Post/Author/DateTime	Post
cellardweller 01-20-04, 10:29 AM	Introduction This began with a post from Snow, suggesting that blade boots be used as an off hand attack for a two handed fighter. The little min/maxer in my head said "why the heck didn't I think about that?" After all, provided that the pseudo off hand attack can do more than 4 damage per hit it would be more efficient than using power attack. This of course assumed that the optimal amount of power attack was greater than two. I remember someone working out a formula for optimal power attacks but as I can't seem to find it any more, so I thought I'd work it out again (I'm getting a little long in the tooth so maybe one of the fresh young minds out there may want to check my math). Having derived the formula though, an number of conclusions become evident – and that is the point of this work. Part One – The simple things in life are often the best Lets begin with a nice simple view of the world. The power attack user only gets a single attack because they are using spring attack or its the surprise round or whatever. We'll give them a two handed weapon because that is the most common use for power attack and this weapon has a critical range of 20 and a critical weapon modifier of 1. The average damage on a given attack can be expressed as y=P(2x+w) where P is the probability that an attack will land and x is the amount of power attack used and w is the average amount of weapon damage on a successful hit excluding power attack The probability for any attack succeeding is given by P=(z-x+21)/20 Where z=min(Attack Modifier (excluding power attack) - AC of opponent,20) and x=amount of power attack used Substituting P into the original formula we have y=(z-x+21)(2x+w)/20 Expanding and simplifying (I'll be explicit so you can catch my errors ;)): 20y = 2xz-2x^2+42x+zw-xw+21w 20y =-2x^2 + (2z-w+42)x + (zw-21w) For any given encounter z and w are constants so differentiating with respect to x we have 20dx/dy = -4x + (2z+42-w) ddx/dy = -1/5 The second derivative of this function is negative therefore the turning point is a maximum. Substituting dx/dy = 0 we can find this maximum, giving us the optimal amount of power attack to use for any given values of z and w. 0 = -4x + (2z+42-w) x = (2z – w)/4 + 10.5 (Magic formula 1) So for example a L4 str 16 fighter wielding a +1 greatsword with which he has specialisation attacks a Barghest should use 3 points of power attack. x=(2(4bab+3str+1weapon-16AC)-(7greatsword+4str+1weapon+2spec))/2+10.5 x=(2(-8)-14)/4+10.5 x=-30/4 +10.5 x=3 There are a number of observations that we can draw from magic formula 1 (MF1) – some of them obvious and others less so. 1) Power attack favours small fighters A halfling fighter has the same attack modifier as an equivalent human fighter, but does less damage because of a lower strength modifier and weapon size. This means that for any opponent the values of z will be the same, but the halfling will have a smaller value of w and as such will have a higher value for x. 2) Energy (flaming, frost, holy etc.) weapons decrease the amount of power attack you should use Weapon enhancements that increase damage without affecting the attack modifier increase reduce the amount of optimal power attack by one for every 4 points of average damage. 3) Damage reduction increases the amount of power attack that should be used Damage reduction has the effect of reducing w without decreasing z and as such increases x. 4) Straight weapon +'s increase the amount of power attack that should be used Every plus increases the 2z – w part of the equation by one, this increases x by 1/4 Part 2 - Frenzy is power In part one a two handed weapon was assumed to make life easier. In this part I will address single weapons and other factors that affect the rate of return on power attack. The original function of part one can incorporate this effect by re-writing it as y=P(fx+w) where f is the rate of return (1 for one-handed weapons, 2 for two-handed and 3 for a frenzied berserker using a two handed weapon etc). Light weapons will be addressed in part 5. Carrying this factor through the same same steps as in part one. y=(z-x+21)(fx+w)/20 20y = fxz-fx^2+fx+zw-xw+21w 20y =-fx^2 + (fz-w+21f)x + (zw-21w) 20dy/dx = -2fx + (fz+21f-w) 0 = -2fx + (fz+21f-w) 2fx = fz+21f-w x = (fz – w)/2f + 10.5 (Magic formula 2) sanity check: substituting f=2 into MF2 should result in MF1 - check 1) Power attack can be just as efficient for one handed fighters Good news for sword and board paladins and bladesingers. fz-w is generally a negative number for opponents of an appropriate CR, but for a single weapon fighter the amount is a much smaller negative number. If the one-handed fighter averages less that half the damage of their two handed counterpart, they will end up using more power attack. 2) Power attack favours power attack boosters such as frenzied berserker No surprises here Part 3- Haven't I seen you somewhere before? Until now we have been assuming that a fighter will only be getting one attack a round, in this section, the effect of power attack on multiple attacks will be examined. The total damage on a full attack can be expressed as y=P1(fx+w) + P2(fx+w) ... y= sum(Pi)(fx+w) Pi can be written as Pi=(zi-x+21-5(i-1))/20 Sum(Pi) = sum((zi-x+21-5(i-1))/20) Sum(Pi) = n(z-x+21)/20 - sum(i-1)/4 Sum(Pi) = n(z-x+21)/20 - n(n-1)/8 Substituting Sum(Pi) in we have y= (n(z-x+21)/20 - n(n-1)/8) (fx+w) 40y/n= (2z-2x+47-5n)(fx+w) 40y/n= -2fx^2 + (2zf+47f -5nf -2w)x + (2zw + 47w -5nw) differentiating 40dy/dxn= -4fx + (2zf+47f -5nf -2w) finding the maximum 0 = -4fx + 2zf+47f-5nf -2w 4fx = 2(fz-w)+47f-5nf x = (fz-w)/2f + (47-5n)/4 (Magic formula 3) sanity check: substituting n=1 into MF3 should result in MF2 - check 1) The more iterative attacks you have, the less power attack should be used. For every interative attack that you have, the amount of power attack is decreased by 5/4 Part 4 – Quick as a rabbit Thanks to WarRabbit for doing all the math for this section :D. Effects of extra attacks at full bab (from haste, flurry etc) can be factored into the power attack formula as follows: The total damage on a full attack can be expressed as y=P1(fx+w)b + P1(fx+w) + P2(fx+w) ... y=P1(fx+w)b + sum(Pi)(fx+w) Where b is the bonus attacks due to haste, flurry, etc. (i.e. extra full BAB attacks) Pi can be written as Pi=(zi-x+21-5(i-1))/20 Sum(Pi) = sum((zi-x+21-5(i-1))/20) Sum(Pi) = n(z-x+21)/20 - sum(i-1)/4 Sum(Pi) = n(z-x+21)/20 - n(n-1)/8 Substituting Sum(Pi) in we have y= (n(z-x+21)/20 - n(n-1)/8) (fx+w) + b(z-x+21)(fx+w)/20 40y/n= (2z-2x+47-5n)(fx+w) + (2bz–2bx+42b)(fx+w) 40y/n=(2z-2x+47-5n+2bz-2bx+42b)(fx+w) 40y/n=(2z-2x-5n+2bz-2bx+42b+47)(fx+w) 40y/n= 2zfx–2fx^2–5nfx+2bzfx–2bfx^2+42bfx+47fx + 2zw–2wx–5nw+2bzw–2bwx+42bw+47w 40y/n= (-2f–2bf)x^2 + (2zf-5nf+2bzf+42bf+47f-2w-2bw)x + (2zw-5nw+2bzw+42bw+47w) differentiating 40dy/dxn= 2(-2f-2bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) 40dy/dxn= (-4f-4bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) finding the maximum 0 = (-4f-4bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) (4f+4bf)x = 2zf-5nf+2bzf+42bf+47f-2w-2bw (4f+4bf)x = 2(fz–w) + 47f-5nf + 2b(fz-w) + 42bf (1+b)x = (fz-w)/2f + (47-5n)/4 + b(fz-w)/2f + 10.5b Simplifying x = ((fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b)/ (1+b) x = ((1+b)(fz-w)/2f + 10.5(b+1) - 5(n-1)/4) / (1+b) x = ((fz-w)/2f + 42/4 - 5/4((n-1)/(1+b)) (magic formula 4) Sanity check substitute b = 0 into the above formula and you get magic formula 3. 1) Extra non-iterative attacks only matter if you also have interative attacks When n=1 the final term = 0 and x becomes independent of b 1) Extra non-iterative attacks decrease the effect of iterative attacks on power attack As b approaches infinity, the final part of the formula approaches 0 and we return to our single attack model. Part 5 – The critical issue What about the effect of higher critical weapons? Well, now things get messy. Earlier formulas assumed that the critical modifier was 20 *1 so factoring criticals in will have an effect no matter what weapon you use. Average damage with criticals factored in can be written as y = P1(fx+w+tmw/20) + P2(fx+w+mtw/20) + ... where t = max(min(threat range,z+21),1) and m = the critical modifier-1 Simplifying y= sum(Pi)(fx+w+tmw/20) Substituting Sum(Pi) in we have y= (n(z-x+21)/20 - n(n-1)/8) (fx+w+tmw/20) 40y/n= (2z-2x+47-5n)(fx+w+tmw/20) 40y/n= -2fx^2 + (2zf+47f-5nf-2w-tmw/10)x + (2zw+47w-5nw-tmwz/10+47tmw/20-ntmw/4) differentiating 40dy/dxn= -4fx + 2zf+47f -5nf -2w-tmw/10 finding the max 0= -4fx + 2zf+47f-5nf -2w-tmw/10 4fx = 2(fz-w)+47f-5nf-tmw/10 x = (fz-w)/2f + (47-5n)/4 - tmw/40f (Magic formula 5) Sanity Check: Substituting t=1 and m=0 into MF4 should result in MF3 – check 1) High Critical modifiers have negative effect on powerattack This one's a little suprising. For any given fighter against any given opponent they should use more power attack if they are using a low critical weapon. 2) The effect the critical modifier has on power attack is independent of your attack modifier or opponents The t*m factor is part of the is not dependent on z so any given critical modifier has as much a negative effect on power attack for a 1st level fighter as a 20th level fighter (provided x>0). Part 6 The lighter side of life Looking at MF's 2-4 it isn't exactly clear how power attack would work for an light offhand weapon. If you substitute f=0 into these equations you will get a division by 0 – not good. In order to model the effect of a light offhand weapon, both hands need to be factored in. y= P1(fx+w+tmw/20) + P2(fx+w+mtw/20) + ... + P'1(w'+t'm'w'/20) + P2(w'+m't'w'/20)+... y= sum(Pi)(fx+w+tmw/20) + sum(P'i)(f'x+w'+t'm'w'/20) since f' = 0 y= sum(Pi)(fx+w+tmw/20) + sum(P'i)(w'+t'm'w'/20) substituting values for sum(Pi) and Sum(P'i) in y= (n(z-x+21)/20 - n(n-1)/8) (fx+w+tmw/20) + (n'(z'-x+21)/20 + n'(n'-1)/8) (w'+t'm'w'/20) simplifying 40y= n(2z-2x+47-5n)(fx+w+tmw/20)+(2n'z'-2n'x'+47n'-5n'^2)(w'+t'm'w'/20) 40y= -2fnx^2 + (2nfz+47nf-5fn^2-2nw-ntmw/10-2w'n'-2n't'm'w'/20)x + (2n'z'+47n'-5n'^2)(w'+t'm'w'/20) + (2zw+57w -5nw-tmwz/10+37tmw/20-ntmw/4) differentiating 40dy/dx= -4fnx + 2nfz+47nf-5fn^2-2nw-ntmw/10-2w'n'-n't'm'w'/10 finding the turning point 4fx = 2fz+47f-5fn-2w-tmw/10-(2w'n'+n't'm'w')/10n x = 2fz+47f-5fn-2w-tmw/10-(2w'n'+n't'm'w')/10n x = (fz-w)/fx + (37-5n)/4-tmw/40f – (2+t'm')n'w'/40nf (Magic formula 6) 1) Amount of power attack depends on the “handed-ratio” The final term that reduces x is directly proportional to n'/n so the more off hand attacks that you have relative to your “main” hand the less power attack should be used 2) The more damage that is being done by your off hand, the less power attack you should use. As w' and t'm' increase the final factor also increases so you should use less power attack. 3) High criticals on your main hand may make power attack a viable option for two-weapon fighting. The final factor is divided by 40f so the final factor can be nullified (but f affects the second last term - its a balancing act!) Part 7 My mum says I'm tough Formula for non-light off hand weapons coming soon. Part 8 Huh? With all these increasing complicated formulas for calclulating optimal power attack what practical use can they be? Perhaps I can illustrate with an example. Let start by plugging the same fighter vs Barghest situation into magic formula 4, but lets up him to level 6 to give him a second attack. x = (fz-w)/2f + (47-5n)/4 - tmw/40f x=(2(6bab+3str+1weapon-16AC) -(7greatsword+4str+1weapon+2spec))/2 +(47-5*2attacks)/4 - 2threatrange*1multiplier*(7+4+1+2)/(40*2) x=(2(-6)-14)/4+37/4 - 28/80) x=-26/4 +37/4 - 7/20 x=2.4 So our advanced fighter now uses 2 power attack against the Barghest defeats it easily. Not happy about the turn of events, evil dm decides that his big brother comes around the corner to investigate. A greater barghest has an ac 2 higher than it's baby brother and therefore decreased z by a comensuate amount. Because f and w are constant, we can instantly see that x is decreased by 2 points for every extra point of AC and the fighter should not use power attack at all (x=0.4). The moral of the story is that not necissary to re-calculate the whole equation for each because z, w and f are more or less static, you just need to know your optimal power attack for a particular AC work out how x varies with z for your fighter. Calculations on the fly are then as easy as Pi! Final Words There you have it, the optimal power attack usage for any weapon configuration against any opponent. For practical use, the value for z is probably an estimation (unless you have been peaking over the dm screen) so magic formula 3 is as far as you will really need to go. Enjoy, CD. Enter the proof readers. V0.1 Initial Version V0.2 Fixed up some random sign swapping Reversed conclusion 3.1 V0.3 Added sections "Huh?" V0.4 Added sections "Quick as a rabbit"
Yekoj 01-20-04, 11:28 AM	Wow. uhh.... Wow. It would be cool to add a "power attack for dummies" formula in its own separate area of this post. I.e. help dopes like me see how to do all the work possible pre-combat so they are ready to toss in a guestimate of the enemy AC and do some simple math before declaring their power attack. I can sort of do this using your attacking a barghest model but I get confused about "n" and such in Magic Formula 3. Also, it would be helpful to know (roughly) how much each of the interesting facts impacts power attack. For example, you note that power attack "favors" small attackers and frenzied berserker power attack boosters. But how much (roughly and perhaps relatively)? Likewise, what degree of precision do you recommend. I.e. do different crit multipliers effect the result by .1-.2 or by 5-6 points of power attack (i.e. can they safely be ignored by players or not). Thanks, Yekoj
Qflash 01-20-04, 11:39 AM	Cellarsweller, you must have had some time on your hands but i have to admit that this is nice work man! I started to get it but remembered that I do enough math at work now!..... But props to this post.... Q
Snow Savant 01-20-04, 12:06 PM	Nice work, CD! :) I found to be most useful, the results of your TWF with 2-Hander & Auxiliary Weapon (Blade Boots, Spiked Armor, etc.). Especially since that is a fairly new and in vogue combat style. That -2 attack penalty for TWF puts a slight crimp on the Power Attack usage of the 2-hander. Although there are ways to circumvent that (KotMC's Combat Sense, etc.). Another interesting thing of note is the recent builds that emphasize Karmic Strike. Since Power Attack attack/damage mods apply until your next turn, a Karmic Strike combatant will be getting a more consistent and multipled use of his Power Attack mods. So I'm guessing that: 1) The more attacks you have, the more power attack should be used. Intuitively I would have said the opposite, but looking at Magic formula 3 it is clear that x increases by 5/4 for every attack available. ... means that Power Attack has good synergy with Karmic Strike users. But perhaps not as much with Karmic Strike / Double-Hit (Double-Hit is also a feat) users. CellarDweller, I'd be curious what your take on that combat style would be in reference to your algorhythmic results. XO, Snow :cloud9:
adiaven 01-20-04, 12:18 PM	Magic Forumla for Dummies Optimal Power Attack = (The difference between your To Hit and target's AC)/2 + (Your average damage)/4 + 10.5 Example: Your To Hit is +21 Target AC is 27 Your average damage is 13 (2D6 + 6) OPA = (21-27)/2 + 13/4 + 10.5 = -3 + 3.25 + 10.5 OPA = 10.75 His formula says your best powerattack is 10 or 11.
