Exploring Weapon Damage

I've done a fair bit of number crunching the past few days, some of it was on the likely damage charts I posted last week. I've been working out what a bonus to hit or damage actually does in the game. I've bee using the S&W hit chances as a base for my math and AC values used on the charts, if one considers the odds to hit the tables are applicable across editions and versions of the game.

I've cut the charts to a smaller AC range this time about to have charts that fit on this blog on most browsers and because a vast majority of predictable combats would likely be occurring in the AC range used of 9[10] for unarmored on to 2[17] for Plate and Shield.
 

Chart 1: Likely Weapon Damage vs AC

Damage Die	Armor Class
	9[10]	8[11]	7[12]	6[13]	5[14]	4[15]	3[16]	2[17]
d4 (2.5)	1.375	1.25	1.125	1.0	0.875	0.75	0.625	0.5
d6 (3.5)	1.925	1.75	1.575	1.4	1.225	1.05	0.875	0.7
d8 (4.5)	2.475	2.25	2.025	1.8	1.575	1.35	1.125	0.9
d10 (5.5)	3.025	2.75	2.475	2.2	1.925	1.65	1.375	1.1

From the above table you can see how much damage an attacker with no adjustment to hit is likely to inflict upon a foe each round based on the foes armor class . A 1d6 weapon with no adjustments to hit is likely to inflict 1.4 points of damage per round vs an AC 6 opponent (14 points in 10 rounds). 

The charts above do not say a d4 weapon would inflict but 1/2 a point of damage per round (for example) but they do indicate the likely damage  that would be inflicted each round by a weapon vs a specific AC across many combats.

Chart 2:Likely damage by die as a % of damage on a d6.

Damage Die	% of Damage Inflicted Compared to 1d6	Average Likely Damage vs AC 9 to 2
d4	71%	0.9375
d6	100%	1.3125
d8	128%	1.6875
d10	157%	2.0625

Take a look at that, eyeballing the raw dice roll tells us a d4 is 2/3rds as effective as a d6, and a d10 is 167% as effective as a d6 but, when we factor in hit probability the numbers shift and damage based on the average damage likely to be inflicted the %’s in the chart above bear out across the board.

So what does a +1 to hit and a +1 to damage actually  compared to a d6 in combat? Traditional tells us each +1 to hit is a 5% improvement in hit chances but the impact on likely damage is more significant.

I'm using a d6 here in this chart and for further analysis as a baseline to compare weapon damage as the d6 was the only die type used for damage in the earliest version of the rules and is still used by some today instead of the more popular variable damage ranges.

Chart 3a: Likely weapon damage with a d6 weapon and a bonus to hit only.

D6 with Hit Bonus	Armor Class								Average Likely Damage
	9[10]	8[11]	7[12]	6[13]	5[14]	4[15]	3[16]	2[17]
+1	2.1	1.925	1.75	1.575	1.4	1.225	1.05	0.875	1.487
+2	2.275	2.1	1.925	1.75	1.575	1.4	1.225	1.05	1.662
+3	2.45	2.275	2.1	1.925	1.75	1.575	1.4	1.225	1.837
+4	2.625	2.45	2.275	2.1	1.925	1.75	1.575	1.4	2.0125

Chart 3b

D6 with Hit Bonus	Average Likely Damage	Percent of damage compared to 1d6 alone
+1	1.487	113%
+2	1.662	126%
+3	1.837	142%
+4	2.0125	153%

A +1 to hit means a lot more than a simple bump in chances to hit of 5%. A character with a 1d6 weapon and but a +1 to hit chance bonus will be dishing out 113% the damage of someone with no hit bonus.

Chart 4a: Likley damage with 1d6 and damage bonus alone.

Dmg. Bonus	Armor Class
	9[10]	8[11]	7[12]	6[13]	5[14]	4[15]	3[16]	2[17]
+1	2.475	2.25	2.025	1.8	1.575	1.35	1.125	0.9
+2	3.025	2.75	2.475	2.2	1.925	1.65	1.375	1.1
+3	3.575	3.25	2.925	2.6	2.275	1.95	1.625	1.3
+4	4.125	3.75	3.375	3	2.625	2.25	1.875	1.5

Chart 4b:

D6 with Damage Bonus of:	Average Likely Damage	Percent of damage compared to 1d6 alone
+1	1.6875	128%
+2	2.0625	157%
+3	2.4375	185%
+4	2.8125	214%

A +1 to damage is pretty telling, with 1d6 each successive +1 in damage is like shifting up 2 in total damage range (from 1d6 to 1d8 for example).

