roguerouge
First Post
two hand builds
Here, here... and with two-weapon wielders too?
Here, here... and with two-weapon wielders too?
Power Attack Optimization
Elder-Basilisk
First Post
I've done some thinking about this on my own and, combined with strategy from the miniatures game, I've come to the conclusion that maximum average damage per round is not the same as optimal use of power attack.
The optimal use of Power Attack is the amount that gives you the best chance of winning the battle at the lowest cost. In some cases, that means taking a huge risk of accomplishing nothing because anything less than a huge hit won't accomplish anything and the enemy is very likely to end the fight next round if you don't end it this round. In most cases, however, the optimum power attack is going to be the one that gives you the best chance to drop the greatest number of foes over a relatively short time frame (usually 1-3 rounds).
your optimal use of Power Attack
depends upon the target's hit points as well as their AC, your feats,
etc. This is further complicated by variable (rather than fixed damage
outputs) Let's look at an example:
Your greataxe wielding fighter--let's call him Roy-- is fighting a
group of hobgoblins with class levels. Because Roy is 4th level and
has a 16 strength, weapon specialization, and a +1 greataxe, his
attack bonus is +9 for 1d12+7 damage--an average of 13.5 points of
damage. (Roy has decided to use a greataxe for this simulation to make
the math simpler). It he's up against AC 20, he deals (excluding
criticals) an average of 6.75 damage per attack. If he uses two points
of Power Attack, that goes up to 7 damage per attack. Wohoo. He scores
an extra 0.25 damage per attack--that was sure worth spending a feat.
Well, maybe not. Now, let's imagine that the hobgoblin fighters he is
fighting have 17 hit points. If we just look at average damage, Roy
will need two hits to drop each hobgoblin unless he Power Attacks for
2. So, instead of going from 6.75 to 7 damage, he is really going from
a 25% chance of dropping a hobgoblin every two rounds (with a 50%
chance of injuring but not killing the hobgoblin and a 25% chance of
doing nothing to the hobgoblin) to a 64% chance of dropping at least
one hobgoblin every two rounds (with a 16% chance of killing two
hobgoblins and a 36% chance of accomplishing nothing). Now Power
Attack is starting to look a lot better.
But since D&D uses variable rather than fixed damage, that's not quite
true. The without Power Attacking, Roy has a 17% chance of dropping a
hobgoblin to negatives with a single hit. If he power attacks for two,
that chance goes up to 50% rather than 100%. In fact, in order to get
the number to 100% of hits dropping a hobgoblin, he needs to Power
Attack for 5 (which he can't do).
It turns out that, while Power Attacking for four decreases his
average damage per attack from 6.75 to 6.45, it actually increases his
chances of dropping the hobgoblin in a single attack from 8.3% to 25%.
In two rounds, Roy's chance of dropping at least one hobgoblin go from
25% (including a 2.7% chance of dropping two hobgoblins) to 43.75%.
(including a 6.25% chance of killing two hobgoblins). On the other
hand, Roy's chances of leaving the hobgoblin completely uninjured are
about 55% rather than 25%.
What about a situation where average damage is enough to drop the bad
guy outright. Revising out scenario to give the hobgoblin 13 hit
points, it turns out that Roy has a 25% chance of dropping a hobgoblin
on each attack if he does not Power Attack at all. However, he manages
a 35% chance to drop a hobgoblin if he Power Attacks for three points.
In two rounds, the percentages are:
Drops 2 hobgoblins: no PA=6.25%; PA=3 12.25%
Drops 1 hobgoblin: no PA=37.5%; PA=3 45.5%
Injures 1 hobgoblin: no PA=12.5%; PA=3 0%
Accomplishes nothing: no PA=43.75%; PA=3 42.25%
All this, despite the fact that Power Attacking for 2 is the optimal
average damage per round number.
Now there are also situations where the Power Attack math doesn't work
out this way. If, for instance, we have a troll instead of a hobgoblin
and the chance for a one-shot kill becomes negligable, we would need
to figure out the odds that power attacking would take a three-hit
kill and make it a two-hit kill. If the hobgoblin had 8 hit points
(where one result in 12 on the greataxe die leaves it staggered rather
than down), then the odds of one-shotting it actually go down by Power
Attacking (from 45.833% to 45%). Since we don't know the actual hit
point totals of our enemies in D&D (unless we have Combat Awareness
from the PHB II), we're making a lot of these decisions in the dark.