Sisyfos 01-20-04, 12:19 PM	Yes... A simple formula which I can do fast in my head would be nice :-) I know that in many gaming groups other players will start to look at the munchkin a bit funny if he whips out a calculator and punches figures in his ready made formula to determine the optimal PA amount :angel: ... we need to be stealthy with this kind of information to keep the other players and DM from our back. Great work! Sisyfos EDIT: So many posts between the time I started to read the thread and posted... fast action guys 'n gals.
adiaven 01-20-04, 12:28 PM	A table would work best, so you dont have to do any math at all at the gaming table... I could whip up some tables for the basic cases (1 attack, 1 full round attack with 1 weapon, 1 full round attack with 2 weapons)
Funny Slaughter 01-20-04, 12:32 PM	wow, some of you seem to be really afraid of letters, a magic formula for dummies thus resulting in writing a whole text instead of a clear variable declaration. should be quite simple to write a little application for this or, even more easy, include this into an excel-sheet. keep the formulas coming for all the different fighting-styles and if nobody else wants to do this i will write a little VB in an xls-file and post a link to it. as long as i dont have to do gauss-distribution with it... gs Funny
SoulLord 01-20-04, 01:39 PM	Very nice so what would be the numbers for a dragon disciple using a TH falchion and armor spikes? bard1/barbarian1/bard3/Dragon disciple 10 SoulLord
thorian 01-20-04, 01:59 PM	Part 5 The lighter side of life Looking at MF's 2-4 it isn't exactly clear how power attack would work for an light offhand weapon. This one is very simple. Power Attack can not be used with light weapons (PHB, pg. 98), unless they are unarmed or natural attacks.
Sisyfos 01-20-04, 02:03 PM	Originally posted by SoulLord Very nice so what would be the numbers for a dragon disciple using a TH falchion and armor spikes? bard1/barbarian1/bard3/Dragon disciple 10 SoulLord Just punch in the numbers.
pawsplay 01-20-04, 03:06 PM	My rule of thumb has been: if you're using a two-hander or two weapons, use about half your to-hit bonus, otherwise use a third. Very useful maths, but there are limitations to what was put forward. It does not address the damage YOU are taking. Ending the fight early is better than ending it later. A weapon with a high crit modifier might not average any more, but its range means that a strong Power Attack has the potential to end the fight in one or two rounds.
michael_noah 01-20-04, 03:20 PM	And if you power attack more than you should with your high critical range weapon, that in turn means that you have a chance of dying before you hit the guy. Especially for a PC, whose life is hopefully long, you should always go for whatever is best on average.
pawsplay 01-20-04, 03:23 PM	It's better to swish a few times and finally take someone out, than to do really good "average" damage every round until you are dead. Sure, you might go for broke and lose. You might also shoot for the average and lose. The average damage per round does not tell you how many rounds, on average, you will need to take out your opponent.
Fwib 01-20-04, 03:37 PM	Originally posted by pawsplay The average damage per round does not tell you how many rounds, on average, you will need to take out your opponent. Errr... how not? you don't know their number of hit points?
mean_liar 01-20-04, 03:45 PM	Actually, my experience with Power Attack (from a plug and chug spreadsheet, no formulas, just results) is that most optimal uses of Power Attack occur in the +0 to +1 range. Only against significantly lower AC opponents (AC roughly 5 greater than your adjusted AB or less) would you use more, and even then only in the 4-5 range. FYI.
Zaruthustran 01-20-04, 03:46 PM	Originally posted by Snow Savant Nice work, CD! :) I found to be most useful, the results of your TWF with 2-Hander & Auxiliary Weapon (Blade Boots, Spiked Armor, etc.). Especially since that is a fairly new and in vogue combat style. Fairly new? Really? I've been using two-handed weapon + armor spikes since 3E first came out. Just seemed like an obvious way to maximize damage and number of attacks. It's even better in 3.5, of course. Unfortunately, there is much, much debate on whether a two-handed weapon can be used in two-weapon fighting. I'm in favor of it, but it seems the majority of rules lawyers are against it. A search of Infinite Monkeys will turn up the particulars (the debate raged for about a week). The crux is the term "off-hand weapon". Anyway, if you're into the two-handed weapon + non-handheld secondary weapon thing you might find the discussion interesting. -z PS: infinite monkeys is a yahoo group for hardcore Living Greyhawk rules lawyers.
adiaven 01-20-04, 03:55 PM	Originally posted by pawsplay It's better to swish a few times and finally take someone out, than to do really good "average" damage every round until you are dead. Sure, you might go for broke and lose. You might also shoot for the average and lose. The average damage per round does not tell you how many rounds, on average, you will need to take out your opponent. ehh? How is: 25, 22, 23, 27, dead worse than wiff, wiff, wiff, wiff, wiff, wiff, 94 - dead It's almost always better to go with the average good damage per round then the rare mega hit, especially against an opponent you are sure you can beat. One streak of bad luck can mean that you die before getting off that mega hit. Sure, you can get lucky and get the mega hit in early and kill him, but you have the same odds of missing a lot and dieing. Why not go for the average damage and the sure win? Also keep in mind that the amount of damage changes the tactics of a fight against an intelligent opponent. If they are taking damage early in the fight, they will usually start to fight more defensively or retreat, which means even less damage and less chance of death for you. The only time you should go for the rare, but huge hit power attack is when you are fighting an opponent that clearly outmatches you, and your only hope is to get lucky and land 1 or 2 mega hits early on. Of course a truly smart fighter would retreat from any battle he does not have the advantage.
Elgonn 01-20-04, 04:00 PM	Average and consistent favors PCs. You never want to count on Luck as a PC.
SoulLord 01-20-04, 05:19 PM	Originally posted by thorian This one is very simple. Power Attack can not be used with light weapons (PHB, pg. 98), unless they are unarmed or natural attacks. assuming one takes improved unarmed strike then you can take a THW and still use kicks as your off-hand weapon and youll have the benefits of using power attack
michael_noah 01-20-04, 05:26 PM	And don't forget, we're not just talking about: Case 1: a) average damage, hits on average b) Big damage, misses a lot c) average is the same we're talking about: Case 2: a) average damage, hits on average b) big damage, misses a lot c) average is better for (a) In fact, it's been mathematically proven for us (thanks!). You can't succesfully argue for option (b).
Ehlonnia 01-20-04, 06:11 PM	The question deals with when it becomes inefficient for a two-weapon fighter to use power attack. It is granted that the light weapon will not get the bonus from power attack, but it will suffer the penalty to hit, regardless. Originally posted by thorian This one is very simple. Power Attack can not be used with light weapons (PHB, pg. 98), unless they are unarmed or natural attacks.
sshuit 01-20-04, 06:29 PM	CD : Can you explain this section here?.. I'm not quite sure what z is supposed to be. what is that last ",20" about? The probability for any attack succeeding is given by P=(z-x+21)/20 Where z=max(Attack Modifier (excluding power attack) - AC of opponent,20) and x=amount of power attack used
pawsplay 01-20-04, 06:49 PM	Errr... how not? you don't know their number of hit points? Because it's calculated a different way. It requires The Calculus. But here's the basic idea. If you use the big whiff method: a) There is a chance you may just keep on missing. b) There is a chance you may end the fight early. a) decreases for more swings, while b) increases for more swings. Thought problem: You are facing an opponent with 20 hp. He is wielding an unholy bane v. humans greataxe. You have 20 hp and you are a human Paladin. Would you rather have: a) a weapon that does 1d8+11 damage b) a weapon that does 1d0+10 damage Now, both weapons average 15.5 damage. But the second one has a 1 in 10 chance of killing your opponent in one hit. Thought problem 2: The Wight Now, would you rather definitely kill an opponent in three rounds, or would you rather have a decent shot at killing him in one, a more likely one in two, and a fair possibility of missing three rounds in a row? Every round you fight, there is a chance you will be hit with an energy drain. Therefore, the longer the fight, the worse off you are. Let's compare 1d20 with 2d10. The first averages 10.5, the second, 11. So 2d10 is better. Now let's suppose you have a limited number of rolls to reach 30 or more total. It's possible to do this on 1d20 with just two 15's, or a 20 and a 10. Not too improbable. But because 2d10 exists on a bell curve, the chances of getting two above average rolls is much less. In other words, the lower your opponents hit points, and the more damage they can do in a turn to you, the better off you are with Power Attack.
Snow Savant 01-20-04, 07:12 PM	Pawsplay said: In other words, the lower your opponents hit points, and the more damage they can do in a turn to you, the better off you are with Power Attack. At least in my metagame environment, too many savvy DM's use exotic and/or templated monsters these days. Especially with the tons of monster & template types now available from all the sourcebooks and the 3 creature catalogs. It's too difficult to determine how many HP's my foes have or their damage capabilities. As it is, when my character sees 4 Orcs walking toward him, I don't trust my knowledge of the Monster Manual anymore to guide me into making definitive mathetical determinations about their game mechanical. So when it comes to damaging these 4 mystery Orcs (or whoever), I want to hit them consistently and often. I don't want to gamble knocking them out with a huge hit that may or may not come. I can also make tactical decisions about adjusting the way I fight by the way my hits make contact with them and judging their reactions. And god forbid I hit that foe *finally* with a sure-thing maxed-out Power Attack only to find out that he has stupid-high DR against something I am not prepared for. Ergo, hit consistently, hit often, make dynamic tactical decisions en route to the creature's demise. There are too many X-factors with foe identification anymore to be able to say for a fact that a wight is a wight .... and not something more, or less for that matter. Now, if your DM gives you simple foes from the MM, with little variation, everything changes for the better for you. But nobody around here has a non-killer DM, do they? ;) XO, Snow :cloud9:
WarRabbit 01-20-04, 07:27 PM	Cellardwellar, In your formula for Pi you have: "Pi can be written as Pi=(zi-x+21-5(i-1))/20 Sum(Pi) = sum((zi-x+21-5(i-1))/20) Sum(Pi) = n(z-x+21)/20 + sum(i-1)/4 Sum(Pi) = n(z-x+21)/20 + n(n-1)/8" I believe the formula should be: Sum(Pi) = n(z-x+21)/20 - n(n-1)/8 Which leaves you with: x = (zf - w)/2f + (37-5n)/4 (Magic Formula 3) However, I"m puzzled why when plugging n=1 back into the formula the result is not Magic Formula 2...so maybe I'm wrong, but I did try some practical examples in excel and the Formula for Sum(Pi) I gave above seems to work. Something isn't right. Maybe you can tell me where my thinking is wrong Cellardwellar? One Example I used: z = total attack bonus = +15 n = # of attacks = 3 x = AC of target = 20 My Formula Sum(Pi) = 3(15-20+21)/20 - 3(3-2)/8 = 1.65 Your Formula Sum(Pi) = 3(15-20+21)/20 + 3(3-2)/8 = 3.15 First Attack Actual Hit Probability = (15-20+21)/20 = 0.80 2nd Attack Actual Hit Probability = (15-20+21-5)/20 = 0.55 3rd Attack Actual Hit Probability = (15-20+21-10)/20 = 0.30 Actual Sum(P) = 1.65, which matches my formula. Edit: Actually, after double checking my math I believe the Magic 3 Formula is: x = (zf - w)/2f + (47 - 5n)/4 And substituting n=1 into this formula does give you Magic Formula 2. Thus the Sum(Pi) formula should have been: Sum(Pi) = n(z-x+21)/20 - n(n-1)/8
Funny Slaughter 01-20-04, 07:35 PM	Average and consistent favors PCs. You never want to count on Luck as a PC. how about a cleric of fharlanghn? seriously, i think the use of power-attack is one of the basic mechanics of the game. in sword and fist there is a very similar section about the use of flurry attack so i dont think one is totally off in munchy-land by using this. i think nearly every experienced fighter could teach one how to use power attack. in fact every PC who knows this feat should know this, too. its you, as a player, who is acting stupid if a character that survived for many years or even decades with fighting experience that could serve for whole armies is swinging his sword into the tree all the time just because you do know the mechanics but ignore them. in my opinion the best use for power-attack is when you get into situations that favor you. your enemy is prone and you flank him, thats +12 to damage, cool! but eventually its smarter to hit him better, after a few strikes you should be able to guess his AC and adjust your use of PA. a formula helps a lot here, experienced gamers use it without even knowing i think. gs Funny
pawsplay 01-20-04, 07:36 PM	I still think for humanoids and NPCs, a few strong Power Attacks are a nice opener. After that, something more conservative. In fact, assuming you can whittle down the opponent, Power Attack becomes less and less useful. Against a dragon or something, averages are probably on your side.
