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Post by xarkon on Mar 16, 2009 23:34:08 GMT
I stand corrected on the description of your numbers, didn't realize you'd normalized to no crit iteration 5 case.
By per round damage, I mean the average damage done per round (think of this as average hits per round enhanced by crits), normalized by the damage of the weapon. Maybe I should have called it average hits per round to avoid confusion. E.g. if a given attack has a 50% chance to hit (w crit mult =1) , that attack contributes 0.5 to hits per round, if you have a crit mult of 3 on 19-20 then that same attack averages 0.6 hits per round, since a hit with a crit, counts as 3x.(see formula below).
So if you have a situation with AC-AB of 10, looking in that ss, the bastard sword base case is 1.61. This is the average hits per round, including enhancement by crits. You'd multiply this number times the base weapon damage (e.g. 1d10 gives avg base of 5.5, with 1d6 fire would be 5.5+3.5 for base damage), to get average damage per round.
The ratio sheet was just to see where this per round calculation differed from your numbers.
As to explanation of the where the 1.61 number came from for base bastard sword. There are four attacks plus haste, use the formula Phit (Pcrit (CritMult-1) + 1) to get hit average for a given attack, where Pcrit cannot be > Phit. So the 5 attacks per round give an average of 0.50 ( 0.10 (2) + 1) = 0.6 Haste at full AB 0.50 ( 0.10 (2) + 1) = 0.6 full AB 0.25 (0.10 (2) + 1) = 0.3 AB-5 0.05 (0.05 (2) + 1) = 0.055 AB -10 0.05 (0.05 (2) + 1) = 0.055 AB - 15 _____________________________ Total per round = 1.61 Hope that helps clarify what I'm trying to calculate here.
Xarkon
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Post by FunkySwerve on Mar 17, 2009 5:26:59 GMT
By per round damage, I mean the average damage done per round (think of this as average hits per round enhanced by crits), normalized by the damage of the weapon. Maybe I should have called it average hits per round to avoid confusion. E.g. if a given attack has a 50% chance to hit (w crit mult =1) , that attack contributes 0.5 to hits per round, With you so far. You're using the same baseline we did, the no-crit scenario. 19-20 means 10% of hits are crits. That means, in this scenario, that 10 or lower misses, 11-18 hits, and 19-20 crits for 3x the damage. Put another way, that's .4 hits per round for noncrits, and .1 x 3 hits for crits, or .7 hits for that attack. Of course, the crit confirmation roll makes half the crits noncrits (second roll has to hit for crit to confirm, and we have a 50% miss rate here), so instead of .4 + .3, we get .4 + .05 + .15, or .6, for that first attack, which is what you have. And, of course, the iterations. With iterations, assuming this is a normal one-handed weapon, that's .6x2, plus 3 lower iteration attacks. The next iteration would be 15 or lower misses, 16-18 hits, 19-20 crits 25% of the time, for .3 + .0075 + .075, or .3825. The next two would hit only on 20, and crit only 5% of the time, meaning you would have .0475 hits per round from normal hits and .0075 hits per round from crits, for a total of .055, which is what you have. So, unless I screwed up my math, you have an error in your math on the third attack (and therefore your formula), since you show .3 instead of .385. Once you work that out, you can then try to calculate how the new power critical feats we're adding will affect all this (they will add 4 and 6 respectively to crit confirmation rolls, for a total of +10 with both). Funky
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Post by xarkon on Mar 17, 2009 11:26:52 GMT
Ahh, but your math is wrong here. Hit on 16-18 gives 0.15, not 0.3 Crit on 19-20 gives .1x3 x 25% of time for another 0.075 and gives regular hit 75% of the time (.1 x 0.75 for another .075, not .0075) So .15 + .075 + .075 is 0.3 as per formula.
