Yes, some of these numbers have been run before.
For given stats at a given level, it's pretty easy to know what ACs optimize damage with PA and which don't. Supply stats and I'll walk through the numbers.
The fact is, yes you might miss more when you PA, but when cleaving, the potential payoff is also bigger...TWICE as big, in fact. I think it's worth it.
Ignoring critical hits altogether...
When attacking one foe normally, this fighter should Power Attack monsters of AC 22 or lower. At AC 23, the power-attacking fighter does 2.1 DPR versus 2.2 without PA. At AC 22, the PA fighter does 2.8 DPR vs. 2.75 without.
When Cleaving two foes, this fighter should Power Attack monsters of AC 21 or lower instead. The DPR at AC 22 rounds to 3.4 either way.
The fact is, yes you might miss more when you PA, but when cleaving, the potential payoff is also bigger...TWICE as big, in fact. I think it's worth it.
The problem is that second hit is much less likely than the first, since it depends on the first. The contribution of total DPR of the second hit is very low until you get into the range where you're hitting a lot.
And since the loss of to-hit probability occurs twice for the second hit, there's a clear range where it's optimal to PA only if you're not cleaving.Of course, for a FTR 1, that range is very small. When PA has a larger effect starting at level 4 (or when average damage gets much higher), that range of numbers is also broader.
AvalonXQ,
Thanks! One hopes that a 1st-level character won't be fighting AC22 or greater, so it looks like the general rule for him would be "always use Power Attack, with or without Cleave".
Unfortunately, DPR isn't the only thing to consider (particularly at level 1). Since you're swinging a 2-handed sword your average damage is 11 (2d6+4) with a minimum of 6. If you have a good chance of dropping an enemy anyway (say it only has 1 HD), then the extra damage doesn't matter and you shouldn't voluntarily take the penalty to attack.
Also - in situations where your enemies have different AC from each other your DPR is higher if you attack the one with lower AC first. It's pointed out above that 22 AC is the breaking point but what if you have an AC 24 enemy with AC 18 allies. Is it better to use PA? What if you absolutely need to do at least 10 damage to one of the targets?
You could do the same sort of analysis for every case, but it's not really worth it since the damage output is actually very close and your choice will often depend on other circumstances.
Finally, you'll see that the relationship is quadratic which means that even if you wanted to only deal with DPR, there are two break-even points. As pointed out above, we should always PA against AC 21 or lower but we should also PA against very high ACs (26+) since you're hoping for crits.
As a side note - it's not really AC that we're interested in, it's the number we need to roll to hit. If we need 16+ to hit, it could be standing toe-to-toe with an AC 22 enemy, but it could also be that we're shaken and prone on the ground trying to hit an AC 16 enemy.