Power Attack and Statistics

[trentonjoe]

Here is the character:

Dwarven Fighter 9/Bard3
BAB:+11
Attack Bonus with Battle Axe: +21/+16/+11
(11BAB+6 STR+3magic weapon+1 Weapon Focus)
Damage:1-8 +14 (19/x3)

Now, when is it advantagous to power attack? AC's under 23? 20? 15?

I used to Power attack all the time (for anywhere between 6 and 10) but I just got the third attack.

Any suggestions? Is there a simple math formula to help?

Thanks!

 

[Petrosian]

your to hit chance, hits out of 20, needs to be higher than youe average damage in order for power attack to begin to help.

that should give you the AC to begin considering PA.

to figure out the shift that will give you the most benefit, cut H-D (hit chances in 20 minum the average damage before power attack) in half. So if the chances in 20 for a hit are 16 and your average damage is 12, 16-12 is 4 divided by 2 is 2... shift 2 to power attack.

 

[Zenon]

your to hit chance, hits out of 20, needs to be higher than youe average damage in order for power attack to begin to help.

that should give you the AC to begin considering PA.

to figure out the shift that will give you the most benefit, cut H-D (hit chances in 20 minum the average damage before power attack) in half. So if the chances in 20 for a hit are 16 and your average damage is 12, 16-12 is 4 divided by 2 is 2... shift 2 to power attack.

Interesting formula! Did you do some math on it? Does it stand up? (I'm being serious here, I just re-read it and it sounds like I'm being a jerk. I'm not, I'm curious how you arrived at it, and if you've tested it...I have a fighter with PA and always have trouble knowing when to use it.)

 

[Cheiromancer]

I read somewhere that the best amount of power attack to take is given by

P = (47-5N-2D)/4 -T/2

Where N is the number of attacks, D is the average damage per attack, and T is the target number (the number you need to hit your opponent's AC).

So for you, N would be 3, D would be 18.5 (ignoring criticals).

I get P = -5 - T/2

Since the target number is

T= AC - attack bonus

and your attack bonus is 21, we can substitute and solve for P.

I get P = 9.25 - AC/2

Which means that you should only use power attack against critters whose AC is worse than 16. For every 2 full points below AC 18, add +1 to the power attack. So P= +1 against AC 16, +2 against AC 14, and so on.

As your average damage and number of attacks goes up, the optimal amount of power attacking goes down.

edit: criticals were messed up. I took them out.
edit 2: forget to divide by 4 in an important step.

 

[Celebrim]

To keep it simple, ignoring the effects of critical hits, the test is:

If (Avg_Damage * (chancehit_1st_attack+chancehit_2nd_attack+...) < Avg_Damage+Power_Attack * (chancehit_1st_powerattack+chancehit_2nd_powerattack+...)) then Power_Attack(Foe)

In your case, it is clear to me that you don't want to power attack a foe with 20 or 23 AC. I suspect you'll do a little good to power attack a foe with 15 AC if you don't go overboard.

Let's suppose you drop 3-10 into power attack.

Your average damage sans power attack vs. an AC 15 foe is:

18.5*(.95+.95+.85)=50.875

Your 3 point power attack gives you:

21.5*(.95+.95+.7)=55.9

Your 5 point power attack gives you:

23.5*(.95+.85+.6)=56.4

Your 6 point power attack gives you:

24.5*(.95+.8+.55)=56.35

Now that the damage dropped, we don't really need to go further than this, but just to show you what happens:

Your 7 point power attack gives you:

25.5*(.95+.75+.5)=56.1

Your 10 point power attack gives you:

28.5*(.8+.6+.35)=49.875

I've never tried to work out a formula for max damage to calculate how much you want to power attack in a given situation, but in general I find <= 5 works well unless you know you can't miss. I'd love to see a calculation, but I suspect it would be too involved for routine use anyway.

I also suspect that once the effects of criticals are accounted for, power attacking is made even weaker because your latter attacks are more likely to critical if you don't power attack. This is especially true because your axe can already provoke a massive damage save on most rolls without power attacking. When in doubt, don't power attack.

PS: I was composing this message when Petrosian and Cheiromancer were posting and so didn't read their posts until afterwards. I suspect that the calculations they are using are either wrong or else being misused, since clearly you can increase average damage (as shown above) against targets with AC > 13 and with > +2 power attack.

 

[Jens]

It sounds very reasonable (as in I agree.. at leats until I have thought some more about crits )

You can think of expected damage as the area of a square with sides equal to your chance to hit and your damage on a hit:

ExpDam = Chance * Damage

Here Chance is the <number of sides on d20 that his> divided by 20 so it equals

= Sides / 20 * Damage = (Sides * Damage)/20

and to maximize the area of Sides*Damage while keeping Sides+Damage konstant, the two must be equal, which you do by petrosian's formula. (Edit: I state my rule of thumb as Sides = Damage since I find that easy to remember and fairly easy to figure out. Ex: I do 8 damage including crits and hit on 9+. That's 12 sides so I should PA by 2.)

When you've got multiple attacks you should use your average number of 'Sides'. And you should pretty much always PA when you only miss on 1s or only hit on 20s.

(Note: What about crits, by the way? Should they be accounted for in Damage or not? PA damage is multiplied on crits...)

 

[Zenon]

I also suspect that once the effects of criticals are accounted for, power attacking is made even weaker because your latter attacks are more likely to critical if you don't power attack. This is especially true because your axe can already provoke a massive damage save on most rolls without power attacking. When in doubt, don't power attack.

I usually find this is the case. Considering that the PA applies to all of your attacks (including AoOs, Cleaves, etc) until next round I find I hardly ever use it unless the situation is a "sure thing" to hit.

 

[Jens]

Actually, crits may make PA stronger. PA damage is multiplied on crits so you get more that 1-for-1, usually at least 1.1-for-1.

I think the main problem in making a general formula is that with multiple attacks, you often have almost sure hits or misses. The almost certain hits against AC 15 is the reason why trentonjoe should use PA in his example.

Edit: AoOs should make PA stronger since the highest attack bonus is used. In effect the highest number of sides that will hit should have double weight in the average if you expect to get an AoO, and even more if you expect to get more than one. Cleave is more tricky because it's difficult to predict which of your iterative attacks drops an opponent (and hence should have extra weight). Great Cleave makes this problem worse. But in all situations there is one (or two ) amount that is optimal to invest in PA. Sometimes it's just very difficult to determine

 

[Celebrim]

I thought I'd do a brief critical hit update, just to test my initial suspicions.

Your average damage against AC 15 including criticals is:

18.5*(.95+.95+.85) + 37*(.095+.095+.085)=61.05

Note that this is just over 10 damage higher than the calculation for without criticals.

If you drop 5 into power attack your average damage is:

23.5*(.95+.85+.6) + 47*(.095+.085+.060)=67.28

This is just over 11 damage higher than the calculation for without criticals. This means that my initial suspicions are false.

If you drop 6 into power attack your average damage is:

24.5*(.95+.8+.55) + 49*(.095+.080+.055)=67.62

So in fact, criticals (at least x3 or higher criticals) help power attacking, if ever so slightly.

 

[Jens]

Celebrim, I think you give crits too much credit. The chance to crit gives 'normal weapons' (those with 20/x3 or 19-20/x2 crit types) exactly 10% extra damage assuming that a hit is made and all damage is multiplied and that all threats are hits. (Those with 20/x2 give 5% and those with 20/x4 or 18-20/x2 give 15%.)

(I think you let it add 20%. Did I miss Improved Critical or Keen or something?)