Power Attack and Statistics

[Jens]

I think that the correct formula for AT is:
AT = T-2.5*(N-1)
(Consider the trivial case of N=1), and for monks that's:
AT = T-1.5*(N-1)

The additional 2.5 gives you the 47 you want, instead of 42.

Ah, thank you (smacks forehead)... I will go back and correct it

KD, that was a lot of calculations! (The conclusions look right, too )

About crits: I think you're right they shouldn't influence the PA choice. I don't know why I confused myself on that. But since you do seem to take crits into account, they should only add 10% (when using a non-Keen Battleaxe without Improved Critical) not 20%.

Suspect maths: Where it holds, the general formula Cheiromancer suggested gives the 'same' result as you suggest. Unfortunately it only holds against AC 23 to AC 30 for full attack and against AC 23 to AC 40 for single attack, and then it says you should use PA by a negative amount, which of course means you should not PA.

 

[KarinsDad]

About crits: I think you're right they shouldn't influence the PA choice. I don't know why I confused myself on that. But since you do seem to take crits into account, they should only add 10% (when using a non-Keen Battleaxe without Improved Critical) not 20%.

I was merely taking criticals into account to be thorough.

19/x3 is the threat and critical damage given in the original example, hence, it is probably a Keen Battleaxe, or the character has Improved Critical with it.

So, you have a 10% chance of a threat, assuming your opponents AC does not require you to roll a 20 to hit, but in the “when should I PA” mode, that is always the case. In other words, if you have to roll a 20 anyway to hit, you might as well put your full BAB into PA.

Let’s take a 30% chance to hit. Typically, there are a few ways to figure this out:

(20% * normal damage) + (10% * 70% * normal damage + 10% * 30% * 3 times damage) OR

20 + 7 + 9 = 36

36% = 1.2 * 30%

(30% * normal damage) + (10% * 30% * 2 additional times damage) OR

30 + 6 = 36

Again, 36% = 1.2 * 30%.

Another way of looking at it is this:

20/x2 = 1.05
20/x3 = 1.10
19/x2 = 1.10
19/x3 = 1.20

Increasing the critical damage from x2 to x3 for the same threat range doubles the increase damage percentage.

 

[Jens]

Re: Re: Power Attack and Statistics

Full Round Attack:

(23 - AC) / 2 round up = points to add to Power Attack OR
(24 - AC) / 2 round down, depending on your preference

This gives a slightly higher average damage for Full Attack:

1. If the AC is higher than 22, don't use PA (unless the AC is so high you only hit on 20s)
2. PA by (24-AC)/2 rounded up = (25-AC)/2 rounded down, depending on your preference

Examples:

Against AC 21, using PA by (24-21)/2 rounded up = (25-21)/2 rounded down = 2 gives (.95+.70+.45)*(18.5+2)*1.2 = 51.66 which is slightly more than the (.95+.75+.50)*(18.5+1)*1.2 = 51.48 you would get from PA'ing by only 1.

Similarly against AC 19, using PA by (24-19)/2 rounded up = (25-19)/2 rounded down = 3 gives (.95+.75+.50)*(18.5+3)*1.2 = 56.76 which is slightly more than the (.95+.80+.55)*(18.5+2)*1.2 = 56.58 you would get from PA'ing by only 2.

That being said, I think it's usually preferable to PA a little less than what gives the most average damage. PA generally makes hits less likely and therefore makes your damage output more variable, which is usually not desireable.

 

[trentonjoe]

Re: Re: Re: Power Attack and Statistics

1. If the AC is higher than 22, don't use PA (unless the AC is so high you only hit on 20s)
2. PA by (24-AC)/2 rounded up = (25-AC)/2 rounded down, depending on your preference

.

Thank you so much! When I grow up I wan to be Dutch and good at Math.

Wait I am grown up. Crap. Oh well, thanks for the help everyone!

 

[Rashak Mani]

Conclusion: Power Attacks SUCKS at mid to high levels !

USE COMBAT ANALYZER and let these Math Freaks aside !!

I used the program and noticed that only with ACs 15-16 or lower was Power attack worthwhile for my Dwarven Barbarian. Mostly because he already deals so much damage. Power Attack would have to be good in order to compensate any misses it causes. In Rage my damage is d12+13 thats 19.5 AVG damage !!

(Dwarf Fight 5/Barb 4 Str 18(rage22) Wpn Fcs / Wpn Spec / GreatAxe +2 )

+4 damage from power attack = 20% chance bigger of missing. Since a miss = almost 20 damage I would have to hit 5 times (5x4) with PA to compensate 1 Miss !! Hardly worthwhile... unless AC is pathetic.

At mid to higher levels how many AC15-16 creatures do you actually meet ?

Conclusion: Power attack is for very specific foes or situations. Like they said before... the less STR you have the better PA works.

