This is the simplest model I can think of to precisely quantify what damage a ranged attack weapon could have, in contrast to a melee attack weapon.

The approach we'll be looking at to quantify the difference between ranged and melee attack weapons in D&D, is how many attacks a ranged weapon can make on a target melee fighter, before the fighter can chase down and get a hit on the wizard/archer making the ranged attacks (from a distance).

The maximum distance between the fighter and the wizard/archer, will be the maximum range of the ranged weapon.  (The weapon could be a sling, crossbow, magic missile, etc ...).  In 4E D&D terms, this would be the number of squares between the fighter and wizard/archer.  (Many ranged attacks have a range of 5 or 10, and 20 for a magic missile).

The maximum number of squares a character can move per round is 6 for many races.  (Dwarfs can move 5 squares, while elves can move 7 squares).


The idea is to find how many attacks the wizard/archer can make, before the fighter can catch up to them and do an attack, by enumerating all possible distances between the fighter and wizard/archer.  Then we'll take the average of these number of attacks.

Per round, a character can either do a move action and a standard action attack, or do only a double move action.  This is similar to the action economy per round, which is done in 4E D&D.  (Attacks of opportunity, charging, etc ... will be ignored for simplicity).

The scenario of interest will be the wizard/archer first attacking the fighter at an initial fixed distance with a ranged attack.  (The wizard/archer doesn't move on the first round).  The fighter realizes this and runs after the wizard/archer.  If the fighter can't reach the wizard/archer with his maximum move action, then it will do a double move action.  Then the wizard/archer moves away from the fighter at his maximum distance per round, and does a standard action ranged attack against the fighter.  This continues repeatedly until the fighter does a standard action melee attack on the wizard/archer.

(For simplicity and technical reasons, the fighter moves just as fast as the wizard/archer per move action).


For a generic ranged attack in 4E, it will have a range of 10 squares.

For the case of a fighter and wizard/archer that are moving at a speed of 5 squares per round, it will take the fighter one round to reach and attack the wizard/archer if the gap between them is 5 squares or less.  Between 6 and 9 squares between them, the wizard/archer can get in two attacks before the fighter can reach and attack the wizard/archer.  So the average number of attacks the wizard/archer makes is 1.4 before the fighter reach and attacks the wizard/archer.

Similarly for the fighter and wizard/archer that are moving at a speed of 6 squares per round, the average number of attacks the wizard/archer makes is 1.3 before the fighter reaches and attacks the wizard/archer.

Similarly for the fighter and wizard/archer that are moving at a speed of 7 squares per round, the average number of attacks the wizard/archer makes is 1.2 before the fighter reaches and attacks the wizard/archer.


If the fighter's melee weapon is a sword with d8 damage (average 4.5 damage), we could make the wizard/archer's range weapon damage to be reduced by a numerical factor equal to the average number of attacks they can make before the fighter is able to attack them.

So for different move action speeds, the wizard/archer's possible ranged weapon damage could be:

speed 5 -> 4.5/1.4 = 3.2142
speed 6 -> 4.5/1.3 = 3.4615
speed 7 -> 4.5/1.2 = 3.75

The damage which corresponds to approximately these numbers, would be a d6 damage (which has an average 3.5 damage).

Looking through some 4E wizard at-will powers, the ranged 10 attack powers do indeed have d6 + int mod damage (ie. cloak of daggers, scorching burst).  Simple ranged weapons like a sling and hand crossbow have d6 damage.


This analysis could also be done for a magic missile with range 20.  Without going through the details, an analysis with the fighter and wizard moving at speed 7, suggests the damage should be around 2.5 which corresponds to a 1d4 damage.  (The magic missile from the 4E PHB1 has 2d4 + int mod damage).

With you up until the 1.2 attacks before the archer closes.
 
