Math of Power Attack

[shadow_archmagi]

I'm bored, and it's been awhile since I had a stats class so this is good practice for me, and maybe this is new information to some people.

Power Attack lets you trade BAB for damage, at a 2-1 ratio if you're using a two handed weapon (For this reason, everyone uses a two handed weapon.) You can choose how much BAB you trade on each attack, which raises the question "How much BAB should I choose?"

Here's the math that'll get you closer to answering that question.

First off, let's take an example character, Jeremy Barbarian. He's level 5, so he has 5 BAB, and he also has a strength score of 18 and a +1 greataxe.

So on a normal attack, he's rolling 5 BAB+4 STR+1 Magic for a total of +10 to hit, and dealing 1d12+7 (Avg of 13) damage (remember you get your strength to damage normally, and then with a two handed weapon you get 50% of your strength again as a bonus, so a +4 becomes a +6. Then the weapon is still magic so that's another +1)

Now then, if he power attacks for full, he's looking at an extra 10 damage- 1d12+17 (avg of 23). He's nearly doubled his damage output, but at the cost of halving his accuracy. (Specifically, his damage output is ~77% higher)

Well-

That's where things get tricky. He's only halved his accuracy in absolute terms- depending on the enemy's AC, the relevant fraction could be almost anything. Think about it this way.

Let's say that when you compare his to-hit with the enemy's AC, the red numbers represent attacks that won't hit, and the blue ones attacks that will.

If we assume the enemy has 20 AC, then we get this breakdown:

(With power attack)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6/20 odds is 30%

(Without power attack)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11/20 odds is 55%

So now we multiply his accuracy by his actual damage to get an estimate of how much damage per round he's going to do over the course of the fight. (If he only hits on one round in ten, then we average that to figure he's doing 1/10th of his damage every round.)

30% of 23 is 6.9
55% of 13 is 7.15

So on the first round of the fight, Jeremy isn't very likely to hit with a power attack, and actually loses a (in a statistically average world) a fourth of a point of damage by doing so.

Then in the next round, his ally Susan is standing on the far side of his opponent, providing a flanking bonus, (+2) and Jeremy flies into a barbarian rage (+2), and the cleric Harold uses Bless. (+1) Now our breakdown looks like this.

(with power attack)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11/20 is 55%
(Without power attack)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
16/20 is 80%

Now we have 55% of 23 (12.65)
Versus 80% of 13 (10.4)

In the second round of combat, Jeremy is going to have a much easier time hitting the opponent, so Power Attack will give him two and a fifth points more damage over the course of his lifetime.

Do you understand why it was a smart move one round, and not the other?

In the first round, he was looking at hitting on an 11, versus hitting on a 6. 11 divided by 6 is 1.83- In round one, Regular Attacking Jeremy was 83% more accurate than Power Attacking Jeremy, who tried to compensate by dealing 77% more damage. In round two he was hitting on 16 versus 11, so Regular Attacking Jeremy was only 45% more accurate than him, while Power Attacking Jeremy was still dealing 77% more damage.

So the math that you need to do on a regular basis is:

(Number I need to roll to hit) Divided By (Number I need to roll to hit with power attack)

versus

(Damage I do with power attack) Divided By (Damage I normally do)

If the top number is bigger, then you shouldn't power attack because it's better to be accurate. Of course, this system only works if you know your opponent's AC! Most of the time, you won't, so you'll have to take your best guess based on the DM's descriptions of opponents.

[mucco]

Bottom line: if you hit easily, use PA.

Can you elaborate and find out how much one should PA for, in various situations?

[Eonir]

But then you take Shocktrooper so you can subtract your AC instead of your BAB on a PA on a charge :D

[shadow_archmagi]

Bottom line: if you hit easily, use PA.

Can you elaborate and find out how much one should PA for, in various situations?

That's what the formula on the bottom is for.



(Number I need to roll to hit) Divided By (Number I need to roll to hit with power attack)

versus

(Damage I do with power attack) Divided By (Damage I normally do)


You should be able to plug in your damage at any given time and compare it to your odds of hitting and thus determine whether Accuracy (the top) or Power (the bottom) is better in any given situation. It'll vary greatly depending on your build. (A build that has high strength or sneak attack won't benefit as much from power attack, because it won't be as high a percentage of total damage.)

EDIT: this chart (http://www.giantitp.com/forums/showthread.php?t=172050) may be helpful for determining whether to power attack an unknown opponent.