Elgonn 01-20-04, 08:06 PM	Originally posted by pawsplay In other words, the lower your opponents hit points, and the more damage they can do in a turn to you, the better off you are with Power Attack. Isn't this like saying that if you aren't statistically going to win then hope for luck and big hits? Because I think you are actually proving that if you opponent has tiny hit points and does a lot of damage your better off with expertise. You always want consistency. Originally posted by Funny Slaughter how about a cleric of fharlanghn? Let him pray for luck. If he needs it he is already doomed. Now if he could make his opponents reroll. *grin*
cellardweller 01-20-04, 08:34 PM	Snow wrote CellarDweller, I'd be curious what your take on that combat style would be in reference to your algorhythmic results. It all depends on how your strength and extra sources of damage. If you want to find out if it is better or not, plug your values into magic formulas 3 and 5 to find out optimal z plug these into the average formula solve for average damage(thf) > average damage(twf). I may add an extra section on doing this tonight. thorian wrote [B]This one is very simple. Power Attack can not be used with light weapons (PHB, pg. 98), unless they are unarmed or natural attacks. No, but it can be used on the longsword that you are holding in your other hand. Any attack penalty applies to both weapons, but the damage bonus only applies to the one handed weapon. sshuit wrote Can you explain this section here?.. I'm not quite sure what z is supposed to be. what is that last ",20" about? The number of different "numbers" that can be rolled without power attack is z+21. Every point of of power attack reduces that number by one so we get (z-x+21). The number of distict "numbers" that can be rolled is 20 so the probablilty of a "hitting" roll is (z-x+21)/20 WarRabbit wrote In your formula for Pi you have: ... Yep, something looks a bit off here. I'll check it properly when I get back from work tonight. cellardweller wrote Effects of haste, flurry and other sources of extra non iterative attacks can be factored in by adding Magic formulas 2 and 3 together. Effects of two weapon fighting where there are two sets of iterative attacks can be factored in by adding magic formula 3 to itself (with appropriate values for f and z). While the first statement is true, the second is in error. In calculating dy/dx for iterative attacks, I am dividing both sides by n, so for two weapon fighting with two non-light weapons, the "handed-ness" factor (n'/40fn) will be involved. I will add this as section 6 tonight.
Psifon 01-20-04, 10:53 PM	Well, not being a math wiz, I weant ahead and used a spreadsheet program I found on the web to create a table of PA values for my character. Here is a portion of the tables: Av/BAB 0 1 2 3 4 5 6 3/-2 93.9/35.7 96.3/38.1 98.3/40.6 99.7/43.1 100.7/45.5 98.6/45.5 95.7/45.2 4/-1 90.1/35.7 92.3/38.1 94.1/40.6 95.2/43.1 93.5/43.1 91.0/43.0 87.7/42.5 5/0 86.3/35.7 88.3/38.1 89.8/40.6 88.4/40.8 86.3/40.8 83.4/40.4 79.7/39.9 6/1 82.6/35.7 84.3/38.1 83.4/38.5 81.6/38.5 79.1/38.4 75.8/37.9 71.7/37.2 7/2 78.9/35.7 78.2/36.1 77.0/36.3 74.8/36.3 71.9/36.0 68.2/35.4 ------- 8/3 73.2/33.8 72.2/34.1 70.5/34.2 68.0/34.0 64.7/33.5 ------- ------- 9/4 67.6/31.9 66.2/32.1 64.1/32.0 61.2/31.7 ------ ------- ------- 10/5 62.0/30.0 60.2/30.1 57.7/29.9 ------- ------ ------- 11/6 56.3/28.2 54.2/28.1 ------- ------- ------ 12/7 50.7/26.3 48.2/26.1 ------- ------- ------ 13/8 45.1/24.4 42.2/24.1 ------- ------- ------ 1) Power Attack VS Number need to hit (Average Iteritive/Full BAB). Base average damage is 23.5+7, Criticals are figured in. Av/BAB 0 1 2 3 4 5 6 3/-2 76.3/29.0 78.0/30.9 79.3/32.8 80.3/34.7 80.9/36.6 79.0/36.5 76.5/36.1 4/-1 73.2/29.0 74.8/30.9 75.9/32.8 76.7/34.7 75.1/34.7 72.9/34.4 70.1/34.0 5/0 70.2/29.0 71.5/30.9 72.5/32.8 71.2/32.9 69.3/32.7 66.8/32.4 63.8/31.9 6/1 67.1/29.0 68.3/30.9 67.3/31.1 65.7/31.0 63.5/30.8 60.8/30.4 57.4/29.8 7/2 64.1/29.0 63.4/29.3 62.1/29.3 60.2/29.2 57.8/28.9 ------ ------ 8/3 59.5/27.5 58.5/27.6 56.9/27.6 54.8/27.4 ------ ------ ------ 9/4 54.9/25.9 53.6/26.0 51.8/25.9 49.3/25.6 ------ ------ ------ 10/5 50.3/24.4 48.8/24.4 46.6/24.2 ------ ------ ------ 11/6 45.8/22.9 43.9/22.8 ------ ------ ------ 12/7 41.2/21.4 39.0/21.1 ------ ------ ------ 13/8 36.3/19.8 34.1/19.5 ------ ------ ------ 2) Power Attack VS Number need to hit (Average Iteritive/Full BAB). Base average damage is 23.5+7, Criticals are NOT figured in. This character is a ftr 10/weaponmaster 1 with a mercurial greatsword +3 that also has holy (hence the 23.5+7 for average damage) The single diget numbers in the far left column represent the lowest number needed to hit a given AC for an average attack. The number before the slash assumes a full iterative attack, while the number after the slash represents a single attack for the round (hence the 5 point difference) The numbers along the top (that don't line up) are the number of points of power attack put into the equation. The numbers before the slash represent the average damage of a full iteritive attack. The numbers after the slash represent the average damage of a single attack at full attack bonus. While hard to read, in the current format (I'm not a computer wiz either), There are a couple of things that I noticed right away with these tables. I really don't know if this will hold true for all characters, but I thought I would share since it might be usefull to some. 1) At low AC's the amount of damage delt by a single attack was about a third of the whole average damage. At a higher AC, this ratio closed to about 2-1. This obviously makes sense given that you will hit more often with a low AC, but it is usefull to us non-math wiz guys to have this kind of thing spelled out. 2) There is a break point for the best average damage, and there is a second break point for the MOST power attack you can put into an attack routine without hurting your average damage. These two points (while I am sure are already clear to many), have some interesting in-game implications. I tend to think of monsters (of any stripe) in terms of "hit kills" An average orc is a 1-hit kill monster. A hill giant for this particular character is about a 4-hit kill monster. 1) if you are going for better average damage, use small amounts of PA to boost your average damage. Probably, most of the time, this is the better choice. This is a good idea when you are not sure how many hit-kills you are facing, but have a good idea what the AC is. 2) If you can expect to take a lot of full BAB swings in a round, it might be worth it to pump a lot into PA. No suprise here really, but if you are using WWA or expect a lot of AoO's in the round, then PA is your friend. The idea here is that if you can reduce the number of hits it takes to kill the foe, then average damage may not be the best way to conceptualize the attack. Here you might want to use the maximum possible PA value for your routine. This is better used against groups, since they tend to take less hit-kills to drop (and often have worse AC's). So in this case, you may be able to use a lot of PA to turn a 2 hit-kill into a 1 hit-kill. Here follow a couple of tables that show the ideal PA value and the best PA value for the full BAB and the average Iteritive attack. Large Size, W/ Crits Vs Evil Full BAB Ideal Max Average It. Ideal Max -2 5 10+ 3 4 6 -1 4 10 4 3 5 0 4 9 5 2 4 1 3 7 6 1 2 2 3 4 7 0 0 3 2 3 8 - - 4 1 2 9 - - 5 1 1 10 - - 6 0 0 11 - - 7 - - 12 - - 8 - - 13 - - Medium Size, W/O Crits Vs Evil Full BAB Ideal Max Average It. Ideal Max -2 5 10+ 3 4 7 -1 5 10+ 4 3 6 0 4 10 5 2 5 1 4 8 6 1 3 2 4 6 7 1 1 3 3 5 8 0 0 4 2 4 9 - - 5 2 3 10 - - 6 1 2 11 - - 7 1 1 12 - - 8 0 0 13 - - This supports the notion that for the most part, if your foe doesn't take a crit, you want to use more power attack, by like one point or so. OK, so this probably wasn't the most helpfull post (what whith the crappy tables and all), but I am sick of seeing "best power attack" numbers that don't reflect both the full BAB by itself and the Iteritive attack. They are so different it is important to express both. Anyway, I hope someone finds this helpfull.
pawsplay 01-20-04, 11:10 PM	Isn't this like saying that if you aren't statistically going to win then hope for luck and big hits? My main point is that comfortable averages won't protect you from taking damage each round.
Elgonn 01-20-04, 11:40 PM	Originally posted by pawsplay My main point is that comfortable averages won't protect you from taking damage each round. Neither will big hits. It just has a chance to. But the biggest problem with big inaccurate hits is that you are considerably more likely to not just take damage but die. Death is infinitely worse than damage. You 30 HP Opponent 30 HP - Deals 10 damage with a 50% chance to hit. You win init You playing it safe deal 10 damage with an 75% chance to hit You playing it dangerously deal 30 damage with a 25% chance to hit. You deal the same average damage per round either way. Who is more likely to die? Safety boy or Danger boy? How far from statistical average does one or the other have to slide to fail? How likely is it that you can scale damage equally to hit chance?
Psifon 01-21-04, 12:33 AM	I'd like to turn this arguement on it's head. When is it better to go for the big hits, and when is it better to play it safe? I would say that if you are planning to do an iteritive attack it is better to go for average damage with a few points of power attack to maximize your average damage. On the other hand, if you are expecting to be able to run a combination of attacks based on Combat Reflexes and Great Cleave, you want to power attack for more. Assuming that you are more likely to drop a foe with a single hit thanks to the big PA add, you want to draw on an inside straight and hit big, so that you can get yet ANOTHER attack out of the mix. The same would hold true for a situation where you think that you are able to drop a foe with a big PA and you are doing a WWA. In this case, you are striking all the foes in reach, but it really doesn't help you to do average damage to each foe if you aren't going to drop any. Here the PA is actually a DEFENSIVE option, because when you PA and drop a foe, that is one less attack aimed at you this round and after all, you ARE outnumbered or you woudln't be WWA'ing in the first place. Less clear is when you are doing a single attack for the round. One common scenario is when you are first joining combat. You don't really know what you are up agianst at all, so even figuring what the AC is is just a guess. So do you want to PA at all, PA a little or PA alot? I would go for PAing alot, simply because I am probably fresh, and while one hit of average damage probably won't make a huge difference to the outcome of the fight, one hit of alot of damage might. But then a miss might as well, so this is pure judgement call. If you are fighting a creature that has lots of attacks but little relative damage per attack, then you want to spring attack. Ok, so now what? Do you PA for a large amount and wait for luck to shine on you, or do you whittle it down? I would probably go for whittling it down, with only the "optimum" PA (or purhapse even no PA), in this case, counting on my better damage per hit (and my party) to win the fight. This all hinges on my prior post and the observation that there is both an optimum amount of PA to use for an attack routine, and a maximum amount that you can use without hurting your overall optimum damage. You can use enough to increase your average, or you can use enough to keep your average the same, by doing more damage and hitting less often. These two numbers are of course different if you are working on full BAB or average Iteritive attack, so we are really talking about four number here. I really think that the whole analysis of how much PA to use against a given AC is extremely useful, however, I think there is a certain amount of art as to WHEN to use it. I also think that there is a time to use the optimum amount of PA and a time to use the Maximum amount of PA, depending on what your situation is.
cellardweller 01-21-04, 01:10 AM	I'd rather trust statistics than any mysterious "art" ;) The formula's derived optimise for average damage per round, assuming that the resisdual damage will be negligable - If you are fighting many low hp opponents it won't be. To minimise damage you are taking what you are trying to do is kill your opponent as quickly as possible. So instead of maximising damage you do, you want to minimise the number of rounds that the fight goes on for - ie instead of maximising y, minimise (h div y)+1 (where h is the opponents hit points). It will make the formula's considerably more complex because dy/dx becomes a peicewise function, but it is definitely doable. EDIT: Me learn how talk good.
