Negative Armour Class

[Matthew]

Most of us are all familiar with the idea of ascending armour classes versus descending armour classes, and ideas about what might make one more suitable than the other for use with Dungeons & Dragons. No doubt, there is a passing familiarity with the idea that maybe flipping armour classes between Chain Mail and Dungeons & Dragons might have been related to some sort of 2d6 or under system with a range of 2-9, but the reason remains a mystery.

I was thinking today about the numeric range of armour class in D&D (9 to −9) and AD&D (10 to −10), and it occurred to me that these correspond to two probability distributions. In the former case 5% to 95%, and in the latter case 0% to 100%, which makes 55% the "pivot point" in both cases. In order to get access to the full range of probable outcomes, that is to say to be able to hit the full range of armour classes without resorting to repeating twenties, a character needs a THAC0 of about 11, which is the equivalent of around fighter levels 10-12. If in OD&D fighters once had a smoother progression of 2 points for every 3 levels, then it would be just as they hit 13th level: (1-3 = 19, 4-6 = 17, 7-9 = 15, 10-12 = 13, 13-15 = 11). Perhaps also significant is that fact that monsters hit this same THAC0 at around about 9-12 hit dice.

So, I was wondering, if perhaps the positive to negative 19 or 21 point range might have been linked to a developmental stage of Gygax's thinking, where he was looking at what "hit ranges" were possible for characters of various levels. In AD&D, for instance, a level one fighter can hit AC 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, but basically has to advance to level 11 before he can hit AC −10 without repeating twenties, whilst a monster needs to have 10 or more hit dice. Possibly it is more obvious somewhere between OD&D and AD&D where each level of fighter corresponds directly to a negative armour class (Level 1 Fighter hits AC −1, Level 2 Fighter hits AC −2, and so on).

Anyway, this was just rattling around in my head and I wondered if anybody else had any new insights.

[thedungeondelver]

I'm not sure if this helps but Gary said that "armor class" came from Ironsides or Don't Give Up The Ship or something like that and that "AC1" indicated first-class armor. AC2 indicated second class armor, and so on, until you had 10th class armor (virtually nothing or canvas or light wood or the like) and that it made sense that you'd want to have first class armor if you could.

It just made sense to say "Okay, what's better than first class? Class 0. What's better than that?" and it followed along logically.

(Go tell that to 3e and 4e players and watch them have aneurysms.)

[Matthew]

I have heard that theorised before, though I did not realise (or perhaps had forgotten) that it came directly from Gygax himself. My own muggy memory of it was that descending armour class was rumoured to be taken from Arneson's naval war game that Gygax contributed to, but we also have that interview from 1980 where Gygax says "The concept of armour class and weapon size originated in Chainmail. When I put it into Dungeons & Dragons, I just reversed the order of armour class."

[Ghul]

Here is a relevant quote that I find interesting, from the interview Gamespy did with Arneson:

GameSpy: So you started playing Chainmail using the fantasy rules. How did you have to change the rules around?

Arneson: We had to change it almost after the first weekend. Combat in Chainmail is simply rolling two six-sided dice, and you either defeated the monster and killed it … or it killed you. It didn't take too long for players to get attached to their characters, and they wanted something detailed which Chainmail didn't have. The initial Chainmail rules was a matrix. That was okay for a few different kinds of units, but by the second weekend we already had 20 or 30 different monsters, and the matrix was starting to fill up the loft.

I adopted the rules I'd done earlier for a Civil War game called Ironclads that had hit points and armor class. It meant that players had a chance to live longer and do more. They didn't care that they had hit points to keep track of because they were just keeping track of little detailed records for their character and not trying to do it for an entire army. They didn't care if they could kill a monster in one blow, but they didn't want the monster to kill them in one blow.

Here is the link to the interview.

Cheers,
Jeff T

[Matthew]

It occurred to me today that there is another 19 point range in D&D, which is to say attributes ranging from 0-18; the midway point there is "9", which is perhaps less helpful, though in the 3-18 range it is 11-12.

[Bargle]

The way I did my CHAINMAIL to d&d conversion was to have heavy horse represented as a negative AC.

foot
light: 8-10
heavy: 4-7
armored: 1-3
horse
medium: -1-0
heavy -4 -2

taking an armored foot fighting a light foot:
Veteran
att/def:AF
hits: 1c
dmg: 1d6/5-6 (1:1)

Light Foot
att/def: LF
hits: 1c
dmg: 1d6/6

What we have here is a 30.55% chance for the veteran to kill a unit of light foot and a 16% for lightfoot to take a unit of armored. In D&D
Veteran
att/def: thac0: 19/AC 2
def: AC 3
dmg: 1d6

light foot
att/def: Thac0: 20/AC 7
dmg: 1d6


taking average dmg and average hit points (0d&d) what we're left with is the Veteran has a 45% chance to kill with one attack and the light foot has 15% (+-5% based on variable AC) so a negative AC is an analog to the fact that heavy horse (say a dragon) lowering the % of causing a "hit"

How then to have our 1HH Dragon vs. Hero play out?
dragon
att/def: HH
hits: 1c
dmg: 1d6/5-6 (1:2 ratio vs AF)
-----
AC: -2
Hits: 3HD (heavy horse 1:3)
dmg: 2d6 (HH1:2 ratio vs. AF heroes) 1d4/1d4/1d6 claw claw bite

vs. veteran
att/def: AF
hits: 1s
dmg: 1d6/6 (1:3)
----
AC: 2
hits: 1HD
dmg: 1d6/6

In CHAINMAIL our dragon gets hit appox. 1/3 as often as if a AF was attacking another AF (it takes three 6's to score 1 hit--ignoring for the moment that non-heroes can't hurt dragons). Well if AF vs. AF has a 20% of landing a blow (AC 2 vs. thac0 19) in both CHAINMAIL and dungeons and dragons, it comes to no surprise that our veteran has a 5% of hitting the dragon. (AC 19 vs. -2 AC). He hit's about 1/3 as often.