[ericgrau]

I did something like this a while back.
http://www.giantitp.com/forums/showthread.php?t=87339

I found power attack is mostly only worth it with shock trooper or leap attack. At low levels PA alone seems best to blow 2 to 4 attack bonus. Once you get multiple attacks and your average attack bonus goes down PA alone is only useful for single attacks or when you hit on a 2. At higher levels PA alone is only useful when you hit on a 2 (and then only enough that you still hit on a 2). Once I subtract the lost damage from the attack penalty it peaked at +3 damage in the very most ideal situation and averaged about +1 damage in most cases until higher levels where it caused a negative change in damage (unless you can auto hit on a 2).

So in short in core it's a situational feat that's not usually (but sometimes) worth it in general compared to other feats, even for THFers. When you do get it in core only you do -2 to -4 low level or mid level single attacks, or at other levels only enough to still hit on a 2 (including secondary attacks). Out of core you can boost it enough to make it essential for every THFer.

[shadow_archmagi]

I did something like this a while back.
http://www.giantitp.com/forums/showthread.php?t=87339


I figured it had been done before, but I thought I'd enjoy the thought exercise and maybe inform a couple people. I was surprised to find out that Core power attack wasn't great, though!

[Particle_Man]

There is also the matter of DR. If you can't beat the DR and are doing 0 damage without PA, then you would benefit from PA in beating the DR.

[Gnome Alone]

I'm currently playing a duskblade, and some of my favorite words in the universe at the moment are "I quick cast true strike."

And my other favorite words are "...and Power Attack for full and arcane channel Vampiric Touch."

[Eldariel]

This tool (http://donjon.bin.sh/d20/power/) does the math for you (though it doesn't go with TWF). Basically, the more attack bonuses you have, the better PA gets. In Core, as long as you are using Trip, Flank or Charge (or any other single attack scenario), you can generally afford to PA quite heavily.

The math suggests that a fully buffed level 20 Barbarian can afford to PA for 17-18 against a Balor. True Strike of course also makes for PA for 20. You can generally PA enough that your first attack hits on 2 and net damage. Of course, if there are no buffs in play, the numbers are far more modest.

And much depends on the exact opponents too; stock Balor isn't high AC but a Great Wyrm with its wealth and spells used defensively is a different story.

[imneuromancer]

Power Attack Full or go home, that's my motto.

[Zherog]

I found power attack is mostly only worth it with shock trooper or leap attack. At low levels PA alone seems best to blow 2 to 4 attack bonus. Once you get multiple attacks and your average attack bonus goes down PA alone is only useful for single attacks or when you hit on a 2. At higher levels PA alone is only useful when you hit on a 2 (and then only enough that you still hit on a 2). Once I subtract the lost damage from the attack penalty it peaked at +3 damage in the very most ideal situation and averaged about +1 damage in most cases until higher levels where it caused a negative change in damage (unless you can auto hit on a 2).

You should also full Power Attack if you need to roll a 20 to hit the target, because in that situation reducing your attack total has no effect.

Of course, if you're actually in that situation, you probably ought to be making a hasty retreat and/or throwing your PHB at the DM...

[Nich_Critic]

I like power attack when I can get a touch attack vs a heavily armored foe, or a flat footed attack vs a high dex foe. In either case the equation is the same. You're trying to turn excess attack bonuses, which would otherwise be wasted, into damage.

Another way I like to think about it, for back of the envelope calculations, is how much would I power attack if I knew I was going to roll a 10? That gives me roughly 50/50 chance to hit on the power attack, if I guessed the enemy's ac correctly (and you can usually guess, depending on your level, their visible gear, party know-it-all's knowledge check, etc.). You can scale up or down from there, depending on whether you value hitting or damage (you don't power attack vs enemies you know to have less health then normal damage you do, but you might value a chance of dropping them in one turn over a guaranteed two turn kill).

[Particle_Man]

You should also full Power Attack if you need to roll a 20 to hit the target, because in that situation reducing your attack total has no effect.

And bring out your Vorpal sword, because, hey, why not? :smallcool::smallcool:

[Gwendol]

http://donjon.bin.sh/d20/power/

Here's a calculator I use a lot. Very handy, and does account for some various situations.

[Particle_Man]

Speaking of which, there are some cases (like a stance in ToB) where you can control what you roll (like guarantee an 11) and in that case, if you know what your target number is, you can precisely fine-tune power attack to maximize damage.

[Adamantrue]

I made a spreadsheet a while back to try and find the "sweet spot" of a Power Attack. I uploaded a Google Doc version HERE (https://docs.google.com/spreadsheet/ccc?key=0AkMd7HwFURxIdFo1YzA2THFmRXZhU2NfaTc2VlJvd lE).

I believe that version doesn't factor in critical hits, though.

