## Monday, March 28, 2016

### More Monster Metrics, Pt. 2

As mentioned last time, here are the results from v1.08 of the Monster-Metrics function of the Arena simulator. This shows how each monster from the OD&D dungeon tables match up with generic Fighters of levels 0 to 12. Equiv. HD (EHD) is what I would use to award XP now (using the original rule of 100 XP per HD). Or, for greater simplicity, you could look at the number of asterisks in the "Bonus" column and give that number of extra increments to XP (hat tip to the Cook/Moldvay notation).

Shading of the monster names indicates broadly where monsters were in the original six Monster Level Tables (OD&D Vol-3, p. 10-11). Although, if we were to revise those tables based on this data, it suggests that we could do something like this -- Level 1 would be all monsters shown with EHD 1; Level 2 would be EHD 2; Level 3 EHD 3-4; Level 4 EHD 5-6; Level 5 EHD 8-10; and Level 6 EHD 12+.

Thanks to the capacity for Party-on-Party combats in the current simulator, we can now gauge not just balance against one Fighter of similar level, but exactly what it would take to balance a given Monster against fighters of any level. (Recall: All fighter are assumed with 3d6 stats, chain and shield, +1 sword, no other special abilities). Where a fraction appears, it means that it takes several of the monsters to match a given fighter; e.g., in the top right, the "1/16" means that it takes about 16 Giant Rats to take on a solitary Lord of 12th level. Or where an integer appears, the reverse is true: the "17" in the bottom left, indicates that a Vampire is a fair match against 17 normal men-at-arms, under this model.

I think that the most important observation here is that not all monsters scale the same when you put them in groups, or face them off against higher or lower-level PCs. Two distinct categories of special abilities present themselves:
• Low-Level Killers: These are area-effect attacks, which can affect possibly an entire party at the start of a combat, but are limited in terms of times used (e.g., Breath Weapons) or being easily countered (e.g., avert eyes from Gaze Attacks). These abilities are likely to destroy large numbers of low-level fighters, but are of more limited use against higher-level PCs (who are likely to make the save and then keep fighting afterward). This is passingly similar to the magic-user "glass cannon" effect; a nuclear-type option that you can shoot off only once or twice.

• High-Level Killers: These are predominantly save-or-die-on-hit effects, that can only affect one target per round, but can be used round-after-round without limitation (e.g., Poison, Petrifying Touch, or Swallowing). These are unlikely to have any benefit whatsoever against low-level fighters; the target is likely to be dead anyway just from the 1d6 damage attack. But this effect is far more worrisome for high-level characters; if a Lord falls into a pit full of poisonous Spiders, the small amount of direct damage is of almost no concern, but the possibly multiple save-or-die rolls each round is a real problem (and the Lord's high hit points then become effectively irrelevant).

Granted that monsters scale differently in groups, I still wanted to generate a single value that we could use for experience awards (EHD), which incorporated all of the information across different levels of opponents (a more stable, consistent measure than before). So the metric I decided to use was to multiply the number in each cell times the level in question (that is: total raw hit dice value at that level), and then take the average of that across all levels 1-12. That is: $$EHD = (\sum_{n = 1}^N n \cdot f(n))/N$$, where $$f(n)$$ is the monster metric at level $$n$$ in the table above, and $$N$$ is the maximum level considered (in this case, $$N = 12$$). I think that overall this gives pretty good EHD figures.

Using these more robust EHD values, we see that some monsters have increased in value from our prior point estimates. For example: Spiders and Ghouls previously didn't seem to warrant any bonus to XP for their abilities; and we can see above that indeed, their special abilities do not put them at an advantage over a single 1st-level Fighter. But when appearing in groups their save-or-go-down abilities are much more dangerous; according to our data, it only takes 3 Ghouls, or 6 Spiders to threaten a solo 12th-level Lord with likely death in combat. Overall, then, we can confirm that they do warrant an XP boost across all the situations where they might appear.

Anything surprising you can see in that output data? Next time we'll focus specifically about the monsters with the uppermost EHD values in that table.

1. Great stuff. Actually the surprise to me is how few surprises there are, most of the creatures rated well above their HD are the ones I'd expect.

A bunch of wandering ghouls gave me a very nasty surprise in an early game, we had to go back before even getting into the dungeon after a wandering encounter.

I always knew vampires were a nightmare, this confirms it, but I'm still a little surprised they beat the Purple Worm and how few low level types that takes out. The worst thing about vampires is that they should play clever, and that's not really taken into account here, but they're still bad news anyway.

