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Tools for testing:
Sun Axe level 25 - 47 base damage 50-50 split fire and slashing.
Lightforged Axe level 25 - 47 base damage 50-50 split fire and slashing.
so we can assume that slashing and fire damage is about 23.5 damage.
Character with 0 in all stats (no Flame power bonus) and no skills, and no other bonuses of any kind.
Victim for testing:
dual scythe scavenger level 3 (through some additional testing it seems they have ~25% fire resist by default, ~50% if "resisted" message pops up and no slashing damage resistance)
So for testing purposes I'll look for attacks target "resisted", for consistency sake.
Starting damage on target from both axes is 35 damage: 23.5 fire damage, 23.5/2 -> 11.75 inflicted fire damage on enemy that resisted fire damage, now 23.5+11.75 = ~35.25 damage done, seems to add up with 50-50 split assumption and calculated enemy resistance.
Next level up "This is the Way" passive. On paper it boosts magic weapon damage. I would assume since weapon does fire damage - it's a kind of magic damage, no?
So assume we add 10% fire damage: 23.5+(23.5*0.1)=25.85 /2 -> 12.925 effective damage and 23.5+12.925= ~36 damage total.
But attacking enemy we got 35. Looks like damage is not added. I guess it's a bonus exclusively for wands and staves.
Next Arsonist. This one adds 10% damage bonus to ALL fire damage.
By same calculations we should get about 36 damage, but nope... Still at 35.
Pyromaniac (+20% to all fire damage) yields same results - 35 damage.
Let's try Warrior's Path (+10% to all melee damage).
So I assume it should add damage to the "whole" weapon, meaning both fire and slashing.
Resulting damage shows... That it is plausible. 25.85+12.925 = 38.775 and target received 38 damage.
Add one strength (+5% melee damage) for good measure: 27.025+13.5125 = 40.5375
40 damage on target verified it.
Resulting damage from Lightforged axe is 39
Calculating 23.5+9=32.5, now 32.5/2+23.5=39.75 - barely fits, but game seems to display only the numbers before the point, so Lightforged Axe checks out.
Resultind damage from Sunforged Axe 44.
Sunforged Axe is 35+9 = 44... Boy is it a lot easier when target has no resistance...
In conclusion:
♥♥♥♥♥♥♥♥♥♥♥! the awesome +1 all stats ring doesn't work! F*CK!.. And well, melee bonuses apply only to melee weapons, while magic bonuses - only to magic weapons a.i. wands and staves. But the bonus damage from upgrading does matter.
PS: Take it with a grain of salt - my math is bad and testing methods might be even worse, but somehow everything seems to add up, more or less.
My build utilizes Water aura with as much Intelligence as I could get my hands on, but primary focus still on melee tree.
Result - nigh immortal character (~35hp/s regen) with good wand damage for ranged and good melee damage :D
+1 all stats ring not working was unfortunate. Was happy when I found it, only to notice that my health went down, when it should have went up. Hence I noticed it doesn't work.