Taken out of order:
Coredump said:
First: His continual rant about crits being "100% confimred" or "75% confirmed" is just balderdash. ... The math fact is that a crit range of 18-20 will have a confirmed crit on 15% of the *hits*. IOW, the numbers he uses for "100% confirmed" is the actual correct number. The garbage he spouts about "optimum..." and "75%" is wrong and misleading. (okay, there is a slight caveat. the percentage will be *slightly* less, for those times when an 18 or 19 don't hit.)
...
SKR's rant is pathetic. His logic is flawed, and is math is just plain wrong.
And yet, yours is, as well.
A rapier will not confirm its critical on 15% of "hits." That's crazy talk.
A rapier *threatens* a critical 15% of the time - assuming you don't need more than an 18 to hit. It will confirm its critical 95% of the time - assuming
anything but a 1 will hit.
Coredump said:
We are calculating average damage per *hit*, not per attack.
Which is a faulty way of doing things. Rather, you
should calculate expected damage per attack.
IOW, the expected damage for a given attack is:
(Chance of Normal Hit * Expected Normal Damage) + (Chance of Confirmed Critical * Expected Critical Damage) = Expected Damge per Attack
Let's assume a rapier and a longsword, both used with a damage bonus of +X. Expected Normal Damage and Expected Critical Damage are thus easy to calculate:
END(R): 3.5 + X
END(L): 4.5 + X
ECD(R): 7 + 2X
ECD(L): 9 + 2X
Chance of Hit: MIN(95%, (AC-AB)/20)
Chance of Threat: MIN(Chance of Hit, Threat Range)
Chance of Confirmed Critical: Chance of Threat * Chance of Hit
Chance of Normal Hit: Chance of Hit - Chance of Confirmed Critical
Now, assuming you hit on anything but a 1 (i.e., Chance of Hit = 95%), then the expected damage for an attack with a Rapier is 14.7 damage per hit - when X is equal to 10. For the longsword in the same situation? 15.2. That's equivalent to a 30 Strength score, by the by.
They're roughly equivalent - 23.5 damage per attack - at a Strength score of 46.
Reduce the chance to hit (to, say 50%), and the longsword wielder retains his lead. Drop it below the critical threshhold of the rapier (15%), and the longsword's lead increases.
Now, take the same situation, and give the Rapier wielder stacking Keen and Improved Critical. We'll give the longsword wielder Flaming.
The rapier-wielder is now down a feat compared to his longsword-wielding buddy.
At a damage bonus of +10 (again, equivalent to a 30 Strength), and when anything other than a 1 hits, the rapier wielder is ahead of the longsword wielder - by 0.12 damage per attack. Should the longsword wielder decide to spend that feat in, say, Weapon Specialization (for a +2 to damage), he's back out in the lead again - by 2 points per attack.
EDIT:
For kicks and giggles, let's throw in a battleaxe in that last scenario. It is exactly equal to the longsword - as expected. In other words, a suped-up rapier wielder *barely* breaks even at +10 to damage vs. the "standard" melee weapons, but only so long as those weapons have nothing fancy going for them. A single extra damage enhancement - flaming, shocking, an additional +1 enhancement, - or a single extra feat - like Weapon Spec. - and they handily beat the optimized rapier.