Dungeons and Dragons Challenge Ratings

[jack]

In DnD, monsters are assigned a challenge rating, and approximate measure of how hard they are for an average party of adventurers to defeat.

The challenge ratings are obviously ordered[1], but the question remains, what scale? There are two obvious candidates.

(a) Linear. A CR10 monster is as difficult to defeat as two CR5 monsters[2]. This has the obvious advantage of being easy to add.

(b) Logarithmic. A CR10 monster is as difficult to defeat as two CR9 monsters. (In actual fact, there's an arbitrary scaling factor, it supposedly equals two CR8 monsters.) This has the advantage that it matches character progression by level, and notionally monster progression by hit dice (related to character level). This means a CR10 monster is appropriate for Level 10 adventurer characters, and might well have 10 hit dice, or at least hit dice proportional to 10.

Go on, guess which method they used. I'll give you a clue, it seems the worst possible.

That's right, they used both. (a) for CR<=1 and (b) for CR>=1. (In actual fact, this makes some sense -- you often would use CR<1 monsters only with each other. But it still seems very arbitrary. Not that I care, but it amused me :))

Footnotes

[1] Is it obvious? Well, in actual fact, you might easily have rock-paper-scissors monsters, but because they're defined in terms of the average party, the challenge ratings *are* transitive. Also anti-symmetric.

Is it a well-order? Well, the monsters listed anywhere, there are only finitely many of them, so yes. And if you consider typical attributes of monsters, eg. health, strength, damage output, these are defined by positive integers, and lower is weaker, so of any such set, there'll always be a weakest.

However, it is conceivable to have a set of unboundedly weak monsters. Let there be a monster, a proto-nth-orc[3]. This has, on encountering adventurers, a 1/n chance of morphing into an orc, and an (n-1)/n chance of disintegrating entirely. This obviously has a challenge rating of approximately 1/n that of an orc -- so the set of all such meta-nth-orcs is ordered, but has no least member.

[2] The "two together" is an approximation, it's incredibly situational, but it's the standard to start working from.

[3] I so want to throw this at some players now :)

Comments

[simont]

I think you've written quite a lot of text here without making explicit the purpose for which you're adding challenge ratings.

If you add two (or more) monsters' challenge ratings together, do you expect the result to measure how hard it would be for the average party to defeat the two monsters (a) consecutively with plenty of time to rest and recuperate in between, (b) consecutively without recovery time, (c) concurrently, (d) something else?

(a) seems relatively tractable: if you define difficulty as some function of the probability of surviving the encounter, then the probability of defeating two monsters in essentially independent encounters is the product of the probabilities of defeating each one. So if your difficulty was defined to be, say, minus log p, then it would be additive in the obvious sense; or if it were defined to be 1/p then it would "add" by multiplying.

For (b) you'd have to take into account how much of the party's resources – HP, mana, expendable weapons like arrows, wear and tear on armour, etc – the encounter with the first monster was expected to use up, and how that affected their chances against the second. I'd guess that at best it might be possible to produce a rule of thumb that was roughly right for most combinations of monsters, but it would depend on the precise ruleset.

For (c), it would all get a lot more complicated and might easily involve judging how the two monsters' available attacks complemented each other (if one, for example, had a bullwhip attack which could jerk out of your hand the only weapon that would work against the other).

I note with interest that (b)-style addition could easily fail to be commutative but would be constrained to be associative, whereas (c)-style addition has to be commutative but need not be associative. (a) is both, of course.

[cartesiandaemon.livejournal.com]

Ah, maybe I should have put in some more background. I wasn't sure if I could have enough to make it penetrable, without putting in an entire primer of the rules, which is just distracting...

If you add two (or more) monsters' challenge ratings together,

Notionally, to fight them both at the same time. (But then automatically covers the other cases, as they have the same problems, but less so.) It explicitly hand-waves away all the problems with that -- encountering monsters may well not be linear, eg. if their attacks synergise well, they may be much more deadly together, which is often the case if they have random magical abilities.

The DM is supposed to take that into account when planning, though there's no official guidance on how, just to use his common sense for what is likely to kill everyone or not. More controversially experience points by default depend on the challenge rating as compared to your level (there's a formula), so some DM will basically ignore all that and make everyone level up after three sessions, and some will allocate experience points for the challenge ratings as listed in the book, regardless of circumstances.

(The are also lots of reasonably constant modifiers, such as a party being more or less powerful than average, or being better against some sorts of monsters and worse against others, or if the monsters typically attack with strategy or not, or if they typically fight to the death or not. But you can fudge all that once you get the hang of it because the adjustment should remain about the same from the notional average...)

The official guideline is that a challenge rating equal to party level should be "moderately" challenging, defined as taking up 20% (?) of the party's resources. Of course, some characters are more resource based than others. And of course, that ignores the difference between a monster with a high chance of 1/5 killing everyone, and one with a low chance of totally killing one person, you need some variety, but too deadly is generally bad.

[megamole.livejournal.com]

Of course, some characters are more resource based than others.

Yup. From smallest to greatest (assuming we waive material components) it would go something like:

Monk, Druid, Sorcerer, Ranger, Bard, Wizard, Rogue, Barbarian, Cleric, Paladin, Fighter.

