D&D 3.x [3.5] Crit stacking?

[Mike Sullivan]

The problem is that you're leaving out the most important factor, that of hitting in the first place. That has a great affect on average damage in any situation, and it most certainly affects how well two weapons compare to each other. It's like comparing keen to flaming (Sword & Fist shows three examples). If you only calculate average damage per hit, you're assuming everything hits. This simply isn't the case, and it will have a profound affect on statistics.

No, it won't.

As you've been told several times, the reason you can ignore chance to hit in this analysis is that it doesn't change from person to person.

However, I'll just demonstrate it.

Okay, so we're going to compare two people

Person A has a longsword +2 that's not keen, and improved critical. He's a level 8 fighter with a 16 Str, weapon focus and specialization in longsword, and no other bonuses.

Person B has a rapier +2 that's not keen, and improved crit. He's a lavel 8 fighter with a 16 Str, weapon focus and specialization in rapier, and no other bonuses.

Each person has a +14/+9 modified attack bonus. The longsword guy does 1d8 + 7 damage with a 17-20/x2 crit, and the rapier guy does 1d6 + 7 damage with a 15-20/x2 crit. They're attacking a target with AC 20.

First, the analysis that doesn't bother with chance to hit:

• 
  Longsword guy does 1d8 + 7 damage before crits. That averages to 4.5 + 7 = 11.5. His crit is 17-20/x2, which translates to a 1.2 multiplier. Thus, his expected damage per hit is 13.8
  
  Rapier guy does 1d6 + 7 damage before crits. That averages to 3.5 + 7 = 10.5. His crit is 15-20/x2, which translates to a 1.3 multiplier. Thus, his expected damage per hit is 13.65.
  
  Thus, longsword guy does 101.0989% the damage of rapier guy. (13.8 / 13.65)

Second, the analysis that does bother with chance to hit:

• 
  Longsword guy hits on a 6+ with his primary attack and 11+ with his secondary attack. That translates to a 75% chance to hit with his first attack and a 50% chance to hit with his second attack. As we can see above, his expected damage per hit is 13.8, so his expected damage per round is .75(13.8) + .5(13.8) = 17.25.
  
  Rapier guy hits on a 6+ with his primary attack and 11+ with his secondary attack. That translates to a 75% chance to hit with his first attack and a 50% chance to hit with his second attack. As we can see above, his expected damage per hit is 13.65, so his expected damage per round is .75(13.65) + .5(13.65) = 17.0625.
  
  So now we divide 17.25 by 17.0625, and we see that longsword guy does... 101.0989% the damage of the rapier guy.

Tah-dah.

 

[Darklone]

*scratch*
Are you sure it's ok to convert a certain crit range into a flat multiplier or has the AC to hit (and confirm the threat) been taken into account already for this example?

 

[Staffan]

The problem is that you're leaving out the most important factor, that of hitting in the first place. That has a great affect on average damage in any situation, and it most certainly affects how well two weapons compare to each other.

As long as the attack bonuses are the same, the two weapons will hit equally often. Thus one can disregard that and simply calculate damage per hit. This works if you're comparing non-magic weapons to one another (which is what we're doing here), or weapons with the same magic abilities, but not if comparing a greatsword +2 versus a keen falchion +1 or other thing that changes the attack bonus..

 

[Staffan]

*scratch*
Are you sure it's ok to convert a certain crit range into a flat multiplier or has the AC to hit (and confirm the threat) been taken into account already for this example?

Yes. The percentage of hits that are crits is exactly the same as the percentage of attack rolls that are threats, because you then follow up the threat with a hit in order to confirm the crit. The only case where this does not apply is when your opponent has an AC so high that some of the rolls that would normally be threats will instead be misses - essentially wasted threat range.

 

[Storm Raven]

I'm not rushing and I'm not ranting. You are totally correct that a 4th level Fighter would be better off taking Weapon Spec than Imp Crit. But wait, I was talking about characters with the potential to take Imp Crit (BAB +8). So would an 8th level fighter who managed to not have Weapon Spec be better of with it over Imp Crit? Maybe. But are fighters the only ones who use rapiers? What about a rogue with BAB 8+? Isnt it really the best feat he can take? I'm more than slightly baffled you are arguing this point, but if you feel you have a leg to stand on then go for it.

