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A player in my campaing wrote a formula that tells you wen it's beneficial to make a power attack(to maximise your damage).
We thaught it was pretty funny to see the tings we do wen we miss a game or two so I decided to post it here.
The formula is writen in english but in my group were all French Canadian so the explanation were in French.
I did my best to translate them but if you dont understand tell me and I'll try to be more precise.
IF Target_AC < 21 + AB - PA_Penalty - Average_DMG/M - 5/2*(Nb_att -1)
THEN use power attack.
AB: attack bonus without power attack
PA_Penalty: The penalty from power att. (-1 fist level and -1 from every 4 level of Base att. Bonus) (if PA_Penalty = 4 means you take -4 on your attack)
Average_DMG = Average damage the guy make with this weapon (ex: d8+5 = 9,5 of Average_DMG)
M: The multiplier of the power attack (if two handed M =3, one handed M =2, if off-hand, M=1)
Nb_att: the # of attacks the pc get this round (excluding flurry of blows or haste)
Exemple:
Thestosthérosthène (fighter level 1) as +6 to hit for 1d8+6 DMG.
Following this rule if he wants to maximise his damage
Target_AC < 21+6-1- 10,5/3 - 0 = 22,5
That means that the Pc make a power attack on any foes that as an AC inferior to 22.
Is there a freak on this board who can prove him wrong?
. . . And don't tell me that a formula like this take the fun out of the game I already know that. Just dont take it to seriously it's not a philosophical debate.
While doing DPR calculations on various builds, I similarly wondered when Power Attack (or Deadly Aim) would be beneficial and when it wouldn't. I decided to attempt some Algebra, and see if I could find a tipping point for when the damage gained per hit out-values the greater miss chance imposed by these feats. Here is what I did:
Starting out for a single attack I set (h x dmg) = (h - z/20) x (dmg + y).
h is the decimal hit probability, dmg is total average damage, z is the attack penalty, y is the bonus damage from the feat.
I then solved for h to find the tipping point. What I came up with is that the tipping point value for h is determined by the damage while power attacking (or deadly aiming) divided by a multiple of 20 (it is 20 for off hand power atack, 40 for deadly aim and primary hand power attack, and 60 for a two hand power attack)
or mathematically h = (dmg + y)/ 40 for most purposes. h = (dmg +y)/ 60 for 2hand weapon power attackers. Below this hit probability, hitting more often outweighs the value of the added damage. Above this hit probability, the extra damage is worth the hit penalty.
Then I used similar equations for iterative attacks- for 2 attacks I used ((h + (h - .25) x dmg) = (((h - z/20) + (h - z/20 - .25)) x (dmg + y)), and I also solved for 3 attacks as well.
The formulas I came up with for iterative attacks is h = ((dmg + y)/ 40 + .125) for two attacks. h = ((dmg + y)/ 40 + .25) for three attacks, and I extrapolate that the formula will be h = ((dmg + y)/40 + .375) for four attacks.
Those formulas are for deadly aim or power attack with a primary hand weapon. For power attack with a two handed weapon, divide by 60 instead of 40.
I have applied these formulas in DPR calculations, and they seem to be about right.
Edit: I replaced x's with z's in my equations so not to confuse multiplication sign with variable.
Hé hé
Thanks i'll show that to my friend.
Your welcome
That's really cool. There's just one problem ... I don't know any DM (me included) that actually out and out tells you what AC the target is, and you can spend half the combat guessing.
That's really cool. There's just one problem ... I don't know any DM (me included) that actually out and out tells you what AC the target is, and you can spend half the combat guessing.
Agreed, at least until some experience has been gained against the targets.
Shameless but relevant plug: for an automated tool to figure out which abilities are best to use and when, check out my DPR calculator. :)
Probably cool, but my intellect is unable to process your mathematical equations.
I get what you're doing, but it annoys the hell out of me ><, and I am not seeing any percentage results.
I took basic essential math, that isn't basic essential. ><
Actually it's like the old one about flurry of blows - it basically works out that if after modifiers you need a hit on anything less than about a 19 on the dice when flurrying, it's worth flurrying. If it's anything more than a 19 to hit normally, it's still worth flurrying as you have more of a chance of getting a natural 20 which is what you'll likely need to hit anyway. So when in doubt (which is most of the time), you flurry.
It's the same with Pathfinder Power Attack: above a certain AC, you'll only hit on a 20 anyway, so you may as well power attack. A few marks below that is the arena where your lower chance to hit is counterbalanced by your higher expectation of damage, so you can power attack then too. The space between them is so small that it's probably best not to worry about it unless you know your target's AC, and always power attack.
I'm not sure about the math, but I'm concerned that you don't take into account the probability that your average damage without powerattacking will kill the guy. The only reason I usually see to not power-attack is if you will kill them anyway. High str characters at low levels have this. 2d6+6 will kill most goblins outright, so the added hit chance is better.
I just want to add some things that may not have been completely clear. All of the formulas should read as determining the hit probability, without the attack penalty from power attack or deadly aim. For iterative attacks, this is the hit probability of the first attack.
The (dmg +y) term that you plug into the formula is your average total damage from a single hit, including power attack/deadly aim damage. However fractional critical hit damage (like you use in DPR calculations), probably should not be included in this value, since I never included any critical terms in my equations.
The tipping point formulas I posted are really for DPR calculations, and I don't know if they would be at all that useful for combat, but a player might find them useful to see if even taking a certain feat is worthwhile.
If you want to try applying them in combat then you need to know: your own attack bonus (which you should know) and your foe's AC (which you probably shouldn't know). Then your actual hit probability can be calculated h = 1 - ((AC - Att Bns)/20), or at least I think that is how you express it mathematically. [Also, h can really only have a value between .05 and .95, to represent that a 1 is always a miss and a 20 is always a hit.]
Regardless, every d20 result that counts as a hit, gives you a decimal hit value of .05, so for example, when you hit on a 4 or better on an attack roll, your decimal hit probability will be .85. Then compare your actual hit probability with the tipping point hit probability, if the actual is lower - don't power attack or deadly aim. If the actual is higher, then power attacking or deadly aiming shuld maximize your hurt output.