#0 - March 8, 2007, 11:38 a.m.
- This is not a Druid vs Warrior thread, don't make it one.
- This is not a nerf-discussion thread, don't make it one.
- I've not looked at threat generation, it is a different subject that deserves its own thread.
- Try and keep your arguments objective, after all, numbers do not lie.
- Please point out any errors in my calculations or the conclusions i've drawn.
- If someone could put this up on the DruidWiki, that'd be great.
ARMOR vs DODGE - An in-depth investigation
Introduction
The two main attributes to a Druids damage migitation are armor and dodge. Armor provides a garantueed reduction in damage taken from hits, while dodge provides a chance to completely avoid a hit. Most items provide a standard armor bonus based on the item level and the quality of the item, but some provide a higher armor value. These items are interesting for the Druid, since in Dire Bear Form, armor from items is multiplied by 5 (or 5.5). However, as a Druids armor increases, the amount of armor needed to increase your damage reduction by 1% goes up, while dodge doesn't have such effects.
In this text, I investigate the amount of damage reduction gained from increasing armor compared to that gained from adding dodge. Then I will compare the itembudget-costs for both stats and compute which way of increasing damage reduction is cheaper. Please note that the core of this text is mathematical in nature. Readers may wish to skip the mathematical derivations and move on to the conclusions.
Deriving the formulas
I'm assuming a Druid with the Thick Hide talent (any Druid serious about tanking has this). I will denote armor by the variable a, chance to dodge (as a percentage, ranging from 0 to 100) by the variable d and the level of the enemy mob by the variable L.
For now, i'm neglecting critical hits and misses in my calculations. Since crits should occur very rarely (assuming SotF and some defense rating gear) and misses have a percentage-based chance of occurring, this will have a very minimal effect on the outcome of the computations.
Crushing blows do however factor in to the benefits of items that grant dodge chance. Because of the hit-table that WoW uses, dodged attacks replace normal hits and not crushing blows. So if you get hit 100 times and your dodge chance is 20%, you'll dodge 20 hits and get crushed 15 times. If your dodgerate improves to 30%, you will dodge 30 hits, but will still get crushed 15 times, so the relative amount of crushing blows you get will increase. More on the effect of crits, crushes and misses later on.
Let M(a,d) denote the fraction of total damage taken with armor value a and chance to dodge d%. The function will have values between 0 and 1. The dodge component of this function looks like:
M(0,d) = (1 - d / 100)
The armor component looks like:
M(a,0) = (1 - a / (a + 467.5 L - 22167.5))
Since reduction from dodge and armor is multiplicative, the complete function has the following easy form:
M(a,d) = (1 - d / 100)(1 - a / (a + 467.5 L - 22167.5))
Now, we're looking at how this function changes when one of the input values, armor or dodge, changes. Therefore we take the derivatives of this function with respect to these two variables. Let dMd denote the derivative of M with respect to d and dMa the derivative with respect to a.
dMd = -M(a,0) / 100
dMa = -M(0,d)((a + 467.5 L - 22167.5) - a) / (a + 467.5 L - 22167.5)^2
To compare the reduction gained from adding 1 point of armor to that gained from adding 1% dodge, we divide these derivatives to obtain the function R(a,d):
R(a,d) = dMa / dMd = (M(0,d) / M(a,0)) (46750 L - 2216750) / (a + 467.5 L - 22167.5)^2
R(a,d) is the function that gives, for certain dodge and armor, how much reduction 1 extra armor gives in terms of the extra reduction of 1% more dodge. A value of R(a,d) of 0.005 would mean that at that level of armor and dodge, 1 dodge is worth about 200 armor in terms of damage reduction.
Interpretation of R(a,d)
With the newfound function R(a,d) we can find some numerical values of how dodge relates to armor. First, I define the quantity "armor equivalent points" (or AEP) of a certain stat to be the amount of reduction that stat gives in terms of armor. 1 point of armor is always 1 AEP and if R(a,d) = 0.005, then 1% dodge is 200 AEP. The AEP-value of dodge depends on your current dodge and armor level as expressed by the R(a,d) function.
Now, we take a set of common armor/dodge values for feral Druids. I've used 70 as the enemy mob level.
