D&D 3E/3.5 [3.5] Crit stacking?

[Mike Sullivan]

Has anyone actually done the math for the damage loss/gain for these various critical setups? It's logical that cutting the improved critical & keen stacking weakens high crit range weapons, but by how much?

Yes, I've run the numbers before and will again:

1.45 ( 5 + x) > 1.3 ( 7 + x)
7.25 + 1.45x > 9.1 + 1.3x
.15x > 1.85
x > 12.333...

Thus, in 3.0, assuming an imp crit, keen weapon for both parties, once your total damage bonus (including strength, feats, magic, etc) is +13 or greater, against an opponent susceptible to critical hits, it's advantageous to use a scythe or falchion over a greatsword.


In 3.5, the equation is:

1.3 ( 5 + x) > 1.2 (7 + x)
6.5 + 1.3x > 8.4 + 1.2x
.1x > 1.9
x > 19

Thus, in 3.5, assuming either imp. crit or keen for both parties, once your total damage bonus (including strength, feats, magic, etc) is +20 or greater, against an opponent susceptible to critical hits, it's advantageous to use a scythe or falchion over a greatsword.


For rapiers/picks vs. longswords:

3.0:

1.45 ( 3.5 + x) > 1.3 (4.5 + x)
5.075 + 1.45x > 5.85 + 1.3x
.15x > .775
x > 5.16666...

So it's advantageous once your damage bonus is +6 or higher. (Assuming all the conditions spelled out above).


3.5:

1.3 ( 3.5 + x) > 1.2 (4.5 + x)
4.55 + 1.3x > 5.4 + 1.2x
.1x > .85
x > 8.5

So it's advantageous once your damage bonus is +9 or higher. (Again, assuming all the conditions).


I think that's the best way to get the comparison you're looking for -- basically, you need to get an additional +3 to damage for a rapier or heavy pick, or a +7 to damage for a falchion or scythe. Note that these are the minimum damage bonuses for it to EVER make sense to use the better-crit weapons. It's still arguably a bad idea to use a rapier if your damage bonus is +10 in 3.5, because you'll do, on average, about .15 hp more damage per attack against an opponent susceptible to crits, but -1 hp less damage per attack against an opponent not susceptible to crits.



EDIT: The other way of saying this is that the effective damage output of high-crit weapons (rapier, picks, etc) was reduced by 15%, the effective damage output of medium-crit weapons (longsword, battleaxe) was reduced by 10%, and the effective damage output of low-crit weapons (clubs, fists) was reduced by 5%. Assuming that you'd bother to get both keen and imp. critical for the 3.0 version of each such weapon.

 

[Staffan]

Re: Some calculations

Note that there is an alternative way to do the critical rolls
which gives the same critical results. Always roll two dice,
and if the first dice is a hit, the hit is a critical hit if the second
die is in the critical range. I'm still thinking this through, but
it does seem to give the same results.

As long as you demand that the "crit die" is also a hit, it gives the same results. Otherwise, that method will result in more crits than the regular method on opponents that are very hard to hit.

From a math point of view: You have two unrelated events: "roll crit" and "roll hit". It doesn't matter in which order you check the two (e.g. crit then hit or hit then crit), the probability of both being true are still the same.

 

[Hypersmurf]

Re: Re: Some calculations

As long as you demand that the "crit die" is also a hit, it gives the same results. Otherwise, that method will result in more crits than the regular method on opponents that are very hard to hit.

Bear in mind that if the "crit die" is a 20, the attack is a hit even if the "attack die" is a 1.

-Hyp.

 

[Plane Sailing]

Yes, I've run the numbers before and will again:

1.45 ( 5 + x) > 1.3 ( 7 + x)
7.25 + 1.45x > 9.1 + 1.3x
.15x > 1.85
x > 12.333...

I'd just like to make sure I understand all the components of your maths, if you could help me.

(BTW, solving equations on a D&D board? )

LHS is falchion/scythe, RHS is greatsword?

on LHS (5+x) = average damage on 2d4 + break point bonus damage

(on RHS 7 = ave greatsword damage).