Psifon 01-21-04, 01:42 AM	Well, right. At the same time, you aren't going to know how many HP's the enemy has and you aren't going to know what his AC is, so you have to guess. Guessing is an art, not a science. That said, it is extremely usefull to know what your optimum PA value is for any given attack routine. But it is not the only thing you have to know, and there are so many possible variants that the best you can do is estimate. For instance, which formula do you use on a round where you start in base-to-base combat with a foe (who is already wounded no less, and might be able to take 2-3 more hits), but you can reasonably expect that 1-3 more opponents are going to close with you between rounds, and as such you will be able to bring your spiked chain to bear against them using the combat reflexes feat? Do you put a little bit of PA into your iteritive attack, and have a sub-optimal attack routine against the AoO's that are (possibly) comming in, or do you put enough PA to buff your full BAB attack to optimal and increase the risk of not dropping your foe? Your equation cannot answer this question. You HAVE to make a judgement call based on the battlefield conditions. Have the incoming opponents taken a fireball earlier in the combat? Are they likely to take one before they get to go? Are there other targets besides you who they are going for or are you all that stands between them and the rest of the party? Do you have the great cleave feat, and is it likely to make a difference in this fight? Is your crit range and multiplier good enough that you can expect to crit one foe and drop him, allowing yet ANOTHER attack against your primary foe (with cleave) if you failed to drop him during your action? How many HP do you have left, anyway? I mean, the list goes on and on. You can't apply an equation to these questions. Knowing the best PA value is a critical piece of information in making these decisions, but it is not the only piece by a long shot. That is why I love having this info (or I wouldn't have bothered with the tables) but it is not all I want to use. And really what fun would it be if it were any other way? It's an art! an art I tell you! ;)
cellardweller 01-21-04, 02:09 AM	The estimation of z, h and w (due to dr) could be construed as an art, i guess. Unless of course you are the gm :smirk: - but that just mean.
mean_liar 01-21-04, 08:06 AM	MS Excel tells me that the art is either +1 or +0 in most cases, and much higher on the fringes. :)
Funny Slaughter 01-21-04, 08:17 AM	MS Excel tells me that the art is either +1 or +0 in most cases, and much higher on the fringes. i always thought about power-attack being a cleric- and monster-feat. clerical buffings can get his to-hit into regions where its safe to put the BAB into PA completely. and there are quite a lot of monsters that hit the average PC AC (not AC DC) so easy that PA is nearly a must. in other cases its often just a stone on the path to the "i did the most damage award" or simply to take divine might. PA is not good for "most cases", but there are enough situations where you can use it very good gs Funny
pawsplay 01-21-04, 12:17 PM	I don't think going for an average is "playing it safe." There's the old 3rd level character versus an orc warrior thing. An orc warrior, despite having 1 HD, has a pretty good swing with that greataxe, and a truly nasty crit. On the other hand, he only has a few hp. So you swing and kill him. Now, you eventually come face to face with the war chief. He's like a 3rd level barbarian or something, and has the same nasty swing. Now, it's true you may keep missing. But even if you keep hitting, he may drop a few party members. On the other hand, if you put some Power Attack into it, you have a good shot at dropping him in or two rounds. And then there's the Attacks of Opportunity thing. Now, Power Attack means that AoO is more likely to miss. But who is going to want to draw an attack of opportunity from an orc war chief, knowing he hits hard, and knowing he is power attacking from last round?
Elgonn 01-21-04, 12:44 PM	The rogue/monk/fighter with the Elusive Target feat.
WarRabbit 01-21-04, 03:48 PM	cellardweller wrote "Effects of haste, flurry and other sources of extra non iterative attacks can be factored in by adding Magic formulas 2 and 3 together." I don't believe this statement is correct. Let's say you have a fighter with the following setup: 12th level(BAB +12), 18 Strength, Using greatsword+1 with a speed enchantment (2d6 damage(average 14 total) with 4 total attacks: 2 full BAB attacks, one attack at -5, and one at -10). The PA modifier is 2 due to using a two-handed weapon. Now let's calculate the optimum PA against an opponent with an AC of 20: 1st the normal full attack without the extra speed attack: (Magic Formula 3) x = (fz-w)/2f + (47-5n)/4 x = (2*(17-20)-14)/(2*2) + (47-5*3)/4 x = 3 Now the extra single attack at full BAB(this time n=1): (Magic Formula 2) x = (fz-w)/2f + 10.5 x = (2*(17-20)-14)/(2*2) + 10.5 X = 5.50 You state that adding these 2 equations together will give you the optimum power attack when using extra attacks, but in this case that would mean using an 8 or 9 PA (since adding the 2 equations results in 8.5). I believe the absolute highest optimum PA will occur with a single attack...if you add in additional attacks at the full BAB(ala whirlwind attack) then your optimum PA stays the same...if you add in additional attacks at a less than full BAB, then your optimum PA will decrease. In this case the optimum PA is somewhere in between 3 and 5.5, though my brain cannot handle the calculus as well as you, so I don't know what the formula is. On another note: It looks like your two-weapon formula(magic formula 5) has an error with the second hand...you still have + n'(n'-1) instead of - n'(n'-1) when substituting Sum(Pi) into y. Finally, I have to say good job with the calculus work!
RabidWeasel 01-21-04, 08:36 PM	I would imagine a spiked chain tripping power attack build with combat reflexes could get some serious mileage out of power attack, what with AOO's from standing opponents, bonus attack from frenzy, improved trip, etc.
Master of the Squirrel's 01-21-04, 09:34 PM	The work put into the formulas I applaud. And, yes, they do work for an AoO fighter. Any penalties you take simply factor into the rest of your attacks. The 'art' mentioned plays a little role in this, but if you use the formulas, they will serve as true as they can given that we're looking at probablilty. The 'art' comes down to basically doing these formulas in your head, without really actually plugging in your numbers. These formulas assume you have knowledge of your foes AC. Well, if you use the formula for the highest AC that you threaten, you will have optimal conditions. Now, I'm sure there is a way to factor in all the AC's to get the correct number, but currently Highschool Education hasn't got me there (maybe next semester :) ). Of course, when it comes down to it, your more likely going to be doing this in your head, making quick judgements, just like you would in real battle. Of course, if your DM allows you to have your TI-89 with this programmed in next to you, all the power to ya. :) Speaking of which... anyone here a good programmer? :)
cellardweller 01-21-04, 10:17 PM	Originally posted by Master of the Squirrel's Speaking of which... anyone here a good programmer? :) Once sections 6 (twf) and 8 (choosing optimal fighting style) are complete, I'll throw together a quick and dirty javascript calculator that will output a nice table for you to print and bring to your gaming table.
WarRabbit 01-21-04, 10:57 PM	I've prepared an excel spreadsheet that calculates the optimum power attack taking into account the characters BAB, strength, size, weapon feats(focus & specialization) and the character's weapon base damage, usage(light, one-handed, two-handed), bonus and special abilities(including the elemental abilities such as 'flaming' and the burst versions such as 'flaming burst'). The spreadsheet isn't quite finished because I"m hoping Cellardwellar can figure out the formula for additional BAB attacks granted from haste, speed, and flurry/greater flurry. Also, the spreadsheet isn't all that pretty, but you can print out a fairly decent table to use while gaming. If anyone is interested in the spreadsheet you can email me at LordTenser@aol.com. I wouldn't mind some feedback to see if I applied Cellardwellar's formulas correctly.
Psifon 01-21-04, 11:51 PM	Originally posted by cellardweller Once sections 6 (twf) and 8 (choosing optimal fighting style) are complete, I'll throw together a quick and dirty javascript calculator that will output a nice table for you to print and bring to your gaming table. Can you put in an option for how the use of blessed weapon effects your power attack options? I often wonder about this, since it "flattens" the probablity of a critical hit, while not actually effecting the probability of hitting. So how would this figure in Oh Great Math Guru?
cellardweller 01-22-04, 12:03 AM	Originally posted by Psifon Can you put in an option for how the use of blessed weapon effects your power attack options? I often wonder about this, since it "flattens" the probablity of a critical hit, while not actually effecting the probability of hitting. So how would this figure in Oh Great Math Guru? y= (n(z-x+21)/20 - n(n-1)/8) (fx+w +mtw/20) 40y/n= (2z-2x+47-5n)(fx+w-mtw/20) 40dy/dxn= -4fx + (2zf+47f -5nf -2w - mtw/20) x=(fz-w)/2f + (47-5n)/4 - mtw/80f
Psifon 01-22-04, 12:28 AM	Originally posted by cellardweller y= (n(z-x+21)/20 - n(n-1)/8) (fx+w +mtw/20) 40y/n= (2z-2x+47-5n)(fx+w-mtw/20) 40dy/dxn= -4fx + (2zf+47f -5nf -2w - mtw/20) x=(fz-w)/2f + (47-5n)/4 - mtw/80f Wow! Great! I can't wait to see how that looks in the Java Script! I wonder what the answers will be.... Seriously though, thanks.
Psifon 01-22-04, 12:32 AM	Now, I don't see any provisions in your formulas for extra damage dice. Things like sneek attack and holy weapons effect your damage output but are independent of critical hits. Is this in there, or did I miss it?
cellardweller 01-22-04, 12:54 AM	Extra damage is included in the w term
Vysirez 01-22-04, 03:52 AM	I think Psifon was talking about part 4 where you included criticals. Here is a partial quote Average damage with criticals factored in can be written as y = P1(fx+w+tmw/20) + P2(fx+w+mtw/20) + ... where t = max(min(threat range,z+21),1) and m = the critical modifier-1 I may be misunderstanding but you are using w as a constant in this equation to equal average damage but extra dice are not increased by a critical. So if w is your average damage on a normal hit that includes extra dice you can't just modify that by your crit chances and crit modifier. You would have to use some other value that doesnt include your extra dice based damage. However your t definition throws me off a bit so you might have included that.
cellardweller 01-22-04, 04:45 AM	Originally posted by Vysirez I think Psifon was talking about part 4 where you included criticals. Ohhh! I getcha now...Yes I overlooked that part. The tmw/20 part is carried all the way through so if you were going to include non-multiplied component: x = (fz-w)/2f + (47-5n)/4 - tm(w+g)/40f (Magic formula 4) Where g is the average damage from burst qualities - the damage from extra dice. ie bursting increases effect of threat range and extra damage dice reduces it.
WarRabbit 01-27-04, 10:40 PM	The problem of solving a formula for additional full BAB attacks such as those granted from haste, speed, flurry, etc. intrigued me so I decided to give solving the formula a shot...I used Cellardwellar's formula layout for 'Magic Formula 3' (where extra iterative attacks are taken into account, but not critical ranges or multipliers) and edited it: The total damage on a full attack can be expressed as y=P1(fx+w)b + P1(fx+w) + P2(fx+w) ... y=P1(fx+w)b + sum(Pi)(fx+w) Where b is the bonus attacks due to haste, flurry, etc. (i.e. extra full BAB attacks) Pi can be written as Pi=(zi-x+21-5(i-1))/20 Sum(Pi) = sum((zi-x+21-5(i-1))/20) Sum(Pi) = n(z-x+21)/20 - sum(i-1)/4 Sum(Pi) = n(z-x+21)/20 - n(n-1)/8 Substituting Sum(Pi) in we have y= (n(z-x+21)/20 - n(n-1)/8) (fx+w) + b(z-x+21)(fx+w)/20 40y/n= (2z-2x+47-5n)(fx+w) + (2bz–2bx+42b)(fx+w) 40y/n=(2z-2x+47-5n+2bz-2bx+42b)(fx+w) 40y/n=(2z-2x-5n+2bz-2bx+42b+47)(fx+w) 40y/n= 2zfx–2fx^2–5nfx+2bzfx–2bfx^2+42bfx+47fx + 2zw–2wx–5nw+2bzw–2bwx+42bw+47w 40y/n= (-2f–2bf)x^2 + (2zf-5nf+2bzf+42bf+47f-2w-2bw)x + (2zw-5nw+2bzw+42bw+47w) differentiating 40dy/dxn= 2(-2f-2bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) 40dy/dxn= (-4f-4bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) finding the maximum 0 = (-4f-4bf)x + (2zf-5nf+2bzf+42bf+47f-2w-2bw) (4f+4bf)x = 2zf-5nf+2bzf+42bf+47f-2w-2bw (4f+4bf)x = 2(fz–w) + 47f-5nf + 2b(fz-w) + 42bf (1+b)x = (fz-w)/2f + (47-5n)/4 + b(fz-w)/2f + 10.5b x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] Sanity check substitute b = 0 into the above formula and you get magic formula 3. Granted, even if correct this formula isn't practical to use at the gaming table, but it would work for creating a table by using excel or a programming language for use at the gaming table.
michael_noah 01-28-04, 11:52 AM	The average damage on a given attack can be expressed as y=P(2x+w) where P is the probability that an attack will land and x is the amount of power attack used and w is the average amount of weapon damage on a successful hit excluding power attack The probability for any attack succeeding is given by P=(z-x+21)/20 Where z=max(Attack Modifier (excluding power attack) - AC of opponent,20) and x=amount of power attack used This can't be right - you end up with a probability greater than 1 almost all the time. Any time you power attack 20 or less, in fact. Do you mean z=Min(Attack Mod - AC, 20)?
Nail 01-28-04, 03:22 PM	Originally posted by michael_noah This can't be right - you end up with a probability greater than 1 almost all the time. Any time you power attack 20 or less, in fact. Do you mean z=Min(Attack Mod - AC, 20)? I struggled with this too. As I see it, he's made a fundamental error. Even if you max-ed out your power attack, you still have a 5% chance of hitting. Even if you have an attack mod of +66, you still have a 5% chance of missing. Them's the rules. I don't see those rules reflected in his equations....but then again, I feel pretty thick-headed today. Enlighten me. :angel:
Nail 01-28-04, 03:50 PM	Okay. I've wrestled with it for a while. The "P" in his equations must be: P = Min(19, Max(Atk - AC - x + 21, 1))/20 You need to have the power attack within the Min/Max function, or it doesn't work. Now, I've only got a guess at how to differentiate an equation with a Min/Max function in it. Only the barest of a guess, as math is not my strong suit.
cellardweller 01-28-04, 06:00 PM	I deliberately left out the minmax part of the probability, because I thought its effects were self evident - P will never end up > 0 unless x ends up greater than your bab. Think about it this way, if you are hitting on a 2 with 3 or 4 power attack, there is no reason to use 3 - hence the effects can be ignored. edit: oh yes, z is a min function - clerical error. Keep em coming, I will update the main document as soon as I get some spare time.