18000 armor, 16% dodge - 1% dodge = 340 AEP
18000 armor, 20% dodge - 1% dodge = 357 AEP
18000 armor, 24% dodge - 1% dodge = 376 AEP
18000 armor, 28% dodge - 1% dodge = 397 AEP
18000 armor, 32% dodge - 1% dodge = 420 AEP
21000 armor, 16% dodge - 1% dodge = 376 AEP
21000 armor, 20% dodge - 1% dodge = 394 AEP
21000 armor, 24% dodge - 1% dodge = 415 AEP
21000 armor, 28% dodge - 1% dodge = 438 AEP
21000 armor, 32% dodge - 1% dodge = 464 AEP
24000 armor, 16% dodge - 1% dodge = 411 AEP
24000 armor, 20% dodge - 1% dodge = 432 AEP
24000 armor, 24% dodge - 1% dodge = 455 AEP
24000 armor, 28% dodge - 1% dodge = 480 AEP
24000 armor, 32% dodge - 1% dodge = 508 AEP
27000 armor, 16% dodge - 1% dodge = 447 AEP
27000 armor, 20% dodge - 1% dodge = 469 AEP
27000 armor, 24% dodge - 1% dodge = 494 AEP
27000 armor, 28% dodge - 1% dodge = 522 AEP
27000 armor, 32% dodge - 1% dodge = 552 AEP
So, what does it mean? A high AEP means that the 1% dodge is equal to a higher amount of armor. This means that the higher the AEP of 1% dodge is, the better dodge is compared to armor. We notice that the higher your armor, the better dodge becomes when compared to armor. This is because the higher you get, the more armor it takes to get an extra 1% of damage reduction from armor. Getting more dodge also increases the AEP of dodge, because at higher dodge-rates, adding an extra percent helps alot more than adding an extra percent at low dodge. Note that AEP works with armor *after* the bearform multiplier, so while 1 point of armor in bearform is worth 1 AEP, you will only need 0.182 armor on the actual item (or: casterform-armor) in order to obtain this.
At level 70, you need 19 dodge-rating to obtain 1% chance to dodge, so the AEP value of dodge-rating is the AEP value of 1% dodge divided by 19, which will lie between 18 and 29 AEP.
With 2.4 defense-rating you gain 1 defense-skill. Every 25 skillpoints you have decreases your chance to be hit and crit by 1% and increases your chance to dodge by 1% (and does the same for parry and block chances, but those are not relevant for Druids). So for all practical purposes, 60 defense-rating can be considered equal to 3% dodge-chance in terms of long-term damage migitation. Which means that 20 defense-rating is equivalent to 1% dodge, so defense-rating is worth about 5% less AEP than dodge-rating.
Agility adds 2 armor and 0.0691% chance to dodge. So the AEP value of 1 point of AGI is between 26 and 38.
Comparison with ItemValue costs
Items are created based on something called ItemValue. This is the sum of how much stats an item is worth. Some stats cost more than others and the way ItemValue is calculated, makes it so that 10 of one stat and 10 of another stat with the same cost makes for a lower total than just 20 of one stat.
Every armorpiece has a base armorvalue based on the itemlevel of the item, the quality (green, blue, purple) and the type of armor (cloth, leather, mail, plate). This base armor is free and doesn't affect other stats. Some items have higher armor than this base armor and it's the extra armor that weighs in the balance for an items ItemValue.
Lets say that 1 point of armor costs 1 point, then extensive testing by others has yielded that 1 point of base-stats costs 10 points. In Dire Bearform, you get 5.5 armor out of 1 point of armor on the item, so 1 AEP worth of armor costs 0.182 points. 1 dodge-rating also costs 10 points. So 1 AEP worth of dodge-rating costs between 0.345 points and 0.556 points.
1 Point of agility costs 10 points, so 1 AEP worth of AGI costs between 0.263 and 0.385 points. Now, putting this all together, we see that gaining migitation through dodge costs about twice to three times as much as gaining the same migitation through armor. Agility is also more expensive than armor, but significantly cheaper than obtaining AEP through dodge-rating.
1 Point of defense-rating also costs 10 points, so defense-rating is slightly more expensive as dodge-rating. However, defense-rating also reduces burst damage by preventing critical hits, so it has its uses apart from long term damage migitation.
Compared to pre-TBC, the price of AEP through dodge-rating compared to armor has remained more or less the same, but where agility used to be less effective than dodge-rating, it is now significantly more effective, thanks to the new AGI->Dodge formula.
... to be continued ...