Generally spontaneous casters are towards the lower end of the scale; Clerics usually tromp around in heavy armour, though. Interesting how many of the new base classes (especially the sponters like Spirit Shaman or Favoured Soul, or the manifesters like Psion or Soulknife) are also towards the lower end of the spectrum.

And don't even get me started on the really silly Vow of Poverty idea.

[cartesiandaemon.livejournal.com]

From smallest to greatest (assuming we waive material components)

Ah, this severely puzzled me, and then realised what I'd said. I meant, in terms of resources expended in an encounter. I haven't actually played much dnd at all, just enough to get an idea of the rules.

I think I can think of three different metrics: reliance on uses per day; dependency on acquiring new equipment; and dependency on having equipment.

For the first, I would have put the fighter approximately least, I think almost everything he does he can do all day long, except have hitpoints? And the wizard probably most, having a limited number of most powerful spells.

For the third, I'd guess the monk least -- afaik a monk wins the "dropped naked into a dungeon" contest hands down :) And the wizard again most -- assume we waive spell components, requirements, even preparation, a wizard still has to have a spellbook or be stuck, everyone else can at least hit something.

For the second, does that correspond with your list? Or have a just got a very skewed view? I've not played in a high-level campaign.

[cartesiandaemon.livejournal.com]

don't even get me started on the really silly Vow of Poverty idea.

I tried to resist the temptation to get you started... I've never played enough to see VoP in action, I only heard about it. It seems silly that:

* It's orthogonal to character class, so has to be balanced for monks or whoever fits the idea best, which means it has to end up nearly unusable for anything else
* It's supposedly balanced not just by a downside of can't use xx, but by losing everything if you break it, the worse the downside is, the more chance the dm will take pity
* Its utility depends on the wealth available, the less wealth, the better the feature. But then this applies to lots and lots of things.

But the idea that:

* Monks don't horde magic items, but give everything away, and instead get a permanent boost a bit less than everyone else's expected +2 equipment

Sounds cool, thematic, and as balanced as anything else.

[cartesiandaemon.livejournal.com]

(a) LOL. Yes, that works exactly. In actual fact, you generally try to tweak it so people die very rarely, and it doesn't quite apply. Where it does apply is experience points, which, once awarded for an encounter, do add.

But now I wonder if chance of dying would make a good measure in addition to the traditional system -- it's objective, and the second axis would formalise another important aspect of evaluating an enocunter.

(c) is what it's *supposed* to measure. Though (b) is probably closer to what it *does* measure, as all the non-linearities in combining monsters aren't taken account of in the formula.

And in DnD you're either on your feet with full strength, or dying, your effectiveness doesn't really drop. (For spellcasters, that's "have spells left" or "have no spells left"), so (b) doesn't make that much difference.

Actually, I guess there's approximately two timescales that matter. Overnight, you regain spells, and maybe go back to base and renew equipment. Over a few minutes, you can cast healing spells, drink potions, pull people out of pit traps, etc.

Fighting monsters consecutively would be close to "fighting monsters concurrently, but ignoring synergies", which is what they're supposed to measure.

I'm not sure if the term "resources" better tracks hit points or healing potions, or even if it's that well defined (it's certainly not that well thought out :)) That's the end of my musings for this post -- note, this is *mostly* theoretical on my part, I've played some, but not a lot.

[cartesiandaemon.livejournal.com]

Edited at 2007-11-19 03:20 pm UTC

Wait, that also horribly confused me. I thought "now you can edit comments"? But it's not, it's reposted, it's jsut logically edited. (And wisely says so to avoid that "Huh, I thought he said..." moment.)

[simont]

I did edit it rather than reposting. First time I've used the new comment-editing feature. All I did was to correct a shamefully misplaced apostrophe, though.

[cartesiandaemon.livejournal.com]

Ah! In which case I was wrong *twice* in one sentence in opposite directions, which I think is some new record even for me :)

[megamole.livejournal.com]

I thought the canonical answer was that a CR10 monster would provide a reasonable challenge to a party of 4 10th-level characters.

They themselves show examples where CR doesn't really work - for example, the Imp I believe is CR2 or 3 and can come in swarms. Each Imp can fire off 3 magic missiles at will, which could easily kill a 2nd or 3rd level Wizard (or even Rogue) dead... let alone a swarm of them.

[cartesiandaemon.livejournal.com]

I thought the canonical answer was that a CR10 monster would provide a reasonable challenge to a party of 4 10th-level characters.

Right, that's the definition/guideline. Which, if you are to determine that the 2log2 scale applies to adventures (which I didn't, but assume fits[1]), fixes the scale for CR>=1. And, then assuming you don't allow (1/2)-level fighters in your campaign, it makes sense to call half of a CR1 monster CR(1/2 )rather than CR(-1). But it still irks me that the scale suddenly changes :)

They themselves show examples where CR doesn't really work

Oh yes, CR is excessively hand-waved anyway -- see the response to Simon.

[ravingglory.livejournal.com]

It's generally agreed that the CR system isn't very good. It was kind of tacked on at the last minute. It's better than the last system which didn't scale exp. rewards by level at all, but not by all that much.

[cartesiandaemon.livejournal.com]

That too :)