[darkelf]

This tool (http://donjon.bin.sh/d20/power/) does the math for you (though it doesn't go with TWF).

is there anyone who does both TWF and PA? they're kind of opposite builds.
but i'll add it to the to-do list.

[Darth Stabber]

That math is really only useful in core. If you are using it(not just having the feat as a prereq for something), chances are you have shocktrooper. Also leap attack throws your math off a lot, as does Frenzied Berserker's PA ratio increase.

Leap Attack - favors more PA
Shocktrooper - PA = BAB
Frenzied Berserker - favors more PA

If you combine all three and you still have an AC higher than 10 on the round after a charge, you're doing something weird.

[Eldariel]

is there anyone who does both TWF and PA? they're kind of opposite builds.
but i'll add it to the to-do list.

Revenant Blade, significantly, two-handed PAs with both weapons. Builds using Unarmed Strikes as secondary also have primary two-handed and secondary one-handed PA returns. Then there are some fringe builds with one-handed PA on both weapons (and I guess some builds might have PA as a prerequisite who TWF and don't expect to use it but can, with one-handed and no-returns).


That math is really only useful in core. If you are using it(not just having the feat as a prereq for something), chances are you have shocktrooper. Also leap attack throws your math off a lot, as does Frenzied Berserker's PA ratio increase.

Leap Attack - favors more PA
Shocktrooper - PA = BAB
Frenzied Berserker - favors more PA

If you combine all three and you still have an AC higher than 10 on the round after a charge, you're doing something weird.

Well, there are cases like many Cleric-builds and Gish-builds that don't have the feats for Shock Trooper-line, but can still use PA as a massive damage increase thanks to their natural To Hit boosts; it's useful for those.

[Greenish]

I was surprised to find out that Core power attack wasn't great, though!Well, ericgrau has been saying that for quite a while.


Speaking of which, there are some cases (like a stance in ToB) where you can control what you roll (like guarantee an 11) and in that case, if you know what your target number is, you can precisely fine-tune power attack to maximize damage.The ToB stance being 1/round, the best use would be with a high-damage maneuver.

Maneuvers in general, being made at highest attack bonus (and often a bit on top) tend to favour PA.

[candycorn]

Used to have a spreadsheet that calculated optimal power attack between +0 and +20, based on target's AC, your net attack bonus, miss chances (concealment, blink, etc), and critical hit chance and multiplier.

Each item was an entry at the top, so factoring flanking was as simple as changing your attack bonus cell from +18 to +20.

Can't remember what I did with it though. I could probably rebuild it, but it would take a while. As I recall, there were a LOT of cells being used.

[Gwendol]

Or you can use the web- tool I linked to above.

[GreenSerpent]

is there anyone who does both TWF and PA? they're kind of opposite builds.
but i'll add it to the to-do list.

Diopsids. They get 2-handed weapons in each arm, full benefits of each as a 2-handed weapon, the ability to qualify without the DEX requirements for the Two-Weapon Fighting feats.

Currently I'm making a Leap Attacking Shock Trooper Pouncing Diopsid Barbarian/Fighter/Frenzied Berserker. I forsee destruction on a gigantic scale.

[Ravens_cry]

The rules make for a funky bell curve as you want to generally Power Attack less and less as the number you need to roll to hit gets higher and higher, until you need a 20, in which case pile on the Power Attack.
It makes an interesting shape is all.

[shadow_archmagi]

That math is really only useful in core. If you are using it(not just having the feat as a prereq for something), chances are you have shocktrooper. Also leap attack throws your math off a lot, as does Frenzied Berserker's PA ratio increase.

Leap Attack - favors more PA
Shocktrooper - PA = BAB
Frenzied Berserker - favors more PA

If you combine all three and you still have an AC higher than 10 on the round after a charge, you're doing something weird.

The formula I posted at the bottom (Accuracy vs Damage) should work regardless of how much power attack you're getting. If you're getting eighteen points of damage per point of BAB, then you should always see power attack boosting your damage output by much more than it's reducing it via accuracy losses.

[Person_Man]

There is always an optimal Power Attack ratio.

Expected damage = Average Damage * Probability of hitting.

If you don't have Shock Trooper, then you can keep one of the Power Attack calculators open on your laptop or smart phone, or just print out a chart. Keep track of what everyone rolls during combat, which will give you a good indicator as to each enemy's AC and hit points. After a while of doing this, you'll probably be able to guess most enemy's AC, and will get a good feel for how much your character should Power Attack each time.