Now the bit I'd just like a little clarification on - the multipliers on each side. The greatsword has a 10% chance (minus a little bit for confirming the crit, but that is equal on both sides in the example I assume). The falchion and scythe both do 15% more damage on average, whether through threat range or damage multiplier.

So why do we have 1.45 for the scythe and 1.3 for the Greatsword?

I'm afraid I might be being a little dense here, and I want to make sure I understand it properly.

Thanks!

 

[Storm Raven]

To the argument comparing not stacking Improved Critical with Keen being like not stacking Weapon Focus and Weapon Specialization with Enhancement Bonuses, I have got to say that such a comparison is ridiculous.

No, the comparison is exactly on point.

Improved Critical is the skill to make more critical hits, but the Keen ability overrides it due to the fact that it does it its own way, meaning the skill logically will not have MORE effect that way.

No, keen makes the blade sharper and more effective, it makes the skill of the wearer more valuable. The blade iteself does not make your attacks hit more often.

Enhancement Bonuses, however, would not logically override Weapon Focus and Weapon Specialization becasue the ENHANCEMENT (key word there) is direct magical energy and not a magical "effect" per se.

Actually, it would make more logical sense to these sorts of bonuses to override the character's skill. A +3 longsword makes the character more likely to hit. Logically, it must work by guding the character's blows so that they score a hit instead of deflecting off of armor. In effect, the bonuses to attack rolls from magical weapons should obviate a a character's skill with a weapon.

Last but certainly not least, the most important logic of all behind the threat range increases not stacking is simply one of PURE AND SIMPLE BALANCE. +1 or +2 to hit and damage stacking with other stuff does not unbalance things. Stacking things (a feat and a +1 ability) that can eventually result in HUNDREDS of points of added damage, THAT is just plain abusive balance-wise.

It has been shown time and again that critical stacking is not a balance issue. In point of fact, it has been shown repeatedly that energy enhancements add more expected damage to the power of a weapon relative to their cost than the keen enhancement.

Further, many feats, like Weapon Focus and Weapon Specialization can be reliably expected to add hundreds of points of potential aditional damage to a charactrer's output over the life of the character. I'm not sure why it is a unique situation in your mind with respect to Improved Critical other than the fact that you haven't worked through the math very well.

 

[Storm Raven]

My "complaint" is nothing of the sort. What I mean to say is that possessor's of 0 skill (BAB and combat feats) can still make critical hits. Ergo, it is difficult to believe that critical hits are entirely based on skill, since regardless of the user having it or not, the crits get made. Im not a math guy but Im pretty sure that someone sans keen, sans Imp. Critical will get about that same % of crits if they face monsters equal to their level. This, to me, suggests that a critical is a "lucky" blow, perhaps in a "critical" spot on the creature.

Even someone with a 0 BAB and no combat feats has some skill. There is ability, it may not be well-trained, but it is present.

But where does that +3 bonus come from? The sword, not you, not your skill, but a magical enhancement on a weapon you wield. An intelligent sword with the keen enhancement which granted Improved Critical as a bonus feat wielded by a commoner would inflict a lot of critical hits. None of them are based on skill.

A weapon that grants a feat grants skill to the user. He actually has a skill he didn't have before. of course, this is beside the point, since there are no actual examples of such a weapon in any of WotC's published materials.

See above. And when you play a game with luck bonuses in the DMG it seems a little narrowminded to say improving a lucky event is impossible.

And with this, you obviate your own arguments. Since you now state that you can increase the chances of a lucky even with magic, there is no reason not to have keen stack. Your entire premise is that critical hits are lucky events, and thus you cannot have effects that improve them stack. But if you can increase the chances of lucky events via magic, then your entire argument falls by the wayside.

 

[Storm Raven]

For some reason I'm picturing piles and piles of cow manure. Even if we limit ourselves to looking through 3e modules I think you will find my claim true. The fact is that feat and that enhancement are total no-brainers if you are wielding a rapier. I mean, lets say you are high enough that you qualify for Imp Crit. What reason do you have to not pick it up? Its totally awesome for you, its a substantial power-up and nothing short of an in-character disdain (or extreme affetion) for something affecting the decision (another feat) could make someone NOT take Imp Crit.

