Hello everyone.
I've seen questions posted about maximizing DPS output and whether or not Spell Power/ Weapon Damage, Critical %, and/or Magicka/Stamina is best for focusing on in gear selections. As such, I did a search on the official forums for formulas and was surprised that I did not find a post with the exact formulas here. Thus, here they are:
Tooltip = (max_ABILITY + wpn/spelldmg × 10.46) × skill_coef × rank_coef
For the rest of the thread, I will abbreviate these values as such:
max_stamina/magicka: A (for ability, the game's labeling of magicka/stamina)
wpn/spell_dmg: P (for power, which the game uses for these collectively)
skill_coef: S
rank_coef: R
critical hit %: C (will be used later, stay tuned or skip ahead)
Thus, the formulas become:
Tooltip = (A+P×10.46)×S×R
What is my rank_coef?
Base is 1.00, add 0.01 for each rank (morph rank 1 counts as rank 5, or 0.04)
What is my skill_coef?
It varies for each skill, and you can calculate it if you really want to by fiddling with your stats in-game and a spreadsheet. I used to have a list, but it's long, inaccurate in the current version, and I'll leave that as an exercise to the reader. You don't need it really for stat comparison, but I'll explain that below.
How do critical hits and critical hit percent chance factor in?
Critical hits multiply your damage by 1.5 (~1.55 for shadow stone, more with divine trait gear). Thus, a critical hit ADDS 0.5 times your tooltip value. This event occurs only has a critical_hit% chance of happening. Thus, you can take your skill, multiply it by 0.5, and then multiply that by your chance of having a critical hit, and you get your added average benefit from your critical hit percent. Let's add it into our formulas.
Average Skill Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5
- NOTE: C is a percent value, so make sure to use 0.40 for 40% and so on.
This all seems awfully complicated, and my numbers don't match up right!
That's right, it is complicated, and the numbers don't work quite right. That's because these formulas were reverse engineered, and they involve something called truncation and/or various forms of rounding. For really advanced players, or those already comfortable with math, you'll figure out, in fiddling with the math above, that the values in those formulas are truncated at various stages. For the most part, the changes are so small that you can accept your values being off some and just ignore truncation in calculating your best setup of power, ability, and critical percent.
Lovely thread, complicated math, I have no idea what to do with this.
Find out what you want (max burst damage, highest ultimate generation, best overall DPS, etc) and use the math to help you. For simplicity's sake, you can frequently remove S and R from your math for ability/crit/power comparisons, as they'll remain constant (by comparison) no matter what skill you use. In doing calculations.
Resist
Damage Multiplier = 1- (TRUNC((RESISTANCE - PENETRATION) ÷ 63000),2)
TL:DR See above for variable definitions.
Average Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5
To the best of my knowledge, these values are accurate for ESO 2.0.3
Edited by evedgebah on April 2, 2015 6:38PM