Weapon comparison

[Ail]

In case anyone likes this, I made a comparison the other day about the relative damage weapons do. I mean, what the average damage for a weapon over time considering the effects of criticals and the probability of scoring a hit.

I found some neat relations. The most obvious is:

everything else being equal, a weapon with crit 19-20/x2 is exactly equal to a weapon with crit x3.

On the other hand, the advantage of crit values is easy to compute. For example, a rapier has an advantage of 4.(54)% over a short sword with equal attack bonuses.

The mean damage in a single attack is pretty determinant too. All else being equal, a longsword does around 28.6% more damage than a short sword.

But attack bonuses are pretty determinant when your chance to score a hit is relatively low. The general rule is this:
- if you can hit easily, use a weapon with big damage dice.
- if you can hit with more difficulty, favour a weapon with higher attack bonus.

I have not written a document, though I have all formulas ready and some analysis made for my new PC for a Dragonlance campaign. In case , if anyone finds this interesting, post your weapons here and I'll compare them (if they're not too many).

As an aside, the most devastating weapon really seems to be the Lance Charge, though I have not made comparisons for x4 and 2d6 weapons. But event these won't probably match the effect of doubling damage that a lance has... even more because a x3 crit is really good.

Alex

[NeoTiamat]

Release this, please!

I've been drowning in weapons ever since the Arms and Equipment guide came out. While I generally chose them based on style, it might be nice to actually have a technical analysis.

Have you computed effect that the strength bonus has on two-handed weapons?

Also dual-wielding?

I've always had the vague theory that the Greatsword is the most powerful of all the martial weapons, confrim or deny?

Exotic Weapons - are they actually worth the feat slots? Is a Bastard Sword that much better then a Long Sword?

This could be extremely interesting.

[Ail]

Release this, please!

I've been drowning in weapons ever since the Arms and Equipment guide came out. While I generally chose them based on style, it might be nice to actually have a technical analysis.

Have you computed effect that the strength bonus has on two-handed weapons?

Also dual-wielding?

I've always had the vague theory that the Greatsword is the most powerful of all the martial weapons, confrim or deny?

Exotic Weapons - are they actually worth the feat slots? Is a Bastard Sword that much better then a Long Sword?

This could be extremely interesting.

Interesting questions. No, I forgot to add the strength bonus. However, since it is a simple additive parcel, it can be figured out easily as an extra parameter. Basically, I considered these parameters:

- x: number of dice rolls that will give a successful hit. For example, if your opponent has AC 15 and your BAB is 5, you'll hit him on 11 unmodified rolls

- b: modifier to attack (possibly coming from a feat, magic/masterwork weapon, stat bonus, etc)

- a: damage dice (here's where you can add your strength bonus easily)

- d: crit range

- m: crit multiplier

I have not considered dual wielding, but since they have penalties, you could apply them to each weapon analysis and add the average values.

Considering the greatsword, I'd have to make a table. I have not compared all pairs, merely got to the formulas and made piece-meal comparisons for what I needed.

As for BS / LS, assuming they have the same attack bonuses and known that they have the same critical, the BS will deal 22.2% more damage than the long sword. It's your call if this is worth the exotic weapon feat.

The formula for average damage is:

a * (y / 20) * (1 + d(m-1) / 20)

where y = x + b

It's worth noting that for small x, the factor y / 20 is pretty determinant, but for x over 10 or so, it can be dominated by other factors. My examples used these weapos of 1d6 / 1d8 damage, 19-20/x2 or x3 weapons and with bonuses of +0, +1 or +3. I never considered the strength bonus because, frankly, my fighter has Str 11.

Now, typical values:
1d4 --- a = 2.5
1d6 --- a = 3.5
1d8 --- a = 4.5
1d10 --- a = 5.5
2d6 --- a = 7
2d4 --- a = 5

x2 --- d(m-1) = 1
19-20/x2 --- d(m-1) = 2
x3 --- d(m-1) = 2
x4 --- d(m-1) = 3

these values are fixed for weapons so you can compare weapons of equal bonus merely by computing these. I considered a base reference of

a = 1
b = 0
d(m-1) = 1

This is a horizontal line. Actually considering the attack bonus throws in a lot more complication which will cause the line relative to the weapon to become a falling curve (similar to a falling exponential) that is high near the y axis and tends to a horizontal line as x increases. Since x is limited to 20, it never truly becomes horizontal, but anyway, guess I'm digressing.

Alex

[NeoTiamat]

Okay... I lost you about half-way, but that's allright, I'm a mathematical incompetent. You might want to retest in regards to strength with characters with a strength of 11, 14, 18, and 24. (For the really high strength), and see what happens. Obviously two-handers will pull ahead, but by how much?

Other then that, I look forward to seeing your conclusions.

[The Giamarga]

Weapon Comparisons
Fun with math and a representative cross-section of weapons, compared at +1, +1 Keen, and +2.
http://burrowowl.net/wordpress/200208/w ... mparisons/

Weapon Choices
http://burrowowl.net/wordpress/200208/weapon-choices/


Analysis of Attacking with Two Weapons:
http://homepage.mac.com/guyf/DnD/Attack ... apons.html

[Sorti]

Also, I think there's an easy formula to figure how weapons are balanced; I don't remember it exactly, but it's something like:
basic weapon: 1d4 20/x2, and 4 "weapon points"
You can spend a weapon point to increase the weapon's damage (cumulative), crit range or multiplier (not both), give a +2 to trip, or similar. An exotic weapon has 5 points. I don't remember anything else, but probably you can find the whole formula with google.

[Ail]

Hmm... I read the analysis above. The first two are sort of short and I would have to verify if he considered the possibility of a critical in the mean damage.

Maybe I'll write a document one of these days. I couldn't explain it properly without graphs .

As for what Sorti said, sorry, never heard of it.
Basically, I think the 5 statistics I gave completely characterize a weapon. Further things like trip and disarm and such are too odd to put in an equation, I'm afraid.

Well, sleepy right now. Bye...
Alex