Author Topic: Discussion Thread for the Mathematics of Power Attack  (Read 3565 times)

Offline Iainuki

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Offline Gribel

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #1 on: January 04, 2014, 07:26:42 PM »
Equation (1)'s sum shouldn't have the +21, it is already included via h. The way it is, iterative attacks are more accurate than full BAB attacks. Also, the cap of 100% accuracy is not included, i.e. h - p may be greater than 20. I'm still at the begining, I don't know if you adressed this further down. I'll keep on reading though, I liked it.
Oh, and stinking cloud has to be one of my favorate battlefield spells. Combined with sleet stor, you can shut a group down and keep them shut down, trapped inside a fart. When does that ever get old?

Offline Iainuki

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #2 on: January 04, 2014, 08:42:53 PM »
Equation (1)'s sum shouldn't have the +21, it is already included via h.

You're right, that's a typo.  I uploaded a fixed version.

I deliberately ignored the possibility of falling off the RNG because it makes it makes the math more complicated for very little gain.  First, if you're off the RNG, you're either vastly overmatched (if you can only hit on a natural 20) or vastly superior to your enemies (if you can only miss on a natural 1).  Power Attack optimization isn't important in these scenarios because in the first case, your strategy should either be to run away or switch to an attack mode that has a better than 5% chance of working, and in the second case, it doesn't really matter what you do because you're going to win easily.   Second, it's very easy to know what the optimal Power Attack penalty and how much damage Power Attack adds when you're off the RNG.  If you hit on anything but a natural 1 and don't have iteratives or natural attacks to worry about, you Power Attack up to the limit of your excess attack bonus and then the logic in this guide applies again.  (If you have to worry about iteratives and natural weapons, then you have to do the complicated math, which involves piecewise functions and gets annoying.)  If you hit only a natural 20, you want to Power Attack up to your BAB.

I can add some of this logic if you think it would be helpful.

Offline Gribel

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #3 on: January 04, 2014, 09:16:01 PM »
Indeed, after reading on I found your considerations. It's a nice simplification. Not only is your math correct, but you also make great analysis regarding what is relevant, best case scenarios, comparisons, etc..

Further numerical analysis and examples regarding optimized returns for power attack (Leap Attack, Spirited Charge, etc., as you mentioned near the end) would be interesting, though Shock Trooper renders it useless.
Oh, and stinking cloud has to be one of my favorate battlefield spells. Combined with sleet stor, you can shut a group down and keep them shut down, trapped inside a fart. When does that ever get old?

Offline Jackinthegreen

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #4 on: January 09, 2014, 12:37:16 AM »
Going along the lines of PA, have you ever looked at the Arcane Duelist?  Specifically the Dextrous Attack and False Keenness abilities.  Do note they have a typo in False Keenness where the damage should be reduced by 8, not 12.

Offline F50

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #5 on: January 09, 2014, 12:52:16 PM »
It is worth mentioning that a trusty wand of wraithstrike combined (or a heartseeker amulet) with a wand chamber can make the best case frighteningly common, even for on-level enemies, since having a touch AC of 9-11 is not particularly uncommon for giants, golems and the like. That said, excellent math. A more complete assessment would be more useful for the sake of actual optimization and I definitely would find it interesting to see mathematically what power attacking for x3 (leap attack), x5 (combat brute), and x6 (combat brute + leap attack) does to damage calculations, especially in addition to x2, x3, and x4 modifiers to total damage (valorous, battle jump, spirited charge and combinations thereof)
« Last Edit: January 09, 2014, 01:05:57 PM by F50 »

Offline phaedrusxy

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #6 on: January 09, 2014, 01:21:48 PM »
If you're going to talk about wands of wraithstrike, it might be worth mentioning the Impaling enchantment (MiC), which lets you make your next attack as a touch attack 3x/day. It is a +1 equivalent, but only goes on piercing weapons. Also, if you have wings, you can make a diving charge for double damage with a piercing weapon (no feats required!).
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Offline Garryl

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #7 on: January 09, 2014, 03:29:31 PM »
If you're going to talk about wands of wraithstrike, it might be worth mentioning the Impaling enchantment (MiC), which lets you make your next attack as a touch attack 3x/day. It is a +1 equivalent, but only goes on piercing weapons. Also, if you have wings, you can make a diving charge for double damage with a piercing weapon (no feats required!).