That said, it appears that power attacking for enough to make sure you
drop an enemy on every successful hit (and, yes, things like fireball
and magic missiles from your allies can make Power Attack unnecessary
for this goal, but they can also take a tougher foe and make it
possible to one-shot them, so in general, I think they wash out in the
adventuring environment) seems to be a pretty good plan if you can
manage it.
The optimal use of Power Attack is the amount that gives you the best chance of winning the battle at the lowest cost. In some cases, that means taking a huge risk of accomplishing nothing because anything less than a huge hit won't accomplish anything and the enemy is very likely to end the fight next round if you don't end it this round. In most cases, however, the optimum power attack is going to be the one that gives you the best chance to drop the greatest number of foes over a relatively short time frame (usually 1-3 rounds).
your optimal use of Power Attack
depends upon the target's hit points as well as their AC, your feats,
etc. This is further complicated by variable (rather than fixed damage
outputs) Let's look at an example:
Your greataxe wielding fighter--let's call him Roy-- is fighting a
group of hobgoblins with class levels. Because Roy is 4th level and
has a 16 strength, weapon specialization, and a +1 greataxe, his
attack bonus is +9 for 1d12+7 damage--an average of 13.5 points of
damage. (Roy has decided to use a greataxe for this simulation to make
the math simpler). It he's up against AC 20, he deals (excluding
criticals) an average of 6.75 damage per attack. If he uses two points
of Power Attack, that goes up to 7 damage per attack. Wohoo. He scores
an extra 0.25 damage per attack--that was sure worth spending a feat.
Well, maybe not. Now, let's imagine that the hobgoblin fighters he is
fighting have 17 hit points. If we just look at average damage, Roy
will need two hits to drop each hobgoblin unless he Power Attacks for
2. So, instead of going from 6.75 to 7 damage, he is really going from
a 25% chance of dropping a hobgoblin every two rounds (with a 50%
chance of injuring but not killing the hobgoblin and a 25% chance of
doing nothing to the hobgoblin) to a 64% chance of dropping at least
one hobgoblin every two rounds (with a 16% chance of killing two
hobgoblins and a 36% chance of accomplishing nothing). Now Power
Attack is starting to look a lot better.
But since D&D uses variable rather than fixed damage, that's not quite
true. The without Power Attacking, Roy has a 17% chance of dropping a
hobgoblin to negatives with a single hit. If he power attacks for two,
that chance goes up to 50% rather than 100%. In fact, in order to get
the number to 100% of hits dropping a hobgoblin, he needs to Power
Attack for 5 (which he can't do).
It turns out that, while Power Attacking for four decreases his
average damage per attack from 6.75 to 6.45, it actually increases his
chances of dropping the hobgoblin in a single attack from 8.3% to 25%.
In two rounds, Roy's chance of dropping at least one hobgoblin go from
25% (including a 2.7% chance of dropping two hobgoblins) to 43.75%.
(including a 6.25% chance of killing two hobgoblins). On the other
hand, Roy's chances of leaving the hobgoblin completely uninjured are
about 55% rather than 25%.
What about a situation where average damage is enough to drop the bad
guy outright. Revising out scenario to give the hobgoblin 13 hit
points, it turns out that Roy has a 25% chance of dropping a hobgoblin
on each attack if he does not Power Attack at all. However, he manages
a 35% chance to drop a hobgoblin if he Power Attacks for three points.
In two rounds, the percentages are:
Drops 2 hobgoblins: no PA=6.25%; PA=3 12.25%
Drops 1 hobgoblin: no PA=37.5%; PA=3 45.5%
Injures 1 hobgoblin: no PA=12.5%; PA=3 0%
Accomplishes nothing: no PA=43.75%; PA=3 42.25%
All this, despite the fact that Power Attacking for 2 is the optimal
average damage per round number.
