A bit more complicated than that.
Take a look at F2 first:
“F2: (base chance to apply effect of element type vs defense type) (UVHM mode tested)
SLAG (30 vsHealth, 30 vsArmor, 30 vsShield)
Fire (30 vsHealth, 15 vsArmor, 15 vsShield) // 60 vs health in TPS
Electric (15 vsHealth, 15 vsArmor, 75 vsShield)
Corrosive (15 vsHealth, 30 vsArmor, 15 vsShield)”
So slag has equal chance to be applied regardless of defense type (be it shield, armor or health). The other elemental types are a bit more fastidious . Electric DOT for example is really easy to apply vs shields and 75/15 = 5 times less likely vs armor or health.
Fire starts at 30% vs health and 15% vs shields or armor.
F4 >1 in an ability means that ability gets an extra bonus to the chance to apply that effect.
For items (weapons or grenades F4 value is dependent on the weapon/grenade parts. For weapons the BAR extra chance to apply elemental effect and flicker are also calculated in F4 )
So vs equal lvl health enemy 30 * 3 = 90% for Raving Retribution (and 15 * 3 = 45% vs shields or armor).
Firebreath has less of a bonus so 30 * 1.5 and 15 * 1.5
All of this assuming enemies of equal level to krieg. The chance to apply elemental effects is lowered vs enemies of level higher than the caster. (F6 multiplier in the bla bla formula)
And since this is krieg and fire DOTs we’re taking about … very likely his F9 will be >1 from Burn Baby Burn and often from Fuel the Fire killskill (incredibly strong effect).