Actually, no, it is not the best feat you can take for a rogue. A rogue is better off taking a number of toher feats as oppsed to Imrpoved Critical, mostly because improved critical has a relatively minor effect on the damage he deals. Go back and look at the analyses that have been presented in this thread, you will find that the increased damage inflicted by Improved Critical is really quite small.

As far as Energy Bonus +1d6 vs Keen? I've never seen a player who has the option of what enhancement they get not chase Keen. Perhaps statistically it is better in most situations to have the +1d6 Energy, but I can think of a lot of situations where that damage is more useless than doubling your crit range (and vice versa).

Then you have seen a lot of players who are not very smart. The +1d6 bonus from energy damage applies to every hit. With the very limited exception of creatures immune to the particular type of energy your weapon is enhanced with, that is an average of +3.5 points of damage on every attack, effectively doubling the base damage of the rapier.

The bonus from keen only crops up when your threaten a critical, and confirm the critical, and the creature is not immune to ciritcals (which is reasonably common, given that a very common class of opponents, undead, is immune to criticals). Then it adds a +1d6 base damage plus modifiers (and if you are a finesse fighter, like you seem to assume for a rapier wielder, your modifiers are likely to be relatively modest). It is a much less reliable damage bonus.

You still haven't mentioned what else you can do with a rapier besides going for crits. If I want Weapon Spec and Energy Damage then why didn't I pick longsword? Because I wanted finesse? But finesse hoses my off-hand...and it still doesnt really count as another style since if Im a dex-based weapon finesse rapier wielder than *All* Ive got going for me is crits.

The problem is that you haven't figured out that critical hits are exactly as valuable for any given weapon. Rapiers are not especially useful for critical hits, because the damage multiplier is small and the base damage is low. Every weapon has just about the same expected damage increase from Improved Critical or keen as every other weapon. The attributes you are talking about that make the rapier a poor choice for many combat options are attributes of the rapier, not attributes of the feat or the weapon enhancement. The rapier is no worse than a longsword at any of the various combat maneuvers that are available. If Improved Disarm is useless for a rapier wielder, then it is useless for a longsword wielder. Perhaps you should review your thoughts on this matter, since you seem not to be thinking it through very well.

A longsword is a virtually identical weapon as a rapier in terms of value as a method of inflicting damage. The longsword has a higher base damage die, but a smaller threat range. Effectively, they are identical weapons when you evaluate their expected damage, with or without finesse.

Technik "neither ranting, nor rushing"

You should change that to "Tecnik "neither paying attention nor doing math"

 

[Mike Sullivan]

*scratch*
Are you sure it's ok to convert a certain crit range into a flat multiplier or has the AC to hit (and confirm the threat) been taken into account already for this example?

I am absolutely positive that it's okay to convert a crit range into a flat multiplier, with one and only one exception: If you're attacking in such a way as to "waste" some of your crit thresh (eg, you have a crit thresh of 15-20, but require an 18+ to hit). In that case, you have to recalculate your damage such that your crit range is appropriate -- in my example, it's now effectively 18-20.

My feeling is broadly that with the exception of the 12-20 crit range, if this starts to come into play, we're looking at a silly case. Fighters broadly speaking don't need 16-19+ to hit against CR-appropriate opponents.

 

[Anubis]

No, it won't.

As you've been told several times, the reason you can ignore chance to hit in this analysis is that it doesn't change from person to person.

However, I'll just demonstrate it.

Okay, so we're going to compare two people

*Snip*

That stuff doesn't matter. Sure you have the average damage per hit, but that IS NOT an accurate reflection of average damage! The whole point of this exercise was to find out who'd be able to dish out more damage. Not per hit, but overall. For that, you must take hit rates into account. A person with a single rapier can do far more damage then someone with Monkey Grip and Ambidexterity wielding a mercurial greatsword in each hand, although the flat damage will be about ten times greater with the mercurial greatswords.

 

[Technik4]

Ok, slight rant here about energy protection vs immune to criticals.

-Most monsters of CR 5 or higher have some kind of elemental protection, be it racial, magical, from an item they are wearing, whatever.

-There are races with inherent energy protection for as little as ECL +1. Additionally there are feats which grant Energy Protection 5 as long as you have a high fortitude.

-Almost all the elemental energy damage from a weapon can be countered by a first level spell which lasts 24 hours.

-While certain types of monsters inherently have an immunity to criticals, it is never a class ability, nor a racial ability. Additionally, the magic items that give critical protection do so in percentages, and it is far more expensive than elemental protections.