Now there are also situations where the Power Attack math doesn't work
out this way. If, for instance, we have a troll instead of a hobgoblin
and the chance for a one-shot kill becomes negligable, we would need
to figure out the odds that power attacking would take a three-hit
kill and make it a two-hit kill. If the hobgoblin had 8 hit points
(where one result in 12 on the greataxe die leaves it staggered rather
than down), then the odds of one-shotting it actually go down by Power
Attacking (from 45.833% to 45%). Since we don't know the actual hit
point totals of our enemies in D&D (unless we have Combat Awareness
from the PHB II), we're making a lot of these decisions in the dark.
That said, it appears that power attacking for enough to make sure you
drop an enemy on every successful hit (and, yes, things like fireball
and magic missiles from your allies can make Power Attack unnecessary
for this goal, but they can also take a tougher foe and make it
possible to one-shot them, so in general, I think they wash out in the
adventuring environment) seems to be a pretty good plan if you can
manage it.
Ridley's Cohort
First Post
Elder-Basilisk said:
Yup.
Average damage does not always compare directly to average damage when the characters are in the hands of skilled tacticians.
The effect you analyzed becomes extreme when you add in Cleave. (Impressive analysis, BTW.)
In the 1st session I played D&D 3.0, we ran into Zombies. To our surprise, they were not going down with one hit as expected. In fact, the PA/Cleave Fighter with a Great Axe could only kill a Zombie with a single blow if he rolled above average.
In that situation, a 1st-2nd level PC should just go for max Power Attack. His average damage against the primary target may well drop slightly, but the tactical bonanza of removing 1 or 2 full health Zombies in a single attack is extremely sweet, even at the cost of missing outright.
Heck, max Power Attack made sense even if it were one lone Zombie where cleave is not a factor. A Zombie with 1 HP is for all practical purposes a Zombie that is a 50% HP -- a Zombie that survives one hit is almost never going to survive a second.
The other half of the story is that TWF specialist should not try and compete with the heavy offensive fighters in the average damage department. A better approach is to maximize the number of enemies dropped versus number of attacks received. Tempt the enemy into to giving you full attacks.
A TWf specialist standing next to multiple weak enemies can easily be as effective or more effective that a Great Cleave specialist, in spite of a disadvantage in average damage. Cleave and Great Cleave do not yield any bounty if you happen to miss the first attack. A TWF specialist has a hedge against runs of bad luck. As the DMG says, removing luck tends to favor PCs while tempting the luck of the dice eventually yields dead PCs.
For example:
A Cleave fighter might have a 25% of killing one weak foe plus a 25% change of killing two weak foes. (~50% chance of hitting killing the first one, then a ~50% of killing a second.) Average kills = 0.75.
The TWF specialist has two chances and therefore a 50% chance of killing only one weak foe plus a 25% chance of killing two. Average kills = 1.00
Who is the better fighter?
Furthermore, the TWF can take a 5' step in the middle of his full iterative attack. Unless the Cleave fighter has reach, many cleaves do not materialize for lack of a target in the immediate vicinity.
So I tend to laugh about comparisions between fighting styles that focus solely on average damage. Different fighting style demand different tactics to gain the full benefits. If you are obsessing about quantitative damage and not seeing the particular qualitative advantages available, then you still have a lot to learn about tactics.
In our games, the fighter or barbarion with Cleave often position themselves to take advantage of the possibility should it arise. Of course, that can leave them exposed to more attacks that necessary.Ridley's Cohort said:
Absolutely. I strongly advocate having a mix of fighting styles within a party to deal with different scenarios. Usually a two-handed weapon Barbarian and a sword & board (light armor) mobile whirlwind attacker.Ridley's Cohort said:
Great post Elder-Basilisk!
I wouldn't advocate maximizing average damage/round as being an exclusive strategy. Rather, having a number in your head for achieving such a maximum provides a fixed point to hang your hat on, in estimating the best strategy. Power Attacking for a little bit more than that which delivers maximum average, and you may up your chance of ending an encounter one round sooner--but your gut tells you not to go too high over this number...and you're gut is right. I think a nice little math problem I may fix in a sheet is to also provide the proper strategy (or set of strategies)-- ie, PA for 6 in round1 and 3 in round2, etc.--to minimize the #rounds it takes to drop an opponent Hp ___ (enter in a field) with a range of ACs.