If you do have Shock Trooper, then it is always optimal (at least in terms of expected damage) for you to use maximum Power Attack, unless you believe that your enemy has fewer hit points then your minimum damage. To mitigate your low AC, pick up defenses that are not reliant on it, such as battlefield control, a miss chance, Deflect/Block arrows, etc.

[eggs]

Without Wraithstrike/Shocktrooper/&c., Power Attack is pretty crummy on full attacks, but even in Core it's worthwhile. PA's real use is in standard action/charge attacks and AoOs, which are often the only attacks permitted to nonmagical melee, where low iterative attack bonuses don't penalize large PA penalties, and where the melee-types normally struggle to generate meaningful damage.

[Thrawn183]

The real key to using power attack (outside of leap attack/shock trooper, of course) is anything that give a to-hit bonus, but not bonus damage. It also works well if you have any way of debuffing an enemy's AC. Anything from stunning, to knocking them prone to blinding them.

Power Attack is also surprisingly useful against certain types of enemies. Oozes in particular have buckets of HP for their AC. Many hit die advanced enemies also have relatively low AC compared to their HP.

A fully advanced Tyrannosaurus (putting stat boosts into con instead of strength, admittedly) will have 729 HP with an AC of 18 at a CR of 21. You're really going to want some power attack to put out enough damage to drop that thing.

Lastly, you can do fun things like build a character that uses weapon finesse on a spiked chain or elven courtblade. By intentionally building less bonus damage from strength, you can make power attack much more attractive.

[Coidzor]

Indeed, Bards are a Power Attacker's best friends. :smallbiggrin:

[JackRackham]

There's also the matter of tactics and how many hp you believe the enemy to have. Really, the exact amount of damage is irrelevant. What is relevant is how many rounds it takes to neutralise the enemy. So, if you can't one-round the enemy without power attack and your average damage-per-round using that formula is at least half the opponent's hp with or without power attacking, you're better off power attacking, as a chance of one-shotting him, given the probability that he'll last two rounds without power attack, is better than nothing.

For example, if you hit 55% of the time with power attack and do enough to one-round the enemy, but you hit 70% without it and fall 7 or 8 damage short, power attack is the better option.

[Godskook]

is there anyone who does both TWF and PA? they're kind of opposite builds.
but i'll add it to the to-do list.

There's a way to be a TWF+PA build. *EXACTLY* one way to my knowledge, and its Revenant Blade. Basically, you start as a Str-focused skimish build, lag a little through the prestige class and then turn into a combat monster.

[tyckspoon]

There's a way to be a TWF+PA build. *EXACTLY* one way to my knowledge, and its Revenant Blade. Basically, you start as a Str-focused skimish build, lag a little through the prestige class and then turn into a combat monster.

Anything with a sufficient number of arms can do it too, although Revenant Blades still do it better. Thri-kreen of course, it's pretty much the entire reason to be a Diopsid (Dragon Compendium, they have four arms but two of them aren't fully developed so they're not good for wielding a weapon independently), and there's a few templates/spells/spell and item combos that can give you extra usable arms.

[Thespianus]

Maybe I'm not reading things right here, but it seems most posts ignore the PA penalty on subsequent hits in a Full Attack?

If you have three attacks, your PA penalty applies to all those attacks, and the penatly that seemed wise on the first attack might be stupid on the 3rd.

So you should also factor in the number of attacks you make in a round when selecting your PA-penalty.

The PA penatly remains until your next turn, so even AOO rolls get penalized for you using PA on your turn. Not sure if everyone reads that bit, so I just wanted to add this information in here :)

[GreenSerpent]

Anything with a sufficient number of arms can do it too, although Revenant Blades still do it better. Thri-kreen of course, it's pretty much the entire reason to be a Diopsid (Dragon Compendium, they have four arms but two of them aren't fully developed so they're not good for wielding a weapon independently), and there's a few templates/spells/spell and item combos that can give you extra usable arms.

From what I can tell of Revenant Blade it seems that the capstone ability is exactly the same as the Diopsid racial ability. You get to treat both ends of the Double Scimitar as a two-handed weapon? The Diopsid Extra Arms allows it to wield a two-handed weapon in one pair of arms and benefit from the benefits of wielding a two-handed weapon (1.5x STR modifier to damage etc.).

Seems that the Diopsid beats Revenant Blade then as it can wield whatever weapons it wants!
(although for an elf Revenant Blade looks magnificent!)

(on a side note, I'm currently playing a Diopsid who's a Spirit Lion Barbarian, going through Fighter to Frenzied Berserker. Leap Attack into the build. Oh dear - the damage is causing me trouble to calculate!)

[Thrawn183]

If you have three attacks, your PA penalty applies to all those attacks, and the penatly that seemed wise on the first attack might be stupid on the 3rd.