WarRabbit 01-28-04, 08:16 PM	Cellardwellar, I've been thinking about the extra damage from criticals and I believe your formula leaves out a key component...the threat confirmation roll. I believe the analyis of finding the formula for including criticals begins with the formula I"ve included below, but it quickly gets very complicated. So far solving this formula is beyond me. The total damage(including criticals) on a full attack can be expressed as y=P1(fx+w+P1*tmw/20)b + P1(fx+w+P1*tmw/20) + P2(fx+w+P2*tmw/20) Let me know if I've gone wrong somewhere.
cellardweller 01-28-04, 08:45 PM	I made that mistake at first, and only realised it after a page and a half of algebraic acrobatics. The threat confirmation roll is already taken into account in y=P(fx+w+tmw/20) rewriting: y=P(fx+w)+mwP(t/20) ie damage with criticals = damage without criticals + multiplier*damage*proabality of hitting*probablilty of threatening
Qaetar 01-28-04, 09:16 PM	Question: How well does the penalty of -2 for using on offhand one-handed weapon defeat the offhand light weapon loss of PA, or does it lose to it majorly? (Qaetar)
WarRabbit 01-28-04, 11:27 PM	Originally posted by cellardweller I made that mistake at first, and only realised it after a page and a half of algebraic acrobatics. The threat confirmation roll is already taken into account in y=P(fx+w+tmw/20) rewriting: y=P(fx+w)+mwP(t/20) ie damage with criticals = damage without criticals + multiplier*damage*proabality of hitting*probablilty of threatening Yep, you're right...my bad.
Boondoggle 01-29-04, 08:13 AM	Originally posted by cellardweller damage with criticals = damage without criticals + multiplier*damage*proabality of hitting*probablilty of threatening This isn't correct. The probabality to deal critical damage is the probabality to hit times the probabality to threaten times the probabality to confirm. Usually, the probabality to hit & confirm are the same. Your equation should be: y=P(f*x+w+P*t*m*w/20)
cellardweller 01-29-04, 09:26 AM	Originally posted by Boondoggle This isn't correct. The probabality to deal critical damage is the probabality to hit times the probabality to threaten times the probabality to confirm. Usually, the probabality to hit & confirm are the same. Your equation should be: y=P(f*x+w+P*t*m*w/20) Not quite: If you are referring to power critical, then now you're nit picking :P. In that case that case the formula should be y=P(fx+w)+(P+4/20)(tmw/20) y=P(fx+w+tmw/20) + tmw/100 The final part will fall off when differentiating so power critical has no effect on power attack. If you are refering to the fact that a threat is only a threat if it is also a hit, then that is aready taken care of in the definition of t (see first post).
cellardweller 01-29-04, 09:48 AM	Originally posted by WarRabbit The problem of solving a formula for additional full BAB attacks such as those granted from haste, speed, flurry, etc. intrigued me so I decided to give solving the formula a shot...I used Cellardwellar's formula layout for 'Magic Formula 3' (where extra iterative attacks are taken into account, but not critical ranges or multipliers) and edited it: The total damage on a full attack can be expressed as <snip> x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] Sanity check substitute b = 0 into the above formula and you get magic formula 3. Granted, even if correct this formula isn't practical to use at the gaming table, but it would work for creating a table by using excel or a programming language for use at the gaming table. Hey WarRabbit, I was just about to add this into the main document, but as I was writting up the conclusions, I realised that there must be an error in there somewhere. For n=1 and any given values of f, z and w, the value of x should be the same regardless of b (if you think about it you will see why but it is difficult to express)- under your formula it is inversely proportionate. If you want I will try to find the error, but I thought I'd let you have first shot (thats my story and I'm sticking to it :P)
WarRabbit 01-29-04, 11:18 AM	Cellardwellar, For n=1, x does remain the same...check out these examples: Here's the fomula: x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] for n = 1 the formula is: x = [(fz-w)/2f + 10.5 + b(fz-w)/2f + 10.5b] / [1+b] ok, so try b at different values, for b = 0 the formula is: x = [(fz-w)/2f +10.5 + 0 + 0] / [1+0] = (fz-w)/2f +10.5 (checks out) for b = 1, x = [(fz-w)/2f + 10.5 + 1(fz-w)/2f + 10.5(1)] / [1+1] x = [ 2 ((fz-w)/2f + 10.5)]/[2] = (fz-w)/2f +10.5 (checks out) for b =2, x = [(fz-w)/2f +10.5 + 2(fz-w)/2f + 10.5(2)] / [1+2] x = [ 3 ((fz-w)/2f + 10.5)]/[3] = (fz-w)/2f +10.5 (checks out)
Silencer 01-29-04, 12:13 PM	Originally posted by cellardweller I deliberately left out the minmax part of the probability, because I thought its effects were self evident - P will never end up > 0 unless x ends up greater than your bab. Think about it this way, if you are hitting on a 2 with 3 or 4 power attack, there is no reason to use 3 - hence the effects can be ignored. edit: oh yes, z is a min function - clerical error. Keep em coming, I will update the main document as soon as I get some spare time. That's why I would have left it as a Max() function but rather: z=Max(Attack Modifier (excluding power attack) - AC of opponent, -20) ...to illustrate the fact that you'll hit on a natural 20 regardless of your Attack Modifier and the AC of opponent). But maybe we could have this value even more representative (and thus a bit more complex) in such a way: z'=Max(Attack Modifier (excluding power attack) - AC of opponent, -20) z=Min(z', 20) However, most of the time this will end up being "Attack - AC" so that's not so important... unless you only hit your opponent on a nataural 20 without any point spent on power attack already. Good work cellardweller! I had just spent my last game session doing such generic calculus on my notes sheet (each time another player had a private moment with the DM). I was planning to post it on those boards... but you've been faster than me.
michael_noah 01-29-04, 01:29 PM	Originally posted by Boondoggle This isn't correct. The probabality to deal critical damage is the probabality to hit times the probabality to threaten times the probabality to confirm. Usually, the probabality to hit & confirm are the same. Your equation should be: y=P(f*x+w+P*t*m*w/20) This is incorrect. You can only multiply probabilities to determine the probability of both events if the events are independant. Threatening and hitting are not independant (chance to hit increases if you happen to threaten - since it means you rolled a high (or at least >13, etc) number). I can't remember off-hand what the correct way to do this is.
HighlandsTraveller 01-29-04, 03:11 PM	I had derived a different formula : 10*prob - .25*dmg (for the single attack). This did not take into account when you need a 20 or 1 to hit. I figured that's what the z = min(ab-ac,20) part of your equation is for, but I tried testing it with an example and it didn't seem to work although maybe I'm doing it wrong. Suppose a 15th lvl fighter wins initiative and charges his foe with a flatfoot AC of 20. His attk bonus is +32 and his avg dmg is 20. (2z-w)/4+10.5= (2(12)-20)/4+10.5= 11.5 In fact he should PA for 13! Lets take a 2nd lvl fighter with 14 str, mstrwk guisarme, and wpn foc. His attk bonus is +6 and his avg dmg is 8.5. His opponent is a halfling 2wiz/2mnk that has had time to uber buff with shield, mage armor, and drank a ptn of owls wis. His AC is 27 which strangely enough was a bizzarely defensive encounter I played through! The numbers are: (-42-8.5)/4+10.5= -2.1 or with z capped at -20? (-40-8.5)/4+10.5= -1.6 Clearly, you should PA for 2 in this case because you need a natural 20 to hit anyways. Anyways, I'm not clear on what the min function does in the z equation, so maybe that's the problem. If attk bonus - AC is grtr than -1 then you should PA until the diference is -1 then figure out if further PA helps. If attk bonus - AC is less than -19 then you should PA everything. So, the open ended question is what to do when attkmod-AC > -1. The only thing I can think of is to prePA the attk bonus down to 1 below AC and use this modified attk bonus and wpn dmg in the equation to see if further PA is beneficial.
Nail 01-29-04, 03:29 PM	Originally posted by michael_noah This is incorrect. You can only multiply probabilities to determine the probability of both events if the events are independant. Threatening and hitting are not independant ... Nope. The Atk roll and the Crit Confirm roll are independent; one doesn't change the chance for the other. (<EDIT>Perhaps you're unclear how Critical hits work? First roll Atk roll, then roll Confirm roll.) As a simple example: Given two coin flips, I bet you can't get two heads. If you accept my bet, you will lose 75% of the time. You will lose even though you must first flip a "heads", and only then can you flip another "heads". The mechanic is identical to confirming a critical. Regardless of your attack bonus, you have a set percent chance to score a critical (ex: mundane Longsword = 10%). You must then confirm the critical by hitting the opponent's AC, which does depend on you Atk bonus. Reducing the equation yeilds: E = [1 + Pc*(M-1)] where: "E" = factor to determine average extra damage from criticals, "Pc" = Chance to critical (mundane longsword = 10%), and "M" = Critical multiplier. So average damage from one attack is: AveDamPerAtk = P * D * E where: "D" = weapon damage + Str + Magic + ....etc, and "P" = probability to hit the opponent. -Nail
WarRabbit 01-29-04, 03:53 PM	I've completed an excel spreadsheet using average damage tables to determine the optimal PA to use for a full attack or single attack. It takes into account every factor I could think of(including special ability enchantments, whether a foe is immune to criticals or not, blessed weapons, extra attacks from haste or flurry, etc.). The only thing it won't do is calculate the optimal PA for fighting with two weapons. The formulas presented here work pretty well, but I found it hard to set up the formulas with the proper min's and max's for always missing on a 1 and always hitting on a 20...especially with iterative attacks. Because of that difficulty I created this spreadsheet by calculating the average damage you would do for using PAs of 0 through 20, and then had the spreadsheet select the PA with the highest average damage. Anyway, if anyone is interested in the spreadsheet, email me at LordTenser@aol.com and I will send you a copy.
michael_noah 01-30-04, 11:10 AM	Originally posted by Nail [B]Nope. The Atk roll and the Crit Confirm roll are independent; one doesn't change the chance for the other. I didn't say confirm, I said threaten. Also, you don't have a set chance to threaten, unless your weapon only threatens on a 20. If you roll a 19 with a longsword, you might still miss.
Nail 01-30-04, 11:13 AM	Originally posted by michael_noah I didn't say confirm, I said threaten. Okay....... The Atk roll is the same as the "threaten" roll. That is, if you hit your opponent *and* your natural roll is in the threaten range, then you roll to confirm. 2 separate rolls. Perhaps I'm missing your arguement.
Nail 01-30-04, 11:16 AM	Originally posted by michael_noah Also, you don't have a set chance to threaten, unless your weapon only threatens on a 20. If you roll a 19 with a longsword, you might still miss. A-Ha! I *thought* you and I might be talking past each other. Got it. It's true that we're assuming any roll in your threat range is also a hit. That's a pretty good assumption with weapons with a low threat range, no keen, etc. It's a terrible assumption otherwise. Any ideas how to handle that? My method, I'm afraid, is brute force with an Excel spreadsheet.
cellardweller 01-30-04, 11:19 AM	Originally posted by Nail Okay....... The Atk roll is the same as the "threaten" roll. That is, if you hit your opponent *and* your natural roll is in the threaten range, then you roll to confirm. michael_noah is using the he definition of threat roll used in the formula: t = max(min(threat range,z+21),1) You are using t= threat range So you are both correct but are speaking different languages. EDIT: A conclusion I see you reached while I was typing this up :D
Nail 01-30-04, 11:56 AM	Originally posted by cellardweller EDIT: A conclusion I see you reached while I was typing this up :D Cross-posting: Gotta love it. So...how to handle high crit range weapons????? (Other than brute force......'cause I already know how to do that. Brute force I'm good at.)
cellardweller 01-30-04, 11:57 AM	Originally posted by WarRabbit [B]Cellardwellar, For n=1, x does remain the same...check out these examples: So it does. I saw that 1+b on the outside and no factor of b on (47-5n)/4 and leapt to the opposite conclusion (in a single bound I might add). Ok then, I am trying to get that into a format that make that conclusion evident without the need to use examples, but can't get rid of the b dependent value for n=1. Can you spot my error? x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] combine (fz-w)/2f parts x = [ (1+b)(fz-w)/2f + (47-5n)/4 + 10.5b] / [(1+b)] comibine 10.5 parts x = [ (1+b)(fz-w)/2f + 10.5 - 5/4 - 5n/4 + 10.5b] / [(1+b)] x = [ (1+b)(fz-w)/2f + 10.5(b+1) - 5/4 - 5n/4] / [(1+b)] combine the rest x = [ (1+b)(fz-w)/2f + 10.5(b+1) - 5(n+1)/4] / [(1+b)] bring the /(1+b) inside the brackets x = (fz-w)/2f + 10.5 - 5(n+1)/4(1+b) I'm pretty sure the correct answer is x = (fz-w)/2f + 47/4 - 5(n+b)/4(1+b) but I just can't prove it... I'll try again after some sleep...
cellardweller 01-30-04, 12:03 PM	Originally posted by Nail Cross-posting: Gotta love it. So...how to handle high crit range weapons????? (Other than brute force......'cause I already know how to do that. Brute force I'm good at.) the definition for t already does take it into account t = max(min(threat range,z+21),1) That means that if you ordinarily threaten on a 17 (threat range=4) but only hit on an but are up against and opponent that you need an 18 to hit, t =3, not 4.
