D&D 3E/3.5 3.5 power attack: the designers' rationale

[Mike Sullivan]

I'd like this example better if he didn't have a Strength score of 18. The game was designed for 25 point buy, and even though such a fighter could take 18 Strength, he usually wouldn't.

I figured that a 17 base strength, +1 for level 4, wasn't out of line for a character who's planning on a greatsword strategy, since that's obviously a damage-output-focused character, and the big advantage of a two-handed weapon is the ability to get x1.5 Str bonus.

A 16 Strength, however, would yield the following situation:

+9 AB, requires a 7 to hit.

Per hit damage is 2d6 + 4 + 1 + 2 = 14 * 1.1 - 5 = 10.4 per hit.

Per round expected damage, no PA = 7.28

Per round expected damage, PA +1 = 7.475

Per round expected damage, PA +2 = 7.56

Per round expected damage, PA +3 = 7.535

So the optimal PAing is for +2 to damage, and it increases per round expected damage by .28 hit points.

 

[Elder-Basilisk]

IME, 3.0 power attack was wildly useful when facing low AC opponents. It is also useful when facing oppontents with just a few more hit points than the average damage from one or two attacks.

For instance, a large zombie has 29 hit points and AC 11; a huge zombie has 55 hit points and AC 11. Their CRs are 1 and 3 respectively but they usually show up in large groups to be tossed against higher level parties.

A typical 8th level fighter/barbarian: Str 18, +2 (item), +4 rage with a +2 greatsword will have an attack bonus of +18/+13 and will deal 2d6+14 points of damage. He will also have cleave.

Against the large zombie, he will hit with both attacks on a roll of 2 and will deal 21 points of damage per hit. Against a close-packed zombie horde, that lets him kill 1.5 large zombies per round. (his second attack kills the large zombie and then he cleaves into another. The next round, his first attack kills that zombie, he cleaves into a second and finishes it off with his secondary attack).

With 3.0 power attack, he can power attack for 8 points and still hit on a 2 and a 5. However, this brings his zombie-killing potential up to nearly 3/round. His first attack now drops one zombie on average, and he then cleaves into another, dropping it, and takes a 5 foot step and drops a third (80% chance or so).

Against the huge zombies, he can power attack for six and stand a very good chance of dropping 1.5 zombies per round instead of the .75 zombies per round he gets without power attack.

Against hordes of non-zombie mooks, it was still useful. A fourth level fighter (Str 17, +1 greatsword--+9 atk, 2d6+7 damage) with a greatsword against a troop of bugbears (AC 17, 16 hp), for instance, deals an average of 9.1 damage per round against the bugbears. And he's likely to kill one bugbear every three attacks. With Cleave, that's two bugbears every 5 rounds.

If the fighter power attacks for three points, his average damage/round goes down to 8.5. However, he has a 50% chance of dropping one bugbear each round. So, his bugbear kill ratio goes up to about 1 bugbears every two rounds (1.25 bugbears every two rounds with cleave factored in)--almost twice as good as it was without power attack.

When facing multiple opponents with the cleave feat (even more so with Great Cleave), average damage/round doesn't tell the whole story.

An interesting claim that Psion made was that Power Attack would have been a "must have" feat, even if it had not been changed, because you'll more often have to cut through 3.5 DR. I have no idea if this is true, so I thought I'd run the numbers.

<Numbers Snipped>

I don't know, maybe there's something in the middle there where 3.0 PA would be wildly useful.

 

[Shard O'Glase]

also I found power attack to wildly useful in the 1st round of a fight. I could drop a lot form my to hit when I'm only concerned with one attack. It's useful in some circumstances status made it balanced IMO, with the x2 dmg on two handed weapons its useful in all circumstances and really, realy useful in the circumstances it already was good, making it a bit too good of a feat especially as a 1st tier feat.

 

[Mike Sullivan]

IME, 3.0 power attack was wildly useful when facing low AC opponents. It is also useful when facing oppontents with just a few more hit points than the average damage from one or two attacks.

Yes, yes, stipulated that any kind of damage bonus is very useful when it doesn't impact your chances to hit.

On the other hand, seriously, who cares? You're putting an 8th level character up against CR 3 opponents, here. The 8th level character is going to win with minimal effort, it seems clear. That he may or may not win marginally faster seems to me to be pretty irrelevent on the grand scale.

Against hordes of non-zombie mooks, it was still useful. A fourth level fighter (Str 17, +1 greatsword--+9 atk, 2d6+7 damage) with a greatsword against a troop of bugbears (AC 17, 16 hp), for instance, deals an average of 9.1 damage per round against the bugbears. And he's likely to kill one bugbear every three attacks. With Cleave, that's two bugbears every 5 rounds.

If the fighter power attacks for three points, his average damage/round goes down to 8.5. However, he has a 50% chance of dropping one bugbear each round. So, his bugbear kill ratio goes up to about 1 bugbears every two rounds (1.25 bugbears every two rounds with cleave factored in)--almost twice as good as it was without power attack.

