The current weapon chain:
Pistol
Shotgun
Cmbt. Shotgun
Chaingun
Dbl. Shotgun
Rocket launcher
Plasma rifle
BFG9000
I think it should be in between combat Shotgun and chaingun.
In 250 turns, the combat shotgun can cause 180 damage
In 250 turns, the chaingun can dish out some major hurt at 350 damage.
WHOA! Big gap. No wonder when I first did hell's arena I got a highscore.
Keeping in mind that this is at an unarmored enemy at close range. Otherwise the damage may be lower.
In 250 turns, the plasma pistol should do approx. 280 damage. This means that an example of the turn times for the PP is:
Clip size: 10
Damage: 7d3
Firing time: 10 turns
Reloading time: 20 turns
Although the damage looks quite high, this will do just a little above 280 damage in 250 turns.
Fire pistol X 10 (140 damage, 100 turns)
Reload pistol (120 turns)
Fire pistol X 10 (280 damage, 220 turns)
Reload pistol (240 turns)
Fire pistol (294 damage, 250 turns)
Assuming you always roll an average of 14 (the average of a 7d3 anyway)
So there. We have a spot, and a suggested formula, for the PP.
EDIT: My mistake! The double shotgun allready does 270 dam per 250 turns. Possibly the PP could do 230.