this is in advice as people are generally looking for "what's the best weapon".
just looking at weapons without bonuses, for simplicity assume they hit on 11+ (that's an average to hit ratio, 10 out of 20 rolls).
Again, for simplicity don't add any primary ability bonuses or magical bonuses, and don't consider AoO.
Longsword(martial 1hnd melee) 15gp sm:1d6 med:1d8 crit:19-20/×2 type:S reach:- range:- wt:4lbs specials:-.
on average for medium size (4.5dmg/19+ @+dmg)
hits; 11,12,13,14,15,16,17,18,19+C,20+C out of rolls 1-20.
crits, again this will hit on 11+ for; 11,12,13,14,15,16,17,18,19,20.
. . since we hit 10 times out of 20 rolls, average damage bonus on a critical will be (10/20)*average damage or 0.5*average damage.
. . so on a critical, the average damage will be 1+0.5 or 1.5*average damage.
this means our damage from all possible rolls will be(starting at 11); 4.5,4.5,4.5,4.5,4.5,4.5,4.5,4.5,6.75,6.75 or 49.5.
since we had 20 tries (rolls 1-20) the average will be 49.5/20 or 2.475
Longsword has an average damage output of 2.475/r plus 11/20*Str bonus(1hnd).
Falcata(exotic martial 1hnd melee) 18gp sm:1d6 med:1d8 crit:19-20/×3 type:S reach:- range:- wt:4lbs specials:-.
on average for medium size (4.5dmg/19+ @+2*dmg)
hits; 11,12,13,14,15,16,17,18,19+C,20+C out of rolls 1-20.
crits, again this will hit on 11+ for; 11,12,13,14,15,16,17,18,19,20.
. . since we hit 10 times out of 20 rolls, average damage bonus on a critical will be (10/20)*2*average damage or 1*average damage.
. . so on a critical, the average damage will be 1+1 or 2*average damage.
this means our damage from all possible rolls will be(starting at 11); 4.5,4.5,4.5,4.5,4.5,4.5,4.5,4.5,9,9 or 54.
since we had 20 tries (rolls 1-20) the average will be 54/20 or 2.7
Falcata has an average damage output of 2.7/r plus 12/20*Str bonus(1hnd).
Greatsword(martial 2hnd melee) 50gp sm:1d10 med:2d6 crit:19-20/×2 type:S reach:- range:- wt:8lbs specials:-.
on average for medium size (7dmg/19+ @+dmg)
hits; 11,12,13,14,15,16,17,18,19+C,20+C out of rolls 1-20.
crits, see longsword.
this means our damage from all possible rolls will be(starting at 11); 7,7,7,7,7,7,7,7,10.5,10.5 or 77.
since we had 20 tries (rolls 1-20) the average will be 77/20 or 3.85
Greatsword has an average damage output of 3.85/r plus 11/20*1.5*Str bonus(2hnd).
Earthbreaker(martial 2hnd melee) 40gp sm:1d10 med:2d6 crit:20/×3 type:B reach:- range:- wt:12lbs specials:-.
on average for medium size (7dmg/20 @+2*dmg)
hits: 11,12,13,14,15,16,17,18,19,20+C out of rolls 1-20.
crits: 2*average damage.
damage: 9*7 +14 = 77.
average damage:3.85
Earthbreaker has an average damage output of 3.85/r plus 11/20*1.5*Str bonus(2hnd).
Falchion(martial 2hnd melee) 75gp sm:1d6 med:2d4 crit:18-20/×2 type:S reach:- range:- wt:8lbs specials:-.
on average for medium size (5dmg/18+ @+dmg)
hits: 11,12,13,14,15,16,17,18+C,19+C,20+C out of rolls 1-20.
crits: 1.5*average damage.
damage: 7*5 +3*7.5 = 57.5.
average damage:2.875
Falchion has an average damage output of 2.875/r plus 11.5/20*1.5*Str bonus(2hnd).
Interesting. But as you mentioned the falcata is x3. Your calculation for it is for x2.
