## Simplified avoidance formulas

January 30, 2010 at 9:16 am | Posted in Uncategorized | Leave a commentIn this post I describe what defense rating is, how it works, and how it contributes to avoidance percentages. In a later post I intend to discuss the value of defense in an environment where tank health pools greatly reduce the risk of tank death due to critical strikes (ie, heroics). Much of the technical information here I have drawn from Tankspot and Elitist Jerks so while any mistakes are my ownthe credit largely is theirs.

**Defense is for…**

Defense rating performs two primary functions for tanks in PvE encounters:

- Reduces chance to take a critical strike.
- Increases chance to dodge, parry, block or be missed.

**Defense skill versus defense rating**

Defense rating on gear is converted into defense skill, which is displayed on the character sheet, before being used in calculations for avoidance or crit immunity. The conversion between these two quantities varies by level, but below are a few common conversions:

- at 80, 4.918498039 defense rating equal 1 defense skill
- at 70, 2.365385056 defense rating equal 1 defense skill
- at 60, 1.50 defense rating equal 1 defense skill

*(Note: fractional amounts of defense skill are rounded down when using it for subsequent calculations.) *

This conversion does not appear to be subject to diminishing returns. That is, the conversion is fixed across all defense rating levels. In an attempt to verify this, I tried juggling gear items around on a level 80 character. I’m fairly confident that 4.92 is a good approximation of the conversion based on this data:

- 491 dr = 99 ds, 492 dr = 100 ds
- 614 dr = 124 ds, 615 dr = 125 ds
- 737 dr = 149 ds, 738 dr = 150 ds
- 860 dr = 174 ds, 861 dr = ???, 862 dr = 175 ds (can anybody confirm the 861 figure?)

*(Note: I have many more data points available for readers that might be interested in examining this further. I strongly suspect, however, that this work has already been done by others.)*

From defense skill we can calculate the various benefits of defense rating.

**Critical strikes**

When mobs attack, they have a 5% base chance to get a critical strike that hits for twice as much as normal. The base chance is modified by two factors: if the mob is higher/lower level than the defender and the defense skill of the defender. The chance to be crit hit increases or decreases by 0.2% per level. Defense skill lowers the chance to be crit by 0.04% per skill point. So we get the following formula:

- percent chance to be crit hit = 5 + (0.2 * (mob level – player level)) – (0.04 * defense skill)

From this, we can derive the standard ‘magic numbers’:

- At level 80, tanks need
**535**defense skill to be crit immune. (Heroic mobs are level 82 and below) - At level 80, tanks need
**540**defense skill to be crit immune. (Raid bosses are considered level 83)

**Avoidance**

Defense skill also provides a benefit to avoidance stats. The *undiminished* chance to dodge, parry, block and miss are each increased by the same amount as reduction to chance to be crit (without the 5.6% cap). The ‘undiminished’ part, of course, is key. The amount of avoidance gain you will actually realize will vary based on your current avoidance stats with the exception of block chance (it is not subject to diminishing returns). What follows in this section is mostly about the formulas at level 80 after patch 3.2.

The formulas vary slightly by class. Here is the warrior formula for **parry** as I understand it:

- parry percentage (as seen on your character sheet) = P
_{no-DR}+ P_{diminished} - P
_{no-DR}= (number of talent points in Deflection) + (base parry) - base parry = 5 (for all plate tanks)
- P
_{diminished}= (P_{undiminished}* C_{p}) / (P_{undiminished}+ k * C_{p}) - P
_{undiminished}= 0.04 * (defense skill) + [ (parry rating) / 45.25018692] - C
_{p}= 47.003525 (this is the ‘parry cap’ for warriors since 3.2) - k = 0.9560 (for warriors)

Next, **dodge** for warriors:

- dodge percentage = D
_{no-DR}+ D_{diminished} - D
_{no-DR}= (number of talent points in Anticipation) + (base dodge) + 0.0118 * (white agility) - base dodge = 3.664 (for warriors as of 3.2)
- D
_{diminished}= (D_{undiminished}* C_{d}) / (D_{undiminished}+ k * C_{d}) - D
_{undiminished}= 0.04 * (defense skill) + [ (dodge rating) / 45.25018692] + 0.0118 * (green agility) - C
_{d}= 88.129021 - k is same as previous
- white/green agility is displayed on your character sheet when you mouse over your overall agility. their sum is equal to your overall agility.

Miss is a little different as the value is not displayed on the character sheet. Here is the **miss** formula for warriors:

- miss percentage = M
_{no-DR}+ M_{diminished} - M
_{no-DR}= 5 + (racial bonus) - racial bonus = 2 for night elves, 0 for everybody else
- M
_{diminished}= (M_{undiminished}* C_{m}) / (M_{undiminished}+ k * C_{m}) - M
_{undiminished}= 0.04 * (defense skill) - C
_{m}= 16

Block, as mentioned previously, is not subject to diminishing returns. This fact has been used to good effect in tanking the adds for Anub’arak. Here is the formula for **block**:

- block percentage = (base block) + (number of talent points in Shield Specialization) + 0.04 * (defense skill) + [ (block rating) / 16.3949947 ]
- base block = 5

If you don’t want to do the math yourself, I have written a basic **calculato****r** that will perform the calculations for you. I think it still has a couple little bugs, especially for non-warriors, but it should get you close. I have written about it in a previous post. If you find problems with the calculator, please notify; I will fix it as soon as I am able.

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