Maximizing the yield of Power Attack... a formula!

[DracoSuave]

If the opponent's defense against your attack is less than:

19 + your bonus to hit that enemy - (twice the average damage of the attack divided by the bonus damage you get from Power attack)

Then using Power Attack is optimal. Otherwise, do not use Power Attack.

With one handed weapons:

D < 19 + A - x

With two handed weapons:

D < 19 + A - 2x/3

Where D is the defense of the opponent, A is the attack bonus with the attack before Power Attacking, and x is the average damage the attack does on a normal, non-critical hit.

Critical hit damage factors out of the inequation, and it is irrelevent to Power Attack's efficacy.

MATH FOLLOWS

This uses my ED20 calculation system for mean damage for 20 attacks.

r is number of outcomes on a d20 that register hits.
x is the mean damage from the dice of a normal hit.
b is the static bonus damage.
k is the number of outcomes on a d20 that register critical hits.
c is the maximum damage of the dice from a critical hit
d is the mean damage from the bonus dice from a critical hit.

(r)(x+b)+(k)(c-x+d) < (r-2)(x+b+n)+(k)(c-x+d)
[subtract k(c-x+d) from both sides]
rx+rb < rx+rb+rn-2(x+b)+2n

0 < rn-2(x+b)-2n

2(x+b)+2n < rn

(2x+2b)/n + 2 < r
(2x+2b)/n + 2 < 21-R (R is the number you need to roll on the die to hit)
R < 19-(2x+2b)/n
D-A < 19-(2x+2b)/n (D is the defense, A is the attack bonus)

D < 19+A-2d/n (d is the mean damage for the attack, including bonus to damage)


Why do I use a system based on damage over 20 hits and not DPR? Because damage over 20 hits makes for simpler more elegant math using concepts people actually -game- with. Numbers to hit targets. Damage die rolls. Bonus damage. Critical hit damage... it's all added up. If you want to find the mean DPR for an attack calculated by the ED20 (Expected Damage over 20) formulae, you just divide by 20. But for most comparisons, ED20 works better, and allows for the derivation of formulas where you plug in the numbers, and blammo, get an answer for when something is favorable.

 

[Oompa]

Ok.. but i dont know the ac of the monster.. so how i know when to use it?

 

[DracoSuave]

Here's an example. Let's say you're a sword and board fighter wielding a longsword and a shield, you're level 1 with 18 strength, and you've got weapon focus longsword.

Your attack bonus is +4(str)+3(prof)+1(fighter) for a total of +8.

Your damage for the attack pre-power attack is 1d8+5, which becomes 9.5 mean damage on a hit.

D < 19 + 8 - 9.5

If the enemy's AC is greater than 18.5 (greater than or equal to 19 in practice), Power Attack is not optimal.

You can figure out the AC by trial and error. Subtract your attack bonus from the AC threshold. 19-8 = 11. If you're finding yourself missing the opponent with rolls of 11 or above without Power Attack, or with 13 or above -with- Power Attack, it is not optimal to Power Attack.

 

[Bluewyrm]

So, is this accurate?

Heroic tier, with one handed weapons:
D < 19 + A - x

Heroic tier, with two handed weapons:
D < 19 + A - 2x/3

Paragon tier, with one handed weapons:
D < 19 + A - x/2

Paragon tier, with two handed weapons:
D < 19 + A - x/3

Epic tier, with one handed weapons:
D < 19 + A - x/3

Epic tier, with two handed weapons:
D < 19 + A - 2x/9

 

[Goumindong]

Ok.. but i dont know the ac of the monster.. so how i know when to use it?

You can guess based on the type of monster. Soldiers are likely to have High AC. Brutes, skirmishers, artillery are likely to have lower AC. Controllers will be in the middle.

Another good basic idea is "Are you a fighter making an OA with either decent wisdom or combat reflexes/blade opportunity?" If you answer "yes" to that question then power attack is beneficial. Especially if you have a two handed weapon.

Never Power Attack with an encounter or daily power.

Also don't forget adding 2 for CA

 

[Cadfan]

Actually, since you're basically never going to be using a straight attack action, this needs adjusted. A character with Reaping Strike is going to do partial damage on a miss, for example, so he's less concerned about accuracy than he otherwise would be. His sister who took Cleave does extra damage on a hit, so a loss in accuracy penalizes her more heavily.

 

[DracoSuave]

Actually, since you're basically never going to be using a straight attack action, this needs adjusted. A character with Reaping Strike is going to do partial damage on a miss, for example, so he's less concerned about accuracy than he otherwise would be. His sister who took Cleave does extra damage on a hit, so a loss in accuracy penalizes her more heavily.

It's easily adjusted for various at-wills.

Reaping Strike does strength damage whether you hit or miss, which means that miss damage is no longer relevant to the damage inequation.

D < 19 + A - x + m where m is the miss damage.

Cleave is extra damage attached to a hit, so it would simply be added on to x.

D < 19 + A - (x + c) where c is the cleave damage

 

[Stalker0]

It be interesting to combine this with the monster data from the MM, and determine how useful power attack would be overall.

 

[DracoSuave]

It be interesting to combine this with the monster data from the MM, and determine how useful power attack would be overall.

It's ironicly less useful the larger your weapon damage is. But given the average damage of a weapon, you could simply plug in the numbers, and compare.

That's well beyond the scope of what I'm willing to do, however.

 

[ac_noj]

It be interesting to combine this with the monster data from the MM, and determine how useful power attack would be overall.

I did a couple of comparisons and the gist of it is that it's usually useful so long as you're:

A) Not attacking a soldier or higher level monster and

B) Don't get some bonus effect for hitting

Since B happens a lot, I'm going to save my feat for something that is always good.