Final damage from dmg/boss

Definitions

1. Damage refers to the final damage bonus applied by the stat damage %. We'll denote the value of this by DMG.
2. Boss damage refers to the additional final damage bonus which is added with damage % against bosses (and only bosses!). We'll denote the value of this by BossDMG.

The dmg/boss component of the damage formula $$(1 + \text{DMG} + \text{BossDMG}).$$ Warning: A 10% damage bonus almost never means 10% final damage from your current base stats.

Example 1. Suppose an explorer has 200% damage and 100% boss. Let's evaluate the final damage bonus he gets from a 10% damage buff with respect to his base stats.

Against a mob, his final damage bonus is given by $$ \frac{1 + (2 + 0.1)}{1 + 2} \sim 1.033 $$ Against a boss, his final damage bonus is given by $$ \frac{1 + (2 + 0.1) + 1}{1 + 2 + 1} = 1.025 $$ Example 2. Let's now evaluate the final damage bonus the above explorer gets from a 10% boss buff.

His final damage bonus is zero against mobs as the following calculation shows $$ \frac{1 + 2 + 0}{1 + 2} = 1.0 $$ Against a boss, his final damage bonus is given by $$ \frac{1 + 2 + (1 + 0.1)}{1 + 2 + 1} = 1.025 $$