Finding the optimal amount to Power Attack

[Piratecat]

This is cool!

 

[Misirlou]

Crits:

Let M = damage multiplier on crit. Let R = treat range. (i.e. for a 19-20/x2 weapon, M=2, R=2).

On the first attack roll, barring attacks against extremely high AC, the chance to hit is (A-T+21)/20. The chance to crit is R/20. A crit is worth (M-1) extra attacks, assuming the confirmation roll succeeds. Hence the expectation to-hit chance, when crits come into play, is:

(A-T+21)/20 +(A-T+21)*R*(M-1)/400
Factoring:
(A-T+21)(1 + R*(M-1)/20)/20

Note that the presence of crits affects this expression only through the appearance of the factor (1 + R*(M-1)/20). This is a constant multiplicative factor, and as such, has no effect on the location of the maximum (when the derivative of this thing is set equal to 0, all constants will vanish).

Now, there is a very slight error here. If you are in a situation where a 19, which normally threatens, misses, then the formula adds in some erroneous possible crit. damage on a 19. However, the error is very small, since the chance of a crit. is 1/400 in this case.

 

[maddman75]

Thanks

You're right that it doesn't take auto-hits and misses into account. It actually doesn't cause any error, except in the extreme case where you would otherwise miss on a natural 20. I decided to ignore it for the sake of simplicity--most people will never even try to attack something with such a high AC.

Heh - in that case the formula doesn't matter. The optimal choice when you need a natural 20 to hit is to power attack full. Its not like your chances to hit are going to go down, it'll still be 1 in 20.

 

[Kid Charlemagne]

How do you adjust for multipel attack rolls with differing bonuses? My 12th level fighter with the +19/+12/+7 attack sequence would tend to throw that off - I suppose averaging the attack bonuses works well enough.

While playing a FTR with Power Attack, I always found that Power Attacking more on any round where I would only get one attack was an excellent strategy, but if I was facing something with a low AC and lots of HP, I'd rather Power Attack very little on any round where I got multiple attacks - especially since my 3.0 FTR had a 12-20 crit range on his scimitar - it was vital not only to hit, but to be able to verify that crit on as many attacks as possible.

 

[buzz]

Or, you could just use the tables in Goodman Games' most excellent Power Gamer's 3.5 Warrior Strategy Guide and not deal wth math at all.

Best $20 I've spent on a D&D product, period.

 

[Misirlou]

As I noted in an earlier post, I haven't actually done the multiple attack case yet, but I have a pretty good idea what it will do. I think averaging them is too much; the first attacks should count more because they hit more often.

Actually, low AC and high HP is the type of monster against whom you should be Power Attacking the most.

Also, if you're using a character with an enormous crit. range, and you're in a situation which in you might miss within your threat range, the formula will slightly overestimate the amount by which you should PA.

Hmm, I guess I'll try to deal with iterative attacks right now.

Normal exp. damage:
(A - T + 21 - x)(D + x)

With one iterative attack:
(2A - 2T + 37 - 2x)(D + x), is maximized when x =
(A - T - D + 18.5)/2

I think the growth is quadratic, but I'll check the next case to make sure:
(3A - 3T + 48 - 3x)(D + x), maximized at
(A - T - D + 16)/2

Huh. Linear. Ok.

In short, for every iterative attack (beyond the first), subtract 1.25 from your optimal Power Attack.
For a flurrying monk, it's minorly more complicated, but the correction will be slightly smaller.
In fact, I was wrong. What this really works out to is just using the average.

 

[Conaill]

Note that this formula harks back all the way to the early 3.0 days. In fact, there was a min-maxing workshop at Gencon 2000 where this was discussed. I remember seeing a very nice write-up of specifically the Power Attack formula, but I can't find it anymore right now.

I did find a page by Jonathan Tweet on wizards.com about various Combat Calculations (including why crit damage works out to +5% damage per crit range, etc.). There's also an article on Character Strategies and Guidelines by Class.

 

[Particle_Man]

Or, you could just use the tables in Goodman Games' most excellent Power Gamer's 3.5 Warrior Strategy Guide and not deal wth math at all.

Best $20 I've spent on a D&D product, period.

2 weird things with that though:

1) The table in that book (5-9) ignores average weapon damage in its power attack table. It just cross-references the attack bonus vs. victim's ac. Since the above formula takes average damage into account, why does the table not do this? Or does the average damage become irrelevant, allowing us to simplify the above formula?

2) The table and formula both don't take iterative attacks into account. For the table, +8 attack bonus does not distinguish between the +6/+1 BAB fighter with a +2 attack bonus from strength, and the +5 BAB fighter with a +3 attack bonus from strength. Now if iterative attacks are pretty much irrelevant, that's another thing.

 

[Misirlou]

1)I've never seen this book (I'm a pretty new D&D player), so I couldn't guess at how they've put their table together. However, your average damage per hit (sum of weapon damage and any bonuses) is clearly necessary for even an approximation.

Think of a 5th-level human fighter with Str 18, wielding a +2 bastard sword, and using Weapon Focus and Weapon Specialization.
Now think of a 5th-level halfling fighter with Dex 18, wielding a masterwork short bow, and with Weapon Focus.
Say they're attacking an AC 20 target.

Both have +12 to attack. However, the first guy averages 13.5 damage per hit, and the second averages 2.5 damage per hit.

As per the formula, the first guy's optimal Power Attack is 0. The second guy's is 5. Big difference.

2)OP edited for iterative attacks.

 

[Conaill]

1) The table in that book (5-9) ignores average weapon damage in its power attack table. It just cross-references the attack bonus vs. victim's ac. Since the above formula takes average damage into account, why does the table not do this? Or does the average damage become irrelevant, allowing us to simplify the above formula?

2) The table and formula both don't take iterative attacks into account. For the table, +8 attack bonus does not distinguish between the +6/+1 BAB fighter with a +2 attack bonus from strength, and the +5 BAB fighter with a +3 attack bonus from strength. Now if iterative attacks are pretty much irrelevant, that's another thing.

Based on this thread over on Goodman Games' website, you can expect to see some errata (including for the Power Attack table) some time after Gencon...