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Discussion Thread for the Mathematics of Power Attack

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Iainuki:
The main topic is here: http://www.minmaxboards.com/index.php?topic=12229.0.

Gribel:
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.

Iainuki:

--- Quote from: Gribel on January 04, 2014, 07:26:42 PM ---Equation (1)'s sum shouldn't have the +21, it is already included via h.

--- End quote ---

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.

Gribel:
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.

Jackinthegreen:
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.

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