Korak said:
The math is useful because I put it in a context. I took a nearly optimal situtation for the power of the feat to show itself. I tried to break it by analyzing a character designed to have a very high hit bonus and damage bonus. Then I looked at the difference between his damage with and without the feat in optimal conditions (all full attacks). The reason for all this, is that if you look at what happens in the most favorable situation for the feat and it proves to be no more powerful than a very standard PHB feat (weapon specializtion in this case), then you see that the feat can't be overpowered in most campaigns. You missed the context for the math.
You're saying that you reached a conclusion that this feat is no more powerful than weapon specialization. That it will not result in an increase in PC power greater than that achieved by a PC gaining weapon specialization.
Let's say a PC is ready to select either IRS or weapon specialization as his next feat in a campaign. Your saying that IRS, even in a situation most favorable to it, will not be more powerful than IRS.
Let's say that combat takes place mostly in outdoor settings with a lot of open space in this campaign. Combats begin at great distances, so the PC gets to use full archery attacks during (effectively) all rounds of combat.
Before taking the feat, the PC deals d8+4(strength)+2(magic)+d6(fire) [average 14, minimum 8] on a hit. His AB is +12/+7 or +10/+10/+5 when using rapid fire.
The most common encounter, by far, in this campaign are wandering encounters with large packs of CR 1/2 (or less) creatures with 7 hps or less. Each of these foes has an AC of 14 to 20. Orcs, kobolds, goblins, hobgoblins, etc ... These creatures attack in large numbers in order to be effective.
Each shot by that archer will kill one of these foes, even if the PC rolls minimum damage. Having weapon specialization may result in more damage, but not more kills. In this situation, more damage is useless.
IRS, on the other hand, turns 1 out of every 10 attacks from a miss into a hit (on average). When you're making three attacks per round, that adds up rather significantly.
In this style of campaign, IRS is vastly more powerful than weapon specialization.
It will also be far more important in any situation in which it is being used frequently and the percentage increase in chances to hit exceeds the percentage increases in damage per hit (such as when you have a high AC foe and you deal a lot of damage per shot ... perhaps a sneak attacking rogue).
Your conclusion, based upon the very sinsible and well calculated math, ends up in a flase determination because the math doesn't cover the situation fully. Your math lied yo you.