You can't answer without considering your BAB and opponent CA, anyway the answer is preetty easy:.
Example #1:
Suppose you hit on a roll of 15 or more, after a combat you did one roll for each score of 15 or more.
Long sword damage=4.5 ((1+8)/2) * 6 (each roll from 15 through 20) + 2 (critical hit 19 and 20) * 4.5 = 36 HP
Scimitar damage = 3.5 ((1+6)/2) * 6 + 3 (critical hit 18, 19 and 20) * 3.5 = 31.5 HP
So you could think long sword is better than scimitar, but suppose instead you are able to hit only on roll of 18 or more, so you have:
Example #2:
Long sword damage=4.5 ((1+8)/2) * 3 (each roll from 18 through 20) + 2 (critical hit 19 and 20) * 4.5 = 22.5 HP
Scimitar damage = 3.5 ((1+6)/2) * 3 + 3 (critical hit 19 and 20) * 3.5 = 21 HP
You can see that more difficult become to hit the opponent, more the average damage of the smallest weapon (but with wider critical area) is similar to that of the largest one.
But at medium chance to hit (suppose about 12-15 roll on 20) the greater damage of the long sword grant you bigger average damage than scimitar one.
Bye, MadLuke.
Example #1:
Suppose you hit on a roll of 15 or more, after a combat you did one roll for each score of 15 or more.
Long sword damage=4.5 ((1+8)/2) * 6 (each roll from 15 through 20) + 2 (critical hit 19 and 20) * 4.5 = 36 HP
Scimitar damage = 3.5 ((1+6)/2) * 6 + 3 (critical hit 18, 19 and 20) * 3.5 = 31.5 HP
So you could think long sword is better than scimitar, but suppose instead you are able to hit only on roll of 18 or more, so you have:
Example #2:
Long sword damage=4.5 ((1+8)/2) * 3 (each roll from 18 through 20) + 2 (critical hit 19 and 20) * 4.5 = 22.5 HP
Scimitar damage = 3.5 ((1+6)/2) * 3 + 3 (critical hit 19 and 20) * 3.5 = 21 HP
You can see that more difficult become to hit the opponent, more the average damage of the smallest weapon (but with wider critical area) is similar to that of the largest one.
But at medium chance to hit (suppose about 12-15 roll on 20) the greater damage of the long sword grant you bigger average damage than scimitar one.
Bye, MadLuke.