When facing multiple opponents with the cleave feat (even more so with Great Cleave), average damage/round doesn't tell the whole story.

This, on the other hand, is interesting. I want to examine it more closely:

Fighter as statted above, facing bugbears as statted above.

The fighter's chance of one-hit killing a bugbear (without PA) is either his chance of rolling a 9+ on 2d6 (10 in 36), or guaranteed on a critical hit. He rolls to hit one per round at +9, so his odds of hitting at all are 65%, and his odds of criticaling are 6.5%, so his odds of normal-hitting are 58.5%. Each normal hit will have a 27.8% chance of dropping a bugbear. Thus, his odds of normal-hit-dropping a bugbear, per round, are 16.25%. Add to that the critical hit chance, and we see that this is the per-round breakdown of the possible outcomes:

Fighter misses: 35%
Fighter hits and wounds: 42.25%
Fighter hits and drops: 22.75%

The fighter, then, has a 22.75% chance of getting a Cleave attack on a round when he's attacking an unwounded opponent.


Now, let's look at the fighter PAing for two.

He now misses 45% of the time, and he still auto-drops his opponent on a critical, but criticals are now rarer -- 5.5% of the time. The other 49.5% of the time (normal hits), he needs to roll a 7+ to drop the bugbear. The odds of this are 58.3%. So that's a 28.875% chance to drop the bugbear on, plus the 5.5% from the critical, is

Fighter misses: 45%
Fighter hits and wounds: 20.625%
Fighter hits and drops: 34.375%

So, he's got a 34.375% chance of getting a Cleave attack.

Now, what are the results of those Cleave attacks? Well, they precisely mimic the normal attacks for those rounds.

So, we can create a total matrix for one round of each fighter:

No PA:

Misses entirely: 35%
Wounds 1 opponent: 42.25%
Drops 1 opponent, misses next opponent: 7.9625%
Drops 1 opponent, wounds next opponent: 9.726%
Drops 2 opponents: 5.176%

PA for 2:

Misses entirely: 45%
Wounds 1 opponent: 20.625%
Drops 1 opponent, misses next opponent: 15.469%
Drops 1 opponent, wounds next opponent: 7.09%
Drops 2 opponents: 11.816%

What's all that translate to? Well, a wounded opponent is dead meat for the next hit, so I think it's fair to say that wounding an opponent constitutes .5 killing an opponent. So, this translates to the following, in terms of "number of opponents dropped per round":

No PA:

.35 * 0 + .4225 * .5 + .0796 * 1 + 1.5 * .09726 + 2 * .05176 = .54026 opponents dropped per round.

PA:

.45 * 0 + .20625 * .5 + .15469% * 1 + .0709 * 1.5 + .11816 * 2 = .600035 opponents dropped per round.

As is broadly the case in this thread, for a low-level fighter, we're looking at mild benefits -- or so it seems to me.

 

[coyote6]

I guessed the rationales were something like that; my first thought was, "Why not use x1.5?" I thought for a while that they might've changed the Str bonus for two-handed weapons...

One player in my group (the guy that plays Pell, the greatsword-wielding half-orc barbarian/fighter) has already said, "Wow, that sounds too powerful*; maybe x1.5 damage instead of double?". I think that may become our house rule.

*Everybody in the group boggled at the double damage bit, but he was the first to suggest x1.5 damage.

 

[satori01]

Thanks PC and Ed Stark for allowing this to be posted. I hope we can see more of these behind the curtain threads, as many of us, will probably be uncouth boars and need to be hit over the head with proof,(myself included).

My largest quibble with the new rulling is the fact that it disallows power attack for small weapons. One of the aspects of 3e that I loved was the combination of classes and feats that allowed the character concept of the dexterous finessed combat warrior.
I have in my campaign a halfling knife fighter. The whole concept is a fighter based on mobility, and defense, that uses his surpluse of to hit bonus,(size, finesse, weapon focus etc) to augment his average damage.

I also wonder if all the comparisson calculations are including the inherent -2 to hit from TWF as well as the negative from the power attack. Power attaking for 2 points results in a -4 to hit which I have to believe effects average damage in a manner similiar to a THF. Sure the TWF receives more attacks but is the percentage increase from the extra attack compensate for the increased negative. A TWF power attacking for 2 points is at a -4 to hit, compared to the THF also power attacking for 2 points at a -2. Are peoples calculations accounting for this? ( I am by no means a satistical machine, so if anyone wants to crunch the numbers thank you)

I am all for increasing the relative use of Power Attack for THF, but I feel it should not come at the expense of a flavorful option like the knife fighter.

 

[Mike Sullivan]

*Everybody in the group boggled at the double damage bit, but he was the first to suggest x1.5 damage.

The reason that I flinch at this kind of thing is that people in general (perhaps not your group in particular) broadly feel that they have an intuitive grasp on what's the "better" thing to do in a given circumstance...