WarRabbit 01-30-04, 12:15 PM	Originally posted by cellardweller x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] combine (fz-w)/2f parts x = [ (1+b)(fz-w)/2f + (47-5n)/4 + 10.5b] / [(1+b)] comibine 10.5 parts x = [ (1+b)(fz-w)/2f + 10.5 - 5/4 - 5n/4 + 10.5b] / [(1+b)] x = [ (1+b)(fz-w)/2f + 10.5(b+1) - 5/4 - 5n/4] / [(1+b)] combine the rest x = [ (1+b)(fz-w)/2f + 10.5(b+1) - 5(n+1)/4] / [(1+b)] bring the /(1+b) inside the brackets x = (fz-w)/2f + 10.5 - 5(n+1)/4(1+b) your line right after 'combine 10.5 parts' is wrong, it should be +5/4, not -5/4: x = [(fz-w)/2f + (47-5n)/4 + b(fz-w)/2f +10.5b] / [(1+b)] combine (fz-w)/2f parts x = [ (1+b)(fz-w)/2f + (47-5n)/4 + 10.5b] / [(1+b)] comibine 10.5 parts x = [ (1+b)(fz-w)/2f + 10.5 + 5/4 - 5n/4 + 10.5b] / [(1+b)] x = [ (1+b)(fz-w)/2f + 10.5(b+1) +5/4 - 5n/4] / [(1+b)] combine the rest x = [ (1+b)(fz-w)/2f + 10.5(b+1) - 5(n-1)/4] / [(1+b)] bring the /(1+b) inside the brackets x = (fz-w)/2f + 10.5 - 5(n-1)/4(1+b) for n = 1: x = (fz-w)/2f + 10.5 - 5(1-1)/4(1+b) = (fz-w)/2f +10.5
cellardweller 01-30-04, 12:22 PM	Originally posted by WarRabbit your line right after 'combine 10.5 parts' is wrong, it should be +5/4, not -5/4: x = (fz-w)/2f + 10.5 - 5(1-1)/4(1+b) = (fz-w)/2f +10.5 Ah-ha! Thankyou kindly.
michael_noah 01-30-04, 12:50 PM	It might be that brute force is the best way to go about it, but we can certainly find a better way than with a spreadsheet. I may verify all these formula's this weekend - but in order to differentiate the ones with all kinds of Min and Max functions we're going to need some sort of math tool. Is anyone around here at a university with access to Maple or Mathematica or something like that? p.s. damn cross-posting. glad we got that cleared up.
cellardweller 01-30-04, 09:43 PM	Originally posted by michael_noah It might be that brute force is the best way to go about it, but we can certainly find a better way than with a spreadsheet. I may verify all these formula's this weekend - but in order to differentiate the ones with all kinds of Min and Max functions we're going to need some sort of math tool. Is anyone around here at a university with access to Maple or Mathematica or something like that? p.s. damn cross-posting. glad we got that cleared up. I think you may be getting a little confused and embarking on a wild goose chase. In all cases you are differentiating damage per hit with respect to power attack (ie dy/dx) as neither x or y is contained within the min or max functions they are treated as constants. Hence there is no problem.
Nail 02-02-04, 10:46 AM	Originally posted by cellardweller neither x or y is contained within the min or max functions.... They should be. You still hit on a "20", even if you max out your Power Attack.
Nail 02-02-04, 11:38 AM	Originally posted by cellardweller the definition for t already does take it into account t = max(min(threat range,z+21),1) That means that if you ordinarily threaten on a 17 (threat range=4) but only hit on an but are up against and opponent that you need an 18 to hit, t =3, not 4. Okay. I've been pondering this for some time, scratching out arcane symbols on legal pads, etc. I think you're wrong, here. Although it's correct to include z here (a fact I overlooked, BTW), you must also include x. The amount of power attack will affect whether or not you confirm a critical. t and x are linked.
mean_liar 02-02-04, 12:11 PM	I know you guys are deep into the formulation of a Power Attack GUT, but I did track down the spreadsheet that does all the work for you. Power Attack Calculator (at bottom of site) (http://www.geocities.com/frisbeet/DandDandFightin.html) ...which is funny, since I used to have such disdain for statisticians until actually getting a job and leaving the university. Now its all Monte Carlo simulations and approximations to the nearest .05%. Speedy accurate estimation outweighs ponderous absolute perfection everywhere but the most fringe cases. And I think we can agree that Excel crunching Power Attack to the nearest 1/1000000th damage point per round is probably good enough for our purposes. :)
ShameOnU 02-02-04, 12:40 PM	Dunno if it's just me, but to me the link's dead..... BTW that's some NICE :censored::censored::censored::censored: you guys are doing here. i bow to you :bow::bow::bow:
Nail 02-02-04, 12:43 PM	Originally posted by mean_liar ... And I think we can agree that Excel crunching Power Attack to the nearest 1/1000000th damage point per round is probably good enough for our purposes. :) Oh great, the site is down due to high traffic. As it happens, I also have an excel spread sheet which calculates the best power attack, given any number of variables. I don't need this thread to tell me how to do that. "Brute force" using excel is easy. The fun for me is seeing what sorts of generalizations we can make....and that's easiest if you have the master equation in front of you, rather than doing umpteen simulations. Although I know, from personal experience, how fun those monte carlo simulations can be. ;)
michael_noah 02-02-04, 12:55 PM	If anyone has that web-pretty spreadsheet (I don't site's down), I can probably put in on a server that isn't bandwidth-limitted.
Joshua Randall 02-04-04, 10:27 AM	Bump. I was enjoying the mathematical discussion. Hope it hasn't petered out in the face of brute force Excel sheets.
frisbeet 02-21-04, 08:18 PM	I love the analysis you've all put into this topic. It's a breath of fresh air...I used to post more about it, but while I couldn't always generate interest, it seemed like every time someone would respond along the lines of "you're crazy, that's meta-gaming". Not true, of course, but that's not what gets me. What gets me is the lack of imagination exhibited by such posts: they presume that these forums should only be about D&D and that any good math problem derived from D&D should be bottled up. (Sorry for the awful pun.) Anyway, the spreadsheet mean_liar refers to is in my sig. Still haven't got around to implementing liar's incredibly good idea of allowing for generic attack bonus and damage bonus implementation, or standard attack average damage/round calculation, but otherwise some of you may find it useful. Sorry for the bandwidth limitation...I'd be happy to have it hosted somewhere else. (Though it looks like I'm averaging only a few hits a day so patience may be an almost unnecessary sol'n). Ok you analytical solution guys, how are you going to handle average weapon damage when DR makes some hits 0 damage, with a crappy damage roll, but other hits for positive damage?
frisbeet 02-25-04, 12:03 AM	Still haven't got around to implementing liar's incredibly good idea of allowing for generic attack bonus and damage bonus implementation, or standard attack average damage/round calculation Well, now I have. Click sig. Interestingly, a few examples have shown that the optimum PA for a standard attacking fighter isn't much different than a full attacking one...in general, a couple more PA points for the std attacker in the middle AC ranges. This for a level 12 fighter, 24 str, two-handed weapon. If this thread even gets re-read, don't fret too much about high site traffic...I can guarantee in a couple hours, certainly by tomorrow, everything will be back to baseline.
Chesterfield 03-23-04, 03:39 AM	:bump: Seems like Frisbeet's question haven't been answerd yet... I think this is one of the most interesting threads I've seen for a very long time. :D
KashGarinn 03-23-04, 05:40 AM	nice! I've never truly seen the beauty of calculus displayed in as fine light as this. I'll probably amuse myself by going over the numbers the next few days, thinking how some of the feats vary the playing ground. great work guys! K.
KashGarinn 03-23-04, 12:59 PM	I have a few things to ask.. I was going through the basics with the formula.. here's what I did and found odd. Fighter lvl 1, STR modifier = 0, extra bonuses = none, weapon = greatsword, using 2-handed = 2d6 = 7 average damage. x = (fz-w)/2f + (47-5n)/4 just so that I have the terminology correct: x = minus to AB which is converted to power attack dam. f = powerattack multiplier (1 for 1-handed, 2 for 2-handed etc..) z = chance for someone with AB to hit AC, or AB-AC w = average normal damage n = number of attacks f = 2, w = 7, n = 1, z = (1-AC) x = (2(1-AC)-7)/2*2 + (47-5)/4 x = (2 - 2AC - 7)/4 + 42/4 x = -AC/2 - 5/4 + 42/4 = -AC/2 + 37/4 = -AC/2 + 9,25 Now, he can only decide between 0 PA, or 1 PA. x = 0 = -AC/2 + 9,25 => AC = 18,5 = 19 (rounded up) X = 1 = -AC/2 + 9,25 => AC = 16,5 = 17 (rounded up) ...So this is telling me that if an opponent has 17 or less AC, I should use power attack? Let's create a 6th lvl fighter, STR modifier = 0, extra bonuses = 0, AB = 6, weapon = greatsword, 2 handed = 2d6 = 7 average damage x = (fz-w)/2f + (47-5n)/4 , f = 2, n = 2 x = (2z-7)/2*2 + (47-5*2)/4 x = z/2 - 7/4 + 37/4 = z/2 + 7,5 x = (6-AC)/2 + 7,5 = 3 - AC/2 + 7,5 = -AC/2 +10,5 A 6th lvl fighter can PA from 0 to 6, let's take 0 to 6 x = 0 => AC = 21 x = 1 => AC = 19 x = 2 => AC = 17 x = 3 => AC = 15 x = 4 => AC = 13 x = 5 => AC = 11 x = 6 => AC = 9 Ok, on a 1d20, a 6th lvl fighter with AB 6 will hit 50% on ac = 16 let's look at the probability for the listed types. AC = 21, no PA. number needed on d20 = 15 AC = 19, PA = -1, number needed = 14 AC = 17, PA = -2, # needed = 13 AC = 15, PA = -3, # needed = 12 AC = 13, PA = -4, # needed = 11 AC = 11, PA = -5, # needed = 10 AC = 9, PA = -6, # needed = 11 ... Can someone explain to me why the ratios are so skewed? I it really good for a lvl 1 fighter to put 1 into PA until after AC 17? Is it really good that only between 25% and 50% success rate should u use PA? I think it's strange for instance when you PA for -1, you go from 45% down to 40%.. but at PA -5, you go from 75% down to 50%.. I need to put this into excel and play with a few graphs.. I'll post a maxed Frenzied berserker later.. let's see how that goes. P.S. if there are any errors in my calculation (simple as they are) lemme know :) K.
Qaetar 03-23-04, 01:30 PM	What do you find strange about losing 25% to hit by taking -5 and only losing 5% by taking -1? (Qaetar)
KashGarinn 03-23-04, 05:42 PM	hehe, I phrased it badly.. I can see that.. hmm.. not exactly sure how to phrase what I mean. Well, I'm just wondering why for instance the first increment to x.. the -1 to AB.. why does it start at AC where I need a 14 on the 1d20 to hit? btw, there's no real point I'm trying to make.. at least not yet.. just throwing out a few numbers :) Well, I did the low-end earlier.. let's do the high end.. meet 18ECL FB called Puk. when not frenzying we can use MF3. x = (fz-w)/2f + (47-5n)/4 f = 4, z = (AB-AC), w = 2d6+str19+enhancement4 = 30, n = 4 x = (4z - 30)/8 + (47 - 5*4)/4 x = z/2 - 3,75 +6,75, AB = bab17+wpnfcs1+str13+enhancement4 = 35 x = 35/2 - AC/2 +3 x = -AC/2 + 20,5 - Let's see how the AC mark changes from x = 0 to x = 17, first/last attack = what number you need on a d20 to hit the specified AC. x = 0 => AC = 41 , first attack= 6 ,last attack=20 x = 1 => AC = 39 , first attack= 5 ,last attack=20 x = 2 => AC = 37 , first attack= 4 ,last attack=19 x = 3 => AC = 35 , first attack= 3 ,last attack=18 .... x = 10 => AC = 21,first attack= -4,last attack=11 x = 11 => AC = 19,first attack= -5,last attack=10 x = 12 => AC = 17,first attack= -6,last attack=9 x = 13 => AC = 15,first attack= -7,last attack=8 x = 14 => AC = 13,first attack= -8,last attack=7 x = 15 => AC = 11,first attack= -9,last attack=6 x = 16 => AC = 9 , first attack= -10,last attack=5 x = 17 => AC = 7 , first attack= -11,last attack=4 hmm... from x = 1 we see that first attack needs 5 to hit AC 39, second attack needs 10 to hit AC 39, third attack needs 15 to hit AC 39, and the fourth a solid 20. I wonder why x = 17 means the AC-mark gets so low.. first attack -11, second attack -6, third attack -1, and fourth attack 4.. why? If we say we want 50% chance on the last attack and PA for 17, meaning 10 on a d20, the AC mark should be at 13.. why is it at 7? If we want 50% on the third attack and PA for 17, then the AC mark should be at 18.. if we want 50% on the second attack, and PA for 17 (similar to what it's like for x = 1) then AC could be up to 23.. I don't quite get the reasons behind this.. where is the probability factor set? Am I using the formula correctly? I think I am.. I don't want to create the numbers for when Puk goes frenzying if my calculations are wrong.. I'll wait for somebodys input/verification on this before I continue. K.
Qaetar 03-23-04, 07:11 PM	Ah. Well, if you don't understand the math behind it all, it's kinda hard to explain. My guess, not having read the thread in a long time, is that the gain in damage is greater than 5% of your current output or some such. Meaning, if I only hit 25% of the time and +2 damage is more than the average damage I lose by only hitting 20% of the time, it's beneficial for me to PA for 1. (Qaetar)
Raging Halfling 03-23-04, 10:02 PM	Kash, this is nitpicking a bit, but your examples don't work because the characters can't use Power Attack. You have to have a Str bonus of at least +1 to qualify for the feat. I'm afraid I'm not really an expert on the math, so somebody else will have to answer your question. Just thought I'd point that out.
KashGarinn 03-24-04, 07:22 AM	Qaetar: If you check out the 17lvl FB, you can see that the last attack needs a 20 to hit, and the higher you PA the number needed on a d20 lowers linearly.. Shouldn't it stabilise around a preferred to-hit ratio rather than just go down linearly? I'm guessing that the answer can be found in the definition of z. I'll think about it more.. this is fun :D disclaimer, I only have rudimentary knowledge of mathematics, and maybe not doing this right.. K.
Nail 03-24-04, 11:29 AM	Originally posted by Raging Halfling You have to have a Str bonus of at least +1 to qualify for the feat. Nope. You need a Str score 13 or greater. That's different than +1 "Str bonus". After all, you could have a 12 Str and yet not qualify for PA.
Raging Halfling 03-25-04, 06:07 PM	Originally posted by Nail Nope. You need a Str score 13 or greater. That's different than +1 "Str bonus". After all, you could have a 12 Str and yet not qualify for PA. Don't be obtuse. A Strength score of 13 means that you have a minimum of a +1 Str bonus. I was abbreviating that concept for the purpose of his formula.