I know that flying creatures can do double damage with claw and talon attacks, but I thought that double damage with piercing weapons was not a general rule and was only found in the Raptoran and Dragonborn flight abilities?

Offline Jackinthegreen

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #8 on: January 10, 2014, 12:46:34 AM »
If you're going to talk about wands of wraithstrike, it might be worth mentioning the Impaling enchantment (MiC), which lets you make your next attack as a touch attack 3x/day. It is a +1 equivalent, but only goes on piercing weapons. Also, if you have wings, you can make a diving charge for double damage with a piercing weapon (no feats required!).

I know that flying creatures can do double damage with claw and talon attacks, but I thought that double damage with piercing weapons was not a general rule and was only found in the Raptoran and Dragonborn flight abilities?

Those are the only two places I've ever seen it.

Offline phaedrusxy

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #9 on: January 10, 2014, 10:27:16 AM »
If you're going to talk about wands of wraithstrike, it might be worth mentioning the Impaling enchantment (MiC), which lets you make your next attack as a touch attack 3x/day. It is a +1 equivalent, but only goes on piercing weapons. Also, if you have wings, you can make a diving charge for double damage with a piercing weapon (no feats required!).

I know that flying creatures can do double damage with claw and talon attacks, but I thought that double damage with piercing weapons was not a general rule and was only found in the Raptoran and Dragonborn flight abilities?

Those are the only two places I've ever seen it.
Perhaps you're right, but those are probably the most common sources of Extraordinary flight for PCs (excluding polymorph and other body-changing tactics).
I don't pee messages into the snow often , but when I do , it's in Cyrillic with Fake Viagra.  Stay frosty my friends.

Offline Iainuki

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #10 on: January 10, 2014, 11:08:28 PM »
Going along the lines of PA, have you ever looked at the Arcane Duelist?  Specifically the Dextrous Attack and False Keenness abilities.  Do note they have a typo in False Keenness where the damage should be reduced by 8, not 12.

I did a brief write-up on this class at one point, though I forget if I posted it.

Dexterous attack has no restriction preventing you from using it with a two-handed melee weapon, so with dexterous attack and Power Attack, a literal reading of the rules allows you to use dexterous attack to convert damage from your weapon damage die or dice to attack bonus and then Power Attack to convert attack bonus into damage.  This results in a very favorable conversion ratio because each 1 point of potential damage on a weapon die is only worth .5 expected damage while you get to convert potential damage one-to-one into attack bonus and then two-to-one back into actual damage with Power Attack for a net ratio of 4 damage for every 1 damage on your weapon's damage dice once your BAB is high enough, or 1.5 damage/BAB assuming your weapon's dice are larger than your BAB.  However, you lose damage from your non-dice damage bonus first and the conversion ratio on that is only two-to-one or 1 damage/BAB.  This means that dexterous attack pays off the most with whatever two-handed weapon has the highest die size and with the lowest possible non-dice damage bonus, so with low Str, weapon enhancement bonus, and fixed damage bonuses from feats and class features.  Weapons with two or more damage dice are also disadvantaged.  If your immediate thought is that the way to optimize dexterous attack is with a spiked chain (despite its two dice), Weapon Finesse, and sneak attack, skirmish, Arcane Strike (CW 96), or Dragonfire Inspiration (DrM 17-18), you'd be right.  There are also some non-core finesseable two-handed weapons, or one-handed finessseable weapons that can be used in two hands, that would work; I'm sure Captnq's weapon handbook has a list.  On the whole, the numbers aren't spectacular for an investment of two feats (Dodge, Mobility) and three to four class levels (three levels for the ability, one for the ability to cast 1st-level arcane spells), but it might useful for some niche builds.