I think with a slight elaboration we can make the model prove that melee damage should actually be downgraded instead.
So, the archer gets 1-2 free attacks before the fighter can close with that; after closing however the fighter gets a free attack on the archer each round (for fighting next to them, or for shifting with the fighter class feature). So for a combat that lasts for 1-2 rounds after closing (probable I think with 4E hit points), the number of free attacks on each side is actually equal. If it lasts 3+ rounds, then the fighter actually is getting more free attacks and it is melee damage than needs to be downgraded.
 
(This is in the case where the archer or wizard can't themselves pull out a sword and go melee as well. If that's the case I think your analysis probably holds).

Quote from: Bloody Stupid Johnson;528365(This is in the case where the archer or wizard can't themselves pull out a sword and go melee as well. If that's the case I think your analysis probably holds).

I was assuming the wizard/archer didn't have a sword or any means to do a melee attack.

My original motivation behind the model, was to examine whether there exists any possible technical justification (besides coincidence or trial and error) for why some of the ranged attacks could have a d6 or d4 damage.

For a long time, I thought the d6 or d4 damage for basic ranged attacks wasn't much more than Gygax et al "shoehorning" combat into the type of dice available.

Alot of the ranged weapons (like longbows) do d8 or d10, I think ?
A number of wizard powers do d6, but most have some other special effect and usually target a non-armour-defense ?

Quote from: Bloody Stupid Johnson;528373Alot of the ranged weapons (like longbows) do d8 or d10, I think ?
A number of wizard powers do d6, but most have some other special effect and usually target a non-armour-defense ?

Yup.

I haven't been able to figure out any technical justification for the damage of other cases of ranged attacks.

On the surface, it doesn't appear to be much more than "shoehorning" combat into mechanics of the dice available.  (ie. Bigger or more badass weapons have larger damage).

Quote from: Bloody Stupid Johnson;528365With you up until the 1.2 attacks before the archer closes.

The 1.2 attacks is easy to figure out for both characters moving at speed 7, with the wizard/archer doing a range 10 attack.

If the initial gap between the fighter and wizard/archer is 0 to 7 squares, the fighter can reach the wizard/archer in one round and melee attack him.  (The wizard/archer is only able to get off one shot on the fighter).

For an initial gap of 8 or 9, the wizard/archer can get off two ranged attacks on the fighter, before the fighter reaches him.  (The fighter does a double move on the first round, and a single move on the second round).

So the average of the number of ranged attacks the wizard/archer makes before the fighter catches up with him and does a melee attack, in this case is:

(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2)/10 = 1.2


For the case of both characters moving at speed 6, the average number of attacks the wizard/archer makes is:

(1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 2)/10 = 1.3

For the case of both characters moving at speed 5, the average number of attacks the wizard/archer makes is:

(1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 2)/10 = 1.4

(For completeness, these are the details for characters moving at speed 7 with a wizard/archer doing range 20 attacks on the fighter).

If the initial gap between the fighter and wizard/archer is 0 to 7 squares, the fighter can reach the wizard/archer in one round and melee attack him. (The wizard/archer is only able to get off one shot on the fighter).

For an initial gap of 8 to 14 squares, the wizard/archer can get off two ranged attacks on the fighter, before the fighter catches him. (The fighter does a double move on the first round, and a single move on the second round).

For an initial gap of 15 to 19 squares, the wizard/archer can get off three ranged attacks on the fighter, before the fighter catches him.  (The fighter does doubles moves in the first and second rounds, and a single move in the third round).

So the average of the number of ranged attacks the wizard/archer makes before the fighter catches up with him and does a melee attack, in this case is:

[8(1) + 7(2) + 5(3)]/20 = 1.85

If the fighter's melee weapon is a sword with d8 damage (average 4.5 damage), we could make the wizard/archer's range weapon damage to be reduced by a numerical factor equal to the average number of attacks they can make before the fighter is able to attack them.

So for speed 7, the wizard/archer's possible range 20 weapon damage could be:

speed 7 -> 4.5/1.85 = 2.4324

The damage which corresponds approximately to these numbers, would be a d4 damage (which has an average 2.5 damage).


(This case doesn't correspond to any range 20 weapons or powers in 4E D&D, which I can think of).

