Now, one of my major game-design principles is that finding the right in-game value or "price"for different unit types is very hard. And by very hard I mean: (1) A table or formula of added components for this purpose is certain to be insufficient for this job (c.f. Traveller spaceship construction, War Machine unit values, D&D 3E magic items, etc.); the only way to properly gauge the interaction of all the different moving parts is through actual playtesting, each unit as a coherent individual piece. And (2) This correct playtest-balancing is by far the hardest part of game design, like, a whole order of magnitude more work than all the rest of the design put together.
So given that, I'd like to use my extensive playtests for Book of War as a resource, since over the years I've lost track of how many hundreds of millions, or billions, of computer-simulated combats I've run for each unit type; that is, I'm pretty confident about the relative "cost" values for each unit there. And even if you don't trust that (although you could verify with the simulator program here), note that the cost values generated eerily match those found in the Chainmail Fantasy Supplement, or original D&D Vol-3 Men-At-Arms costs, so you could just reference Gygax there if you prefer.
The original XP table for D&D only considers Hit Dice, but of course other factors can make a monster much weaker or more powerful. Greater movement, armor class, attacks, and damage can enormously change the value of a type. That's even before we consider "special abilities" like flying, poison, paralysis, turn-to-stone, fire breath, regeneration, etc. Even just having a ranged attack will at least double the value of a piece (e.g., see Vol-3 Men-At-Arms), because that effectively gives many more attacks on the table. Let's reduce our sample space by only looking at units from BOW that are foot, melee-only units with the identical armor value of 5 (same as AC 5, chain mail). Here's what that part of the BOW database looks like:
And let's chart the Hit Dice versus the Cost values:
That's an interesting chart, because there's a very clear outlier: Trolls, the very example given in Vol-1 which allows us to extrapolate any kind of XP awards in the first place. (Again I'll point out that both my Book of War game and Gygax's Chainmail Fantasy agree that Trolls should have a cost of about 70 [75 in Chainmail], with Hill Giants at the lower cost of 50, etc.) If we remove the Troll outliers, then the rest of the chart is basically a linear progression, as shown below:
So this says that for those simple medium-foot units, you could approximate the proper cost in BOW by just taking the hit dice and multiplying by 6 or 7 in each case, and this would account for over 98% of the variation from the mean for those types.
In other words: The value of raw Hit Dice is really linear -- it's not geometric or parabolic or higher-powered in any way. I find this unsurprising for a few reasons: (1) Taking higher-HD creatures generally reduces the number of attacks on a per-HD basis (10 orcs get 10 attacks, but a 10-HD giant only gets one attack; in most cases I'd prefer the former when attacking). (2) We also know that higher individual hit dice are effectively devalued in hits taken, because it presents a simpler "packing problem" to the attacker in applying damage (see here). Now, that two-fold devaluation for higher hit dice is somewhat offset by higher to-hit chances; but you also need some other assumed improvements in movement, damage, and minor special abilities (e.g., throwing rocks) just to maintain parity on a per-HD basis (i.e., to maintain even a linear price increase).
So that argues for the original Vol-1 XP system (linear) over the Sup-I alternative (parabolic). However: What the Vol-1 system was certainly blind to was the need to account for special abilities in some way -- with a canonical case in the very Troll that Vol-1 used for its example; it certainly needs to be worth more than 700 XP no matter how you slice or re-slice it (they are very dangerous in practice). Of course, as we saw in the last post, the Sup-I "special ability" awards were pretty close to the base awards themselves; you don't really need a new table for that, as even in Vol-1 you could broadly just "double" (or: add a like amount to the base XP) the award for a powerful special ability like regeneration, and, for example, give out 1,400 XP for defeating a Troll. (That's just about the proportional difference we see between Troll and Giant costs in the table above.) And it would be justified to likewise give this same doubling adjustment for other statistical improvements like high armor class, ranged attacks (at least for numerous low-HD creatures), etc., etc.
Thus, it seems that the Vol-1 linear system really presents the best true "value" per Hit Die (with appropriate special ability adjustments, as for Trolls). But here are a few possible counterarguments to this theory: One is that in Original D&D's fairly small monster list, high-HD creatures almost uniformly had more deadly special abilities (spells, petrification, breath weapon, swallowing whole, etc.); so perhaps that was accounted for in the system in the first place, and only needed to be disentangled when a greater variety of monsters appeared later on (although I think that's disproven by the relative value of Giants and Trolls in Chainmail, which gets flip-flopped in Vol-1 XP in the absence of any such modifier).
A second counterargument is that the Sup-I adjustment (parabolic through level 9, then linear) may be intended to reflect the progression in the class XP tables: geometric through about Name Level, and then a constant addition for higher levels. This is a somewhat stronger counterargument. Let's look at the relative "number of monsters defeated to gain a level":
The Vol-1 system presents a sliding scale: A single 1st-level fighter in this system must defeat about 20 1st-level monsters to level up (ignoring treasure considerations); and this number slowly increases up to around 100 after name level. But the Sup-I system is more consistent in this sense: At almost every level the fighter needs to kill about 100 monsters to level up (ignoring the anomalous 200 monster requirement at 1st level).
But on the other hand: The depressed Sup-I monster XP implies that about 95% of earned XP will be from treasure at 1st level, sliding to some 70% at level 21+ (link). By my calculations, the original Vol-1 XP system has a more constant proportion in that regard, with around 65-80% XP coming from treasure across any level; and in that way, monster XP is still the smaller part, but not totally negligible, as in the later system.
So the relative merits seem to boil down to this:
- Original Vol-1 XP System: This linear system is easier to use, requiring no table. It better reflects the actual added "value" per raw monster hit die (although manual additions are needed for "special abilities"). It supports a convenient linear conversion to unit values shown in Chainmail Fantasy, Men-At-Arms costs, Book of War costs, etc. It allows lower-level characters to level up after defeating a fairly reasonable 10 or 20 monsters (instead of hundreds in the Sup-I system, excluding treasure). And it has a more even and constant monster/treasure XP split, in a ratio of about 1:3 across all levels.
- Revised Sup-I XP System: This piecewise-parabolic system better reflects the class XP tables, and so generates a nearly constant number of monsters needed to gain the next level in each case (although this number is very high, approximately 100 monsters per level; or in other words, monster XP is nearly negligible compared to treasure XP). And it's compatible and familiar to players of any later edition of D&D.
At the moment, to my eye, it appears that the original, simple Vol-1 system has more qualities in its favor. What do you think?