Monday, January 11, 2016

XP: The Big Switch, Pt. 2

In the last blog we looked at the two different systems for awarding XP for defeated monsters in D&D: (1) in the the original white box set, Vol-1, a simple linear progression of 100 XP for HD, and (2) in the revised Supplement-I (and later editions), a much-depressed parabolic progression up to about 9 HD, and then effectively the same linear 100 XP per HD for levels after that. So which is really better?

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?


33 comments:

  1. I have to agree with your assessment the original system is pretty elegant in its simplicity - I'm all for game subsystems with calculations you can do in your head. The devaluation of monster xp seemed to lead to things like 75k gp gems to allow for advancement. I wonder if a new assessment of xp needed would also be warranted?

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  2. Seems like if you did not like the rate of advancement, it would be easier to change the level charts; more work at first, but something you look up a lot less often than monster xp

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  3. I think you've sold me on using {base rate} x {hit dice} x (1 + {special ability stars}).
    Now I'm mostly thinking about a schema for how what abilities should be worth one or more stars, especially for things like AC (which, since higher level/HD implies a better to-hit, seems like it isn't just simple matter of AC of X or better is worth 1 star).

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    1. I probably wouldn't bother making anything worth more than one special ability star. It seems overly complicated for what's supposed to be a simple XP system. I'd probably give one star for any of the following major abilities:

      Negative AC
      Poison, paralyze, stone, or energy drain
      Regeneration
      Breath weapon
      Spellcasting
      Magic resistance
      Immunity to normal weapons
      Exceptional damage (considering an ogre or giant of similar hit dice to be the baseline)
      Flying plus a ranged or "swoop"-type attack (i.e., able to deal damage while staying out of melee range)
      Other unique special attack or defense

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    2. I agree that this is the next step to consider. At the moment I'm planning on awarding a single doubling for any abilities of note, much like Daniel Wakefield's list. Ideally I'd have a simulator that could give suggestions on how well that stuff is balanced, but that's off in the future for now.

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    3. Consider also how many special abilities it can use during any combat. Defensive abilities, even if they don't come into play (such as PCs refusing to Fireball a Red Dragon), affect the party's options without the monster using its round. But a wizard with a suite of spells probably won't get off more than a couple before he's toasted. Having exceptional offensive abilities should be worth a star, while each exceptional defensive ability might be worth one.

      Immunity to normal weapons is an example that's more complex. At some level, all attackers will have magic weapons, meaning it will have little effect. Unless the + required to hit, in order to qualify for a star, is a minimum based on HD because of an assumed party level and magic equipment content arrayed against it. Maybe +1 per 4 HD is the minimum to matter.

      If you handle Magic Resistance such that attacking caster level reduces the percentage, this should work the same way.

      I don't think an NPC with high CON getting regeneration 1 HP per 2 turns being worth extra XP.

      I think you'd need a threshold for each ability is what I'm saying, and sometimes that threshold will be dependent on the monster HD.

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    4. I certainly agree with what 1d30 just said.

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    5. Honestly, I think that for practical purposes, several of those problems are solved by using OD&D rather than AD&D.

      In OD&D, there is no regeneration for having a high CON. Regeneration as an ability would only refer to trolls or NPCs with a ring of regeneration or the like - healing that occurs every combat turn and can potentially bring the creature back from the dead.

      As for immunity to normal weapons, consider this - a fighter or thief has a good chance of getting a usable magic weapon since swords make up fully one-fifth of all magic items, but clerics and wizards have no such luck. The odds of any given magic item being a magic dagger (and thus usable by wizards) are 1 in 100; the chance of receiving a magic mace or war hammer (for clerics) is no better. Add that to the fact that old school parties are expected to be sizable and contain numerous henchmen, and even a creature that requires +1 weapons to harm will likely be invulnerable to some of them. Also, any party member who has to resort to using spells or magic arrows is consuming precious resources that cannot be quickly replenished.

      As for magic resistance, that's only reduced for casters above 11th level in OD&D. By the time you're that high of a level, whether you give 1000 XP or 2000 XP for killing a Balrog is just a drop in the bucket, really.

      In summary, my view is that the defense doesn't need to be useful against every PC or be able to shut them down completely; as long as it reduces their effectiveness or makes them consume resources in a meaningful way, I'd say it's worth a star.

      As a side note, by the time a party is such a high level that they can casually overcome most special defenses, that's where you could bring in the XP penalty for being over-leveled; so a wight is worth double XP because of its special abilities, but against a 6th-level party (which is sure to have plenty of silvered and/or magic arrows to slay it with) the XP would then be halved due to the level difference.

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    6. Cogent. I'd like to point out that while 0D&D might not have sub-par special abilities (like weak regeneration), I think a lot of DMs will end up throwing stuff like that in at some point. But, like the amount of magic weaponry in the party, it has a lot to do with the DM's taste. Finessing the XP awards is probably, as Delta described, ultimately a judgment call in some cases regardless of the elegance of the rules.

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  4. Very good assessment, thank you for doing the numbers.

    I've been using the Vol1 approach for a long time now. I started off doing it because it helped to advance 1st level characters faster and it was easier to calculate. I've since kept it because I like the effect it has at later levels - rather than just slicing and dicing your way to name level, you either have to do some serious exploring (for my houseruled eXPloration bonuses) or some serious treasure hunting to advance.

    Your post just gives me yet more info and support on sticking with the Vol 1 approach.

    Question... given your analysis, if you were calculating XP for an opposing group of bandits, would you double the XP for the clerics/magic-users/archers in the group?

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    1. Great, thanks for sharing your prior experience with it! And good question: I think I would give the double-XP bump to spellcasters. And yes, probably archers, too.