That said, step back for a moment. If you've got one opponent with a lot of HPs, or lots of opponents with intermediate HPs and a DM who rarely allows a cleave configuration (reach weapons, etc.), you're going to do better hitting for maximum average than any othe strategy, on average (over lots of scenarios, this will be the best strategy). That should be stressed here.
I wouldn't advocate maximizing average damage/round as being an exclusive strategy. Rather, having a number in your head for achieving such a maximum provides a fixed point to hang your hat on, in estimating the best strategy. Power Attacking for a little bit more than that which delivers maximum average, and you may up your chance of ending an encounter one round sooner--but your gut tells you not to go too high over this number...and you're gut is right. I think a nice little math problem I may fix in a sheet is to also provide the proper strategy (or set of strategies)-- ie, PA for 6 in round1 and 3 in round2, etc.--to minimize the #rounds it takes to drop an opponent Hp ___ (enter in a field) with a range of ACs.
That said, step back for a moment. If you've got one opponent with a lot of HPs, or lots of opponents with intermediate HPs and a DM who rarely allows a cleave configuration (reach weapons, etc.), you're going to do better hitting for maximum average than any othe strategy, on average (over lots of scenarios, this will be the best strategy). That should be stressed here.
Elder-Basilisk
First Post
I don't think this is actually the case. I specifically excluded Cleave from my analysis above. The point of it is that what you want to do is not inflict as many hit points of damage as possible; what you want to do is drop your foes.
Let's take that intermediate hit point foe you're talking about. Let's say we're talking 8th level or so, so intermediate is 30-45 hit points. Now, if we analyze an iconic style fighter-- +1 flaming bastard sword and shield, 20 strength (one handed) or +1 greatsword, 22 strength, both with weapon specialization and weapon mastery: slashing, we find that they do:
1 handed: 1d10+1d6+10 damage
2 handed: 2d6+14 damage
The one-handed fighter is going to have a good shot at dropping the intermediate hit point foes in two hits if he power attacks. It will take him three hits, more often than not if he doesn't Power Attack.
The two-handed fighter is going to drop them in two hits pretty often without Power Attacking. If their hit points are in the mid thirties, he can reliably (> 50% of hits) one-shot them by Power Attacking for 8 points.
I would suggest that, in this situation, Power Attack for maximum average damage is still not a good idea. The one-handed weapon fighter is almost certainly best off power attacking for a moderate amount in order to make them reliable two-hit kills. The two-handed fighter is probably best off either not power attacking at all/power attacking for very little or power attacking for full.
In the case of a really high hit point monster, the optimal Power Attack number is probably closer to the max average damage per round, but even there, a lot will depend upon how the battle has progressed. After the first or second round, an injured high hit point monster, may well reach the stage where Power Attack should be used to reduce the number of hits to kill from three or two to two or one just like the mid-hit point monsters discussed above. I'm almost certain that over lots of battles, a flexible approach that minimizes the number of hits to drop a foe will do significantly better than maximum average damage/round.
Let's take that intermediate hit point foe you're talking about. Let's say we're talking 8th level or so, so intermediate is 30-45 hit points. Now, if we analyze an iconic style fighter-- +1 flaming bastard sword and shield, 20 strength (one handed) or +1 greatsword, 22 strength, both with weapon specialization and weapon mastery: slashing, we find that they do:
1 handed: 1d10+1d6+10 damage
2 handed: 2d6+14 damage
The one-handed fighter is going to have a good shot at dropping the intermediate hit point foes in two hits if he power attacks. It will take him three hits, more often than not if he doesn't Power Attack.
The two-handed fighter is going to drop them in two hits pretty often without Power Attacking. If their hit points are in the mid thirties, he can reliably (> 50% of hits) one-shot them by Power Attacking for 8 points.
I would suggest that, in this situation, Power Attack for maximum average damage is still not a good idea. The one-handed weapon fighter is almost certainly best off power attacking for a moderate amount in order to make them reliable two-hit kills. The two-handed fighter is probably best off either not power attacking at all/power attacking for very little or power attacking for full.
