Weapon Balance - A Statistical Analysis

[Cadfan]

Also, two handed weapons don't give you a -2 armor check penalty. That has to factor in somehow.

 

[eamon]

Also, two handed weapons don't give you a -2 armor check penalty. That has to factor in somehow.

And you can actually use your off-hand. The lack of off hand is quite annoying when it comes to picking things up, or drinking a potion.

 

[Ferdil]

Also, two handed weapons don't give you a -2 armor check penalty. That has to factor in somehow.

It's your choice to wear a heavy shield instead of a light one.
Since the two are balanced, the free hand to use a shield is worth the same if you use a light or a heavy shield.

 

[mattdm]

First of all, great spreadsheet.
Second, to balance the greatsword and the glaive it would be enough to give them 0,5 extra damage.
The glaive is easy, from 2d4 to 1d10, but the greatsword? 2d5? 1d4+1d6?

As I mentioned above, 2d4 is very different from a theoretical 1d9 — it has the property of being more consistent. 5 is the average damage, but you'll get 4, 5, or 6 almost ⅔ of the time. This gives the weapon a different feel in play than the "swingy" big dice.

 

[Crazydwarf]

Also, two handed weapons don't give you a -2 armor check penalty. That has to factor in somehow.

And you can actually use your off-hand. The lack of off hand is quite annoying when it comes to picking things up, or drinking a potion.

Hmm good points that I didnt consider.
But still very situational since they are easy to work around unless you are in acctual combat.

The DM would have to setup a comlicated encounter.
Or more possibly the players come up with some strange and out-of-the-box plan as an answer to an encounter.

I must admit to only have one gaming session under my belt sofar due to time restraints on me and my friends so I'm not sure how often this would even be an issue.

 

[Nail]

+3 Prof (P, -1.22): ...

This is interesting.

Higher (+3) Prof weapons do (on average) 1.22 hp less damage than +2 Prof weapons. Do I have that right?

Given that many (many, many) powers key off hits, the lesser damage has to compensate for that. I'm pretty sure lowering damage by 1.22 hp DOES NOT compensate. It's far more important to hit - and activate your power - than miss slightly more often and do a bit more damage.

 

[Crashy75]

This is interesting.

Higher (+3) Prof weapons do (on average) 1.22 hp less damage than +2 Prof weapons. Do I have that right?

Given that many (many, many) powers key off hits, the lesser damage has to compensate for that. I'm pretty sure lowering damage by 1.22 hp DOES NOT compensate. It's far more important to hit - and activate your power - than miss slightly more often and do a bit more damage.

It is a little more complicated than that. First of all, it depends entirely on the type of attack you are using. A +3 weapon garners, on average, an additional strike per 20 attacks over +2 weapons.

+3 weapons are superior to higher damage weapons (as long as they are not that much higher) when making basic and at-will attacks. Period. The reason is because the extra damage from higher damaging weapons is not there because you are not rolling enough (W)'s to compensate for the extra attack. And of course, logically, +3 weapons are better with multi-attack powers and low (W) status affecting powers.

Higher damage weapons are better with the high (W) powers, especially daily 1/2 damage on a miss powers. The higher the X in X(W), the better they are over +3 weapons (assuming a reasonable 50% base accuracy). I had originally thought that +3 weapons were superior here as well (X(W) benefits +3 weapons as well along with increased attributes and magic bonuses), but the math doesn't lie.

+3 weapons are also, in general, superior to High Crit. High crit gives, on average, an additional (W) per 20 attacks at heroic tier. Compare with the additional X(W)+Attribute/magic bonuses from a +3 weapon. At paragon tier, High Crit garners an additional 2(W) compared with X(W) +attributes/magic. Depending on the attack you are using this is a little better, but, in general it is not enough all by itself. There are special feats and equipment that do even things a little more but they cost you in some way.

I can go over the specifics if you want, but I warn you, I've already killed one thread that way...

 

[LightPhoenix]

+3 weapons are superior to higher damage weapons (as long as they are not that much higher) when making basic and at-will attacks. Period. The reason is because the extra damage from higher damaging weapons is not there because you are not rolling enough (W)'s to compensate for the extra attack. And of course, logically, +3 weapons are better with multi-attack powers and low (W) status affecting powers.

While I'd bet this is true the majority of time, this is not absolutely true. This is not the case when you are extremely likely to hit.

For example, if you hit on a 2 or greater (95%) with a Prof+2 weapon, using a non-magical longsword and the battleaxe, same damage mod (for this purpose, +4), for twenty rounds of combat:

Longsword: Hits 100% of the time (Prof + 1) for 20d8+80 damage, average 170.
Battleaxe: Hits 95% of the time for 19d10+76 damage, average 180.5.

Honestly, I don't have the time or desire to do the rigorous statistical analysis, though I'd be interested in seeing it. I didn't add in the critical damage (benefits the battleaxe more), nor other at-will effects. I'm betting there's a certain hit percentage where it is better to use a higher damage weapon with an at-will or basic attack, and I bet it's pretty high (80%+). I just wanted to point out that it is not, as put forward, an absolute.

 

[Nail]

It is a little more complicated than that.

Sure. It always is...

Higher damage weapons are better with the high (W) powers, especially daily 1/2 damage on a miss powers.

Good point.