And they're broadly wrong.

Most people can't handle the attack damage tradeoff in their heads, even as a rough approximation, though a lot of people seem to think that they can.

Yes, the *2 PA seems really strong. I thought it was really strong too until I ran the numbers. I now don't think that it's really strong. It's useful, but not overwhelming. It'll add a point or two to average damages in non-degenerate cases.

So house ruling on what it "seems" like is, I think, often a bad idea.

 

[Mike Sullivan]

I also wonder if all the comparisson calculations a including the inherent -2 to hit from TWF as well as the negative from the power attack. Power attaking for 2 points results in a -4 to hit which I have to believe effects average damage in a manner similiar to a THF. Sure the TWF receives more attacks but is the percentage increase from the extra attack compensate for the increased negative. A TWF power attacking for 2 points is at a -4 to hit, compared to the THF also power attacking for 2 points at a -2. Are peoples calculations accounting for this? ( I am by no means a satistical machine, so if anyone wants to crunch the numbers thank you)

I can't speak for the comparison figures on this thread, but when I ran a comparison in another similar thread, yes, I accounted for them. I'll try to dig up a link and edit it into this post.

EDIT:

http://enworld.cyberstreet.com/showthread.php?s=&threadid=52971

 

[Elder-Basilisk]

On the other hand, seriously, who cares? You're putting an 8th level character up against CR 3 opponents, here. The 8th level character is going to win with minimal effort, it seems clear. That he may or may not win marginally faster seems to me to be pretty irrelevent on the grand scale.

On the other hand, mowing down zombie hordes seems like a staple of gaming. And groups of zombies are an appropriate challenge for mid level characters like the ones we're discussing here. 8 huge zombies or 16 large zombies, for instance are EL 9. Toss in a 8th or 9th level evil cleric to command them (ignoring HD limitations for the moment) and that's a very tough encounter for the PCs (EL 10-11)--one suitable for a boss fight. And in that case, how quickly the fighter can plow through the zombies is going to be one of the deciding factors of the fight. (The cleric can probably only turn one or two at a time). I've been in quite a few situations like that with my characters....

This, on the other hand, is interesting. I want to examine it more closely:

Fighter as statted above, facing bugbears as statted above.
<matrix calculations for fighter v. Bugbear snipped>

As is broadly the case in this thread, for a low-level fighter, we're looking at mild benefits -- or so it seems to me.

I'll grant that these are often mild benefits but they do apply in a lot of cases. The bugbear, for instance is a case where the average damage/round calculation would indicate that power attacking is a poor idea. However, it turns out to be mildly beneficial.

I suspect that similar calculations might move the benefits from mild to significant where average damage/round calculations also reveal an advantage.

Now, mind you, I don't think that the new power attack is a bad idea. (I like it because it somewhat makes up for the loss of the partial charge-full attack manuever popular in 3e). I'm just maintaining that power attack was already a very useful feat--possibly even "must have" before the change.

 

[Mike Sullivan]

Now, mind you, I don't think that the new power attack is a bad idea. (I like it because it somewhat makes up for the loss of the partial charge-full attack manuever popular in 3e). I'm just maintaining that power attack was already a very useful feat--possibly even "must have" before the change.

I don't know that I agree that mowing down zombie hordes is a gaming staple. It's a staple of a particular horror genre, sure. And I think that Large or Huge zombies are a particularly dubious "generic challenge" -- and PA is much less useful against the medium sized ones in the scenario you proposed.

I also am unconvinced by the "mildly useful in a broad number of situations" argument. In general, I see it as useful for a big-weapon fighter in three scenarios:

1. When you are fighting fairly small bands of AC and hit point opponents at level 5 and below (before you get iterative attacks).

2. Briefly in the level 6-10 range when you're charging or otherwise denied your iterative attacks.

3. When all of your attacks for a given round hit on a 2+, and only when you aren't affecting your odds to hit at all.

I think that number 1 is fairly common for a brief level range. Numbers 2 and 3 will come up fairly frequently, but they're turning a rotten situation into a mildly less rotten situation -- increasing your damage from 35 expected per round to 40 expected per round, when your full-attack damage is 65 expected per round, just means you're killing time until you get to full attack.

That said, I think we can agree on one thing:

Clearly, 3.0 PA is at its most useless when we're talking about the archetypical greatsword fighter. Sword-and-boarders benefit more from it, and it's huge for a TWFer.

The change, then, is meant to equalize its utility for everyone -- centering around the sword-and-boarders. Thus, they're making it less useful for the TWFers, and more useful for two-handed guys.

They're making a seperate series of changes to make TWF more competetive (GWS, removing Ambidexterity, and ITWF and GTWF), as it was otherwise by-and-large the weakest style. I think that the goal here -- and, despite what people want to claim, there's no evidence that they've fallen short on this goal -- is to make the three different melee styles be an interesting and tough choice.