Weapon Balance - A Statistical Analysis

[Amphimir Míriel]

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? )

I would suggest longswords+shields for warlords and greatclubs for clerics

 

[Scholar & Brutalman]

Great analysis, but I have to make one comment:

(every class that does not have military weapon proficiency is a class that does not use melee attacks as its main attack powers)

This isn't true of the Str-based battle cleric. Of course, they end up using military or superior weapons they just have to pay a feat tax. Like Wizards end up with Leather Armour proficiency.

 

[pemerton]

Crashy75, another factor that I'm not sure your analysis picks up is that, on a crit, the benefit of the axe over the sword is +2 rather than +1.

So, assuming a 50% chance to hit with the axe or 55% chance with the sword, and +5 mods (+4 stat, +1 feat) the average damage per 20 attacks from each weapon is:

Axe: in 20 attacks, 9 hits plus 1 crit = 49.5 +10 + 10*5 = 109.5

Sword: in 20 attacks, 10 hits plus 1 crit = 45 + 8 + 11*5 = 108

I'd call that pretty close.

A +1 weapon gives one extra hit per 20 rounds, and +1 damage per hit (I'll ignore the 1d6 crit as that is indifferent across weapons):

Axe: in 20 attacks, 10 hits plus 1 crit = 55 +10 + 11*6 = 131

Sword: in 20 attacks, 11 hits plus 1 crit = 49.5 + 8 + 12*6 = 129.5

So no change.

The sword is pretty clearly better if hitting counts (because of conditions/effects). It's also better against minions (more hits, less overkill). The axe is better for bigger damage/damage on miss powers, as you said above.

I'm fairly happy with the balance between the +3 weapons and the +1 dice step weapons. High crit is pretty dependent on increasing the crit range, however.

 

[Saben]

Heavy Blades have more Paragon Paths and classes exclusive to them (Swordmage/ Sword Marshall) and it is possible this is factored into them being "low tier".

I think it is important to note that for all intensive damage purposes at Heroic tier +3 prof and High Crit are equal.

If you hit on a 11+ and crit on a 20 with a High crit weapon you do 9[W] plus 1[MW] (maximised weapon damage)+ 1[W] (high crit). At 3+ it becomes 18[W]+ 1[MW]+ 1[W]

If you hit on a 10+ and hit on a 20 with a +3 weapon you do 10[W] plus 1[MW]. At 2+ it becomes 19[W]+1[MW]

At paragon tier High crit does take a lead of 1[W], but at epic the 2[W] nature of basic attacks mean that +3 stays only 1[W] behind. And given that some powers do up to 7[W], the +3 is substantially better than High crit on those attacks. But again High crit benefits more from the epic weapon powers.

 

[Crashy75]

Crashy75, another factor that I'm not sure your analysis picks up is that, on a crit, the benefit of the axe over the sword is +2 rather than +1.

You are correct. I had forgotten that. Once we get into weapon mastery territory, this bonus becomes larger, though ultimately, it equals +2Y per 20 attacks. So, at heroic tier, it equals 2 point per 20 rounds assuming you were only comparing weapons with one die difference. It's not much, but these little things can add up if they're not all accounted for (and this makes more of a difference when one starts doing comparisons between a fighter with a greataxe and a rogue with a small blade).

So, assuming a 50% chance to hit with the axe or 55% chance with the sword, and +5 mods (+4 stat, +1 feat) the average damage per 20 attacks from each weapon is:

Axe: in 20 attacks, 9 hits plus 1 crit = 49.5 +10 + 10*5 = 109.5

Sword: in 20 attacks, 10 hits plus 1 crit = 45 + 8 + 11*5 = 108

I'd call that pretty close.

A +1 weapon gives one extra hit per 20 rounds, and +1 damage per hit (I'll ignore the 1d6 crit as that is indifferent across weapons):

Axe: in 20 attacks, 10 hits plus 1 crit = 55 +10 + 11*6 = 131

Sword: in 20 attacks, 11 hits plus 1 crit = 49.5 + 8 + 12*6 = 129.5

So no change.

The sword is pretty clearly better if hitting counts (because of conditions/effects). It's also better against minions (more hits, less overkill). The axe is better for bigger damage/damage on miss powers, as you said above.

I'm fairly happy with the balance between the +3 weapons and the +1 dice step weapons. High crit is pretty dependent on increasing the crit range, however.

Overall, I agree. (Didn't check your math but to looks about right) I think 1 handed weapons are, for the most part, balanced as long as you use the 'right' weapon for your class and powers. Personally, I do think two handed weapons should be looked at a little closer, particularly when comparing the great axe to the two handed sword. This has been done to death on the wizards boards (can't find the thread but it's in the house rules section called 'weapon damage and house rules regarding it' or some such. If I come across it again, I'll link it.

