## Monday, May 14, 2018

### Underworld Overhaul, Pt. 4: Monster Numbers Appearing

Here we get to an issue that's a little bit more tricky, because the advice given in the OD&D books are somewhere between ambiguous and self-contradictory: how many monsters appear in an encounter? Again I'll quote the foremost passage from Vol-3, p. 11:
Number of Wandering Monsters Appearing: If the level beneath the surface roughly corresponds with the level of the monster then the number of monsters will be based on a single creature, modified by type (that is Orcs and the like will be in groups) and the number of adventurers in the party. A party of from 1-3 would draw the basic number of monsters, 4-6 would bring about twice as many, and so on. The referee is advised to exercise his discretion in regard to exact determinations, for the number of variables is too great to make a hard and fast rule. There can be places where 300 Hobgoblins dwell...
In particular, in the first sentence, the parenthetical comment ("Orcs and the like will be in groups") makes no sense as a reasonable balancing factor; if a "single creature" at Level 1 is a reasonable challenge for some (small) party, then any multiple number of Orcs will be deadly (to say nothing of 300!).

For the following, we make the following baseline assumptions: (1) As specified in the last post, we use a formula for numbering appearing of NA = scaleFactor × level / EHD, where level = dungeon/character level (presumed equal). That is: we interpret "level of monster" in the quote above to be EHD, not the 1st to 6th level tables on the same page (contrast usage of "level [of] monster" on Vol-3 p. 11 with Vol-1 p. 18, say). (2) Standard party size is 4 characters/fighters (this seems like a common expectation; is about median for the sample party sizes in the book quote above; and seems like a reasonable balance between safety and fast advancement seen in last week's article). In the Arena code, scaleFactor is the same as party size, so 4 in this case. (3) We are simulating dungeon lair encounters, each with a roll on the dungeon treasure table (waiving the 50% chance for treasure, but also no DM-fiat high-value "important treasures"), not wandering encounters.

Granted that, Let's investigate the effect of a few different options for monster numbers appearing in the dungeon. First we repeat the demographic results from the last post; a party size of 4, and equivalent scaleFactor fixed at 4 (so, if dungeon level = EHD, monster numbers are equal to party size, and otherwise proportionally adjusted):

Now we consider if we change the "basic number" in this case, i.e., the scaleFactor, to a variable 1d6. This has an average of 3.5 (slightly less than our prior 4); in 3 cases less, in 2 cases more than our prior fixed value. (This is done by a one-line code change to Arena, so can't be directly executed via the current release application). This results in the following population:

Despite what we might have expected (with a lower average encounter size), we see here that the extra variation in the 1d6 actually makes for a significantly more dangerous campaign. Compared to the prior chart, there are only one-half or fewer fighters at the 5th, 6th, or 7th levels. Even if the PCs may be happy to sometimes fight only 2 or 3 same-level monsters, they will easily be overwhelmed sometime when they are outnumbered by 5 or 6 same-level monsters. (On the flip side, it's a bit weird to occasionally have a treasured lair with only 1 single monster.) Also, the Strength scores for the high-level fighters start to hint that the game may have turned into something of a random meat grinder, regardless of character ability, which we do not want. So let's dial down the variation a bit and look at instead rolling 1d4+1 for the scaleFactor:

Even with the same average as on a 1d6 (i.e., 3.5), this is clearly better for the PCs. Compared to the fixed scaleFactor = 4 table, there are roughly the same number of fighters at 1st to 5th level. The numbers at 6th and 7th level are reduced, but, e.g., there are over three times as many characters at 6th level as in the 1d6 experiment. And the ability score averages at high level look reasonable. And we avoid having single-monster lairs. So: This looks pretty good for dungeon lair numbers. (Side note: In each case, XP from treasure is roughly two-thirds of the total, with monsters accounting for the other one-third.)

Based on this, now consider wandering monster encounters. Seems like this could be around half the size of a "lair" encounter, say: scaleFactor × 1d3. Obviously this is somewhat subjective, because these encounters don't generate treasure, are not critical to advancement, and hopefully avoided entirely by discriminating PCs (and not simulated in our program in any meaningful way). Note that in this case, with our default party size of 4, and an average wandering encounter with 2 monsters, we exactly match the guideline text in Vol-3, p. 11, repeated here:
If the level beneath the surface roughly corresponds with the level of the monster then the number of monsters will be based on a single creature... 4-6 [party size] would bring about twice as many...
In order to make this synch up, we've had to: (1) interpret "level of the monster" as meaning Equivalent Hit Dice, (2) strictly read the "based on a single creature" phrase, and (3) entirely ignore the parenthetical note about groups of Orcs, and the follow-up example of hundreds of Hobgoblins. Our construction gives "lair" encounters again twice this size, which seems to be the upper bound for what PCs can confront and survive more than a few times.