But what about the Warlord or Cleric, which have significant effects based on their attack connecting? Is the extra damage from a +2/high damage weapon enough to off-set the effects that are lost? (and how much extra damage are we taking about? 2 points? )

 

[Crashy75]

But what about the Warlord or Cleric, which have significant effects based on their attack connecting? Is the extra damage from a +2/high damage weapon enough to off-set the effects that are lost? (and how much extra damage are we taking about? 2 points? )

It's hard to give a numeric value to an effect if we are not talking about pure damage. Certainly ongoing damage can be done, but other effects are really hard. Keep in mind that the bonus a +3 weapon gives is the equivalent to an extra strike over 20 attacks. So, to compare, you have to look at how muc extra damage the higher damage weapon deals over 20 attacks. Your question should be modified as such: 'does the extra 2 points = 5% of the effect?' Give me some examples and I'll see what I can do for you.

While I'd bet this is true the majority of time, this is not absolutely true. This is not the case when you are extremely likely to hit.

For example, if you hit on a 2 or greater (95%) with a Prof+2 weapon, using a non-magical longsword and the battleaxe, same damage mod (for this purpose, +4), for twenty rounds of combat:

Longsword: Hits 100% of the time (Prof + 1) for 20d8+80 damage, average 170.
Battleaxe: Hits 95% of the time for 19d10+76 damage, average 180.5.

Honestly, I don't have the time or desire to do the rigorous statistical analysis, though I'd be interested in seeing it. I didn't add in the critical damage (benefits the battleaxe more), nor other at-will effects. I'm betting there's a certain hit percentage where it is better to use a higher damage weapon with an at-will or basic attack, and I bet it's pretty high (80%+). I just wanted to point out that it is not, as put forward, an absolute.

While you are correct, I don't believe this happens in 4e. It is my understanding (and assumption for this analysis) that accuracy stay's around 50% from levels 1-30. It is definitely true that the more accurate one's attacks, the more heavy damage weapons benefit over and above +3 weapons. There is a variance between enemy types that reflects this (+3 weapons will do better vs. soldiers while high damage weapons will do better vs. brutes for example). I don't have that exact information, however, so I can't really calculate that.

And there were a couple of at-will powers I forgot about- mostly because they're not very good: Sure strike and Careful strike. Even a high crit weapon is superior to a +3 weapon at paragon and beyond with these two and is pretty much equal at heroic tier, though it falls behind at later heroic when the pc gets a magic weapon.

Now, let me give a quick rundown:

Let:

W=Average Weapon Damage. This does not include attribute and other modifiers to damage.

M=Damage Modifiers. This will include attribute and magic bonuses. This is a quick analysis so we're going to leave out Sneak Attack and similar modifiers.

N=Number of hits from 20 attacks for the least accurate weapon in the sample. (generally a +2 weapon). I will generally assume 50% accuracy, but the numbers can be tweeked using the formula for any accuracy.

D=Difference in average damage. This will always compare to W.

So if we were comparing a dagger₁ with a longsword₂ and a battleaxe₃, W=2.5, D₁=0 D₂=2 and D₃=3.

X=the number of die rolled.


Y represents the tier. In the heroic tier, Y=1. In the paragon tier, Y=2. In epic tier Y=3.

All weapons start with the following value and are modified by their relative values.

Y= N(XW+M) This represents the damage done using the weakest weapon's damage and the least accurate weapon's, uh, accuracy. Note that this probably (unless we bring in a simple weapon) doesn't represent any single weapon- this just sets the bar for all weapons, and once this is canceled out, we can see exactly how the weapons compare. Now, let me plug in a few weapons. I want to keep this short so I'll go with some standard 1 handed military weapons.

Battleaxe=N(XW+M)+N(XD)

Longsword=N(XW+M)+X(W+M)

War Pick=N(XW+M)+Y(W)

W=4.5, so D=1. We'll keep N as an unknown so we can compare later.

Explanation:

The battle axe does extra damage per attack (over W), so we add that damage x the number of hits.

The longsword is more accurate, gaining an additional hit over 20 attacks. Therefore we add an additional hit to it's total.

The War Pick does extra damage when it makes a crit (avg. 1x per 20 attacks) Y is defined by the tier. It equals 1 in Heroic tier, 2 in paragon, and 3 in epic.

Cancel out the equalities we are left with:


Battleaxe=N(XD)

Longsword=X(W+A)

War Pick=Y(W)

Now, we know that Y=1 in heroic tier, so automatically, unless the longsword wielder has no damage bonuses (careful strike et al) The warpick=W while the Longsword=X(W+A). Clearly, the longsword is better at heroic tier. As long as the longsword is used at least a 2(W) power at paragon, he's still going to be better than the pick. Even with a 1(w) power, the longsword will be better as long as the weilder has a+5 bonus to damage from attributes and magic weapons (very likely).

The battleaxe vs. the longsword is more nuanced. If N(XD)=X(W+A) then the Battleaxe=the Longsword. That is, if the extra damage that the battle axe dealt over those 20 attacks=a single strike from the longsword, they are virtually equal. Also, it's interesting to note that the base accruacy only benefits the battleaxe (as LightPhoenix noted), while increases in damage modifiers (also including things like hunters quarry) only benefit the longsword (relative to the great axe of course!).

More later. My wife has to go to bed!!!