Average Weapon Damage

[Fortain]

I'm currently making a list of average weapon damage for a given set of weapons, but one part is confusing me at the moment. When dealing with a weapon that has a X3 or X4 crit multiplier, should I add the averages together, or average the averages, or something else? My end result is going to look like this:

Base Weapon: Dagger (WotC 3.5E PHB)
Base Damage Die: 1d4
Critical Range & Multiplier: 19-20/X2
Average Damage: 2.5 w/o crit; 2.75 w/crit

Thanks in advance for any info.

EDIT: Sorry, should've pointed this out earlier. I'm using the averaging system by Sean K. Reynolds, where your crits would average out to a certain amount of damage with each swing (seen here: http://www.seankreynolds.com/rpgfiles/rants/keen_medium.html).

 

[Ilium]

Well the average damage for a dagger on a crit is 5, not 2.75. You roll 2d4 and the average for that roll is 5.

A heavy pick (normal damage 1d6, crit 20/x4) has an average critical damage of 14. 3.5 x 4.

Is that what you're asking?

 

[Nail]

I'm unclear on your question...but I'll take a stab at it anyway. With a large Heavy Pick (x4)!

The total average damage for any weapon is:

Total Ave Damage = D[1 + Pc(Mc-1)]

where:
D = average for the weapon damage dice (ex: d6 = 3.5)
Pc = Probability to critical, as a fraction (ex: a threat range of 19-20 = 0.10)
Mc = Multiplier of critical (x4 = "4", etc)

So for a large-sized Heavy Pick, the total average damage would be:

= 4.5 [1 + 0.05(4 - 1)] = 5.175 hp

Is that what you needed? What's this for?

 

[starwed]

The total average damage for any weapon is (some mostly accurate formulas)

This is, of course, the average damage assuming a hit. Since the chance to confirm a crit is the same to hit in the first place, this is a common factor that you can ignore... except when a threat is not necessarily a hit.

Against a creature that you can hit only on a natural 20, for instance, an expanded crit range doesn't help in the least. But since the distribution of enemy ACs isn't something that we can predict, it's best just to ignore this element here.

 

[Ilium]

Ok, now with your edits the question is very different.

As Sean shows on the page you link, you have to decide how often you expect the crits to be confirmed. He shows his numbers based on 25%, 50%, 75% and 100% of threats confirmed. Once you have that number decided on, I think you'd plug it into Nail's equation so it looks like this:

Total Ave Damage = D[1 + (Pc * Pcf) * (Mc-1)]

Where Pcf = your probability to confirm the critical. Basically, Nail is assuming a 100% confirmation rate, right? Let's say you pick a 50% chance. Then Nail's example with the heavy pick is:

= 4.5 [1 + (0.05 * 0.5) (4 - 1)]
= 4.5 [1 + (0.025) * 3]
= 4.5 [1.075]
= 4.8375

Now take Improved Critical (or cast Keen Weapon) for your pick:
= 4.5 [1 + (0.1 * 0.5) (4 - 1)]
= 5.175

 

[comrade raoul]

The easiest way to think of critical hits is that they offer an x% chance to deal an additional y00% of your modified weapon damage, where x is 5 * your threat range and y is your multiplier - 1. (Thus, a pick has a 5% chance to deal +300% damage.) You can multiply these two values to find that the pick deals +15% (5 * 300) expected damage from crits. So you'd do the same thing you do with the dagger, if it had a base 20 threat range, but multiply the extra damage by 3.

So your entry for the light pick would be:

Base Weapon: Light Pick (WotC 3.5E PHB)
Base Damage Die: 1d4
Critical Range & Multiplier: 20/X4
Average Damage: 2.5 w/o crit; 2.875 w/crit

But, I think this way of looking at crits is really misleading, because crits multiply your modified damage. (These numbers assume you don't have any damage bonuses.) If you had a +5 bonus to damage rolls, your light pick would deal 8.625 points of average damage with a crit: note that there's obviously a bigger difference between 7.5 and 8.625 and 2.5 and 2.875! (This difference gets really pronounced when you're comparing high-damage, high-crit weapons, like greatswords or falchions wielded by someone with Improved Critical.)