D&D 3E/3.5 Statistical Analysis of 3.5 Power-Attack: UNDERpowered?

[Halivar]

I developed a program to do this. It's written in Delphi, so if you want it, let me know.

Ok, folks, with a random distribution of dice rolls, covering 5000 rounds per calculation, using my lvl 17 fighter with a greatsword and improved crit., and STR bonus of +7, 4 attacks a round:

First off, let's do vs. AC 20, no fancy stuff:
+27 2d6+18 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 3.545
Damage per Round: 129.1246

With 3.0 Power Attack:
+20 2d6+25 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 2.6428
Damage per Round: 134.8626

More damage... no surprise there. What about 3.5 power attack?
+20 2d6+32 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 2.665
Damage per Round: 167.0366
Pretty awesome. +30 damage a round is very nice. One prob... at CR 17 you'll be hard pressed to find AC less than...

AC 25. Plain vanilla attack:
+27 2d6+18 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 2.9454
Damage per Round: 113.6628

With 3.0 Power Attack:
+20 2d6+25 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 1.7046
Damage per Round: 95.9444
A little less. In general, I think we all knew that Power-Attack falls apart against higher AC opponents.

Now 3.5 Power Attack:
+20 2d6+32 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 1.6874
Damage per Round: 115.842
Hrmm... this feat yields 2 more damage per round. Is that worth a FEAT?

Here's where is all falls apart. I frequently run across AC 30 NPC's. First, vanilla swing:
+27 2d6+18 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 2.0696
Damage per Round: 89.275

3.0 Power Attack:
+20 2d6+25 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 0.9
Damage per Round: 57.0042
At this point, PA is completely worthless.

Can 3.5 fix the worthlessness of this feat? Will the extra damage bonus offset the fact that I don't hit enough? Let's see:
+20 2d6+32 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 0.909
Damage per Round: 70.3216
No. Using +7 Power-Attack (3.5) against AC 30, I lose 30 points of damage a round.

In short, PA is a worthless feat, at least for my character. 3.5 PA continues to be worthless, and is not over-powered.

Can anyone tell me how I could be misinterpretting the data?

If you have any data-sets you like me to run through, let me know.

 

[Storminator]

Things to consider:

1) use a variety of power attack numbers, not just 7

2) use power attack on single attack rounds. Power attack is great when you charge. You only get one attack, and it's likely to hit since its at your full BAB.

PS

 

[Enceladus]

In short, PA is a worthless feat, at least for my character. 3.5 PA continues to be worthless, and is not over-powered.

In short you need to go back to the drawing board with your program. Our party's barbarian uses PA to devistating effect. I hate that feat.

 

[EricNoah]

You know that pithy little saying "If it doesn't fit, you must acquit?" Well my saying is "If it has math, it goes in Rules." I know, I know, it doesn't rhyme....

 

[Halivar]

Well, the effect of picking a "middle number" between +0 and +7 is pretty predictable, since it's a linear progression of damage.

As for the charging thing; yes, that is very true, and I should have thought of that. Perhaps I have been using PA wrong, since the feat itself seems to indicate wild, unfocused energy being put into the swing.

But that pretty much limits the usefulness of PA to once in a combat (unless you disengage and charge in again).

Let's look at just one attack per round (I used =7, but remember it's a linear progression):

Following the same non-PA, 3.0 PA, 3.5 PA sequence:
+27 2d6+18 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 1
Damage per Round: 35.3458

+20 2d6+25 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 1
Damage per Round: 44.937

+20 2d6+32 vs. AC:20 Crit. 17-20 x2:
Hits per Round: 1
Damage per Round: 55.0014

+27 2d6+18 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 1
Damage per Round: 34.87

+20 2d6+25 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 0.8068
Damage per Round: 38.2812

+20 2d6+32 vs. AC:25 Crit. 17-20 x2:
Hits per Round: 0.8034
Damage per Round: 46.9394

+27 2d6+18 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 0.8976
Damage per Round: 32.1486

+20 2d6+25 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 0.5444
Damage per Round: 30.103

+20 2d6+32 vs. AC:30 Crit. 17-20 x2:
Hits per Round: 0.5492
Damage per Round: 36.9216

Notice against AC 30, we still only net 4 extra damage per round with 3.5 PA, while we lose 2 with 3.0 PA. 3.5 PA, however, does much nicer against AC 25.