One thought. The more permanent effects of damage (level drain, disease, not leaving a body that can be recovered) is also not allowed for. This comes up because I know I'd rather face a weasel than a wraith, but your system actually swaps them, just. Maybe it's partly psychological and partly how this is interpreted by DMs, but I'd be tempted to give a little exp boost to these types of monsters. I've just convinced myself that the vampire is still worse, oh no...

1. The thing with the purple worm is that its AC is truly awful, so even if it's killing two low-level fighters per turn like clockwork, the rest will meantime be making mincemeat out of it.

2. Right with all that; including how relatively few surprises there were. Like: the spiders and ghouls snapped back to almost exactly the measures given to them in traditional D&D. Of course, not that Ghouls here are given only 1 attack. If you give them 3 paralyzing attacks as in Sup-I and later editions, then they really become a lunatic nightmare for their hit dice (in the list above, no monster but the purple worm has more than a single save-or-die attack per round).

The long-term effects really are a bit of a problem. Part of me doesn't want to hand out extra XP for that when you haven't really wrestled with those lingering effects until a later date... ?

3. Maybe the solution would be to provide better-than-normal treasure for those monster types? Much like how those lingering effects are something that the party must wrestle with later, treasure isn't worth anything to the party until they manage to haul it back to civilization.

Might also be an interesting mechanic to apply to rust monsters; maybe they crap out diamonds or something. It would certainly give a plausible reason for why the intelligent denizens of the dungeon allow them to live, rather than hunting them to extinction. It could also be interesting from a dungeon ecology perspective, as they could potentially form symbiotic relationships where carrion crawlers eat creatures and leave their metal behind, rust monsters scavenge the metal and excrete gems, xorns eat the gems, and they all contribute to mutual defense against predators and/or adventurers.

4. Ooh, that's interesting.

2. Great stuff! I notice that a Hero can only take on three ordinary men and a Super-Hero can only take on six; I'd be interested to know how much of an equipment disparity would be necessary to increase this to four and eight, as specified in Chainmail.

As a matter of fact, I'd love to see this re-run with the equipment tinkered with based on level. For example, I might give the following:

Level 0 - chain, shield, sword
Level 1 - plate, shield, sword, ranged weapon(?)
Level 2 - one +1 weapon, armor, or shield
Level 3 - two +1 items
Level 4 - full set of +1 equipment
Level 5 - +1 damage adjustment (see below)
Level 6 - one +2 item
Level 7 - two +2 items
Level 8 - full set of +2 equipment
Level 9 - +2 damage adjustment (see below)
Level 10 - one +3 item
Level 11 - two +3 items
Level 12 - full set of +3 items

These are just a first shot at approximating average gear by level; obviously good or bad luck could cause significant departures. My basic premise is that as you gain levels, you'll be finding more and more magic items per level, but your rate of advancement will remain fairly constant because of the fact that as your gear improves, a smaller percentage of the items you find will actually be upgrades. Also note that I gave damage adjustments after a while based on the likelihood of rolling up at least one magic miscellaneous weapon, gauntlets of ogre power, or girdle of giant strength.

1. Good idea, probably I should run that at some point (i.e., presume plate instead of chain at most levels). And I think from experience it works out better to apply a probabilistic chance for magic bumps at each level. Initially I tried an "expected" equipment list much like you suggest, but I was getting quantum leaps in efficacy at certain levels. I vary between wanting to using 5%/level (as stated for NPCs) and up to 25%/level (which would match your expectations here for PCs).

2. I had thought about simulating magic item rolls, but I didn't want to suggest something that would be an excessive amount of work. I also wasn't sure if simulating a bunch of extra things within each simulation would have an adverse effect on performance or run-time.

Big jumps might not be the worst thing in the world, either. If the effectiveness leaps could be timed so that they happen at 3rd and 7th level, that might actually be appropriate. I select those on the following basis: if you opt NOT to use the Alternative Combat System, those are when the big jumps in Fighting-Man effectiveness occur. Specifically, 3rd level is the first time a FM is able to participate in Fantasy Combat (as Hero - 1), and 7th level is when he makes the jump to a better row on the Fantasy Combat Matrix (to Superhero - 1).

3. Also, it's actually a lot easier to have a flat percentage roll every level (as implemented for NPCs) rather than a maintain a list of distinct items at different levels. :-)

4. I had quite forgotten that you'd already coded that previously; copy-pasting certainly would make things easier! I may also be biased in my thinking toward expecting discrete lists, as working with healthcare-related statistics tends to involve primarily discrete events - a percentage is a result, not a starting point! XD

3. Great idea from Daniel above about more treasure for wights, mummies and friends. That makes perfect sense, after all, if they weren't buried with some decent grave goods I wouldn't go messing with them!