 

[KarinsDad]

Re: Re: Re: Power Attack and Statistics

This gives a slightly higher average damage for Full Attack:

1. If the AC is higher than 22, don't use PA (unless the AC is so high you only hit on 20s)
2. PA by (24-AC)/2 rounded up = (25-AC)/2 rounded down, depending on your preference

That is why I also called the Full Attack equation a rule of thumb. Without a spreadsheet (or being a Rain Man at math), it's harder to come up with an easy actual equation that works in every case. So, I put up an equation that at least does not decrease the damage by adding too much PA (hence, your need for #1 to limit the AC 23 case).

There are, however, break points at which the equations change and a different rule applies. For example, against AC 9 in the full round attack equation (which obviously would rarely or never happen at level 12, I'm just showing one example that I know of), using your method PA by (24-9)/2 rounded up = 8 gives (.95+.90+.65)*(18.5+8)*1.2 = 79.5 which is slightly less than the (.95+.95+.70)*(18.5+7)*1.2 = 79.56 you would get from PA'ing by only 7 (my method).

But, your equation is more accurate at the higher ACs (with the exception of AC 23 for which you needed the special case) which will tend to be encountered. Good job! That's what happens when I do math extremely late at night.

PS. Did you use a spreadsheet to figure out the error at the odd ACs or did you just stumble on it trying out different ACs?

 

[Jens]

Re: Re: Re: Re: Power Attack and Statistics

...using your method PA by (24-9)/2 rounded up = 8 gives (.95+.90+.65)*(18.5+8)*1.2 = 79.5 which is slightly less than the (.95+.95+.70)*(18.5+7)*1.2 = 79.56 you would get from PA'ing by only 7 (my method).

I should probably have guessed that things would change when the last attack is almost sure to hit, but... ok, I don't really have any good excuse . Edit: I'm pretty sure the amount to PA by should increase 1-for-1 as AC decreases below the lowest attack bonus; there is no real loss in the chance to hit.

PS. Did you use a spreadsheet to figure out the error at the odd ACs or did you just stumble on it trying out different ACs?

Well, that would probably have been the smart thing to do, but I wanted to try using my old 'programmable' calculator . It works but the output is not the best.

It would be neat to have formulas like Cheiromancer's that covered the whole range of ACs.

 

[KarinsDad]

Re: Re: Re: Re: Re: Power Attack and Statistics

I should probably have guessed that things would change when the last attack is almost sure to hit, but... ok, I don't really have any good excuse . Edit: I'm pretty sure the amount to PA by should increase 1-for-1 as AC decreases below the lowest attack bonus; there is no real loss in the chance to hit.

Actually, that was just a side effect of this particular example.

Imagine a character with two weapons and a BAB of 16 or 5 attacks per round.

Dropping 1 to hit for many ACs (i.e. where the highest attacks are at the 95% level, even if you drop some to hit from them) will drop 3 different attacks by 5%, but increase 5 different attacks by 1.

Well, if you are doing D8+8 at that point, 1 additional point is about an 8% increase in damage for 5 different attacks (or 40% increase in damage) at the cost of 15% (0.15) in the to hit column.

So, a drop of 3 AC might result in 4 or 5 being lowered from the BAB to PA.

The equations worked out so well in this example since the to hit was near 20 and the damage was near 20. Hence, the nice smooth curves until you add a LOT (e.g. AC 9 example) to PA. But, there are a lot of to hit/damage ratios where that smooth curve does not exist. Things like the following occur:

AC PA
30 +1
29 +1
28 +2
27 +3
26 +3
25 +4
24 +5
23 +6

with no consistent pattern, just depending on what the to hit/damage ratio and how many attacks per round you are talking about. Ditto for the single attack case, but the curve for that tends to be smoother, but not always a 1 to 1 ratio.

 

[Mal Malenkirk]

Oooh, the headache! I tend to wing my use of the power attack. Since I'm the DM, it's not too bad. So the big bad monster got too hungry for his own good and missed because he put too much points in powerattack. Too bad.

But I have a friend who has a degree in math/physic and who's working at a master degree in math who designed a nifty little program that allowed him to always get the optimum amount of power attack. It accounted for everything including critical damage, fighting two handed etc.

He printed charts based on the stats of his team mates at any given level.

The most amusing thing is that he has a relatively low opinion of the feat and never selects it unless he's playing a big burly warrior going for cleave, sunder etc.

He only did this because he was tired of seeing the barbarian and the fighter waste attacks by overextending their use of powerattack!

''Don't use the feat on the first round. Once you know the armor class, USE THE CHART *shove it in their face*''

I crack a smile every time he comes up at the game with a new chart. I swear he makes charts for everything!

 

[Disease]

Where were you people when this: ( http://solo23.abac.com/spikeyfreak/Melee_Damage_Calculator.htm ) was in the works?