Chart 5a: Likely damage with 1d6 including Hit and Damage bonus

Bonus	Armor Class
	9[10]	8[11]	7[12]	6[13]	5[14]	4[15]	3[16]	2[17]
+1	2.7	2.475	2.25	2.025	1.8	1.575	1.35	1.125
+2	3.575	3.3	3.025	2.75	2.475	2.2	1.925	1.65
+3	4.55	4.225	3.9	3.575	3.25	2.925	2.6	2.275
+4	5.625	5.25	4.875	4.5	4.125	3.75	3.375	3

Chart 5b:

D6 with Hit and Damage Bonus	Average Likely Damage	Percent of damage compared to 1d6 alone
+1	1.9125	145%
+2	2.6125	199%
+3	3.4125	260%
+4	4.3125	328%

A +1 to hit and damage with a 1d6 weapon likely produces 145% of the damage of a straight 1d6, pretty sweet.  A +3 to hit and damage is better than 2 normal attacks a round, a +4 hit and damage is better than 3 normal attacks.  Level, ability bonuses, magical bonuses and situational bonuses likely have much more impact then typically expected.

Chart 6a: Average likely damage by die with a hit bonus only vs AC 9[10] to 2[17]

Damage Die	Hit Bonus Only
	+1	+2	+3	+4
1d4	1.0625	1.1875	1.3125	1.4375
1d6	1.4875	1.6625	1.8375	2.0125
1d8	1.9125	2.1375	2.3625	2.5875
1d10	2.3375	2.6125	2.8875	3.1625

Chart 6b: above as % of unmodified d6  (see chart 2)

Damage Die	Hit Bonus Only
	+1	+2	+3	+4
1d4	81	90	100	109
1d6	113	127	143	153
1d8	145	163	180	197
1d10	178	199	220	241

The above shows that hit bonus alone while beneficial is not a significant bonus in regards to likely damage inflicted upon opponents. A weapon that does 1d4 damage would need a +3 bonus to hit to do the same damage as a 1d6 with no bonus to hit. A d10 weapon essentially doubles vs a d6 with a +2 to hit bonus.  

Chart 7a: Average likely damage by die with damage bonus only vs AC 9[10] to 2[17]

Damage Die	Damage Bonus Only
	+1	+2	+3	+4
1d4	1.3125	1.6875	2.0625	2.4375
1d6	1.6875	2.0625	2.4375	2.8125
1d8	2.0625	2.4375	2.8125	3.1875
1d10	2.4375	2.8125	3.1875	3.5625

Chart7b:  above as % of unmodified d6  (see chart 2)

Damage Die	Damage Bonus Only
	+1	+2	+3	+4
1d4	100	129	157	186
1d6	129	157	186	214
1d8	157	186	214	243
1d10	186	213	243	271

A damage bonus alone is clearly more significant than a hit bonus alone. A 1d4 weapon with a +1 to damage done is likely to do as much damage as an unmodified d6 is on average.  Damage bonus is also more significant relative to the unmodified roll of the same dice than one finds with a hit bonus (but no damage bonus).

Chart 8a: Average likely damage by die with hit bonus and damage bonus vs AC 9[10] to 2[17]

Damage Die	Hit and Damage Bonus
	+1	+2	+3	+4
1d4	1.4875	2.1375	2.8875	3.7375
1d6	1.9125	2.6125	3.4125	4.3125
1d8	2.3375	3.0875	3.9375	4.8875
1d10	2.7625	3.5625	4.4625	5.4625

Chart 8b: above as % of unmodified d6  (see chart 2)

Damage Die	Hit and Damage Bonus
	+1	+2	+3	+4
1d4	113	163	220	285
1d6	146	199	260	329
1d8	178	235	300	373
1d10	210	271	340	416

Having modifiers applied to hit and damage is obviously a significant bonus, even a meager +1 to hit and damage bonus would have a 1d6 weapon putting out more damage on average than an unmodified d8. Even a +1 to a d10 weapon allows that weapon to inflict damage above that of 2 attacks with an unmodified d6.  

A whole lot of data, I'm going somewhere with this in a future post but felt it was worth sharing the above before I got there.