-There is no spell which grants immunity to critical hits, certainly not one at 1st level.


By and large, energy protection is easier to come by than immunity (or even partial immunity) to critical hits. Especially since it only takes 5 points of energy protection to shut down an energy weapon.

Furthermore, according to Mike Sullivan:

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).

So, the rapier will come out ahead in 3.5 when you have +9 bonus to damage.

Speaking of the rogue, his position is at its worst when he is fighting against creatures with critical hit immunity. I don't think there are any agruemnets so far. Lets say a 9th level rogue has taken dodge, weapon finesse, mobility, and spring attack. What phb feat is better for his 12th level - Imp Crit, Expertise, or "other"?

Since we're talking about a rogue, they dont have access to the longsword, the biggest weapon they can use is in fact a rapier. This may be why you see a lot of rogues with rapiers, why rogues with rapiers eventually get keen rapiers, and why high level rogues with keen rapiers used to take Imp Crit. Granted, I know this hasn't been *your* experience, and I'm positive my math and logic are horribly skewed, but this has been mine.

Now that we've proven that rogue + rapier + higher crit range = good, lets talk about the finesse fighter. A character with at least a few levels in fighter (so getting some feats is no biggie) who took weapon finesse and is trying to make a strong PC. Since he has weapon finesse and the rapier is the best weapon to be finessed (short of taking exotic weapon proficiency) will this character eventually take Imp Crit and acquire a Keen Rapier? Bing. Yes, he most probably would.

If I wanted to make a disarm fighter I would use a flail, a trip fighter I might also go for a flail or a reach weapon, if I'm going sword and board Im taking the best 1-hander I can wield, if I'm going 2-handed the best 2-hander I can wield, and "if I'm going for crits" I will always take the rapier. These are no-brainers.

Technik

 

[Mike Sullivan]

That stuff doesn't matter. Sure you have the average damage per hit, but that IS NOT an accurate reflection of average damage! The whole point of this exercise was to find out who'd be able to dish out more damage. Not per hit, but overall.

Did you even read my post? I demonstrated, in the simplest possible terms, why, in this case, you can do that just by comparing per-hit damage rates. I worked out a full example with the extraneous to-hit rates and demonstrated that it gave exactly the same result as the simpler example that ignored to-hit rates.

For that, you must take hit rates into account. A person with a single rapier can do far more damage then someone with Monkey Grip and Ambidexterity wielding a mercurial greatsword in each hand, although the flat damage will be about ten times greater with the mercurial greatswords.

Yes, Anubis. I know. I also know the difference between comparing two cases in which one case incurs a to-hit penalty, and the other does not.

If you're comparing, for example, two weapon fighting to one-weapon fighting, you have to include to-hit rates because the attack bonuses of otherwise comparable characters are, by necessity, different between a one-weapon fighter and a two-weapon fighter.

If you're comparing two characters who have the same fighting style, but simply use two different weapons -- as we are doing, then the to-hit chances neatly cancel themselves out.

Yet another way of looking at this is that what we've been comparing is something of the form crit multiplier * (base damage + damage bonus). So:

Falchion base damage = fc (it'd be 5 in the real world)
Falchion damage bonus = fd
Falchion crit multiplier = fm

Greatsword base damage = gc (it'd be 7 in the real world)
Greatsword damage bonus = gd
Greatsword crit multiplier = gm

So, what we've been comparing is of this form:

fm * (fc + fd) > gm * (gc + gd)

If we wanted to, we could add two additional factors

Falchion chance to hit = fa
Greatsword chance to hit = ga

fa * fm * (fc + fd) > ga * gm * (gc + gd)

However, we're assuming that we've got comparable characters. In that case, fd = gd, and fa = ga. So we can simplify the inequality:

fa * fm * (fc + fd) > fa * gm * (gc + gd)

And then cancel out the fa's

fm * (fc + fd) > gm * (gc + gd)

And we see we're back where we started.

Once again: You're not wrong that chance to hit is important. In this particular instance, it doesn't impact the analysis.

 

[Grog]

My feeling is broadly that with the exception of the 12-20 crit range, if this starts to come into play, we're looking at a silly case. Fighters broadly speaking don't need 16-19+ to hit against CR-appropriate opponents.

He might with his worst attack, especially at higher levels. A 20th level fighter with +38 to hit, vs. AC 39, would need a 16 or better to hit with his fourth attack.