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I've edited that before you guys replied, but yes, brainfart on the 1 damage.
However, Charon:
Say, guy has 20 HP, lvl 3-ish. You only have a damage bonus of +8-ish (Stat(5)+power attack(2)+misc(1)). Would you take the weapon with +5% to crit or the one with +1 average dmg?
Increase the HP by 4 or decrease the static damage by 2 and the answer changes. This is a moot argument.
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Lowering the damage bonus is moot since an 8 is a good average for that level.
+5 stat mod before level 4 is unusual for any but SAD casters. And depending upon their AC, power attack might not be worth it. (Especially if the character isn't a full BAB class.) Even a +1 weapon isn't common at 3rd level. (WBL is 3000. If you get full plate, you don't have enough gold for a +1 weapon.)
But anyway - as I said before - examples are meaningless. The raw math isn't. And according to the raw math, the average damage needs to be 20 for a 18-20 crit to average the same damage as 19-20 with one point more base damage. And again - between the overkill damage being more likely with crits, and not everything being crittable, it'd probably need to be several points higher to be worth it.
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if you increase the HP by 4 you still have a good chance of one shotting him (50% after a crit) and you still have a pretty good chance of killing him in the same amount of time as the +1 average damage weapon.
With 20 hp & a +8 static damage bonus, both the longsword and the scimitar will take two average hits to drop the target or 1 average crit. Advantage goes to the scimitar.
With 24 hp & +8 static damage bonus, or 20 hp & +6 static damage bonus, the scimitar will take 1 above average crit, 1 average or below crit and 1 average hit, or three average hits. The longsword will require 1 average crit or two average hits. Advantage goes to the longsword.
Lowering the damage bonus is moot since an 8 is a good average for that level.
What are you basing this off of? My experience is not that the average meleer has a 20 Strength, Power Attack and a +1 Weapon at third. You are again deliberately picking examples that are beneficial to your argument.
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What does any of this have to do with a scorpion whip? It seems quite off topic.