The ghouls I met were indeed Sup1, which was assumed when I started. Correct that they are nightmares, you realise rapidly why the Cleric was invented. (Actually to deal with Sir Fang, of course, in Blackmoor, and again this table confirms the need for something to help, although I appreciate that turning is less than perfect as a mechanic).

One question: did you allow multiple attacks for heroes and superheroes against 'normals' (however defined)? In that case I'd have expected them to do better there. In Chainmail a hero was literally four men in normal combat, I'd probably expect them to kill more with four attacks per turn. Appreciate this is an uncertain area and would probably just change the first column or two. Delving Deeper goes further and allows monsters to have HD attacks against normals as well (following CM and the troll example in LBB, which is unclear). Not sure what I think about that, but low levels would get mown down by the PW then!

1. Good question: No, all the fighters just get one attack per round. Partly I just really don't want to look at a wild outlier value against only the 1-HD types (potentially biasing the whole EHD metric). Definitely if you give full CM/AD&D attacks against 1HD then exponentially more will be killed (subject to interpretations, such as movement/contact issues).

2. To my mind, movement and contact probably aren't big issues even with multiple attacks. Other than high-level fighters and vampires, the only things with more than 6 HD are uniformly larger-than-man-sized. I would posit that at least 9 or 10 men could attack something the size of a giant or wyvern - and many more for something like a purple worm or sea monster. That's only for melee; that's not even getting into the possibility of shooting over the heads of your allies at the easily-picked-out 10+ foot tall enemies.

3. True; I was thinking more of multiple attacks for say, 15th- or 20th-level fighting men (where size differential isn't an issue). And of course missiles are a whole different ballgame; they give more power to weaker individual creatures in big groups, assuming terrain is open enough to permit it (which is an advantage to an above-ground castle, now that I think of it).

1. There is just a switch for that. I'll note that I should do a run with it turned on at some point.

5. Beautiful. This is exactly what I wished for. At first glance there are hardly any surprises, except those you already mentioned. Well, maybe the cockatrice with its very flat distribution. Later I will have a more thorough look at the results.

I have a questions though. Will you make the data available, like you did with the previous simulations (ascii, xls, or anything is fine, really).

I would also be interested to see what the table would look like when fighters are pitched against fighters.

One final thought. You mentioned to base XP on EHD. If you have n monsters, the XP will change linearly, but the challenge rating will not; eg. 2 lvl 12 fighters are sufficient to take out a basilisk, but I bet there are a lot more than 10 fighters needed to take out 5 basilisks.

Will you change XP for these non-linear cases? Or is it up to the players to gauge the reward vs. risk of such encounters?

1. If you look carefully, the table does include fighters vs. fighters. That's what those entries of Warrior, Hero, Myrmidon, Champion, and Superhero are.

2. Yes, I realize that, but I could imagine (never played OD&D, so I don't know for sure), that the weapon/armour is not strictly identical to the assumed fighters (chain/shield and +1 sword).

Also, I am not sure about the actual stats of Warrior, Hero etc. are.

But, you are right of course. These are indeed fighters of various level.

3. Above we were actually discussing the possibility of implementing better gear for higher levels, but that's not in as of right now. For now, they're all statted and equipped the same, with the only differences stemming from hit point and THAC0 progression.

As for the definitions:

Warrior: Level 2
Hero: Level 4
Swashbuckler: Level 5
Myrmidon: Level 6
Superhero: Level 8
Lord: Level 9

Swordsman and Champion don't seem to have made the cut, but they'd fill out 3rd and 6th level if they were present.

I believe they get 1d8 for hit points and +1 to hit for each level in Original Edition Delta; you can check the OED quick ref doc to confirm if you want.

4. Good stuff. Of course, Daniel's identified the NPC fighter levels correctly: and those exactly the types that appear in the OD&D dungeon encounter tables (Vol-3).

These types do get fleshed out as full NPCs in the system: 3d6-straight ability scores, 1d8 hit points per level, +1 attack bonus per level, wearing plate & shield, 5% chance for a magic bump at each level to armor, shield, and melee weapon. I was actually surprised (being in plate) that they don't rank better against the PC fighters, but I've checked it a bunch of times and it looks correct (I guess the guaranteed +1 sword offsets that advantage).

In practice, I would in fact just give EHD-based XP multiplied by the number of creatures, principally because that's so simple. I'm actually not sure that different proportional scaling would make so much difference, actually; my educated guess would be that 10 Ftr10 would be about right vs. 5 Basilisks (subject to interpretations: if you confront 5 gaze creatures, do you make 5 saves or just 1? I'd lean towards the latter, and in that case the Basilisks would be less effective in that matchup.)

