I think it depends on the gun. And most guns that proc BloodBath also LOVE +grenade damage. ( guns
with splash . More than half of the non-crit DPUH damage for example comes from the splash. Higher the BAR higher the damage gap ).
The bonus to guns is obviously inferior to what BloodBath gives to guns but the the skills are not mutually exclusive .
And +grenade damage applies to bloodsplosion (not tested by me yet), buzz axe bombardier (both components), grenades, …
Level 43 Double Penetrating Hole Puncher used in test
8438 134970.406 Max 76677.672 Cur 80917.203 Prev 4239.531 Damage
0 134970.406 Max 71908.336 Cur 76677.672 Prev 4769.336 Damage
0 134970.406 Max 67668.805 Cur 71908.336 Prev 4239.531 Damage
16 134970.406 Max 62899.469 Cur 67668.805 Prev 4769.336 Damage
Triggered 7/5 Fuel The Blood using the axe Throw (without BAB)
1109 154156.531 Max 124335.938 Cur 128575.469 Prev 4239.531 Damage
0 154156.531 Max 115784.938 Cur 124335.938 Prev 8551.000 Damage
0 154156.531 Max 111545.406 Cur 115784.938 Prev 4239.531 Damage
16 154156.531 Max 102994.406 Cur 111545.406 Prev 8551.000 Damage
I did not video record so the math will tell how many bloodlust stacks I had (0 before the axe kill) but it is already obvious the FtB increases weapon splash damage.
The math:
On card weapon damage (scaled to lvl 43) : 3249.367
BAR : gun damage ~13.5 ; Grenade Damage ~12.5.
5/5 Strip flesh 15% explosive damage
3249.367 * (1 + 0.135) * (1 + 0.15) = 4241.236 // gun’s impact damage
3249.367 * (1 + 0.135) * (1 + 0.125) * (1 + 0.15) = 4771.3 // splash without FtB
8551 / (3249.367 * (1 + 0.135) * (1 + 0.15)) = 2.016 // explosive damage multiplier
(2.016 - 1 - 0.125) / 0.014 = 63.64 // 64 stacks ? seems a bit high (taste the blood 5/5 +30 and FtB 7/5 +14) …
3249.367 * (1 + 0.135) * (1 + 0.125 + 0.014 * 64) * (1 + 0.15) = 8571.538 … // big error
repeat test - this time I payed attention ~40 bloodlust stacks
4329 154156.531 Max 149917.000 Cur 154156.531 Prev 4239.531 Damage
0 154156.531 Max 141128.594 Cur 149917.000 Prev 8788.406 Damage
0 154156.531 Max 136889.063 Cur 141128.594 Prev 4239.531 Damage
15 154156.531 Max 128100.648 Cur 136889.063 Prev 8788.414 Damage
seems like I’ll have to do it properly with BAR off and strip flesh off to figure it out