Differentiating Damage

In Chainmail, in AD&D, and in various homebrews around the net, changes have been made regarding the accuracy and effectiveness of weapons based on the armor type of the target. Most of the time, these modifications are made and tweaked around the attack roll, itself - however recently conversing with some old-school experimenters, the idea was floated that maybe the attack roll isn't the only place where tweaks might be applied.

Advantage by Armor

On a successful hit, the type of weapon causing the hit should be compared against the type of armor being worn by the target:

• If the weapon's type is considered effective against the given type of armor, damage dealt should be rolled with advantage: that is, rolled twice and the higher result taken.
• If the weapon's type is considered ineffective against the given type of armor, damage dealt should be rolled with disadvantage: that is, rolled twice and the lower result taken.
• If the weapon's type has no rating for the given type of armor, damage should be rolled as normal.
  

To determine whether a weapon is effective or ineffective, a suggested method here is that the should be categorized based on the physics behind its effect:

• Crushing or Puncturing (maces, flails, picks, hammers, crossbows)
  
• Slashing or Hacking (axes, swords, bladed pole-arms)
  
• Piercing or Perforating (spears, knives and daggers, bows)
• Bludgeons (staffs, slings, clubs, unarmed strikes)
  

A weapon so categorized can then be determined effective or ineffective against armor types as follows, an effective weapon result being marked with a plus sign (+); an ineffective weapon result with a minus (-):

	Armor Class (Armor Equivalence)
Damage Type:	<3 (or Plate)	3-5 (or Mail)	6-8 (or Leather, Gambeson)	>8 (or Unarmored)
Crushing or Puncturing	+	+
Slashing or Hacking	-	-		+
Piercing or Perforating			+	+
Bludgeons	-		-

At the referees option, the table may be expanded to accommodate more armor types or unlisted armors might be lumped in with the closest category.

Further, the referee is encouraged to revisit effective and ineffective markings: as the above is based very loosely on AD&D's Weapon Types, General Data, and "To Hit" Adjustments table (PHB, p. 38) - it does not take into account any sort of "rock, paper, scissors" that might make more enticing the option to carry multiple weapons "just in case."

While initially a thought exercise, this satisfies both a minor nod to verisimilitude without overwhelming the referee with complexity nor without slowing gameplay with sequential dice or unnecessary arithmetic and a side-line desire to make fighters "more interesting." That is, with something like the above, based on the nature of foes encountered, a fighter may be tempted to bring several weapons along rather than just the one big one that does the most damage - as their effectiveness may be tempered or exacerbated by the foe they encounter. 

How does stack up?

Rolling advantage or disadvantage has the effect of skewing the result up or down in the direction corresponding to the high or low roll taken. It logically then follows that on a smaller die, the range of possible results being tighter, the gross deviation (that is, the average amount by which the raw number rolled will change) and the proportional impact (that is, the difference between the normal average and the new average) will be smaller.

In B/X, there are four dice used in the variable damage table: four-sided, six-sided, eight-sided, and ten-sided. So, for each of those die sizes, the average result (and thus average damage inflicted on a hit) can be calculated as follows:

	d4		d6		d8		d10
Ineffective	1.88	-25%	2.53	-28%	3.19	-29%	3.85	-30%
Normal	2.5		3.5		4.5		5.5
Effective	3.13	+25%	4.47	+28%	5.81	+29%	7.15	+30%

So, for a dagger at 1d4 striking against a vulnerable armor type, it will see an increase of effectiveness around 25%, or 0.63 damage per hit; whereas a sword dealing 1d8 would see around a 29% difference, or 1.65 damage per hit.

Additionally - looking at the numbers - an interesting trend emerges as the die size increases. When a weapon is used against armor it is effective against, there is of course a trend towards parity with the upward damage die - however, this is muted by the "effective" average being still below the "normal" average of the next die in line until you get to the d8/d10 comparison. Why muted? Because there are only two 1d8 weapons in B/X - the Battle Axe and the Sword - and only two 1d10 weapons - the Pole Arm and the Two-Handed Sword: as such, by the time you get to the top of the range, there isn't much difference in the types and there isn't much room to diversify - R.A.W. However, when a weapon is used against armor it is ineffective against - the trend is observable almost immediately: with the average damage on 1d6, at disadvantage, being only 0.03 different from the average damage rolling a normal 1d4. 

This is more pronounced on 1d8 - where the average at disadvantage is 0.31 points worse than rolling a normal 1d6! Given the opportunity to use a 1d6 weapon or a 1d8 weapon is obvious: while at the same time, if the 1d6 weapon is strong against the armor being worn by the enemy and the 1d8 weapon is weak against it, the choice is equally obvious in the total opposite direction!

Because of this mechanism, a character which would normally be eligible for a sword - which, by many estimates, is the optimal melee weapon to use on the table - suddenly has reason to bring along a pick or a mace, as well. Expand the table out a bit, add various monster vulnerabilities into consideration? Suddenly the fighter has to decide between which weapons to bring weighed against being able to carry back treasure.

Math Breakdown

Comparing the above to a bonus or penalty to hit - on the general consensus that 2 points of "to hit" is about the equivalent, in terms of damage per round, as is 1 point of damage, the benefit of advantage or disadvantage on the die roll ranges from about +/-1 "to hit" using a 1d4 weapon up to +/-4 "to hit" using a 1d10 weapon. So, on the heavier hitters, it's more pronounced. It's likely to be quicker at the table than applying said modifiers - and definitely takes up a tad less space in your house-rules binder, as the one table is a slight smaller than having to have the same cells duplicated or filled out four times each: one for each die type.

In any case, for further reading, in case you're having trouble getting to sleep, here are the numbers, probabilities, and charts - courtesy of AnyDice - that correlate to the conclusions drawn above.

Delve on, readers!

For 1d4 weapons:
output [highest 1 of 2d4] named "D4 At Advantage" output 1d4 named "D4 On Average" output [lowest 1 of 2d4] named "D4 At Disadvantage"
For 1d6 weapons:
output [highest 1 of 2d6] named "D6 At Advantage" output 1d6 named "D6 On Average" output [lowest 1 of 2d6] named "D6 At Disadvantage"
For 1d8 weapons:
output [highest 1 of 2d8] named "D8 At Advantage" output 1d8 named "D8 On Average" output [lowest 1 of 2d8] named "D8 At Disadvantage"
For 1d10 weapons:
output [highest 1 of 2d10] named "D10 At Advantage" output 1d10 named "D10 On Average" output [lowest 1 of 2d10] named "D10 At Disadvantage"

    -- Edit: 1/23, 7 PM --

Per suggested feedback, edited the armor vs weapon table to include Armor Class ranges rather than just the names of armors in B/X. That having been the intended interpretation, but having used armor equivalences to make the ruling more compatible with clones or other OSR systems, you had also pointed out that AC ranges makes the ruling applicable to monsters simultaneously with no internal conversion necessary.

Thank you, community, in helping to make this blog better!

 

Public domain artwork retrieved from Wikimedia Commons and the National Gallery of Art and modified for thematic use. Attribution in alt text.