There has been some discussion of my numbers and analysis in my original rant on this subject. Let's take an absolutely basic approach and just compare the longsword to the rapier. This table shows all of the math involved for Strength values between 10 and 30.

• "1x Str Bonus" is just the normal Strength bonus to damage for that Strength.
• "Crit Rate" is the rate of crits for that weapon (longsword = 19-20 = 10%, rapier = 18-20 = 15%)
• "Ave Die Damage" is the average damage of the base die (longsword = 1d8 = 4.5, rapier = 1d6 = 3.5).
• "Die Damage +1x Str" is Ave Die Damage + 1x Str Bonus
• "Crit Bonus Damage (100% confirmed)" is the average crit damage (which = "Die Damage +1x Str") times the Crit Rate of the weapon. In other words, if your crit rate is 10% (one in ten hits is a crit) and the average crit damage is 10 points, those 10 points averaged over all 10 hits equals +1 point per hit. This assumes you always confirm your critical hits; in other words, it's the ideal situation for the critseeking player. In situations where you're not always able to crit, your Crit Bonus Damage will reflect that (the next three columns -- 75%, 50%, and 25% -- represent that).
• Note that because your iterative attacks are each 5 points worse than the previous attack (+10/+5/+0, for example), the 75%, 50%, and 25% columns reflect that reduced chance of confirming exactly, assuming that your primary attack has a 100% chance of confirming the crit.
• Note that you can't really be in a situation where you have a 100% chance to crit because a roll of 1 on a d20 always misses, but in an idealized example we can ignore that small chance of failure to make our tables cleaner.
• The columns then repeat similar data except that it's based on using the weapon two-handed, and thus getting x1.5 Str Bonus.

Table 2: Comparative Stacking Damage For Longsword and Rapier

Weapon	Str	Str 1x, With keen and Improved Crit stacking	Str 1.5x, With keen and Improved Crit stacking
Longsword	10	5.9	5.85
Rapier	10	5.1	5.08
Longsword	12	7.2	7.15
Rapier	12	6.5	6.53
Longsword	14	8.5	9.75
Rapier	14	8.0	9.43
Longsword	16	9.8	11.05
Rapier	16	9.4	10.88
Longsword	18	11.1	13.65
Rapier	18	10.9	13.78
Longsword	20	12.4	14.95
Rapier	20	12.3	15.23
Longsword	22	13.7	17.55
Rapier	22	13.8	18.13
Longsword	24	15.0	18.85
Rapier	24	15.2	19.58
Longsword	26	16.3	21.45
Rapier	26	16.7	22.48
Longsword	28	17.6	22.75
Rapier	28	18.1	23.93
Longsword	30	18.9	25.35
Rapier	30	19.6	26.83

From Table 2 you can see that even if you let keen and Improved Crit stack, the one-handed longsword is still better than the one-handed rapier until you reach Str 24, and the two-handed longsword is still better than the two-handed rapier until you reach Str 18 (the points where the rapier starts to do better are marked in red). In other words, the rapier needs these two abilities to stack just to maintain parity (i.e., "keep up") with the longsword; both are martial weapons of the same size, and should therefore be about equal. Otherwise the longsword's +1 damage relative to the rapier means it's consistently doing more damage, and is therefore a better weapon.

Now back to Table 1.

Just by looking at the numbers, you can see that the Crit Bonus Damage (100%) doesn't average out to much ... in most cases, it's less than 2 points, and in all cases presented here it's less than 3 points. You have to think of it in these terms:

1. If I add keen to my weapon, I'm adding the Crit Bonus Damage (100%) to every primary attack I make with that weapon.
2. If I take Improved Critical with that weapon, adding the Crit Bonus Damage (100%) to every primary attack I make with that weapon.
3. If I add an energy property (flaming, frost, shock, etc.) to my weapon, I'm adding and average 3.5 damage to every primary attack I make with that weapon.
4. If I take Weapon Specialization with that weapon, I'm adding 2 damage to every primary attack I make with that weapon.