, special attacks cannot land as a glancing blow.

A two-roll system operates in a functionally similar way to a single-roll system; there are just a few minor differences. When a special attack is made, the server rolls a single "dice" first to resolve how the attack lands. The first roll that is made determines whether the attack misses, is dodged, blocked, parried or lands normally. After that roll is completed, a second roll is made to determine whether the attack lands as a critical hit or a normal hit. To this end, the crit cap for special attacks is different than that of normal attacks. Instead of capping at 71.2% as with white attacks, special attacks have a crit cap of 95.2%.

Another difference between the two-roll system of special attacks and the single-roll system of normal attacks is that results from different tables are not mutually exclusive. This means that even if a special attack is blocked, it is still capable of landing as a critical hit. Obviously, however, critical attacks are still exclusive against misses, dodges and parries.

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