In 2 weeks I'll post the full data, code, and a command-line program designed to let you run the simulation yourself in various configurations (assumes you have Java and know how to type).

5. That said, the thing you definitely can't do is take a random monster, multiply its numbers, and use a fixed formula to figure how the EHD changes against a single opponent. That kind of thing is demonstrably unworkable.

6. Ah, I had overlooked that the "Monster" fighters were worked up as NPCs with full chances for magic and everything. You could actually get a piecemeal indication of how much of a difference equipment makes just by altering the percentage chance of a magic bump, perhaps to 20 or 25 percent per level if the goal is to simulate a PC adventurer.

7. Thanks for all the answers by all of you.

Some observations:

Looking at the entries of warrior/hero/swashbuckler/myrmidon/superhero/lord vs. Ftr 2/4/5/6/8/9; the results are indeed very symmetric. For instance Superhero vs. Ftr 2 is 3 and Warrior vs. Ftr 8 is 1/3.

Warrior vs. Ftr 2, Hero vs. Ftr 4 etc. have all a value of 1 and of the 15 remaining pairs, only 3 are not symmetric (Warrior vs. Ftr 6 and Myrmidon vs. Ftr 2, Warrior vs. Ftr 9 and Lord vs. Ftr 2, and Myrmidon vs. Ftr 9 and Lord vs. Ftr 6), but I presume that these are due to rounding effects.

If you plot the rows in the Table of warrior, hero, ..., lord, as function of Ftr level, all the curves are very similar when normalized (I normalized wrt. Ftr 0).

Also, in the range of Ftr 0-4, these (normalized) curves can be described by y = 0.5^(Ftr lvl/2), meaning that you need twice as many fighters when going down 2 levels (so, when n Ftr 3 are needed to defeat an opponent, you could also have used 2n Ftr 1). I think this is in line with the rule within 3E of doubling monsters equaling a +2 in challenge rating.

However, this rule breaks down for Ftr 5+, where the actual curve is much less steep than said function, meaning that the CR explodes when doubling numbers. It also means that the power level of Ftr 5+ does not increase a lot anymore when leveling up.

I always suspected this, but I had endless discussions with one of my players (who strongly believes that in view of power balance all characters should be of roughly equal level, or at least earned XP) and I am happy that I can give some numbers to support my argument.

Regarding the 5 basilisks. I do not think I would ever run such an encounter, but I would rule that multiple Basilisks can in principle have a gaze attack. Maybe an Int check to avert the eyes before crossing a gaze by another Basilisk.

8. That's a really good point and I do agree with that. Back when I did a similar but simpler analysis for 3E, just raw fighting ability (no special abilities), I was also pleasantly surprised by how well the 3E ×2/+2 rule worked out (at least at the lower levels where would start the analysis). Frankly, based on that, I was really hoping here for evidence of a simple scaling formula that would worked in a broader context? But obviously that turns out not to be the case.

9. Speaking of CR, I'd be interested to see the reverse of this table - specifically, how many of each monster it would take to win half the time against PC parties of various levels. That seems to me a more practical measure, as in most cases the party size won't vary much in the course of a particular dungeon expedition. Thus it's mostly academic that a 9th level fighter can take on 5 gnolls; what I want to know is how many gnolls might prove deadly to a party of (for example) five 6th-level adventurers.

10. Right... so I think that would just be the reciprocal of what's shown here, times the party size, e.g., 5/M in your case (assuming the party is all fighters since we can't simulate other effects). That's just spreadsheet work, but I can see how that would be a convenience in that format.

11. What I was really thinking is that the numbers might actually change, but then I remembered that targets are being randomly assigned. I was thinking of the case where a single 3rd-level fighter could take on 3 kobolds, but two 3rd-level fighters might not be able to take on 6 kobolds if all the little buggers gang up on one of them and ignore the other.

12. Right! I guess it's an interesting question if allowed (gang-ups & picking out wounded for attacks)) who would benefit more, the fighters or the kobolds. Maybe that specific case we could guess the kobolds, but I'm not sure cases where the monster can take more than a single hit on average.

13. From the fighter vs. fighter entries in the Table, you may conclude that taking the reciprocal holds. But these are (mostly) identical vanilla creatures.

I suspect that it also holds for non-identical vanilla creatures (in case of random targeting).

However, special abilities do not necessarily scale with number and I suspect for these cases deviations from 5/M.

14. Could be (again, depending on interpretations; if a mob of monsters all has the same area special I tend to just roll once, maybe with a modifier).

6. Yes, I agree; it depends on how the ability is put to play.