So you should also factor in the number of attacks you make in a round when selecting your PA-penalty.

The PA penatly remains until your next turn, so even AOO rolls get penalized for you using PA on your turn. Not sure if everyone reads that bit, so I just wanted to add this information in here :)

The more AoO's you make, the better for power attacking, as it decreases the percentage of the damage you're putting out from iterative attacks. Extra attacks from things like haste or a speed weapon also benefit power attacking by making iterative attacks matter less.

So, doing a little tiny bit of math crafting here to show the extreme ends of the spectrum gets us:
Unoptimized Barbarian 20: Large, 2 handed weapon (+5 guisarme of speed), 16 Str +2 racial +6 item +5 level +5 inherent +8 Rage = 42 Str. This comes out to 2d6+29 damage at +40/+40/+35/+30/+25 on a full round attack.

Optimal Power Attack vs...
Frost Giant Jarl (AC 29/CR 17):8
Pit Fiend (AC 40/CR 20): 2
Balor (AC 35/CR 20): 5
Nightcrawler (AC 35/CR 18): 5
Advanced Tyrannosaurus (AC 18/CR 21): 19
Titan (AC 38/CR 21): 4


Unoptimized Fighter 20 (Power Attacker): Small, +5 Elven Courtblade of Speed, 16 Dex +2 racial +6 item +5 inherent +5 level with Weapon Focus and Greater Weapon Focus. This comes out to 1d8+6 damage at +38/+38/+33/+28/+23.

Optimal Power Attack vs...
Frost Giant Jarl (AC 29/CR 17): 11
Pit Fiend (AC 40/CR 20): 5
Balor (AC 35/CR 20): 6
Nightcrawler (AC 35/CR 18): 6
Advanced Tyrannosaurus (AC 18/CR 21): 19
Titan (AC 38/CR 21): 6


Even with the Barbarian example, once you take into account a buff or two that adds a bonus to his attack rolls and maybe a small penalty to the enemy's AC, Power Attacking is really good against pretty much everything.

[Thespianus]

At level 20, the WBL-curve nets you a good amount of bonuses to strength (or dex) and makes PA more efficient. Even though I haven't run the numbers properly, if we're looking at a level 11 barbarian (BAB 11/6/1) , the benefit of Power Attacking on regular attacks goes down a bit.

Charging, and with Shock Trooper and Leap Attack, etc changes the field a bit, but mid level Core PA-builds aren't super awesome. Granted, almost no melee is great in Core-only.. ;)

[Eldariel]

At level 20, the WBL-curve nets you a good amount of bonuses to strength (or dex) and makes PA more efficient. Even though I haven't run the numbers properly, if we're looking at a level 11 barbarian (BAB 11/6/1) , the benefit of Power Attacking on regular attacks goes down a bit.

Charging, and with Shock Trooper and Leap Attack, etc changes the field a bit, but mid level Core PA-builds aren't super awesome. Granted, almost no melee is great in Core-only.. ;)

Like I said before though, combat modifiers like prone (if you e.g. Trip), higher ground and flanking can pretty much invariably be slammed into PA efficiently. And of course, flat-footedness against high Dex targets.

[Thespianus]

Like I said before though, combat modifiers like prone (if you e.g. Trip), higher ground and flanking can pretty much invariably be slammed into PA efficiently. And of course, flat-footedness against high Dex targets.
True. Intelligent maneuvering can remedy a lot of that.

[ericgrau]

Basically in core-only you can still take PA but you can't take the feat blindly nor use it blindly, especially on full attacks with enough secondary attacks screwing up your average attack bonus. But waiting for the right extremely low AC monsters, buffzilla-ing the fighter, situational combat modifiers, etc. let you PA under the right circumstances. I actually like splat-free PA better because it's not an automatic choice on every melee but it's sometimes a good idea if you plan it out right and/or expect certain foes. Even after you take it you have to think when to use it or not. That's what I think all feats should be. Unfortunately the high OP builds tend to increase its popularity and influence people into getting PA even without the high op feats. Even on medium BAB melee with minimal buffs <shudder>.

With higher optimization you of course shocktrooper/etc., PA for full and don't need math. Which is boring IMO as it increases "This turn I full attack again" syndrome.

[Darth Stabber]

Which is boring IMO as it increases "This turn I full attack again" syndrome.

This is why ToB exists.

[Gwendol]

The good thing about the calculators (or tabulating the results) is that you see exactly how much difference PA makes, and thus can make an informed decision on wether to or not. Still, if you play a melee oriented character using a 2H weapon, you want the feat no matter what.