As for false keenness, the long and short of it is that it and dexterous attack don't work well together.  A weapon with the minimum possible critical multiplier, 2, does 2 damage/point of fixed  damage bonus on a critical.  If we assume that the 12 is a typo, converting that same point with dexterous attack does 2 damage via Power Attack, but you lose 2 damage from the interaction so your critical does the same damage as if you didn't have or use dexterous attack.  If your weapon has a higher critical multiplier, your criticals lose damage relative to not using dexterous attack.  You can make dexterous attack net positive with false keenness if you have increased Power Attack multipliers or little fixed damage bonus, but this is a lot of work for little reward.  Beyond that, optimizing false keenness's damage requires you to do the exact opposite of optimizing dexterous attack's damage, because to maximize damage from criticals, you need to maximize your fixed damage bonus, but to maximize damage from dexterous attack, you need to minimize your fixed damage bonus.  There's probably some way to thread the needle by finding an appropriate non-core weapon that's one- or two-handed, finesseable, and has a 19-20 or 18-20 threat range and getting things that add extra dice on criticals, but criticals are not good for lots of reasons entirely independent of false keenness's problems, and false keenness still gives a penalty to your attack bonus that you could instead use for Power Attack to get more damage on all your attacks.  Basically, it's not good.
« Last Edit: January 11, 2014, 12:21:48 AM by Iainuki »

Offline Iainuki

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #11 on: January 11, 2014, 12:36:12 AM »
It is worth mentioning that a trusty wand of wraithstrike combined (or a heartseeker amulet) with a wand chamber can make the best case frighteningly common, even for on-level enemies, since having a touch AC of 9-11 is not particularly uncommon for giants, golems and the like.

Non-core touch AC is nearly constant on average over monsters at around 10, so yes, this works quite well.

A more complete assessment would be more useful for the sake of actual optimization and I definitely would find it interesting to see mathematically what power attacking for x3 (leap attack), x5 (combat brute), and x6 (combat brute + leap attack) does to damage calculations, especially in addition to x2, x3, and x4 modifiers to total damage (valorous, battle jump, spirited charge and combinations thereof)

The reason I didn't do those calculations in the guide is they have little general applicability.    The number of combinations is huge, there's no clear, succinct way to present the results, and I didn't feel like adding pages of tables or graphs would be very useful.  If you have ideas about how to compress those variables down into one or two tables or graphs, I can look at them.  At an individual character level, Equations 8 or 12 will tell you when you should Power Attack and Equation 7 will tell you how much.  You can precalculate everything except your hit chance and then plug that into a computer, phone, or programmable calculator during a game.
« Last Edit: January 11, 2014, 02:34:04 AM by Iainuki »

Offline Iainuki

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #12 on: January 11, 2014, 02:32:13 AM »
I know that flying creatures can do double damage with claw and talon attacks, but I thought that double damage with piercing weapons was not a general rule and was only found in the Raptoran and Dragonborn flight abilities?

The relevant rules:

``A dive attack works just like a charge, but the diving creature must move a minimum of 30 feet and descend at least 10 feet. It can make only claw or talon attacks, but these deal double  damage'' (MM 312/http://www.d20srd.org/srd/specialAbilities.htm#fly).

``A raptoran with flight can make a dive attack. A dive attack works like a charge, but the raptoran must move a minimum of 30 feet and descend at least 10 feet. A raptoran can make a dive attack only when wielding a piercing weapon; if the attack hits, it deals double damage'' (RotW 68).

``You can make a dive attack. A dive attack works like a charge, but you must fly a minimum of 30 feet and descend at least 10 feet. You can make a dive attack only when wielding a piercing weapon; if the attack hits, it deals double damage'' (Improved Dragon Wings feat, RotD 100).

There is no general rule about dive attacks with piercing weapons, AFAIK.

Offline Powerdork

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #13 on: October 26, 2017, 01:16:07 PM »
Dead guide? File not found.

Offline Stratovarius

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Re: Discussion Thread for the Mathematics of Power Attack
« Reply #14 on: October 26, 2017, 01:26:13 PM »
Dead guide.

Offline Jackinthegreen

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