One can relaxing the speed constraints on the fighter and wizard/archer.

Though the one restriction which still applies, is the wizard/archer can't have a faster movement speed than the fighter.  Otherwise in this model, the fighter will never be able to catch and melee attack the wizard/archer.  (ie. For a fighter with speed 7, the wizard/archer has to be speed 7 or less).


Easiest case to calculate is the wizard/archer with a range 20 weapon/power moving at a speed 5 squares, while the fighter has speed 7 squares.

(Arguments and calculations are similar to the previous post, covering the range 20 weapon/power calculation).

If the initial gap between the fighter and wizard/archer is 0 to 7 squares, the fighter can reach the wizard/archer in one round and melee attack him. (The wizard/archer is only able to get off one shot on the fighter).

For an initial gap of 8 to 16 squares, the wizard/archer can get off two ranged attacks on the fighter, before the fighter catches him. (The fighter does a double move on the first round, and a single move on the second round).

For an initial gap of 17 to 19 squares, the wizard/archer can get off three ranged attacks on the fighter, before the fighter catches him. (The fighter does doubles moves in the first and second rounds, and a single move in the third round).

So the average of the number of ranged attacks the wizard/archer makes before the fighter catches up with him and does a melee attack, in this case is:

[8(1) + 9(2) + 3(3)]/20 = 1.75

(Similarly for the case where the wizard/archer is moving at speed 6, the average of the number of ranged attacks the wizard/archer makes before the fighter catches up with him and does a melee attack is 1..

...

So for a speed 7 fighter chasing these different speeds of the wizard/archer, the wizard/archer's possible range 20 weapon damage could be:

wizard/archer speed 5 -> 4.5/1.75 = 2.5714
wizard/archer speed 6 -> 4.5/1.8 = 2.5
wizard/archer speed 7 -> 4.5/1.85 = 2.4324

The damage which corresponds approximately to these numbers, would be a d4 damage (which has an average 2.5 damage).

Quote from: ggroy;528430

Quote from: Bloody Stupid Johnson;528373Alot of the ranged weapons (like longbows) do d8 or d10, I think ?
A number of wizard powers do d6, but most have some other special effect and usually target a non-armour-defense ?

Yup.

I haven't been able to figure out any technical justification for the damage of other cases of ranged attacks.

On the surface, it doesn't appear to be much more than "shoehorning" combat into mechanics of the dice available.  (ie. Bigger or more badass weapons have larger damage).

Looking through the weapons list in the 4E PHB1 and other sources (AV1, etc ...), the bigger/badass melee weapons can have d10 (ie.  broadsword, morningstar, battleaxe, warhammer, etc ...) or d12 (ie. greataxe, waraxe, etc ...).

Here are the calculations done again, but using d10 or d12 for the fighter's weapon damage (instead of d8).

---> range 10 weapon

-> d10
both at speed 5 -> 5.5/1.4 = 3.9286
both at speed 6 -> 5.5/1.3 = 4.2308
both at speed 7 -> 5.5/1.2 = 4.5833

(Approximately a d6 or a d8).

-> d12
both at speed 5 -> 6.5/1.4 = 4.6428
both at speed 6 -> 6.5/1.3 = 5
both at speed 7 -> 6.5/1.2 = 5.4167

(Approximately a d8 or d10).

(Some 4E D&D range 10 weapons have a d8 damage, such as a repeating crossbow).


---> range 20 weapon

-> d10
wizard/archer speed 5 -> 5.5/1.75 = 3.1429
wizard/archer speed 6 -> 5.5/1.8 = 3.0556
wizard/archer speed 7 -> 5.5/1.85 = 2.9730

(Approximately a d4 or d6).

-> d12
wizard/archer speed 5 -> 6.5/1.75 = 3.7143
wizard/archer speed 6 -> 6.5/1.8 = 3.6111
wizard/archer speed 7 -> 6.5/1.85 = 3.5135

(Approximately a d6).

(None of the 4E D&D heavier/superior range 20 weapons have a d4 or d6 damage).