Falchion and improved critical

[Nail]

About two weeks ago I was involved in a thread about this. IIRC, Scion and I were on opposite sides of the issue.

Since then and after running through lots of numbers, I've changed my mind. Impr. Critical isn't that great, even for a Falchion; and stacking Keen on top of that wouldn't be outragous either. I know it sounds like a no-brainer: surely something that threatens 45% of the time should be incredibly powerful?!?

No so, in this case. Run the numbers and see for yourself!

The equation is:
A = PD[1+Pc(Mc-1)] + PDb

Where:
A = average damage per attack
P = probability to hit, as a fraction (remember: max of 0.95, min of 0.05!)
Pc = Probability to critical, as a fraction (threat range of 18 - 20 would be 0.15)
Mc = Critical multiplier (for a Falchion it's = 2)
Db = Damage dice that are not multiplied by a critical, like energy or sneak attack

I'd be happy to walk you through it, if you wish.

Compare your uber-crit falchion vs a greatsword. Greatsword still wins! Huh.

 

[Garnfellow]

Personally, I made the falchion an exotic weapon in my campaign. I haven't broken out the math, though -- that was just a gut response.

 

[Enkhidu]

which I personally see as a direct result of the change to power attack being a bad one rather than improved crit being odd. 2 for 1 is just too good.

Yet even at 1 for 1 instead of 2 for 1 (and with the a grasp of the "art" of partial power attack), a falchion gets a fairly decent boost in damage from Improved Crit.

 

[Nail]

Personally, I made the falchion an exotic weapon in my campaign. I haven't broken out the math, though -- that was just a gut response.

Nothing against yer gut, but: falchion ain't nothin' special. The numbers do not support your hunch. Revert it back to a martial weapon.

 

[silentspace]

Pc = Probability to critical, as a fraction (threat range of 18 - 20 would be 0.15)

Pc for a threat range of 18-20 should be lower than 0.15, since every threat is not an automatic critical.

If this is factored in, it will tend to increase damage for the falchion vs the greatsword (by how much I don't know - I'm not running the numbers).

Power attack against lower AC creatures will further increase damage for the falchion, as can be seen in the formula.

 

[Nail]

Pc for a threat range of 18-20 should be lower than 0.15, since every threat is not an automatic critical.

Already factored in, my friend. Look at the formula again.

 

[silentspace]

Ah...

 

[silentspace]

But then Pc is a variable number.
For a falchion:
If P >= 0.15, Pc = 0.15
If P = 0.10, Pc = 0.10
If P = 0.05, Pc = 0.05

No?

 

[Nail]

Here, let's try this:

Average damage is gonna be: (using the symbols above)

P * D <= that's the average damage from a normal hit

plus

P * D *Pc *(Mc -1) <= that's the extra damage from a confirmed critical. See how the Probability to critical (Pc) is multiplied by the Probability? That takes into account confirming the threat. The multiplier has 1 subtracted from it to account for only the extra damage from a confirmed critical.

Put the two peices together:

P * D + P * D *Pc *(Mc -1)

.....and factor out the common "P*D":

=PD[1+Pc(Mc-1)]

It's all good!

 

[kigmatzomat]

If you want to make your DM twitch, buy a Sunblade but have it crafted as a falchion. That way instead of the Bastard/Shortsword profiency it uses Falchion/scimitar. Now get two of them and go glowing TWF on some poor undead with massive curving swords in each hand.
Booya!