Final damage from attack
Types of attack- Non-multiplicative attack, which we'll denote by FlatATT.
- Multiplicative attack, which we'll denote by ATT.
- Attack %, which we'll denote by ATT%.
The attack component of the damage formula $$(1 + \text{ATT} \%) * (\text{ATT}) + \text{FlatATT}.$$ Example 1. A lucky noob with 100 total ATT, 0 ATT%, and 0 FLAT_ATT finds himself a 6% ATT emblem.
The initial attack component of the damage formula in this case is $$(1 + 0) * (100) + 0 = 100.$$ The attack component of the damage formula after equipping the 6% ATT emblem is $$(1 + .06) * (100) + 0 = 106.$$ The final damage given by 6% ATT is given by the ratio $$106/100 = 1.06.$$ If the noob's damage output was 1000, his damage output is now $1000 * 1.06 = 1060$.
Example 2. The same noob above then finds a replacement for his weapon which is 5 attack higher than his current weapon.
Prior to equipping his weapon, the attack component of the damage formula is $$(1 + .06) * (100) + 0 = 106.$$ After equipping his weapon, the attack component of the damage formula is $$(1 + .06) * (105) + 0 = 111.3.$$ The final damage given by 5 ATT is then $$111.3/106 = 1.05.$$ The noob's damage output was 1060, so his damage output is now $1060 * 1.05 = 1130$.
Common misconception. Gains from ATT are amplified by the existence of ATT%.
This is false for all classes except Kanna. In the absence of FlatATT, the final damage from x attack is $$\frac{(1 + \text{ATT} \%) * (\text{ATT} + x)} {(1 + \text{ATT} \%) * (\text{ATT})} = \frac{\text{ATT} + x} {\text{ATT}}. $$ So despite the misleading relationship between ATT and ATT% it is best to treat these two stats as being independent from one another.
To demonstrate this with our above example, notice that the 5% increase in final damage is the exact same as dividing the new ATT by the old ATT, without considering ATT% $(105/100)=1.05$.