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This would be a lot easier if you check out a book on probabilities, and learn to do it the short way.
DPR can be easily calculated as:
H*D+CT(H+c)*((CM-1)*D+CX)
Where:
H= Chance to hit
D= Average Damage
CT= Chance to threaten a critical
c= Extra bonuses to confirm a crit, such as Critical Focus
CM= Critical multiplier
CX= Extra critical effects, such as flaming burst
For your first example of a 1-handed longsword, you assumed:
H= 0.5
D= 4.5
CT= 0.1
c= 0
CM= 2
CX= 0
Which gives us:
(0.5*4.5)+(0.1*0.5*4.5)=2.475
Now instead of writing out every possibility, you can just plug the numbers into that formula.
Elven curve blade(exotic martial 2hnd melee) 80gp sm:1d8 med:1d10 crit:18-20/×2 type:S reach:- range:- wt:7lbs specials:-.
on average for medium size (5.5dmg/18+ @+dmg)
hits: 11,12,13,14,15,16,17,18+C,19+C,20+C out of rolls 1-20.
crits: 1.5*average damage.
damage: 7*5.5 +3*8.25 = 63.25.
average damage:3.1625
Earthbreaker has an average damage output of 3.1625/r plus 11.5/20*1.5*Str bonus(2hnd).
Elven branched spear(exotic martial 2hnd melee) 20gp sm:1d6 med:1d8 crit:20/×3 type:P reach:10ft range:- wt:10lbs specials:brace,reach.
on average for medium size (4.5dmg/20 @+2*dmg)
hits: 11,12,13,14,15,16,17,18,19,20+C out of rolls 1-20.
crits: 2*average damage.
damage: 9*4.5 +9 = 49.5.
average damage:2.475
Falchion has an average damage output of 2.475/r at 10ft reach plus 11/20*1.5*Str bonus(2hnd).
I agree RainyDayNinja... I was just spelling it out so people could easily see the effects of *2 and *3 criticals and the variance these add to Strength bonuses, and they could work it out simply for themselves. My post would be the proof for most of your formula. There is considerable handwaving about what's the better weapon without any numbers or math.
This was also my attempt to get people to post some numbers ON the messageboards for easy look up.
typo corrected
Elven branched spear(exotic martial 2hnd melee) 20gp sm:1d6 med:1d8 crit:20/×3 type:P reach:10ft range:- wt:10lbs specials:brace,reach.
on average for medium size (4.5dmg/20 @+2*dmg)
hits: 11,12,13,14,15,16,17,18,19,20+C out of rolls 1-20.
crits: 2*average damage.
damage: 9*4.5 +9 = 49.5.
average damage:2.475
Elven branched spear has an average damage output of 2.475/r at 10ft reach plus 11/20*1.5*Str bonus(2hnd).
RainyDayNinja wrote: ...
DPR = H*D+CT(H+c)*((CM-1)*D+CX)
Where:
H= Chance to hit
D= Average Damage
CT= Chance to threaten a critical
c= Extra bonuses to confirm a crit, such as Critical Focus
CM= Critical multiplier
CX= Extra critical effects, such as flaming burst
For your first example of a 1-handed longsword, you assumed:
H= 0.5
D= 4.5
CT= 0.1
c= 0
CM= 2
CX= 0
Which gives us:
(0.5*4.5)+(0.1*0.5*4.5)=2.475
Now instead of writing out every possibility, you can just plug the numbers into that formula.
chance is the ratio of successes divided by attempts, or H is probability of a hit, P(hit) and CT is P(critical).
the average damage term D in the first half of the formula (H*D) is the damage done on a regular hit. This could include consistent damage such as +3.5 from flaming burst.
the term ((CM-1)*D +CX) is the damage done on a critical.
you should mention that c is the bonus probability to confirm, thus +4 means c=0.2 rather than 4.
CX should be the average of the additional damage.
Ability bonus can be added into D or calculated separately using the same formula less a variable. D=Ability damage bonus; StrDPR = H*D +CT*(H+c)*((CM-1)*D).
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