Also, Nail has gotten me thinking about numerical values of different affects.

I am going to add a couple of variants. Let:

X=The number of die rolled

Z=Affect on a hit.

A quick formula for such an affect would be something like:

N(XD)-XW+M= Z. You have to subtract the damage from the extra hit to isolate the affect and see if the values are about equal. I suspect (as has been reasoned but not specifically played out to my knowledge) that, in general N(XD)-XW+M< Z I'm going to do a quick one to see how this plays out.

Lets take Healing Strike. In this case, Z= A mark and a healing surge. Assuming 50% accuracy, using the longsword and battleaxe and +5 Modifier to damage this becomes (after reduction):

20 - 2(4.5)+5=Healing Surge+ Mark for one round.

Reduce further...

6=Healing surge+ Mark for one round.

Thanks for catching that LightPhoenix. That does even things out a little more. I’d still say that 6<A healing surge and a mark mostly because it’s much harder to heal than it is to inflict 6 points of damage. YMMV however. I’d still go with the longsword (or better, the bastard sword since you’ll probably have to spend a feat anyway).

This does get better in the higher die's favor if we were comparing lesser damaging weapons or the D was much different. For example, if we were comparing the battleaxe to the dagger this would become:

60 - 2(2.5)+5= Healing Surge +Mark for one round. or...

50=Healing surge +Mark for one round.

I'd say the battleaxe would win out there rather convincingly but, of course, it should. Any weapon that has a (relative) D of 2 or more will probably 'win' with this power (barring m/c exceptions like a rogue or ranger that got this power via m/c). Come to think of it, I wonder how the longsword would compare to the battleaxe... Well, comparing two handed weapons to 1 handed weapons is (like everything else) much more complicated. I'll leave that for another post if it comes up.

 

[Nail]

Also, Nail has gotten me thinking about numerical values of different affects.

Yup. That would be most helpful.

Lets take Healing Strike. In this case, Z= A mark and a healing surge. Assuming 50% accuracy, using the longsword and battleaxe and +5 Modifier to damage this becomes (after reduction):

20 - 2(4.5+5)=Healing Surge+ Mark for one round. I can see where this is going.

Reduce further...

1=Healing surge+ Mark for one round.

No. Clearly, with that specific power, it is better to use a longsword than a battle axe. Interesting.

This.

This is *very* helpful! Thanks!

 

[Nail]

Y= N(XW+A)

Errr...wait.

What's "X"? What's "A"?

 

[Crashy75]

Errr...wait.

What's "X"? What's "A"?

Oh, I'm sorry. "A" should be "M". I kept thinking of the "A" in Attribute bonus rather than the "M" in Damage Modifier. X=number of die rolled. I should have just made it 2 as it is defined. Sorry about the confusion.

 

[LightPhoenix]

Oh, I'm sorry. "A" should be "M". I kept thinking of the "A" in Attribute bonus rather than the "M" in Damage Modifier. X=number of die rolled. I should have just made it 2 as it is defined. Sorry about the confusion.

I wondered that myself. The post with equations makes more sense to me now. Perhaps you could edit that post? Also, it took me a minute to realize X is the number of [W] per power.

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.

No, I fully expect it not to happen in 4E, or in any addition, because it's boring. Even though it's a fringe case, it's important. If for no other reason that to try and get you thinking about other fringe cases.

It was very clever of you to set up the equations so as to remove the minimum damage. I do have one question regarding the formulae for the weapons though. You list the longsword as N(XW+A)+X(W+A), for the extra hit due to the proficiency increase. However, shouldn't the added term be XW+A, rather than the X(W+A)?

 

[Crashy75]

I wondered that myself. The post with equations makes more sense to me now. Perhaps you could edit that post? Also, it took me a minute to realize X is the number of [W] per power.

Yes, I will do that if ENWorld cooperates!

No, I fully expect it not to happen in 4E, or in any addition, because it's boring. Even though it's a fringe case, it's important. If for no other reason that to try and get you thinking about other fringe cases.

That's true. And certain feats, powers and equipment definitely present fringe cases.

It was very clever of you to set up the equations so as to remove the minimum damage. I do have one question regarding the formulae for the weapons though. You list the longsword as N(XW+A)+X(W+A), for the extra hit due to the proficiency increase. However, shouldn't the added term be XW+A, rather than the X(W+A)?

D'oh. Good catch. I'll have to edit that as well.

EDIT: So I was able to edit the post and it changed the value to:

6=Healing surge and a mark. I'll still take the healing surge and mark though.