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  5. Given that people these days can play at most weekly, I tend to favor generous XP systems, so the straight up OD&D way seems good.

    I remember when playing AD&D back in the 80's (twice a week) that we only leveled up at a decent rates because of the huge xp awards for finding magic items. I only award xp for magic items sold for cash, but use 100/HD and also let players spend money on carousing for extra, making treasure doubly valuable.


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  6. I used the 100/HD award method for a campaign, and found that once the PCs got ahold of Fireball they tended to blow away big encounters of low-HD wilderness monsters and rake in the XP. I used the partial XP award rule (where a 1 HD monster is worth 1/5 its XP value to a 5th level PC). Seemed to work fine. Mainly I hate the 1E AD&D table because (1) my analysis of the monster's special abilities often doesn't match the XP award table in the appendix, (2) it takes a long time to do it myself, especially with the per-HP bonus, and (3) I use a ton of my own monsters that I need to calculate anyway so the table doesn't help.

    In adventures I write ahead of time I will write in the XP values for monsters so I can give XP that session instead of doing it over the week. I think it's important to provide the quicker response to the players, that X behavior led to gaining Y experience. I think it helps reinforce that the XP came from the big treasure haul or whatever.

    Will definitely go back to the Vol.1 style awards.

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  7. >> I used the 100/HD award method for a campaign, and found that once the PCs got ahold of Fireball they tended to blow away big encounters of low-HD wilderness monsters and rake in the XP.

    And the monsters didn't learn how to defend that... why?

    The orcs in my campaign would have an answer by the third time they tried that. :)

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    1. In my games, intelligent monsters typically scatter into an open formation to prevent too many from getting destroyed by area-of-effect spells, Cleaves, etc. Fireball just takes up a lot of room, and Orcs aren't gonna march 40' apart in a giant line. The typical "answer" is to make sure a good percentage of your party has missile weapons in hand, so in the initial round they can direct their fire to disrupt any casters (whose spells must be cast throughout the round and go off at the end - as a houseruled way to retain disrupted casting without using individual initiative + casting times and weapon speeds) and hope at least one of them hits.

      Also, few enemies got a chance to report back to base on the tactics of the party ...

      Unintelligent monsters stick close enough together for Fireball to take out a good chunk.

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    2. I think that the classic glitch of D&D scaling, setting 1" = 10 ft or 1" = 10 yards for man-to-man action, exacerbates area-effects like fireball overmuch (esp. the latter if uncorrected). Since I interpret 1" = 5 ft uniformly, fireball is useful without being overpowered in this way (takes out about 10 orcs, not a whole order of magnitude greater than sleep). I find that more efficient than, say, changing all the battleground tactics away from medieval tradition.

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    3. You don't scale up area of effect outdoors, only range.

      pg 39 of the rules "IT
      IS IMPERATIVE THAT OUTDOOR SCALE BE USED FOR RANGE ONLY, NEVER
      FOR SPELL AREA OF EFFECT"

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    4. Gygaxian Caps

      YOU CAN NOT HAVE A MEANINGFUL CAMPAIGN IF STRICT TIME RECORDS ARE NOT KEPT

      NO SKILL OF MEASURABLE WORTH

      YOU MUST CONSTRUCT ADDITIONAL PY- uh sorry :P

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    5. Yeah cut and paste directly from the pdf, sorry about the caps.

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    6. "Since I interpret 1" = 5 ft uniformly, fireball is useful without being overpowered "

      Wait are you saying you only do 10' radius fireballs in your campaign?

      /points
      "Heretic!!"

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    7. Fireballs that fill up four 10' x 10' x 10' dungeon cubes are a lot more reasonable than fireballs that fill up 33 of them. And much safer! At least they would be in our game: the elven wizard has a tendency to impulsively cast fireballs in enclosed spaces. (If I was the DM, I would make that PC lose a point of INT every time.)

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  8. Suppose I were toying with awarding XP for monsters fought only to fighters, and XP for treasure only to thieves. In this scenario, what modification of the standard awards for each in 1E would you use to make the rate of experience earned roughly equal for each class? Multiply combat XP by 10? Divide gold XP by 10? or 4?

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    1. I've never done stats on the 1E-style XP-per-hp system. In Vol-1 it would a fairly easy multiply monster XP by 3 (or so). In Sup-I it turns into a sliding scale by level, unfortunately -- like let treasPercent = 0.95 - 0.01 * (level - 1), then new monster XP = 1/(1 - treasPercent) * oldMonsterXP.

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    2. There's also an XP method floating around that grants XP for damage dealt and received instead of for monster kills. It has some fine points that might answer some of the objections the description immediately raises. Can't remember who was doing it though.

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    3. Yes, that would be Alexis over at "Tao of D&D"
      http://tao-dnd.blogspot.com/

      Here's a link to the wiki page explaining his XP system.
      http://tao-of-dnd.wikispaces.com/Experience

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  9. Note that the outlier at level 1 is due to the XP table, not the monster XP award (you double the XP required each level, except for at level 1, because you start from 0 XP, not 1000 XP as would make sense from the progression -- the cost of leaving the level 0 masses!).

    I've always used 100 XP / HD or *, because I don't need to look anything up, and it gets players to level 2 really quickly (perhaps too quickly). The game was intended to slow down as you got to higher levels, as you got a reduction in XP for taking on lower HD monsters, so even with linear increases needed, you get diminishing returns for fighting the same monsters.

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    1. Right, I agree with that. Interesting that you've also been using that system!

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  10. I don't usually have a lot to add to these analytical/statistical posts, but I always find them fascinating and informative.

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