In the case of a really high hit point monster, the optimal Power Attack number is probably closer to the max average damage per round, but even there, a lot will depend upon how the battle has progressed. After the first or second round, an injured high hit point monster, may well reach the stage where Power Attack should be used to reduce the number of hits to kill from three or two to two or one just like the mid-hit point monsters discussed above. I'm almost certain that over lots of battles, a flexible approach that minimizes the number of hits to drop a foe will do significantly better than maximum average damage/round.
frisbeet said:
Ultimately the answer lies in either an analytic analysis or emperical testing. I bet I'm right, most of the time, but without proof I can't be dogmatic. This is something I'm interested in revisiting with much more detail...but time isn't on my side so it may be a while. Stay tuned...what would help is if you (EB) could be transparent in a couple of exemplary calculations, eg:
Because there is, after all, only one answer to the question, "what's the best strategy?" however gray it may be.
It's not that I don't believe you, but to be rigorous and absolutely convincing everything must be made clear to reasonable people with a modicum of algebra/probability education, from first principles. Otherwise its bullsh (I'm not saying this about your post!) and I'm not a prolific poster as I don't waste time. This is the standard I'll hold to myself.
Because there is, after all, only one answer to the question, "what's the best strategy?" however gray it may be.
Elder-Basilisk
First Post
In answer to the question about the figures, see the top of the post:
Unfortunately, I redid the math and it's not entirely correct so you were right to ask me to show my work
Against AC 20, Roy hits on an 11: 50% chance to hit. That's part 1. Part 2 is the damage. Roy will stagger the hobgoblin on a 6 (not considered in this analysis) and drop the hobgoblin on a 7 or better. So, that's a 50% chance to drop any uninjured hobgoblin he hits.
So, with no Power Attack:
50% chance to hitx 50% chance to drop= 25% chance to drop a hobgoblin with his first attack.*
Over two rounds, that comes out to:
Drops 2 hobgoblins: .25*.25
Drops 1 hobgoblin and injures a 2nd: .25 (drop 1st)*.25 (injures 2nd)
Drops 1 hobgoblin: .25 (drops 1st round)*.5 (miss 2nd round)+.5 (miss 1st round)*.25 (drops 2nd round)+.25 (injures 1st round)*.5(hits 2nd round--any hit being a kill)
Injures 1 hobgoblin: .5 (miss 1st round)*.25 (injures 2nd round) +.5 (miss 2nd round)*.25 (injures 1st round)
Accomplishes nothing: .5 (miss 1st round)*.5 (miss 2nd round)
Answers
Drops 2 hobgoblins: 6.25%
Drops 1 hobgoblins and injures a 2nd: 6.25%
Drops 1 hobgoblin: 37.5%
Injures 1 hobgoblin: 25%
Accomplishes nothing: 25%
Now the answers actually add up to 100%.
On to the Power Attack for three answer which should have much simpler math:
Power Attacking for 3, Roy is attacking at +6 for 1d12+13. He hits AC 20 on a 14 or better which is a 35% chance. Minimum damage is 14, so every hit drops a 13hp hobgoblin below 0.
So:
Drops two hobgoblins: .35 (drop round 1)*.35 (drops round 2)
Drops 1 hobgoblin: .35 (drops round 1)*.65 (misses round 2)+.65 (misses round 1)*+35 (drops round 2)
Accomplishes nothing: .65 (misses round 1)*.65 (misses round 2)
answers:
drops 2 hobgoblins: 12.25%
Drops 1 hobgoblin: 45.5%
Accomplishes nothing 42.25%
So, the answers are a little less clean cut now, but by power attacking for 3, Roy still manages a 57.75% chance of dropping at least one hobgoblin with a 12.25% chance of dropping two included in the figure instead of a 50% chance of dropping at least one hobgoblin with a 6.25% chance of dropping two hobgoblins included in the figure.
That's still a pretty strong shifting of the odds in Roy's favor.
*You'll notice that these numbers exclude crits--really it should be a little more than that because if Roy crits the hobgoblin (2.5% chance=5% chance to roll a 20 and 50% chance to confirm) minimum damage will drop the hobgoblin.
Elder_basilisk said:
Unfortunately, I redid the math and it's not entirely correct so you were right to ask me to show my work
Against AC 20, Roy hits on an 11: 50% chance to hit. That's part 1. Part 2 is the damage. Roy will stagger the hobgoblin on a 6 (not considered in this analysis) and drop the hobgoblin on a 7 or better. So, that's a 50% chance to drop any uninjured hobgoblin he hits.
