I have another question on "Added Cold Damage Support". As you can see from the screenshot below: It says that supported skills have 6 to 9 added cold damage. This support gem is linked to Burning Arrow gem: I am having troubles understanding my resulting damage for Burning Arrow: Why is main hand cold damage 16-24? What exactly was enhanced by this support gem? This is what is equipped on me: This my skill tree: From the skill tree you can see that I have 71% increased projectile damage and 10% increased attack physical damage (does this damage even apply to rangers?)
Physical Attack damage applies to all physical attacks including bow attacks, however cold is elemental not physical so we ignore the 10% you have for the calculation.
Burning Arrow has 155% effect of added damage. Since added cold damage obviously adds damage we multiply what it gives by 155%:
6-9 * 1.55 = 9.3 - 13.95
You have 71% increased projectile damage. This increases all the damage of your burning arrow (because it is a projectile) which includes the 9-14 damage we got in the last calculation:
9.3-13.95 * 1.71 = 15.9-23.85.
The game rounds to the nearest whole number so you see 16-24 on your character sheet.
As for your Physical and Fire damage these are the calculations. Starting with the 9-37 physical damage from your bow.
Again Burning Arrows damage effectiveness affects your bows damage:
9-37 * 1.55 = 13.95-57.35
Your passive skill tree has 71% projectile damage and 10% physical attack damage. Since these are both increases they are added together for a total 81% increase:
13.95-57.35 * 1.81 = 25.2-103.8 physical damage
Burning arrow converts 50% of this physical damage to fire damage:
25.2-103.8 * .5 = 12.6-51.9 rounding to 13-52 for both physical and fire damage.