But here's a complication: We assume that encounters (esp. wandering ones) will be scaled in proportion to both party size and monster EHD on the fly, and in practice this would require a calculator for the number-crunching (and also the complete list of monster EHDs). Here's a shortcut rule-of-thumb to make that more practical on the fly, based on the average EHDs at each level. (Bunch of spreadsheet number-crunching occurred here, not shown.) Look at the revised Monster Level Matrix we're using. There are six "tiers", and for each, a die-roll of 3-4 lands on a level-column which provides a "median monster", where EHD approximately equals the dungeon level (and so, presumably character level). The number appearing can then be adjusted by where the result is to the left or right of that median 3-4 result column:

You may note that a result of "Left 2" can only ever result from a die roll of "1" on the matrix; a "Left 1" result only from a "2"; and so forth. The multiplier shown might also be used for lair encounters (recommended base 1d4+1) and so forth. For clarity, the exact number appears for each pip of the 1d3 wandering encounter roll. I've got this jotted into my copy of OD&D Vol-3, p. 11.

Final thought: In contrast to this system, broadly in synch with what's related in that key page of OD&D Vol-3, Gygax's module creations tend to be a lot more dangerous, with larger numbers of monsters than we see here (even in proportion to party size). For example, the suggested monster numbers in Mike Carr's module B1 are much less than Gary Gygax placed in module B2. Another example: The wandering monster groups in the DMG Sample Dungeon have an average EHD of about 6 total, any one of which is an existential threat to a group of only 5 1st-level PCs, as depicted in the example of play, to say nothing of the variation which allows them to regularly be up to twice that size. (If the lair groups are any larger than this, then it's hard to see how they'd even fit in the rooms indicated.)

One "solution" I have tentatively set on is:
NA = scaleFactor × level / EHD

Where scale factor = 1d3 per 2 characters or fraction thereof.
- Hirelings of 1HD are worth 1/2 character (which neatly addresses our hireling issue from the last post).
- To make rapid play easier, assume that EHD is the middle of the range for the level of monster generated.
- To put it on a curve, roll two extra D3 and discard the highest and lowest results.
- If there is a remainder of "unspent" monster HD then sprinkle in a few level 1 monsters (random orcs, skeletons, etc). This results in fairly smooth scaling for parties of different sizes.
- Finally, D3 allows use of common D6s (I've been on a jihad to purge dice other than D6s and D20s from my table for common rolls).

I also thought about higher variability inherently increasing lethality. However, in actual play, I suspect that this is mitigated via (a) multiple classes and (b) running away. For example, one of those extra-deadly larger than normal encounters should be ID'd and result in the magic-user dropping one of their precious Sleep Spells, or a cleric turning undead and making the problem go away, or some sort of consumable (potion/scroll) being used. Or, if all else fails, running away.

I don't know if it would be possible to run the Arena code with a variation for extra deadly encounters, perhaps giving something like a 33% chance to "auto-win" (simulating potion/sleep spell/etc) and a 33% to flee. I suspect that would increase character survival quite a bit, at least assuming skilled play.

2. Sorry for the pile-on...

Just to be very clear, numbers below for LAIR encounters (not wandering):
- Host's proposal (IIRC): NA Scaling Factor = 1d4+1 for every four PCs.
- My proposal: NA Scaling Factor = 1d3 for every two PCs or fraction thereof. Thus, 2d3 for every four PCs. Or, if you prefer a more "natural" curve, 4d3 drop the highest/lowest for four PCs.

Delta, if you don't mind -- how should the 1d4+1 scale factor vary for groups <4 PCs, or >4 PCs?
- Could it be generalized as "1d4 for every three PCs, +1 for each additional PC?" This is easy to remember but results in less variability in NA as the PC group grows larger (and <variability works in the PC's favor).
- Or "1d4+1" for every four PCs or fraction thereof? This results in "cliffs" with high lethality when adding a 5th or 9th PC. It also makes adventuring with 1-2 characters pretty lethal I'd think.

Maybe I missed that detail in the writeup above...

As always thanks for the care you put into this analysis!

1. Thanks for the kind words and the attention for detail! Your observations sound solid to me. I also agree with the jihad vs. non-d6/d20 dice; in fact, it significantly pained me to observe the 1d6 scale factor as clearly too dangerous, and to suggest the 1d4+1 instead.