KashGarinn 03-25-04, 08:54 PM	Well, I've discovered that the formulas are a very simplified model of when to optimally use power attack. They work, but they do not take into account extra attacks, extra crit-range, extra crit factor, the doubling of hitting a 20 on a d20 and so on and so forth.. So I've just created an excel sheet which does that. I'm not contending that the formulas don't work, infact they do work.. within a certain range. http://www.pc.is/dnd/new_odds.xls I'd like it if people would check it out to see if it works. I've locked the workbook, if you want a non-locked version send me a message. you can see from chart 2 when the average damage seems to drop suddenly off, meaning beyond that point you shouldn't be powerattacking for any more. (y axis is average damage, x-axis is the minus to attack bonus because of power attack [or x as it's in this thread] each line represents AB-AC [or z] when AB-AC is between -20 and 20 From chart 1 you can see relative changes between the various amounts of power attack. Each line represents amount of power attack used [x]. If somebody finds this interesting, great. K.
Psifon 03-25-04, 10:39 PM	Playing around with your spreadsheet, I am finding it a little hard to use. Would you mind explaining some of the fields? For example: What are the 5th lvl + 10th level FB? What is the Odd number (21) is this the basic D20+1? Should it ever be changed? Where do you put extra damage dice? Average it and put it in the "other" field on the damage line? What is that little chart in the middle that has bold numbers from 1-20 and a column for AC? Does it do anything? It appears to be labled: "When you should power attack for:" But it is unclear what it does or how you use it. The numbers don't change when I change the values. How do you read the Opp AC? do your read it accross (for those numbers ranging from 61-21 (or whatever they change into) or do you read it down for the numbers ranging from 1-20. What is the row of numbers at the top of the big chart? What is the row of numbers on the second line with of the big chart? The one that has the box drawn around it. Is it the number I should be power attacking for? I notice that the spreadsheet is calculating values for up to 4 attacks per round. Does it exclude these tables if I have a BAB of less than 16? I assume that the Total attacks in a fullrnd field means the number of attacks I get in a full round before haste and similar effects, and the total extra attacks is from haste, AoO's etc. Is this correct? How do I use the spreadsheet if I only want to calculate all attacks at my full BAB (for things like standard action - attacks and WWA and whatnot)? Assume I am not a person that does math for fun here, and explain what you are doing with this tool. It looks highly useful, but we of normal intelligence are having a bit of difficulty interpreting the results. Could you label the table more clearly?
frisbeet 03-25-04, 11:48 PM	Hey KashGarinn, I applaud your efforts. I know exactly how complicated this problem can be. I encourage you to use the "Power Attack Calculator" I've created (click signature) to check your results, at least through AC 50. I've tested it for almost a year now, and all the bugs have been ironed out, except for some difficult monk TWF/flurry issues (do they stack--if they do, crap, I've got a lot of work to make it right) and monkey grip is still 3.0. Anyway. But I suspect the reasons you've made this sheet are the same reasons I've made mine: to prove to ourselves that we can master this optimization. It is not fun for me trying to unravel what other people have done, even if their work proves better. And since we went to all the effort, why not make it available to everybody. That's partly why I've done my work in Excel. As obtuse as it can be, it is still much more transparent than code. When I get a chance I'm gonna comb over your sheet. Good job!
KashGarinn 03-26-04, 08:23 AM	- I've updated the sheet. Check it out now. Psifon: Thanks for checking it out, by your post I see I have alot of work ahead of me to make it cleaner and easier to use, which I will do. "What are the 5th lvl + 10th level FB?" - ah.. that's improved power attack, which FB gets at 5th lvl, and superior power attack.. I'll rename that to their correct names :) Do you know of any other things which increase "What is the Odd number (21) is this the basic D20+1? Should it ever be changed?" - yep.. I had no clue what to call it.. so I called it the odd number. Shouldn't really be changed, so I'll lock it and make it invisible. "Where do you put extra damage dice? Average it and put it in the "other" field on the damage line?" - hmm.. yep. You can do that. I'll add two columns to that, sneak attack and magical.. That reminds me burst weapons need their loving too.. right now you can't add burst weapons to this, as it won't be calculated in correctly. Ok need to throw that in there. thanks for the heads up. "What is that little chart in the middle that has bold numbers from 1-20 and a column for AC?" - ah, that's just a memo for yourself.. you can remove the numbers and add in your own. The main reason for this is I haven't a clue how I can script it so that the highest number in the column will go bold.. if I could do that, then it would be much easier to automatically catch what amount of PA you should be using. If someone knows how to script it so that the highest number in a column will always be bold, I'd like to know. "How do you read the Opp AC?" Ah, I'm sorry. I've corrected it on the sheet. The AC is read left to right, and the power attack factor is read down. I've clarified this. "What is the row of numbers at the top of the big chart?" - That's the opponent's AC. I've clarified it in the excel sheet. "What is the row of numbers on the second line with of the big chart?" - that's the relative minus or plus to your 1d20 roll.. I.e. AB-AC from -20 to +20. I think I should just cover that up.. it's not really important to know, and people would rather like to know the AC then relative +/- to 1d20 roll. So I'll cover it up and u don't have to worry about it :) "I notice that the spreadsheet is calculating values for up to 4 attacks per round." - yup.. But I really should have erased the extra tables.. but it's fun to see the hard-data.. I'll set it up better so that your value to BAB is what controls the amount of attacks in a full round action. Right now TWF is not in this whole kaboodle.. It takes a while to do it as you have to add a whole 3 extra tables especially, so I'll do that when I have the time. "Does it exclude these tables if I have a BAB of less than 16?" - yep, it does now at least.. well that's not right, it ignores the other tables. Don't take any notice of the extra tables unless you're interested in the breakdown on averages for each attack in the full-round attack action. "I assume that the Total attacks in a fullrnd field means the number of attacks I get in a full round before haste and similar effects, and the total extra attacks is from haste, AoO's etc. Is this correct?" - yep. "How do I use the spreadsheet if I only want to calculate all attacks at my full BAB (for things like standard action - attacks and WWA and whatnot)?" - you put a 0 in extra attacks, and a 1 in total attack in fullrnd (or you did before I changed it so that fullrnd field is now based on BAB).. it really should be clearer.. I'll have to think about this. I think it's easier if there is only one table which changes.. so I'll add somekind of a option between a standard attack and a full-round attack. Thanks for pointing it out :) "Could you label the table more clearly?" - Yep, will do. And thanks for your input, highly appreciated :D Frisbeet: "I applaud your efforts." - thanks man.. appreciate it :) "I encourage you to use the "Power Attack Calculator" I've created (click signature) to check your results, at least through AC 50." - I checked it out, and didn't find it explicit enough to know what was happening with the data. "But I suspect the reasons you've made this sheet are the same reasons I've made mine: to prove to ourselves that we can master this optimization." - well, and the fun in the exercise.. This was only supposed to be an exercise in calculus, but statistical analysis was sorely needed to prove or disprove the theory. "When I get a chance I'm gonna comb over your sheet. Good job!" - Thanks alot man, and please do. tear through it and lemme know of anything which is wrong or needed in it.
frisbeet 03-26-04, 09:42 AM	- I checked it out, and didn't find it explicit enough to know what was happening with the data. Like I said, it's usually not a ball trying to figure out what other people have done. The secret to my spreadsheet is unhiding (format drop-down menu)the "compilation", "calculation", "rolls", "weapon selection" & "weapon table" worksheets. The compilation worksheet, together with the non-hidden "comparison" worksheet, put together all possible attack parameters & weapon info and make sure the feat & class feature selection are correct--in short, apply 3.5 rules to the user's parameterization. The weapon info and composite damage bonus get passed on 1st to the rolls worksheet, which is quite large, and takes into account the discrete probability distribution of outcomes for all possible damage dice rolls. This allows me to implement damage reduction. For example, the P distribution for 4d4 is: outcome #ways probability 4 1 0.00390625 5 4 0.015625 6 10 0.0390625 7 20 0.078125 8 31 0.12109375 9 40 0.15625 10 44 0.171875 11 40 0.15625 12 31 0.12109375 13 20 0.078125 14 10 0.0390625 15 4 0.015625 16 1 0.00390625 The "# of ways" column counts the # of ways of rolling, say a 12, with 4 d4s (31), for example. (This comes from a rather complicated formula re-derived awhile back on the EnWorld board.) This distribution is needed if you're wielding a Falchion (2d4 18-20 x2) and hit for critical damage. If you're opponent has DR of 10 and you do no extra damage from strength or weapon enchantment or feats, the probability distribution looks instead like: outcome #ways probability 4 1 0 5 4 0 6 10 0 7 20 0 8 31 0 9 40 0 10 44 0 11 40 0.15625 12 31 0.12109375 13 20 0.078125 14 10 0.0390625 15 4 0.015625 16 1 0.00390625 Why does this matter? With an opponent with no DR, the average Falchion crit damage is 2 x <2d4>, or 10. Take the product of each outcome with it's probability and sum this up, for the 1st distribution I've listed. That's 4 x 0.00390625 + 5 x 0.015625 + 6 x 0.0390625 + ... This sum is 10, as it should be. Now look what happens when you do the same thing for DR 10. The average crit damage is not zero! (10 - 10). Instead, it's exactly 0.890625. That's (11-10) x 0.15625 + (12-10) x (0.23209375) + ... + (16-10) x 0.00390625. So anyway, that's what the "Rolls" sheet does. Together, then, with the appropriate average weapon damage/hit and weapon crit dam/hit from "rolls", and attack bonus progression from "compilation", the "calculation" worksheet calculates the average full attack damage round. That's the P(normally hitting an AC)*average weapon damage + P(critically hitting an AC)*average crit weapon damage. Parameterized by DR, as I've shown. But it does it for all valid PAs up to 20 simultaneously. This is the downfall of static calculation with spreadsheet--to account for all possible things, you have to calculate all possible things. It's why an explicit calculus-derived solution to the problem is attractive--though by its discrete nature, isn't technically a calculus problem, and I'm a little surprised others haven't brought this up in this thread--because it could significantly cut down on file size. So then, with some simple comparison functions provided handily by Excel, the maximum full attack damage is reported together with the power attack value which delivers it. That's the spreadsheet, in a nutshell. Why take the trouble to post all this? I suppose I'm advertising a little. But really it has to do with credibility. KashGarinn's spreadsheet, while not as refined (yet) as mine, has its guts spilled out for everyone to see. Makes it hard to get results (only because there's not a lot of superficial styling), but how those results were calculated is easier to follow. My spreadsheet does a lot of work behind-the-scenes; if you're patient enough and unhide everything, you could follow it. I'm not sure who would want to however. But the final #s, I can say with 99.9% confidence, are exact. The other reason I'm replying is to show that DR really screws up the calculus of optimizing PA, since (average weapon damage, 0 PA)/hit is no longer a constant. Bummer. Edit: WTF was I thinking with the DR example. It's now correct. Sheesh. 3/27/04 Try again 4/10/04.
Nail 03-26-04, 10:45 AM	Originally posted by Raging Halfling A Strength score of 13 means that you have a minimum of a +1 Str bonus. This is also incorrect. "A Strength score of 13" means you have a +1 Str bonus. Nothing "minimum" about it. Yank, yank. ;)
Nail 03-26-04, 10:57 AM	Originally posted by frisbeet Why does (DR) matter? With an opponent with no DR, the average Falchion crit damage is 2 x <2d4>, or 10. Take the product of each outcome x 2 (the crit factor) with it's probability and sum this up, for the 1st distribution I've listed. That's 4 x 2 x 0.00390625 + 5 x 2 x 0.015625 + 6 x 2 x 0.0390625 + ... This sum is 10, as it should be. Now look what happens when you do the same thing for DR 10. The average crit damage is not zero! (10 - 10). Instead, it's exactly 0.890625, a little less than 1. (slaps forehead) Duh! DR really is a big problem. Thanks, Frisbeet! You mention the probability equation derived on ENWorld boards....what is it? Of course, that DR problem throws off my entire spread sheet, should I chose to account for it. Crap. Originally posted by frisbeet .... My spreadsheet does a lot of work behind-the-scenes; if you're patient enough and unhide everything, you could follow it. I'm not sure who would want to however. But the final #s, I can say with 99.9% confidence, are exact. FWIW, I've run it against my own version many times, and always come up with the same numbers. ...and since your PA Calc is prettier, it's the one I use when doing demonstrations. Thanks!
frisbeet 03-26-04, 12:16 PM	Probability Distribution of Dice on EN World (dates back 1 year) (http://enworld.cyberstreet.com/showthread.php?t=43696&page=1&pp=25) Though others in the EN World cast the formulae in much easier to read pictures, here's my input. oc = outcome n = number of identical dice s = sides of die Also, COMB(a,b) = a!/[b!(a-b)!] SUM(i=a,b) {term} = sum all terms starting with the "ath" and ending with the "bth", where i = index) and IF(condition,if true do this,if false do this) = you get the picture Then the # ways = COMB(oc-1,n-1) + SUM(i=1,n-1) {(-1)^i * IF[oc<(i*s+n),0,COMB(n,i)*COMB(oc-i*s-1,n-1)]} LazarusLong42's posts I think recast this more clearly, and generalize it for any scrambled set of dice. A more recent challenge has been to figure out the explicit formula for outcome distribution for drop lowest methods, like 4d6 drop lowest and 5d6 drop two lowest. LL42's got a sol'n for drop single die, but I haven't been able to corroborate it yet. Seems like recently I've only had enough time to post occasionally (or I'm lazy). Math play can be a lot a lot of fun, but it is temporally draining.
KashGarinn 03-26-04, 12:54 PM	Well, I've finally gone through all the things which I could quickly check. So now it's up to alpha version 4 :) Changes include easier time in seeing where to put in your stats, and the highest average damage is highlighted. I'm still always seeing things which can get better.. mostly though GUI things which I should have hidden. I haven't given DR much thought.. it's a variable that the DM can spring on you randomly, and often you don't have the luxury to use excel while playing to check if the optimum PA has changed. I see how having your odds table is better than just a linear average number which I have.. I'll have to do something about that.. Keep the reviews coming! I need more input! K.
