Khopesh vs Rapier DPS

[Valezra]

I couldn't find this anywhere on the forums so if it's been done before I apologize.

Assumptions:
1. Improved Critical or Keen Weapon.
2. Total bonus damage of 10, 25, 50 before base weapon damage or race considerations for calculations.
3. Land all hits on rolls 2-20.
4. Bloodstone.


Khopesh:
1d10 Base for Greensteel = 5.5 Avg

F(10):
Avg Hit = (10+5.5) * (15/20) = 11.625
Avg Crit = (10+5.5+6) * (4/20) * 3 = 12.9
Total = 24.525

F(25):
Avg Hit = (25+5.5) * (15/20) = 22.875
Avg Crit = (25+5.5+6) * (4/20) * 3 = 21.9
Total = 44.775

F(50):
Avg Hit = (50+5.5) * (15/20) = 41.625
Avg Crit = (50+5.5+6) * (4/20) * 3 = 36.9
Total = 78.525


Rapier (and Scimitar for Elf):
1d8 Base for Greensteel = 4.5 Avg

F(10):
Avg Hit = (10+4.5) * (13/20) = 9.425
Avg Crit = (10+4.5+6) * (6/20) * 2 = 12.3
Total = 21.725

F(10) elf/drow:
Avg Hit = (10+4.5+2) * (13/20) = 10.725
Avg Crit = (10+4.5+2+6) * (6/20) * 2 = 13.5
Total = 24.225

F(25):
Avg Hit = (25+4.5) * (13/20) = 19.175
Avg Crit = (25+4.5+6) * (6/20) * 2 = 21.3
Total = 40.725

F(25) elf/drow:
Avg Hit = (25+4.5+2) * (13/20) = 20.475
Avg Crit = (25+4.5+2+6) * (6/20) * 2 = 22.5
Total = 42.975

F(50):
Avg Hit = (50+4.5) * (13/20) = 35.425
Avg Crit = (50+4.5+6) * (6/20) * 2 = 36.3
Total = 71.725

F(50) elf/drow:
Avg Hit = (50+4.5+2) * (13/20) = 36.725
Avg Crit = (50+4.5+2+6) * (6/20) * 2 = 37.5
Total = 74.225

Comparison:

@ Damage (10) - Khopesh does 12.8% more damage than a rapier and 1.2% more damage than a drow/elf rapier.

@ Damage (25) - Khopesh does 9.9% more damage than a rapier and 4.2% more damage than a drow/elf rapier.

@ Damage (50) - Khopesh does 9.5% more damage than a rapier and 5.8% more damage than a drow/elf rapier.

***Edit*** It should be noted that for any setup as the bonus damage increases the advantage of the Khopesh over the Rapier eventually levels out at 8% regardless of the Elf/Drow bonus.

Burst Damage Comparison:
(Assume 1d10 on x2 crit, 2d10 on x3 crit, and 3d10 on 4x crit)

Khopesh Added Burst Damage = 11 * 4 / 20 = 2.2 damage/swing avg
Rapier Added Burst Damage = 5.5 * 6 / 20 = 1.65 damage/swing avg

Discussion:

When looking at the avg hit and the avg crit for a khopesh we find that more than 50% of the khopesh's total damage is coming from regular hits. In fact, Rapiers do more base crit damage than the Khopesh for drow/elf races (this can be offset by a loss in Burst damage for Rapiers however). This means that a miss on a 2 will have a greater DPS loss for the Khopesh user than it will for the Rapier user. Furthermore, elf/drow can take an additional +2 to hit meaning in some circumstances where the AC of the monster or boss is very high the drow/elf rapier user can do slightly higher damage than the Khopesh user.

Notice that as the total damage output increases the advantage of being elf/drow diminishes from only a 1.2% loss at 10 bonus damage to a 5.8% loss at 50 bonus damage.

This is of course circumstantial depending on the mob you are attacking but a good rule of thumb would be to go drow/elf rapier for 3/4 BAB classes such as bards and clerics to offset the loss in BAB and put the DPS on a closer playing ground to a full BAB khopesh user. If you are a paladin, fighter, barbarian, or cleric who spams Divine Power a lot then Khopesh will always provide the highest DPS. If you are an elf/drow and want to free up a feat (such as for the feat starved Paladin) you can go Rapiers and be confident that at the very worst you will probably only be doing 5% less damage than your Khopesh clone counterpart.

Val