TWF math
Someone emailed me having discovered my math was howlingly wrong. So, correction:
Assuming TWF & Ambidexterity, or Rapid Shot, and two attacks (+6/+1 - +9/+4) it's worth using the feats so long as AC is no more than primary bonus + 14. Primary bonus is the first attack bonus, so a character with 18 Str and BAB of +6/+1 would have a primary bonus of +10.
P = Primary attack bonus
The odds of a hit are: (20 - AC + P)/20
So AC 10, P of +6, odds are .8
The average damage of an attack is: (20 - AC + P)/20 x avg dmg roll
2 attacks, compared to 3 attacks with TWF/Ambidexterity or Rapid Shot
Interested in when the 2 attacks are better than the 3 attacks:
(avg dmg roll)(20 - AC + P)/20 + (avg dmg roll)(20 - AC + P - 5)/20 >
2(avg dmg roll)(20 - AC + P - 2)/20 + (avg dmg roll)(20 - AC + P - 7)/20
Since avg dmg roll is everywhere, as is 1/20, we can eliminate the factors.
(20 - AC + P) + (20 - AC + P - 5) > 2(20 - AC + P - 2) + (20 - AC + P - 7)
35 - 2AC + 2P > 49 - 3AC + 3P
AC - P > 14
AC > P + 14
IE: 2 attacks are better than 3 when AC is more than 14 above primary attack bonus. This is, granted, not going to happen a heck of a lot... but will happen sometimes.
This is more important for rogues and others with lower BAB.
For the curious, the same derivation can be worked out for single vs. double attacks.
20 - AC + P > 40 - 2AC + 2P - 4
AC > P + 16
And so on.
If my math is wrong, please let me know.