So, with no Power Attack:
50% chance to hitx 50% chance to drop= 25% chance to drop a hobgoblin with his first attack.*
Over two rounds, that comes out to:
Drops 2 hobgoblins: .25*.25
Drops 1 hobgoblin and injures a 2nd: .25 (drop 1st)*.25 (injures 2nd)
Drops 1 hobgoblin: .25 (drops 1st round)*.5 (miss 2nd round)+.5 (miss 1st round)*.25 (drops 2nd round)+.25 (injures 1st round)*.5(hits 2nd round--any hit being a kill)
Injures 1 hobgoblin: .5 (miss 1st round)*.25 (injures 2nd round) +.5 (miss 2nd round)*.25 (injures 1st round)
Accomplishes nothing: .5 (miss 1st round)*.5 (miss 2nd round)
Answers
Drops 2 hobgoblins: 6.25%
Drops 1 hobgoblins and injures a 2nd: 6.25%
Drops 1 hobgoblin: 37.5%
Injures 1 hobgoblin: 25%
Accomplishes nothing: 25%
Now the answers actually add up to 100%.
On to the Power Attack for three answer which should have much simpler math:
Power Attacking for 3, Roy is attacking at +6 for 1d12+13. He hits AC 20 on a 14 or better which is a 35% chance. Minimum damage is 14, so every hit drops a 13hp hobgoblin below 0.
So:
Drops two hobgoblins: .35 (drop round 1)*.35 (drops round 2)
Drops 1 hobgoblin: .35 (drops round 1)*.65 (misses round 2)+.65 (misses round 1)*+35 (drops round 2)
Accomplishes nothing: .65 (misses round 1)*.65 (misses round 2)
answers:
drops 2 hobgoblins: 12.25%
Drops 1 hobgoblin: 45.5%
Accomplishes nothing 42.25%
So, the answers are a little less clean cut now, but by power attacking for 3, Roy still manages a 57.75% chance of dropping at least one hobgoblin with a 12.25% chance of dropping two included in the figure instead of a 50% chance of dropping at least one hobgoblin with a 6.25% chance of dropping two hobgoblins included in the figure.
That's still a pretty strong shifting of the odds in Roy's favor.
*You'll notice that these numbers exclude crits--really it should be a little more than that because if Roy crits the hobgoblin (2.5% chance=5% chance to roll a 20 and 50% chance to confirm) minimum damage will drop the hobgoblin.
green slime
First Post
Which brings us to the point, where power attacking or not is entirely mute: As a player, you cannot know how many hit points the creature has left.
At the start of the scenario, you don't even know what the correct AC is. After a few swings, a round or two, you have the AC narrowed down (George missed monster X vs AC 30, Bill hit AC 32)
The only thing the players really know are; the hits they connected, and the amount of damage they dealt (which is not equal to the amount of damage the monster recieved).
All this speculating about the number of hits it takes to down an opponent, and the number of hit points is just guesswork on the part of the player. Might work against large numbers of mooks, but is much harder to do against a specific single BBEG.
Add in the fact, that "merely" injuring opponent is not a lost action; it enables those less capable of dealing Megahits to actually be a tad useful: In EB's example, that would include a non-buffed Cleric, a non-flanking rogue, neither of which are likely, by themselves, at that level, to deal the neccessary 14 points of damage to instantly down opponents.
At the start of the scenario, you don't even know what the correct AC is. After a few swings, a round or two, you have the AC narrowed down (George missed monster X vs AC 30, Bill hit AC 32)
The only thing the players really know are; the hits they connected, and the amount of damage they dealt (which is not equal to the amount of damage the monster recieved).
All this speculating about the number of hits it takes to down an opponent, and the number of hit points is just guesswork on the part of the player. Might work against large numbers of mooks, but is much harder to do against a specific single BBEG.
Add in the fact, that "merely" injuring opponent is not a lost action; it enables those less capable of dealing Megahits to actually be a tad useful: In EB's example, that would include a non-buffed Cleric, a non-flanking rogue, neither of which are likely, by themselves, at that level, to deal the neccessary 14 points of damage to instantly down opponents.
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