Nail 03-26-04, 01:47 PM	Originally posted by KashGarinn I haven't given DR much thought.. it's a variable that the DM can spring on you randomly, and often you don't have the luxury to use excel while playing to check if the optimum PA has changed. You do, however, have time before the game to look at its effects......all is simply a matter of availble time, effort, and possible reward for doing so. I've found frisbeet's sheet (or any PA optimization scheme) to be most useful to the player, rather than the DM. The player has just one set of stats to worry about, and can even go so far as calulating the optimal PA for all ACs (10 - 50) and all possible DRs (0, 5, 10, 15; perhaps even Bbn DR). Then the player just whips out the appropriate sheet at the appropriate time. Not that I, as a player, will ever admit to doing such a thing. Oh no. My victories in battle were not affected in any way by knowing the optimal PA. I am a role-player, and merely enjoy the "theater" my playing provides. :)
KashGarinn 03-27-04, 12:59 AM	Well, version is up to alpha 5. here's the link: http://www.pc.is/dnd/new_odds.xls I've made it so that PA is only calculated up to your BAB, and a few other minor tweaks. Check it out to see if you think it's intuitive enough. only thing which I feel I ned to iron out is when threat range is for instace 17-20, but you need 19 or higher to hit.. the doubling for 17 and 18 is still counted in the formula.. I'll fix that soon. I'll also fix it so that 2 weapon fighters can do their thing. hmm... I still need to make the 'when to PA' table automatic, and the DR thing.. what else could there be... Lemme know, ok ? K.
Psifon 03-27-04, 02:18 PM	Great work KashGarinn! Thanks so much. It is MUCH easier to use. I really like the highlighted high numbers, I am glad you figured out how to do that, it give a great grafic depiction of your PA curve. I am running into a couple of minor problems though.... First off, the weapon damage field is too restrictive. It works fine for a medium sized opponent, but when you cast say, an enlarge person on a greatsword wielder (which I routinely do), then you need 3d6 damage dice from the weapon's base damage. If you could simply make it so that you entered the number and type of dice for the weapon damage that would be much better. That way the guy who is polymorphed into a titan can still use the thing. Secondly (and this is probably just my ignorance in working a lot of statistics) I am having problems interpreting the charts. Some things are obvious (like average damage) but other things I am not quite gettng. For instance, in chart one, what are the different series (from 5 to -20) representing? The amount of power attack used? This seems to be what the bottom represents. And for chart 2 I am not at all sure what I am looking at. Could you explain these please? Anyway, thanks again for your great work, and for making it more user friendly.
KimHal 03-27-04, 05:44 PM	20dx/dy = -4x + (2z+42-w) ddx/dy = -1/5 Just nit-picking, but this should be 20dy/dx=... and ddy/dxdx=... Since you venture into doing maths, you'd rather be precise... :smirk:
KashGarinn 03-30-04, 11:43 AM	Ok, up to beta 1 ! In here are clarifications, and 2-weapon fighting option, so go check it out. http://www.pc.is/dnd/new_odds.xls I need some critiques on it, so don't be shy! K.
Psifon 03-31-04, 11:29 PM	Something isn't right. When I change the critcal factor of my weapon, only the numbers after the optimum power attack are changing on the chart. In effect only the numbers on or after the yellow line are registering the change. Is this an error, or is this an artifact of the math involved? I have to assume it is an error, since the average damage of the weapon for each hit has to include the extra damage done by the critical factor and the threat range. Also (and this isn't really important I don't think), the critical damage is not factored into the average damage of the weapon in the field "Total Damage, Main" and "Total Damage off Hand" Not a big deal, but it may be nice to have for comparing basic weapons.
KashGarinn 04-02-04, 08:03 AM	Psifon: "When I change the critcal factor of my weapon, only the numbers after the optimum power attack are changing on the chart. In effect only the numbers on or after the yellow line are registering the change." - Ok, fixed that. I also fixed the problem with when your weapon as a higher crit than the number needed to roll. There were some errors in how it handled critical damages, and sometimes it multiplied more than it should to the crit modifier, that's been changed. So regarding to PA.. I think this is getting pretty complete :) "Also (and this isn't really important I don't think), the critical damage is not factored into the average damage of the weapon in the field "Total Damage, Main" and "Total Damage off Hand" Not a big deal, but it may be nice to have for comparing basic weapons." um.. .. ok.. well.. ah, how to explain this.. it's all calculated in the tables.. meaning you can take the highest number in the PA=0 row, set the chart to "standard action" and that's your 'default average damage' which you are looking for, based on your abilities and strengths. Lemme know if you find anything else you would like or if you find something which is odd. K.
Psifon 04-03-04, 07:49 PM	I found something odd. The field where you put in your character's damage bonus due to Strength is write protected, and therefore cannot be changed. This renders the whole spreadsheet unusable. So are all the blue fields for attack and damage in the off-hand weapon section. Not to nit pick....;)
KashGarinn 04-04-04, 08:34 AM	blah, *bonk* thanks for the heads up. Fixed. K.
Psifon 04-04-04, 12:42 PM	It's still doing it. Hmm... In fact the fields for the secondary weapon labled: Threat range Critical factor Magical extra dice are doing it now too.
KashGarinn 04-04-04, 02:17 PM	hmm, I've re-uploaded it, try now. K.
Psifon 04-04-04, 07:32 PM	Much better, thanks
frisbeet 04-09-04, 06:17 PM	Hi Kash, Looks like maybe you've got a little calculation to iron out. Here's a check example. BAB 20 Str 26 +3 GS Feats of WF, gWF = + 2 in your wpn focus field Feats of WS, gWS = + 4 in your wpn spec. field Feat of improved critical = 0.2 in your Threat range field Caculating by hand and by my spreadsheet, against AC 33 I get 81.12, with no PA. Optimum PA is 2, for 82.80. Looks like you're undercalculation slightly. For example, your first attack damage is 27.3. It should be 29.64. That's (15/20 + 4/20*1/20)*26 + (4/20*19/20)*26*2 Still it's a nice effort and you're almost there.
frisbeet 04-10-04, 02:06 PM	It's a confusing enough calculation that I've had to re-edit my original post on the subject twice (turns out I had it right the 1st time). I'll repost it because I don't want to screw anybody up who may have cared to note the original. Plus, I don't feel like saying anything terribly original right now. The "# of ways" column counts the # of ways of rolling, say a 12, with 4 d4s (31), for example. (This comes from a rather complicated formula re-derived awhile back on the EnWorld board.) This distribution is needed if you're wielding a Falchion (2d4 18-20 x2) and hit for critical damage. If you're opponent has DR of 10 and you do no extra damage from strength or weapon enchantment or feats, the probability distribution looks instead like: outcome #ways probability 4 1 0 5 4 0 6 10 0 7 20 0 8 31 0 9 40 0 10 44 0 11 40 0.15625 12 31 0.12109375 13 20 0.078125 14 10 0.0390625 15 4 0.015625 16 1 0.00390625 Why does this matter? With an opponent with no DR, the average Falchion crit damage is 2 x <2d4>, or 10. Take the product of each outcome with it's probability and sum this up, for the 1st distribution I've listed. That's 4 x 0.00390625 + 5 x 0.015625 + 6 x 0.0390625 + ... This sum is 10, as it should be. Now look what happens when you do the same thing for DR 10. The average crit damage is not zero! (10 - 10). Instead, it's exactly 0.890625. That's (11-10) x 0.15625 + (12-10) x (0.23209375) + ... + (16-10) x 0.00390625. Here's the rather complicated little formula which calculates the distribution for any set of n identical dice with s sides. oc = outcome n = number of identical dice s = sides of die Let COMB(a,b) = a!/[b!(a-b)!] SUM(i=a,b) {term} = sum all terms starting with the "ath" and ending with the "bth", where i = index) and IF(condition,if true do this,if false do this) = you get the picture Then the # ways an outcome can be rolled = COMB(oc-1,n-1) + SUM(i=1,n-1) {(-1)^i * IF[oc<(i*s+n),0,COMB(n,i)*COMB(oc-i*s-1,n-1)]} This is really a snap implementing on a single spreadsheet. It's kindof cool (for a very few of us) to see the distributions, how their spread changes and stuff. Here's 3d8 vs. 6d4 oc 3d8 # ways P 6d4# ways P 3 1 0.001953 4 3 0.005859 5 6 0.011719 6 10 0.019531 1 0.000244 7 15 0.029297 6 0.001465 8 21 0.041016 21 0.005127 9 28 0.054688 56 0.013672 10 36 0.070313 120 0.029297 11 42 0.082031 216 0.052734 12 46 0.089844 336 0.082031 13 48 0.093750 456 0.111328 14 48 0.093750 546 0.133301 15 46 0.089844 580 0.141602 16 42 0.082031 546 0.133301 17 36 0.070313 456 0.111328 18 28 0.054688 336 0.082031 19 21 0.041016 216 0.052734 20 15 0.029297 120 0.029297 21 10 0.019531 56 0.013672 22 6 0.011719 21 0.005127 23 3 0.005859 6 0.001465 24 1 0.001953 1 0.000244 You can check to see if the distributions are correct by calculating the average as above and comparing to the known average: 3 x 0.001953 + 4 x 0.005859 + ... + 24 x 0.001953 for 3d8 = 13.5. The same number is found by taking the average of d8 and multiplying by 3: 4.5 x 3 = 13.5 So that's nice, 3d8 distribution checks out. FYI
Nail 04-14-04, 11:12 AM	Thanks! ...and yes, that is cool. :cool:
darkwing_bmf 07-08-04, 01:32 AM	Edit: I found an error that had already been found, doh! Is there any way the original poster can update the top message with the correct formulas? Thanks
gruuletheaxe 07-09-04, 03:14 AM	Is there a spreadsheet of all this floating around somewhere? Sure would be handy. Amazing work. Thanks.
roguebfl 07-09-04, 07:02 AM	Originally posted by adiaven Magic Forumla for Dummies Optimal Power Attack = (The difference between your To Hit and target's AC)/2 + (Your average damage)/4 + 10.5 Example: Your To Hit is +21 Target AC is 27 Your average damage is 13 (2D6 + 6) OPA = (21-27)/2 + 13/4 + 10.5 = -3 + 3.25 + 10.5 OPA = 10.75 His formula says your best powerattack is 10 or 11. Just to be clear the OPA of 10 or 11 representes your attack modifer After adding the Power Attack Mod? (ie lowering your +21 buy 10 or 11 to leave you with +10 or +11? humm bad numbers to be asking Players has a Attack mod of +12 and an ave dam of 18 (2d6+11) agaist an AC 19 OPA = (12-19)/2 + 18/4 + 10.5 = - 3.5 + 4.5 + 10.5 = 11 .6 is Suggesting to do no more than Powerattack of no more than lowring the attack by 1 ?
frisbeet 08-12-04, 01:39 AM	FYI have updated power attack optimization spreadsheet on my site (signature) to allow for the Power Critical feat (Complete Warrior) and a power attack multiplier to model PrCs/feats which do better than the standard damage:AB penalty ratio. A lot of PrC/character combos can now be modeled by virtue of these improvements, relevant core feat and item enhancement inclusion, and generic attack and damage bonus fields. Have fun, one of you.
Aerk 11-13-05, 04:19 PM	What occurs if you allow Keen and Improved Critical to stack (as has been advocated by Sean K. Reynolds here (http://www.seankreynolds.com/rpgfiles/rants/keenimprovedcritstacking.html). Basically, my question is this: If you have a "high" threat weapon, such as a Falchion, with improved critical and keen stacking on it (18-20, i.e. 15% doubled to 30% doubled to 60%) This would result in a threat range of 9-20. I thought about it and went over the factors: 1) the expanded critical hit range and 2) how this figures into confirming the crits and what effects the minus to hit from power attack has on it - even with the expanded range, PA means the chances to hit and confirm are lowered. My thing is, in a campaign that allowed improved critical and keen to stack, the leap attack + shock trooper (headless charge) + two-handed keen improved critical falchion = a very good chance to drop the enemy in a single round - making the falchion the Weapon of Choice over, say, the greatsword or bastard sword for the initial charge. However, in round-by-round fighting, would the falchion loose this edge, or would imp. crit + keen + normal "optimal" power attack usage allow it to outperform a greatsword with the same feats? I understand the falchion only begins to outperform when you are dealing ridiculous amounts of bonus damage - but on an initial charge, with the right feats, that bonus damage is there. On a side note, now that Leap Attack is +100% with a 2-handed weapon, we get 4:1 ratio, right? How does valorous factor in with that? 8:1? 6:1?
nihility 11-30-05, 09:31 PM	:bump:
Cannonballninja 12-23-05, 08:36 AM	On a side note, now that Leap Attack is +100% with a 2-handed weapon, we get 4:1 ratio, right? How does valorous factor in with that? 8:1? 6:1? Valorous and Leap attack would follow the multiplier rules. x2 from leap attack would become x3 with valorous so you'd be getting a 6:1 return.
Psifon 05-04-06, 01:49 AM	Valorous and Leap attack would follow the multiplier rules. x2 from leap attack would become x3 with valorous so you'd be getting a 6:1 return. Not so. You would be getting X8. Leap attack multiplies the bonus damage from power attack. Valorous multiplies the total damage. They multiply different things. So what you get is: Leap attack = PA + 100%PA Valorous = 2(Base Damage + All Modifiers) So The combo = 2(Base Damage + PA +100%PA) So with a 20 STR and a +3 valorous greatsword (7 points average damage), and a -10 attack penalty on a leap attack, you get: 2 (7 base + 3 Enhancement + 7 STR + 40 PA/Leap Attack) = 114 average damage. On a crit the same weapon would do: 3 (7 base + 3 Enhancement + 7 STR + 40 PA/Leap Attack) = 171 average damage. Note that the double damage from the crit adds a multiplier to the double damage from the valorous weapon. This is because they both multiply the same thing: Total damage. In both cases, added dice from energy weapons, sneak attack, etc. add on afterwards.