Crit calculations

[Garryl]

His chart is correct for average damage on a hit.  However, I'm adding base accuracy into the equation, which lowers his numbers 5%.  Thinking about it more I suppose it's inappropriate to include accuracy results in for those who just want to see the pure average damage without the accuracy factor, but getting accuracy in there will eventually help calculate how much damage on average a character can expect to do with various attacks.  In short, I want to get the statistics of how much accuracy and damage play together to eventually put a handbook together that will give accurate information on what kind of gear to use to maximize damage.

Then I don't understand why you're comparing pairs of specific weapons against each other, or why you're only running your numbers when you hit on a 2. It seems like those just obfuscate the variables you are actually looking at and changing across your tables (base damage + misc modifiers, crit multiplier, threat range). In particular, I don't see why you mention looking at how accuracy affects things since you aren't even looking at different hit chances.

[Jackinthegreen]

His chart is correct for average damage on a hit.  However, I'm adding base accuracy into the equation, which lowers his numbers 5%.  Thinking about it more I suppose it's inappropriate to include accuracy results in for those who just want to see the pure average damage without the accuracy factor, but getting accuracy in there will eventually help calculate how much damage on average a character can expect to do with various attacks.  In short, I want to get the statistics of how much accuracy and damage play together to eventually put a handbook together that will give accurate information on what kind of gear to use to maximize damage.

Then I don't understand why you're comparing pairs of specific weapons against each other, or why you're only running your numbers when you hit on a 2. It seems like those just obfuscate the variables you are actually looking at and changing across your tables (base damage + misc modifiers, crit multiplier, threat range). In particular, I don't see why you mention looking at how accuracy affects things since you aren't even looking at different hit chances.

The work in here is a starting point to make sure I have what I need to get future calculations done.  Just because I haven't yet fully added in different levels of accuracy alongside the damage doesn't mean I won't later on, because indeed I will.

For example, if a battleaxe and heavy pick have the same bonus damage and are both base crit, but the battleaxe has +1 accuracy, the battleaxe always wins.  The gap widens as the damage is increased.  However, adding Keen onto the pick pulls it ahead again, even if the battleaxe is also Keen.  Hence, a masterwork battleaxe will always be better than a normal heavy pick if the accuracy boost helps.  A character with improved crit, however, can get more out of the heavy pick than he could with a slightly better battleaxe.  It's pretty obvious of course, but there is full mathematical proof of that now.

Keep in mind this also started as attempting to redo Reynolds's calculations, and I was asked to make more calculations until I realized I screwed up the math.

[Maat Mons]

If you want to do in-depth analysis, you might want to look at abilities like battle ardor (Tome of Battle, p22) that make the chances of hitting and the chances of confirming a critical different.  It's not too much of an adjustment: [chance of hit] * [non-critical damage] + [chance of critical threat] * [chance of confirmation] * [extra critical damage]

[Jackinthegreen]

Actually, I think one of those equations you gave me already works for that.

=(((A42)*18)+(0.95*(A42)*2*1)+(0.05*(A42)*1))/20 is an example.  .95 in the second part represents the crit confirm and then the .05 in the third part is regular hits when they don't.  Changing those along with the accuracy in the first part would allow tweaking for stuff like Battle Ardor and Power Critical.

[Snowbluff]

If you want to do in-depth analysis, you might want to look at abilities like battle ardor (Tome of Battle, p22) that make the chances of hitting and the chances of confirming a critical different.  It's not too much of an adjustment: [chance of hit] * [non-critical damage] + [chance of critical threat] * [chance of confirmation] * [extra critical damage]

ToB adds some interesting options to crits. Aura of Perfect Chaos messes things, since the Disciple of Dispater class in BoVD plus Improved Critical (They explicitly stack) can get you guaranteed crits.

Also, Aptitude Weapon arguably allows weapon to work with feats they shouldn't work with. Like Lightning maces. Maybe other critical based, weapon specific feats exist.

[nijineko]

You can't use a rapier in two hands to get 1.5x Str.  A scimitar has the same stats (1d6, 18-20/x2) and can be used two-handed, so your numbers are still valid.

Seems like yet another screwup for the Sean K Reynolds guy, as well as myself of course.  I'll change the weapon.

elven thinblade or courtblade is usable as a two-handed weapon.

[Jackinthegreen]

You can't use a rapier in two hands to get 1.5x Str.  A scimitar has the same stats (1d6, 18-20/x2) and can be used two-handed, so your numbers are still valid.

Seems like yet another screwup for the Sean K Reynolds guy, as well as myself of course.  I'll change the weapon.

elven thinblade or courtblade is usable as a two-handed weapon.

That I know, and they do have great threat ranges.  It's mostly a trivial problem with how he did things since he's rules-lawyering but didn't realize rapiers don't get a benefit from being used two-handed.  Oddly enough, there's artwork in Complete Scoundrel for the Deadly Defense feat showing the guy using what looks like a rapier two-handed.

If you want to do in-depth analysis, you might want to look at abilities like battle ardor (Tome of Battle, p22) that make the chances of hitting and the chances of confirming a critical different.  It's not too much of an adjustment: [chance of hit] * [non-critical damage] + [chance of critical threat] * [chance of confirmation] * [extra critical damage]

ToB adds some interesting options to crits. Aura of Perfect Chaos messes things, since the Disciple of Dispater class in BoVD plus Improved Critical (They explicitly stack) can get you guaranteed crits.

Also, Aptitude Weapon arguably allows weapon to work with feats they shouldn't work with. Like Lightning maces. Maybe other critical based, weapon specific feats exist.

Oh yes, Aptitude Lightning Maces cheese is great fun.  I'd need to reread Aura of Perfect Chaos, but I think I can account for its math.  As for Disciple of Dispater, there's a 21 level build that combines it and Arcane Duelist to get a 6-20 crit range.  If using the Bladed Gauntlet before errata which had a base 17-20, the build can get it to 1-20.  Aptitude Weapon with Lightning Maces on that could literally give infinite attacks since every roll is a threat even if it doesn't land.

Edit:  I see Aura of Perfect Order in there to let the character treat a d20 roll as an 11 once per round.  Getting that to be within a crit threat range might be difficult depending on what rules are allowed.