SpikeyFreak said:
The one that's there now has the final damage unprotected.
I just wish I could figure out the formula for calculating the best power attack without using macros.
Xeovke - that sheet is cool.
--Excel-lent Spikey
I just looked at your sheet, and it's quite impressive! BUT, I was incredibly disappointed to find there is no autocrit option, ha! At least mine has .... errr.... the "lightning fist" option?...
As for the formula, I don't think it would be possible to find a nice one that gives you the optimal pow.att. for any number of attack and any average dmg dealt for such attacks, because function F (of variable the pow.att., call it PA) of the probability to hit has a broken shape: it becomes constant under and above certain values, but is linear in between (shaped like ¯\_ ). Then you must multiply this by dmg which is linear in PA plus the possibility of criticals which is F times a linear funtion of PA. So far it's not so bad (...), but add to this multiple attacks... it gets very ugly and you cannot use derivatives to optimize. As I see it, I can think of two solutions:
1) you approximate F by a derivable function (the one I can think of right now which has the good shape is the inverse of tan(-x) ) but then I think it would get comlicated.
or
2) at the end of my "readme.txt" file that goes with my worksheet, there is a little formula that gives you an approximate optimal pow.att., you can make some comparaisons and check it is not that bad most of the time: its main problem is that it very bad for AC's that are way out of the league of the attacker. You could fix it with a MAX function:
MAX( "your damage function for pow.att.=BAB","YDF for pow.att.=MIN( "formula's result" , BAB )" )
Why is it a good fix parenthesis:
for one attack the average dmg looks like Prob*(dmg+PA) where prob is the ¯¯\__ function, now (dmg+PA) is linear in P so has a shape like / . Now these are both positive function so when you multiply them, its shaped like / when Prob was __, /¯\ (that is quadratic) when Prob was /, and / when Prob was ¯¯. I know it is silly to talk about shapes like that, but if you look at it that way, notice the maximum can only appear in the middle or the right segment.
i) If it is in the middle segment it appears on the summit which we know its location: in that part Prob= T-PA (T is the chance to hit, T=21-target's AC+attacker's attack bonus), so
Prob*(dmg+PA)=T*dmg+(T-dmg)*PA-PA^2
hence its summit is at (T-dmg)/2
ii) If it is in the right segment, it is when PA is as great as possible, that is when PA equals your BAB.
so you could make it like as an ecxel command (is that what you had CRGreathouse?)
MAX( "your damage function for PA=BAB","YDF for PA=MIN( (T-dmg/2) , BAB )" )
If you want to get the quantitty PA, use IF( YDF(a) > YDF(b),1,0)*a+IF( YDF(b) > YDF(a),1,0)*b , where "a" and "b" are the candidates for the quantity PA.
If you use the formula I gave at the end of the readme.txt instead of (T-dmg)/2, you would get a nicer approximation of the real optimal pow.att., but this leaves us with one question:
As CRGreathouse noted, there might be a nice way to combine the optimal pow.att. you get for each attack separately to get an even better approx. of the optimal result, something like making an average of PA*(some weight). But I don't really have time to investigate, and I'm actually not sure I would find it.
Also as an improvement on my formula (which does not take acount of the critical hits) you could multiply the pow.att. it gives by about 1+(m/20), where m is the "critical multiplier type" of your weapon, to have better value of the best pow.att. By "critical multiplier type" I mean, for 20/*n then m=n-1, for 19-20/*n then m=2*(n-1), and in general it is (crit. multiplier -1)*(crit. range size).
I think the simplest thing to do is to go "macro", but if you are reticent, with both these changes (the MAX function and the 1+(m/20) modification) to the formula I gave, you will be quite close to the right number, but I have no time to test (you could modify one of my macros to see the result, the one that compares different use of pow.att.). The formula was mostly designed (as you might have seen in the readme.txt examples) to know at which AC you can start usin pow.att., and also to be possibly usable in-game (though I never did, in fact I never used it: I am just happy to know it) without a computer (or even a calculator) at hand.
Hope it helps,
Xeovke
Let yourself go to the macro-side of Excel!
