From Kama to Khopesh -- the value of Criticals

[cforce]

Recent discussions on the change to helpless states got me thinking, and I realized that while I knew critical profile is an important-to-dominant factor in DPS, I didn't have a good sense for how it compared to other sources of damage. What's the real difference between a Khopesh and a Scimitar? I have a good sense for how much Power Attack adds, or Holy, or Holy Burst -- but no intuitive sense for how iCrit compares to Power Attack for added DPS.

So, I took a quick look at base damage across a variety of the top DPS builds. Generally speaking, a fully-raid-buffed DPS build will do somewhere in the neighborhood of mid-60's on-hand, mid-50's off hand for base damage if TWF, and somewhere in the neighborhood of 100 for top-tier THF builds. There was some variation, but it's in the 10% range on base damage among the variants trying to be DPS builds.

This makes the calculation pretty straightforward! I'm going to define something I'll call a "critical unit", which is the component of critical damage above base damage done across the d20 span. So, for example, a critical profile of 20/x2 is "one unit" -- the weapon gets one extra dose of base damage, on a roll of a 20. 19-20/x2 and 20/x3 are each two units: the first gets on extra dose of base damage on 19 and 20, and the second gets two doses on a 20 -- in each case, the total is two. 19-20/x3 is 4 units, 15-20/x2 is 6, etc. A Frenzied Berserker with a Khopesh and improved crit maxes out at 14 units: 4 for 17-18/x3 and 10 for 19-20/x6.

So, we'l use 60 for TWF and 100 for THF as our base damage reference. Each critical unit adds to the overall average damage of a weapon, in about the same amount as if you simply added basedamage/19 to the base damage for each critical unit. So, a critical unit for twf is worth about the same amount of DPS as adding +3.15 to the base weapon damage. A critical unit for THF is about the same as adding +5.26 to base damage.

Let's put this to use in a practical example. I've got iCrit:Slashing. How much better are Khopeshes than Scimitars? Well, the Khopesh has 2 more critical units (8) than the scimitar (6), which is equivalent to about +6.3 point of damage. So, if we were talking about the deciding between a +5 Holy Scimitar and a plain ol' +5 Khopesh, we'd choose the Holy Scimitar -- barely. But wielding a Khopesh with Power Attack *off* is going to do slightly more damage than wielding a similar Scimitar with Power Attack *on*.

How much better is a Falchion's crit profile than a Greataxe's, with Improved Crit? 2 Units, or about the same a 10.5 points of base damage. Again, roughly the equivalent of an (unmodified) power attack.

What's the difference between a Khopesh and a Kama, in the hands of someone with iCrit? 6 critical units, worth 18.9 points of average damage. A simple +5 Khopesh does more damage than, say, a +5 Shock Kama of Greater X Bane in the hands of a DPS build.

Of course, this doesn't even start to take into account Burst effects, but I'll leave that as an exercise for the reader -- just wanted to share my napkin-scratches with the rest of the class.

[Yaga_Nub]

Very interesting.

[karl_k0ch]

Are there any applications?

j/k, very interesting post, indeed.

[zealous]

If only seeker effects and alignment burst followed the rules, right?

[cforce]

Ah, you know what? I didn't even factor in any seeker bonus! Figure 6 points of seeker is worth another ~+0.3 per unit, as well, if you happen to have it...

[Angelus_dead]

This makes the calculation pretty straightforward! I'm going to define something I'll call a "critical unit", which is the component of critical damage above base damage done across the d20 span. So, for example, a critical profile of 20/x2 is "one unit" -- the weapon gets one extra dose of base damage, on a roll of a 20.

1. The term "Critical Power" has been in limited use for years: CP = ((crit mult -1) * (threat range) + 19) / 20. It is the number by which a nominal per-attack damage boost is multiplied to determine the actual average per-attack increase. (Whether you divide it by the 19 or 20 factors is an arbitrary convention)

2. It's probably simpler to consider a 20/x2 weapon to have zero of the increase factor, because the 2x on 20s is canceled out by 0x on 1s. Thus that weapon adds 100% of damage boosts to damage, while things with better crits add more.


Here is a table of Critical Power, which was composed back when Barbarian Critical Rage was first announced:
Club: 20/x2 -> 20/20 = 1.00
Sword: 19-20/x2 -> 21/20 = 1.05
Keen Sword: 17-20/x2 -> 23/20 = 1.15
Axe: 20/x3 -> 21/20 = 1.05
Keen Axe: 19-20/x3 -> 23/20 = 1.15
Rapier: 18-20/x2 -> 22/20 = 1.10
Keen Rapier: 15-20/x2 -> 25/20 = 1.25
Pick: 20/x4 -> 22/20 = 1.10
Keen Pick: 19-20/x4 -> 25/20 = 1.25
Khopesh: 19-20/x3 -> 23/20 = 1.15
Keen Khopesh: 17-20/x3 -> 27/20 = 1.35
SOS: 18-20/x3 -> 25/20 = 1.25
Keen SOS: 15-20/x3 -> 31/20 = 1.55

[cforce]

1. The term "Critical Power" has been in limited use for years: CP = ((crit mult -1) * (threat range) + 19) / 20. It is the number by which a nominal per-attack damage boost is multiplied to determine the actual average per-attack increase. (Whether you divide it by the 19 or 20 factors is an arbitrary convention)

2. It's probably simpler to consider a 20/x2 weapon to have zero of the increase factor, because the 2x on 20s is canceled out by 0x on 1s. Thus that weapon adds 100% of damage boosts to damage, while things with better crits add more.


Here is a table of Critical Power, which was composed back when Barbarian Critical Rage was first announced:
Club: 20/x2 -> 20/20 = 1.00
Sword: 19-20/x2 -> 21/20 = 1.05
Keen Sword: 17-20/x2 -> 23/20 = 1.15
Axe: 20/x3 -> 21/20 = 1.05
Keen Axe: 19-20/x3 -> 23/20 = 1.15
Rapier: 18-20/x2 -> 22/20 = 1.10
Keen Rapier: 15-20/x2 -> 25/20 = 1.25
Pick: 20/x4 -> 22/20 = 1.10
Keen Pick: 19-20/x4 -> 25/20 = 1.25
Khopesh: 19-20/x3 -> 23/20 = 1.15
Keen Khopesh: 17-20/x3 -> 27/20 = 1.35
SOS: 18-20/x3 -> 25/20 = 1.25
Keen SOS: 15-20/x3 -> 31/20 = 1.55

Right. What I stuggled with was this. Yep, 1.15 is better than 1.10. How much? The answer "Well, 0.05" -- that doesn't really tell me anything.

Translating the above, each 0.05 worth of critical power is worth 3.15 points of extra damage (TWF) or 5.26 points of extra damage (THF). While I don't really know what 0.05 points of critical power was worth, I sure do know what +3 damage feels like!