2009-04-16

Friends-Romans-Countrymen, Games and gaming, Math and Science

If you don’t play Pathfinder (or D&D), you might as well skip this post, unless you’re really interested in some math. It’s a post for novice math geeks, and RPG players. How much Power Attack should a fighter use when pimp-slapping the Monster of the Day? It’s a good question worthy of thought. If you’re a gamer, odds are you want to munch-out for the maximum overall damage, so this information is required.

Power Attack is a feat which allows the character to take a penalty on his to-hit roll from 1 to his Base Attack Bonus, and apply a bonus to his damage equal to the penalty taken. If the character is using a 2-handed weapon, the bonus is doubled. This is quite handy for use on critters that are generally easy to hit. If you’re a risk taker, it can be used to some advantage on more “average” to hit monsters. It’s real benefit is for 2H weapon users who get double the bonus (vice 1.5x strength, rounded down).

Our sample character is Tengu. A level 10 fighter with a 16 strength and a +2 heavy flail. Tengu has appropriate other feats for his level: Weapon focus, Weapon specialization, and whichever greater version of the previous two he can get by level 10. The net effect is a +10 base attack bonus, and +7 other bonuses for an attack bonus of +17 / +12, and does base damage of 1d10+8. Tengu also has improved critical for this weapon, so on rolls of 17 or better there is a chance to roll again, and a hit does double damage.

Sample creature 1 has an armour class of 16.

Tengu, whacking away, only misses his first attack on a roll of natural 1. On a roll 17, 18, 19, 20, there is a second roll that misses only on a natural 1 and will do double damage if it hits. Average damage for the first attack can therefore calculated as (15/20)*(1d10+8)+(4/20)(2d10+16)*(19/20)+(4/20)(1d10+8)(1/20). Green is the damage for a normal hit, red for a critical hit, and pink is a missed critical hit.

For Tengu’s second attack, the bonus is +12 so the probabilities are reduced, although the critical thing remains. A 5 or better is needed on the die to hit at all, and thus the average damage of the second attack can be calculated as: (13/20)*(1d10+8)+(4/20)(2d10+16)*(13/20)+(4/20)(1d10+8)(7/20).

The average damage of 1d10 is 5.5, so these numbers add up to 15.39 for the first attack, and 13.23 for the second attack, for an average damage of 28.62 points per round in straight attacks.

With a power attack of -5 applied, Tengu gets +10 damage, but the probablilities change. The numbers become (13/20)*(1d10+18)+(4/20)(2d10+36)*(13/20)+(4/20)(1d10+18)(7/20) and (8/20)*(1d10+18)+(4/20)(2d10+36)*(8/20)+(4/20)(1d10+18)(12/20). This makes a total average damage of 39.01 for the round. That is a substantial improvement.

What about a full-out -10 Power Attack? That’s +20 to damage. The numbers are: (8/20)*(1d10+28)+(4/20)(2d10+56)*(8/20)+(4/20)(1d10+28)(12/20) and (3/20)*(1d10+28)+(4/20)(2d10+56)*(3/20)+(4/20)(1d10+28)(17/20). That comes out to an average of 35.51 damage dealt per round… almost a 10 percent decline from the lower power attack despite the potential for much larger single hits. The extra damage is offset by the greatly decreased hit probability.

It can be seen, therefore, that munching out to the max of the Power Attack feat is not necessarily the optimal choice, although it does allow you a chance to put some impressive smack-down into play. It is possible to work through those formulae for any character and determine the optimum power attack for a given situation. In Tengu’s case, optimum can be calculated to be -6 on the power attack (39.27 damage per round). After that, it’s trading average damage for spot damage that might be higher… a gamble at best. The optimum number varies with the armour rating of the target. The harder the critter is to hit, the lower the number that is optimal for best damage on the power attack.

By way of comparison, a level 10 sorcerer with a 16 charisma casting fireballs at a creature with a +6 reflex save does an average 41 damage per round.