Here comes the math

The basic conversions for defense, dodge and parry rating at level 80 are:

You generally only gain miss chance from defense, though things like the Night Elf racial (which is not subject to diminishing returns) are around. Testing to determine the exact diminishing returns on miss has not been completed. We know that miss is subject to diminishing returns because of Daelo's comment here: WotLK Beta (US-English) Forums -> Avoidance change. (emphasis mine)Code:4.91850 defense rating = 1 defense skill 45.25019 dodge rating = 1% dodge chance 45.25019 parry rating = 1% parry chance 122.9625 defense rating = 1% dodge/parry/miss chance These values are correct as of patch 3.2

Whitetooth has also done the work to isolate the miss cap (link above)Originally Posted byDaelo

There is a coefficient (k) for each class that bounds the diminishing returns:

There is a cap (c) for each class, for each avoidance type:Code:Class k Warrior 0.956 Paladin 0.956 Deathknight 0.956 Druid 0.972 These values are correct as of patch 3.2

Finally, the agility you have beyond your naked agility also affects your dodge chance, based on class:Code:Class type c 1/c Warrior Dodge 88.129021 0.011347 Warrior Parry 47.003525 0.021275 Warrior Miss 16 0.0625 Paladin Dodge 88.129021 0.011347 Paladin Parry 47.003525 0.021275 Paladin Miss 16 0.0625 (presumed since all other caps are the same as warriors) Deathknight Dodge 88.129021 0.011347 Deathknight Parry 47.003525 0.021275 Deathknight Miss 16 0.0625 (presumed since all other caps are the same as warriors) Druid Dodge 116.890707 0.008555 These values are correct as of patch 3.2

Code:Class Dodge/Agility Warrior 0.0118 Paladin 0.0167 Deathknight 0.0118 Druid 0.0209 These values are correct as of patch 3.2Note that your base (naked) avoidance and avoidance given by talents and racials is NOT subject to diminishing returns - do not include them in the calculation

Also note that your base defense (what you have when you're naked) is not used in calculations - only the defense you gain from gear.

The net amount of avoidance you get is given by:

Where

A is the amount of avoidance before diminishing returns

c is the cap for the avoidance stat

k is the constant for your class

Ad is the amount of avoidance after diminishing returns are applied (how much your avoidance actually increases)

Each avoidance type (dodge, parry) is calculated separately from the other. The amount of dodge you have does not affect the diminishing returns on your parry, and vice-versa.

Example 1 - Dodge

Suppose a warrior has 5% dodge when naked with +261 agility from gear, +557 defense on gear, and +368 dodge rating on gear:

First, calculate the base dodge chance from gear:

1a) Convert defense rating to defense skill: 557/4.9185 = 113 defense skill

1b) Convert defense skill to base dodge chance: 113 * 0.04 = 4.52%

1c) Convert dodge rating to base dodge chance: 368/45.25019 = 8.13256%

1d) Convert agility to base dodge chance: 261 * 0.01360 = 3.5496%

2) Calculate k/A: 0.956/(4.52 + 8.13256 + 3.5496) = 0.059

3) Calculate 1/c + k/A: 0.01135 + 0.059 = 0.07035

4) invert the result from step 3: 1/0.07035 = 14.21434%. This is Ad, the diminished amount of dodge actually gained

Now add the diminished dodge from gear to the dodge when naked, and the warrior will end up with 5% + 14.21% = 19.21% dodge

Example 2 - Parry

Suppose a deathknight has 5% parry when naked with +255 defense rating on gear, and +375 parry rating on gear:

First, calculate the base parry chance from gear:

1a) Convert defense rating to defense skill: 255/4.9185 = 51 defense skill

1b) Convert defense skill to base parry chance: 51 * 0.04 = 2.04%

1c) Convert parry rating to base parry chance: 375/45.25019 = 8.28726%

2) Calculate k/A: 0.956/(2.04 + 8.28726) = 0.09257

3) Calculate 1/c + k/A: 0.02128 + 0.09257 = 0.11385

4) invert the result from step 3: 1/0.11385 = 8.78383%. This is Ad, the diminished amount of parry actually gained

Now add the diminished parry chance to the base parry chance and the deathknight will end up with 5% + 8.78% = 13.78% parry

Example 3 - Miss

We know that each point of defense skill increases your chance to be missed by 0.04%, and that defense is currently the only way to increase your chance to be missed. Suppose a human warrior has +689 defense on gear:

1a) Convert defense rating to defense skill: 689/49.18499 = 140 defense skill

1b) Convert defense skill to base miss chance: 140 * 0.04 = 5.6%

2) Calculate k/A: 0.956/5.6 = 0.17071

3) Calculate 1/c + k/A: 0.0625 + 0.17071 = 0.23321

4) invert the result from step 3: 1/0.23321 = 4.2879%. This is Ad, the diminished amount of miss actually gained

The warrior will end up with 5% + 4.29% = 9.29% miss. If the warrior were a Night Elf, the chance to be missed would be 11.29% (because of the Quickness racial.)

You cannotsimply calculate what a given item "should" increase your stats by and just add it to what you have.

Example 4 - Optimum Balance vs. Stamina

Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.

This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

If the warrior trades one stamina gem for +20 parry rating, then the 695/600/120 stats become avoidances of 26.61% and 18.67%, for a ratio of 1.92. Trading another stamina gem for 20 more parry, then the 695/600/140 stats become 26.61% and 19.14%, for a ratio of 1.82. In this case two parry gems brings the warrior back into optimal balance at a cost of 60 stamina.

Example 5 - Trading for Optimum Balance

Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.

This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

If the warrior trades one dodge gem for a parry gem then the 695/580/120 stats become avoidances of 26.30% and 18.67%, for a ratio of 1.88. In this case changing one dodge gem for a parry gem brings the warrior back into optimal balance.

Example 6 - Optimum Balance vs. Defense

Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.

This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

If the warrior trades one dodge gem for defense rating, then the 695/580/100 stats become avoidances of 26.41% and 18.38%, for a ratio of 1.96. Ultimately, three defense gems would be required to bring the ratio below 1.88 if trading dodge gems for them.

If the warrior were to trade stamina gems for defense gems then a trade of 6 gems would be required to bring the ratio below 1.88, or 180 stamina for 120 defense.

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