The formula is derived just as the same way as you've calculated:
(Phit – Pcrit) for the non critting hits Pcrit * Crit Mult*Phit for confirmed critting hits Pcrit * (1-Phit) for non confirmed critting hits ___________
=Phit – Pcrit + Phit *Pcrit*CritMult + Pcrit – Pcrit*Phit
=Phit ( 1 + Pcrit*CritMult – Pcrit)
= Phit (1 + Pcrit (CritMult -1) )
= Phit (Pcrit (CritMult-1 ) +1)
Edit: Note that Pcrit must be <= Phit, i.e. crit range will reduce as hit probability drops
Xarkon
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Post by FunkySwerve on Mar 17, 2009 18:26:17 GMT
I had a feeling I'd buggered up the math. At least I see what you're doing now. Now, how bout those power crit feats? Of course, there's the added complication that many builds simply won't be able to fit all the feats, including those that are already maxed out under the current feats. Are you beginning to see why we resort to guestimates? Funky
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Post by xarkon on Mar 17, 2009 22:26:32 GMT
I had a feeling I'd buggered up the math. At least I see what you're doing now. Now, how bout those power crit feats? Of course, there's the added complication that many builds simply won't be able to fit all the feats, including those that are already maxed out under the current feats. Are you beginning to see why we resort to guestimates? Funky Assuming you mean keen, OC, DC, etc, for "power crit feats", those simply change the CritMult and Pcrit numbers. So a keen + IC + OC + DC bastard sword will have crit range of 14-20 (Pcrit = 0.35) with CritMult of 4. Then use the same formula. Now that you see what I'm doing, hopefully the spreedsheets for various AC-AB will be more clear. They've got all the variations of crit feats that you had in your original spreadsheet. I agree it's complicated just to add in the stuff I did for dependence on AC-AB, nevermind adding strength/weapon size and additional damage modifiers which are not crit multiplied. If the spreadsheets help identify areas where weapons are not balanced, great, if not, the guestimates are reasonable too. Xarkon
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Post by FunkySwerve on Mar 17, 2009 23:12:25 GMT
Not exactly. Once you work that out, you can then try to calculate how the new power critical feats we're adding will affect all this (they will add 4 and 6 respectively to crit confirmation rolls, for a total of +10 with both). Funky Isn't math fun? The real snarl, aside from the 4th dimension, so to speak, is that it's not clear which builds, if any (other than say, CoT and Fighter), can afford the extra feats. You'd basically have to work up an entire set of builds to gauge the impact with precision. Funky
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Post by xarkon on Mar 19, 2009 1:10:03 GMT
Once you work that out, you can then try to calculate how the new power critical feats we're adding will affect all this (they will add 4 and 6 respectively to crit confirmation rolls, for a total of +10 with both). Isn't math fun? The real snarl, aside from the 4th dimension, so to speak, is that it's not clear which builds, if any (other than say, CoT and Fighter), can afford the extra feats. You'd basically have to work up an entire set of builds to gauge the impact with precision. Funky Math is fun! I think I got what you are doing with the new power crit feats. So for single attack damage, use the same calculations, just need to add in the extra hit confirmation bonus probability So sum of (Phit – Pcrit) for the non critting hits Pcrit * Crit Mult*(Phit+CB) for confirmed critting hits Pcrit * (1-(Phit+CB)) for non confirmed critting hits where CB is either 0.2 or 0.5 for the +4 or +10 feats It gets a little uglier because need to make sure Phit+CB is <=0.95 and Pcrit<= Phit, but that's easy in a spread sheet. spreadsheets.google.com/pub?key=pOivG2oeB17Di_v1eyQPDSg I don't know which feats are prereqs or what builds are even possible, but I took a few weapon examples just to see. Certainly helps most at low hit probabilities and for high crit multiples, as would be expected. It would open up some nice possibilities for lower AB classes (e.g. battle cleric w a warhammer), but not if they can't manage to get the requisite feats, alas. Xarkon
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Post by FunkySwerve on Mar 19, 2009 2:30:11 GMT
If you assume that players can afford the new feats, how do our iteration percentiles look, based on your numbers? I realize the values vary based on where ac-ab is, etc, but I'm curious as to your estimation.
Thanks, Funky
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Post by xarkon on Mar 20, 2009 1:01:49 GMT
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Post by xarkon on Mar 21, 2009 22:15:20 GMT
I'm assuming by "interation percentiles" you mean the iteration multipliers you used to get a damage estimate for various iteration weapons. I generated a few calculations as function of AC-AB and also a comparison of double weapon vs a single weapon equivalent. Includes haste attack and 2 bonus for double in addition to offhand. spreadsheets.google.com/pub?key=pOivG2oeB17AcZtOZNze2Lw There really wasn't much dependence on crit multiplier, range, or power crit feats, maybe a few percent. If you want to balance the weapons for AC-AB more in the 10ish range, I'd go with something like this (multipliers relative to iteration 5). Iteration 3, 135% Iteration 4, 115% Iteration 6, 95% Iteration 7, 85% DoubleWeapon, 150% It's true that at either end of the AC-AB scale (always hit or always miss, 'cepting 1's and 20's), the multipliers reduce to just the ratio of attacks, so would be 160%, 120%, 100% and 80% for 3,4,6,7), but in the middle ratio's for 3,4,6 dip and 7 rises. For double weapons at the extremes of AC-AB, it's 150% for iteration 3 doubles and 167% for iteration 4 doubles, but they go up and down somewhat in the middle. Xarkon
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Post by trickypriest on May 4, 2009 9:43:02 GMT
How will this affect medium sized katana users? My WM uses a crafted katana, so it'd really hurt, if after the changes, she's lose str bonus, or anything else from the settings katanas have now. All the more so, because Bastard Swords seem to have a bit unfair advantage over Katanas.
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Post by fasut on Jun 1, 2009 18:25:20 GMT
hope the changes will come soon
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Post by gandoron on Dec 15, 2009 20:52:35 GMT
Do weapons with multiple physical damage types do the most vulnerable now, or is it still broken using the damage type that the mob is strongest against.
-G
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Post by MightyKhan on Dec 16, 2009 12:38:57 GMT
they fixed that in the last nwn update
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