I think in practice I'd be prone to roll 1d6 for the monster number appearing (in a lair), and re-roll any 1's or 6's.

To your question: In theory, scaling by the party size would (I think) be ideal; so a party of 5 gets 5/4 as many monsters, found by a calculator (round to taste). In practice I would probably just dictate "this dungeon is balanced expecting 4 PCs" and not modify things on the fly. On the other hand, if you regularly have 8 PCs (convention tourney?) then double everything shown.

3. Couple random thoughts, seems a good a topic as any to put them.
What is the conceit of scaling Number of Monster with number in the party; just an early rule of thumb for encounter balance, or the notion that More people = more noise = more monsters?

If it is people = noise = monsters, then I guess hirelings should = full people, and actually may be a detriment to overall success.

I am curious how others to "half shares" for hirelings. Do you take their cut off the top, and toss away remainder, or re-calc the splits?
Ex: Part of 3 characters and one hireling defeat a monster for 1000xp.
Do the characters each get 250xp, and the hireling gets 125?
Or do the characters get 286 XP and the hireling 142?

1. Good question. I'm 80% sure that the rule in OD&D Vol-3 that I'm quoting numerous times is purely just about game balance. I've never seen it justified afterward in terms of noise or anything.

Since I first wrote this, it's a bit funny to see how dependent the argument is on that scaling rule, when I don't use it in practice at all. Rather, I just use it to gauge how a dungeon intended for a "typical 4-PC party" should be stocked. (Also that rule was dropped in any later ruleset like AD&D. I recall two TSR adventures that suggested scaling to party size in the very first encounter, and never spoke of it again.)

The issue of hireling XP is perennially a sticky wicket, and was just asked on the Facebook AD&D group a few days ago. My understanding is by the AD&D RAW the extra XP is just lost (your first case). In practice I think most of us (incl. me) add up the fractions and divide by that so nothing is lost (your second case).

4. Yeah I get that, in practice. "This dungeon is scaled for the 5 players that can fit at my dinning room table" :)

5. I wonder, how would the numbers change if you actually assumed that most monsters were singular (albeit multiplied with large parties), and the monsters with x10 Number Appearing appear in groups (of 1d6 or 1d4+1 or whatever you will)?

In the BTB tables this means Goblins, Kobolds, Orcs, Hobgoblins, Gnolls, and Men - with the relevant "Men" in this case being Bandits and Berserkers but perhaps not the classed characters.
(I suppose you can also extend it below the x10 numbers, but it's tricky to figure out the lower limit. In terms of maximum wilderness NA, it's 36 Small Animals, 30 Zombies, 24 Ghouls, 20 Lycanthropes, 18 Ogres, 16 Wraiths.)

When it comes to exact numbers, it's perhaps useful to note the given examples.
Experience points: 1 Troll on 5th dungeon level
Sample Map 2: 4 Ogres
Sample Map 4: 1 Basilisk
Sample Map 8a: 1-2 Trolls
Sample Map 8b: 1 "evil man"
Example dungeon expedition: "Half-a-dozen" gnolls (party size is 6 people)

1. "I wonder, how would the numbers change if... monsters with x10 Number Appearing appear in groups (of 1d6 or 1d4+1 or whatever you will)?"

Fighter-vs-fighter, that would be roughly tripling the threat from those given monsters, and so effectively instant death. (In some sense, that's the exact question that started this investigation.) Assuming you don't have the exact right spell all the time, or attacks-by-level, which we don't assume here.

The Vol-3 dungeon example, is of course, sketchy/suggestive at best (note words such as "suppose", "perhaps, "some evil man", etc.). By my count the total threat/EHD of the ogres is 16, trolls 9 or 18, basilisk 25 (note they're from monster level tables 4, 5, 6). I suppose that might be legitimate for dungeon level 4-5?

The expedition example claims to be on the 1st level. I do think that a 1st-level party facing a like-number of gnolls (EHD 2×6 = 12) would be a clear existential threat. We might imagine the intent in that example being a tough group of monsters guarding the entrance to the 2nd level.

2. Six gnolls isn't that much of an existential threat when it's seemingly the first room they've encountered in the dungeon and they've got an Elf and a Magic-User - Sleep will affect 2d6 of them, after all! (Then again, the magic-user prepared Hold Portal.)

Magic-users are very good at overcoming (a limited number of) existential threats but would also be very overpowered if you assume that they enter every combat "fresh" like in your simulator so I understand why you're not taking them into account.

(Also, again, I'm reminded of the time my players took five first-level characters against 13 Hobgoblins in Keep on the Borderlands: they survived by a combination of Sleep and running away, neither of which are taken into account here.)