Power Attack Returns

[Amechra]

Alright, I'd like to break this to everyone (who didn't, you know, already know this):

Power Attack has limited returns if you aren't using Shock Trooper, or some other means to mitigate the loss of to-hit.

How limited?

I did some calculations (alright, I had software do the grunt work, but I digress), and I arrived at the following formula (it may actually be wrong, if someone a bit better at working these things can take a look):

18x - 1, where X equals the ratio of damage-to-attack-bonus that you are getting from Power Attack.

The above formula gives you the highest average damage you can be able to deal before Power Attack becomes less efficient at dealing damage than just keeping the attack bonus in the first place.

The exceptions to this are the edge cases; i.e., where you could hit on a 2, even with the penalty, or where you were only hitting on a 20 anyway.

Yes, this does mean that once you are cracking into sweet, sweet ToB goodness, or are becoming a massive Monk, or even just running around with a high enough Strength modifier, you have to grab higher and higher multipliers for Power Attack to keep it relevant.

Let's take our trusty friend a Vicious Greatsword, and hand it to a Fighter with a nice Str of 30; it would deal an average of 22 damage, before, say, +5 damage from it being magical (27 damage), and another +7 damage from Bane (34).

He was kinda silly in his youth, and so has Power Attack, Weapon Focus (Greatsword), and Weapon Specialization (Greatsword) for 36 average damage.

Congrats! Now, unless he's a charger, Power Attacking against pretty much anything is going to be a waste of time.

Thoughts? Arguments?

[A_S]

Haven't done the full math on this, so may be missing something, but it seems to me that whether PA is worth it or not can't just be a function of the damage you do; it also varies based on the difference between your AB and your target's AC (i.e., your chance to hit).

Examples: Bob the Fighter does an average of 10 damage with his two-handed pointed stick, and he attacks with it at a +10 attack bonus. Let's avoid edge cases and say he's going up against two opponents, Gretchen the Scantily Clad Ogress (AC 12) and Zen-Boy the Ludicrously Wise Monk (AC 29).

So, if he doesn't power attack, he has a 95% chance to hit Gretchen (only misses on a 1), for an expected damage of 9.5. He only has a 10% chance to hit Zen-Boy (hits on a 19 or 20), for an average damage of 1.

If he does power attack, let's say for 1, then his damage if he hits goes up to 12. He drops down to a 90% chance to hit Gretchen, so an average of 10.8 damage (better), and a 5% chance to hit Zen-Boy, so an average of 0.6 damage (worse). Thus, whether he should power attack depends on the AC of his opponent.

Right?

[Amechra]

The thing is the above calculation is basically designating the "line" where taking even a single point of penalty would be worse than just leaving it.

Basically, the above is the highest damage you can be doing if you hit precisely on a 2 or above where it is worth it; basically, beyond that point, you can take as big a penalty as you can get away with (see the edge cases.)

So the above does take AB and AC difference into account, just in a slightly obfuscated way. I'm going have to do more calculations to see where the point where it becomes inefficient for individual attack bonuses

(Rule of thumb; drop the indicated amount to 8*x to get the average you should be capping at if you hit at about a 10. At least, that's my quick guess.)

[Barsoom]

All these calculations were already done. You're trying to reinvent the wheel. Google "power attack calculator"

[A_S]

Ah, I understand what you're saying. Yeah, cool.

There's so many ways of getting "guaranteed" hits (touch attacks, flat-footed opponents, True Strike, etc., which are all gonna lead to 95% edge case scenarios) that I think it's still often gonna be a worthwhile feat investment, but good stuff to know anyway.

And, come on, it's always more fun to do the calculations yourself than just look them up :P .

[Amechra]

I know about the power attack calculator; they just tell you what amount to power attack for, they don't tell you when you should stop bothering.

Plus, this was pretty much a side effect of trying to figure out crit multiplier/threat range/attack bonus/damage bonus equivalencies, which also revealed that, unless your first attack in a full attack would only succeed on a 17 or better, it will pretty much always be a better idea to use FoB/Rapid Shot/Whirling Frenzy/Snap Kick.

[TuggyNE]

I know about the power attack calculator; they just tell you what amount to power attack for, they don't tell you when you should stop bothering.

Sure they do, it's when it says "-0 Power Attack" a lot (or whatever).

Still, nothing wrong with running the numbers yourself to get a better idea of how things work.