Can’t provide a formula for it but will give you the actual values in the most relevant cases :
At 100 bloodlust stacks:
1/5 UI + 0.2 Actual bonus + 0.2 5/5 UI + 1 Actual bonus + 1.24 ( 1.24 better) 10/5 UI + 2 Actual bonus + 2.54 (~1.25 better) 11/5 UI + 2.2 Actual bonus + 2.8 (~1.28 better)
While the actual Bloodsplosion damage formula is beyond my ability for figuring out, overwhelming gameplay experience shows the grenade damage multiplier applies to its damage. (I know bloodsplosion damage IS a type of splash so grenade damage applying to it was very likely …).
This skill ~ * 4 grenade damage multiplier ( 1 + 2.8 + a little help from BAR) makes Bloodsplosion chains so deadly on melee builds …
This skill (with buzz axe bombardier) also makes the axe throw out-damage his melee swing damage. Without buzz axe bombardier his Axe Throw damage is 3/5 (60%) of Melee Swing damage. Add an extra *4 from the grenade multiplier to his axe throw and … 3/5 * 4 = 2.4 with better crit multiplier than the melee swing. And extra explosive AOE splash damage …So you can start your bloodsplosion chain from range.
I’ll spare you the combat log walls of numbers nobody ever bothers to read or ties to make sense of) this time, and provide an old school BAR off grenade damage pop-up printscreen for 11/5 Fuel the Blood at 100 bloodlust stacks …
91328 * (1+ 2.2) = 292249.6
91328 * (1+ 2.8) = 347046.4 (347 k)