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I would like the modify the DPR formula to take into account the cumulative misfire percentage on firearms. Usually you can just take each of your attacks one by one and modify your damage by your miss chance and crit chance + multiplier, but the assumption I would like to make it so that if your gun misfires, you stop firing (rather than risk explosion with the higher misfire chance of a broken gun).
Here is the formula:
* Damage/round formula: h(d+s)+ft(cd+cb+r)
h = Chance to hit, expressed as a percentage. This doesn't exceed .95 (unless you autohit for whatever reason) and never goes below .05.
d = Normal damage. This is any damage that happens any time you hit.
s = Damage which isn't multiplied on a crit. "s" stands for sneak attack, but this includes elemental/alignment properties on weapons, manyshot damage, and so on.
t = Chance to roll a threat. This is the threat range of your weapon or your chance to hit, whichever is lower.
f = This is your chance to confirm a threat. Most of the time, this is equal to h. If you have Critical Focus, it's (h+.2) or .95, whichever is higher. If you auto-confirm crits, as with a level 20 fighter or Bless Weapon, this is 1.
c = This is the number of bonus multiples you get from a crit. A 2x crit weapon is 1, a 3x crit weapon is 2, etc.
-- Remember to subtract one from your crit multiplier, or your damage will be over-done in the formula!
b = This is elemental burst damage, such as from fiery burst weapons and thundering. Such enhancements self-multiply based on your crit multiplier; if they don't, then they're added to r and not b.
r = This is fixed bonus damage dealt on a crit. No such abilities exist in PF core, to my knowledge.
The main question I am trying to answer involves quantifying the value of having the 5% reduced chance of misfiring a pistol vs the 1d12 damage die of the musket. A standard DPR calc will put the musket ahead, especially with the high crit multiplier for firearms, but misfiring more often will act to reduce the muskets DPR, relatively speaking.
Your help is appreciated.