EDIT: Thanks, Noah, you're right.

 

[Storminator]

Well, the effect of picking a "middle number" between +0 and +7 is pretty predictable, since it's a linear progression of damage.

<SNIP>

You'd think that, but it's wrong.

PA effects the damage, and it effects the probability to hit. Average damage is the product of damage and hit probability, so PA effects your average damage twice, and the resultant average damage is a quadratic function of PA number.

Run some cases and plot average damage against power attack number. It ain't a straight line.

PS

 

[Kid Charlemagne]

I don't think this should come as too much of a surprise. I'v played two fighters of 12th level who used PA, and you have to use if judiciously to make it useful.

Against high- AC opponents the negative to your to hit means you should only use it when you're in a one-attack situation (closing to meet the enemy, striking and moving, possible cleave/great cleave combo). Otherwise, losing the second (or more likely) third attack roll in a full-round attack is a big loss - especially if your PC is built to get more frequent criticals, as both of mine were (one on a 12-20 range with a scimitar, the other a 17-20 range with greatsword).

 

[Halivar]

Wow. Talk about a surprise. I ran some lower stats, with 1 attack per round, and +1 increments of Power Attack.

It would *appear* as if subtracting one from the attack and adding it to damage is self-balancing. But why, in the above calculations, do the power attack numbers increase damage. I think it may be that I was playing with a crit. range of 17-20, which exaggerates the effect of PA by sometimes counting it twice. Here I did 19-20:

+20 2d6+10 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.803
Damage per Round: 15.274

+19 2d6+11 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.769
Damage per Round: 15.505

+18 2d6+12 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.714
Damage per Round: 15.114

+17 2d6+13 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.658
Damage per Round: 15.027

+16 2d6+14 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.605
Damage per Round: 14.903

+15 2d6+15 vs. AC:25 Crit. 19-20 x2:
Hits per Round: 0.55
Damage per Round: 14.084

The effect is pretty consistant (14-15 damage). The difference is that more damage is front -loaded onto your first few attacks. If your're playing with massive damage rules, this can be a significant plus.

 

[Someone]

I did the math once, and ends on the following: you should Power Attack until the expected average damage (including power attack damage) equals the chance of hitting (that is, if you hit with 17,18,19 and 20 that´s 4 numbers out of 20)

That on a single attack. If you make a full attack, I think you had to take the average of the chance of hitting, but I´m not sure.

The conclusion is interesting. If your average damage is 19 per hit(not very hard; say a Str 18 fighter with a +1 flaming greatsword´s damage is 8(weapon) + 6 (strenght) +2(specialization) +3,5 (flaming) = 19,5 and that even without considering criticals) never should power attack unless he would hit rolling a 1 or less.

Also note that the less damage you deal, the more you should power attack. The feat benefits more combatants with low damage per hit; in 3.5, you should get power attack if you fight with one handed weapon and shield, but for 2 handed fighter it quickly lose usefulness unless you fight foes with very low ACs.

 

[Sejs]

I'll try be short and to the point: Power Attack is situational - don't sacrifice more to-hit than you can stand to lose, given the AC of your opponent. Don't PA right off the bat, until you suss out what the other guy's approximate AC is. When PAing, always stack as many favorable to-hit bonuses from other sources, that you can channel into damage. Rage is ideal for PAing, because you can make the to-hit bonus from increased strength do double duty for damage.


3.5ed Barbarian/11. Greater Rage (+6str, +6con). Using a greatsword - When raging, strength mod goes up by +3, modifying to-hit, and damage. 3.5PA w/ 2h weapon can in turn change the +3 to-hit into an additional +6 damage. So either +3 hit / +3 damage, or +0 hit / +9 damage. Additional to-hit mods, such as Flanking (+2), Charge (+2), Bless (+1), Opponent Prone (+4), and Inspire Courage (+1 and up) can all make for much more aggressive power attacking with no functional reduction in ability to land hits successfully.

The Knock-down feat, previously seen as rather lackluster due to it not allowing for the normal Improved Trip follow up attack, becomes much more attractive with 3.5 PA when used with a 2h weapon. You are almost guarenteed to meet the minimum damage requirements to trigger a trip, there's no penalty to failure, and if successful, you can channel 4 more points of to-hit into damage.