FreeTheSlaves
Adventurer
Having delighted in lots of comparative math after being kindly presented with the below formula, I decided on a whim to run some numbers and see what could be seen.
Layout is the following: A = P{D[1+Pc(Mc-1)] + Db}
For bonus critical dice I insert: +Bd[Pc(Mc-1)] after the Db & before the closing }
where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier
Db = Bonus Damage dice that are not multiplied by a confirmed critical
Bd = Bonus die average damage that only occurs on confirmed criticals
The situation:
What are the differences between exotic weapon proficiency (Bastard sword), weapon focus & improved critical feats? The examples use an 8th level fighter with a +2 longsword (50/20 magic item rule), 17 str & gauntlets of ogre str+2 (ab+14/+9 vs AC20). I chose AC20 because it is CR+12, just like SR and eyeballing it & it looks about right.
Vanilla Longsword
7.0125 = 0.75{8.5[1.1]}
4.675 = 0.50{8.5[1.1]}
11.6875
Weapon focus (Longsword)
7.48 = 0.80{8.5[1.1]}
5.1425 = 0.55{8.5[1.1]}
12.6225
Improved critical (Longsword)
7.65 = 0.75{8.5[1.2]}
5.1 = 0.50{8.5[1.2]}
12.75
Exotic weapon proficiency (Bastard Sword)
7.8375 = 0.75{9.5[1.1]}
5.225 = 0.50{9.5[1.1]}
13.0625
What I find interesting is that a feat available at 1st level is the most damage dealing but then I would suspect that by another 2-4 levels or so the average damage increased by Improved critical would offset the Exotic weapon proficiency.
The second iterative attack of Weapon focus actually beats the Improved critical, but this is no surprise because the higher the target AC becomes the better the value of Weapon focus. The value of Weapon focus is highest when it allows a hit on a 19+ when the others require a natural 20, this situation of course spells doom & needs to be taken with a grain of salt.
It is all fine & dandy to take all 3 feats at level 8 but what about level 1, which is the first one you have to survive before anything else. The below assumes that you've only got 1 feat to spare, so which one? The examples use a 1st level fighter with a normal longsword & 15 str (ab+3 vs AC13). I chose AC13 because it is CR+12, just like SR and eyeballing it & it looks about right.
Vanilla Longsword
3.9325 = 0.55{6.5[1.1]}
Weapon focus (Longsword)
4.29 = 0.60{6.5[1.1]}
Exotic weapon proficiency (Bastard Sword)
4.5375 = 0.55{7.5[1.1]}
Before declaring an outright winner let's run the numbers versus a more formidable AC18 (CR+17).
Vanilla Longsword
2.145 = 0.30{6.5[1.1]}
Weapon focus (Longsword)
2.5025 = 0.35{6.5[1.1]}
Exotic weapon proficiency (Bastard Sword)
2.475 = 0.30{7.5[1.1]}
As suspected, the higher the AC the better the mileage gained from WF. The only problem with taking WF over EWP is that you generally* can't go back in time to change the weapon focussed in, although you could wield the Bastard sword 2handed for 1st level as a martial weapon. *I say generally because this doesn't apply to me what with my carefree dm, bwahaha!
Layout is the following: A = P{D[1+Pc(Mc-1)] + Db}
For bonus critical dice I insert: +Bd[Pc(Mc-1)] after the Db & before the closing }
where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier
Db = Bonus Damage dice that are not multiplied by a confirmed critical
Bd = Bonus die average damage that only occurs on confirmed criticals
The situation:
What are the differences between exotic weapon proficiency (Bastard sword), weapon focus & improved critical feats? The examples use an 8th level fighter with a +2 longsword (50/20 magic item rule), 17 str & gauntlets of ogre str+2 (ab+14/+9 vs AC20). I chose AC20 because it is CR+12, just like SR and eyeballing it & it looks about right.
Vanilla Longsword
7.0125 = 0.75{8.5[1.1]}
4.675 = 0.50{8.5[1.1]}
11.6875
Weapon focus (Longsword)
7.48 = 0.80{8.5[1.1]}
5.1425 = 0.55{8.5[1.1]}
12.6225
Improved critical (Longsword)
7.65 = 0.75{8.5[1.2]}
5.1 = 0.50{8.5[1.2]}
12.75
Exotic weapon proficiency (Bastard Sword)
7.8375 = 0.75{9.5[1.1]}
5.225 = 0.50{9.5[1.1]}
13.0625
What I find interesting is that a feat available at 1st level is the most damage dealing but then I would suspect that by another 2-4 levels or so the average damage increased by Improved critical would offset the Exotic weapon proficiency.
The second iterative attack of Weapon focus actually beats the Improved critical, but this is no surprise because the higher the target AC becomes the better the value of Weapon focus. The value of Weapon focus is highest when it allows a hit on a 19+ when the others require a natural 20, this situation of course spells doom & needs to be taken with a grain of salt.
It is all fine & dandy to take all 3 feats at level 8 but what about level 1, which is the first one you have to survive before anything else. The below assumes that you've only got 1 feat to spare, so which one? The examples use a 1st level fighter with a normal longsword & 15 str (ab+3 vs AC13). I chose AC13 because it is CR+12, just like SR and eyeballing it & it looks about right.
Vanilla Longsword
3.9325 = 0.55{6.5[1.1]}
Weapon focus (Longsword)
4.29 = 0.60{6.5[1.1]}
Exotic weapon proficiency (Bastard Sword)
4.5375 = 0.55{7.5[1.1]}
Before declaring an outright winner let's run the numbers versus a more formidable AC18 (CR+17).
Vanilla Longsword
2.145 = 0.30{6.5[1.1]}
Weapon focus (Longsword)
2.5025 = 0.35{6.5[1.1]}
Exotic weapon proficiency (Bastard Sword)
2.475 = 0.30{7.5[1.1]}
As suspected, the higher the AC the better the mileage gained from WF. The only problem with taking WF over EWP is that you generally* can't go back in time to change the weapon focussed in, although you could wield the Bastard sword 2handed for 1st level as a martial weapon. *I say generally because this doesn't apply to me what with my carefree dm, bwahaha!
err...