In point of fact, in terms of increased damage dealing capability for a rapier, you are better off taking Weapon Specialization and an energy enhancement than Improved Critical and keen. If you actually looked at the math as opposed to ranting, you'd have figured this out.

Any munchkin powergamer who thinks that the Improved Critical combined with keen path is the superior progression for a rapier is a munchkin powergamer who isn't very bright.

 

[Mike Sullivan]

I'd just like to make sure I understand all the components of your maths, if you could help me.

(BTW, solving equations on a D&D board? )

LHS is falchion/scythe, RHS is greatsword?

Yup.

on LHS (5+x) = average damage on 2d4 + break point bonus damage

(on RHS 7 = ave greatsword damage).

Yup.

Now the bit I'd just like a little clarification on - the multipliers on each side. The greatsword has a 10% chance (minus a little bit for confirming the crit, but that is equal on both sides in the example I assume). The falchion and scythe both do 15% more damage on average, whether through threat range or damage multiplier.

So why do we have 1.45 for the scythe and 1.3 for the Greatsword?

I was assuming a fully-upgraded scythe and greatsword for the 3.0 case (since that's where it differs from 3.5): In other words, a keen scythe whose wielder has improved critical (or, alternatively, a scythe whose wielder has improved critical and who has cast keen edge on it), and similarly, a keen greatsword whose wielder has improved critical.

Thus, the scythe has a range of 18-20/x4, and the greatsword has a range of 15-20/x2. That means that 15% of the scythe's hits are criticals, which means that its damage can be expressed (if its damage is "y") as .85y + .15*4*y = .85y + .6y = 1.45y.

Similarly, the greatsword crits on 30% of all of its hits, and does twice its normal damage on crits, so its damage is exprssed as: .7y + .3*2*y = .7y + .6y = 1.3y.

If we were looking at unupgraded weapons (in either 3.0 or 3.5, which are identical in this case), then the inequality would be as follows (you'll see your ten percent figure here -- by the way, it's exactly 10% of all hits, though it's not exactly 10% of all attacks):

1.15 ( 5 + x) > 1.1 (7 + x)
5.75 + 1.15x > 7.7 + 1.1x
.05x > 1.95
x > 39

So, that would mean that you'd need a +40 damage bonus to make a scythe or falchion worthwhile if you had neither keen nor improved critical.

And, similarly for rapiers/picks versus longswords:

1.15 (3.5 + x) > 1.1 (4.5 + x)
4.025 + 1.15x > 4.95 + 1.1x
.05x > .925
x > 18.5

So you'd need a +19 damage bonus to make a pick or rapier worthwhile over a longsword, if you had neither keen nor improved critical.

 

[Mike Sullivan]

In point of fact, in terms of increased damage dealing capability for a rapier, you are better off taking Weapon Specialization and an energy enhancement than Improved Critical and keen. If you actually looked at the math as opposed to ranting, you'd have figured this out.

Any munchkin powergamer who thinks that the Improved Critical combined with keen path is the superior progression for a rapier is a munchkin powergamer who isn't very bright.

Though, in all fairness, a fighter has plenty of feats to take both improved critical and weapon specialization, and you can get a keen effect through means other than the weapon-enhancement of that name (like, through a scabbard of keen edges).

 

[Anubis]

Similarly, the greatsword crits on 30% of all of its hits, and does twice its normal damage on crits, so its damage is exprssed as: .7y + .3*2*y = .7y + .6y = 1.3y.

This part I understand, although you aren't taking AC into consideration obviously.

If we were looking at unupgraded weapons (in either 3.0 or 3.5, which are identical in this case), then the inequality would be as follows (you'll see your ten percent figure here -- by the way, it's exactly 10% of all hits, though it's not exactly 10% of all attacks):

1.15 ( 5 + x) > 1.1 (7 + x)
5.75 + 1.15x > 7.7 + 1.1x
.05x > 1.95
x > 39

Sorry, but you need to go through this part and explain. It sounds to me like you're pulling these numbers out of thin air, and your equation's answer also seems to just come out of thin air. Maybe I've been out of school for too long, but when you have a double variable, I wasn't aware you could solve one side first in only two steps. You're missing some in there somewhere. Go through each step of the equation. Also explain precisely where the entire top line comes from.