## 2016-04-11

### More Monster Metrics, Pt. 4

Some final results from our project to measure monster threat levels (in terms of Equivalent Hit Dice, EHD; usable as a basis for XP awards), by means of a Monte-Carlo measurement simulator (link):

First, at the outset, we were hoping that we could reduce power levels to a single rating, together with, say, some formula for how many of the same type of monster interact. Our results show that this effectively impossible; interactions of complicated powers are, as we see again and again, fundamentally irreducible, and trying to use a simple formula or table will be essentially broken. For example: 3rd Edition D&D gave every monster a "Challenge Rating" and a simple formula: doubling the monsters increased this value by +2. But we are more keenly aware that some monsters have abilities that are lower-level-killers (area effects), and others high-level-killers (save-or-die on hit), and these interact totally differently against masses of low-level opponents, or small numbers of high-level opponents. If you want to use our ratings for encounter balancing, then you have to look at the individual cell in the master table for the level that you're considering (EHD alone is less dependable). A graph shows that some monsters are working in totally different probability distributions for mass combats: for example, Red Dragons have a power-curve regression, while Purple Worms have a logarithmic-curve regression, and those curves actually criss-cross each other (reverse advantage) as we advance in opponent level:

Second, in our master Monster Metrics table we summarized certain variable monster types the same way as they appear in the D&D encounter tables (e.g., Lycanthropes, Giants, and Hydras as single listings). These probably deserve their own detailed analysis, but there's not too much surprising here: Lycanthropes' ability to infect opponents doesn't make much difference within one melee. Giants are brutes whose EHD remains about equal to the HD throughout. Hydras with their multiple attacks and maximized hit points are always worth about double their base HD. Also shown below: Vampires with variants for summoned Wolves and Rats (but don't entirely trust that, subject to rulings discussed in the last article).

Third, of course, Dragons are the most complicated and possibly dangerous type in the entire ruleset. The master list only assessed Red Dragons, and represented an average across all age levels (randomly determined for each dragon encountered, a d6 roll indicating age level and points for each hit die). So they also deserve to be broken out for each type and age category, as below. We see that Young and Very Young dragons are worth about the same as their base HD. Sub-Adults are worth double value (a one-asterisk "bump' in XP). Adult dragons are worth triple value (two-asterisk bumps). Old and Very Old dragons can be worth anywhere from triple to sextuple value -- up to EHD 62 for the Very Old Gold Dragons, and that's not even accounting for any spell abilities!

Fourth, I went through the Moldvay/Cook rules to compare the "asterisks" they gave to each monster to the ones I've got here (the notational notion, of course, being taken from those luminaries). Where we differ, my results suggest that XP bonuses were somewhat overvalued in the B/X rules; this is compatible with the observation that while prior writers usually gave an XP "bump" for every significant special ability, not all work in synthesis for a monster at once.
• Same in B/X: Centipede, spider, berserker, ghoul, ant, beetle, giant, troll, scorpion, gorgon, medusa, purple worm.
• Higher in B/X: Lycanthrope, gargoyle, snake, mummy, cockatrice, spectre, hydra, wyvern, basilisk, chimera, dragons.
• Lower in B/X: Manticore, vampire.
B/X gives no XP bump for the manticore's tail spikes (too mundane at first sight?), and probably overlooks the value of the vampire's tremendous summoning ability. One thing that also jumps out at me: Even though B/X agrees that the medusa should get a two-asterisk bump to danger level (raw HD 4, EHD 12+), and it's arguably among the top-tier of monsters in the game, that monster was put in the Basic Ruleset (B-level, for PCs of 1st-3rd level)! I guess you could say the same for dragons, but there are extenuating circumstances in that case.

Finally: If you want to run, double-check, or measure your own monsters with this same system, here's the program that will let you do that: MonsterMetrics is a Java executable JAR file, so it should run on any computing platform on which you have Java installed. Here's how to get it: (1) Download and unzip the first file below, MonsterMetrics.zip, to a location of your choosing (includes executable MonsterMetrics.jar and necessary data files). (2) Open a command-line prompt in that location and type: java -jar MonsterMetrics.jar. This will go through the entire included monster list and assess the strength at each level of opponent Fighter (running 200 mock combats per level/number combination in a binary search to find the best match), and also print a combined value for EHD at the end of each line (copy to a spreadsheet program for additional analysis). If you want to measure just a single monster, then append the name of that monster at the end of the line (for example: java -jar MonsterMetrics.jar vampire). Feel free to inspect the data file Monsters.csv and check out exactly how I adjudicated statistics for each monster in OD&D, and edit or add your own monsters to see how they stack up. (In addition, files for the source code and Java documentation are included for those who want to modify that, but as a standard user you can ignore those.)

Tell me how that works for you and your game!

1. You are a god.

1. I've been informed to "Say yes!" any time that's inquired. :-)

Anyway, I was thinking about your use-case in skipping the whole compilation process. Thank you for the earlier feedback!

2. There is no LWSCHURTZ, only Zuul! =P

2. Thanks so much for this. I'll certainly have a play, when my work next allows.

I'd love to include magic, but it's so hard to see how. I have access to the computing power, it's more about how to design it in any reasonable way.

1. Right, I agree! As an initial stab I imagined trying to focus on a few critical spells and maybe expanding from there. But it's well outside my work time available.

3. I'll have to take more time to look at this in a couple weeks, but thanks for letting us peek under the hood!

4. Hmm, we could have a mixed party for the monster to fight. Thieves wouldn't be so bad; if they make a hide throw, they could have one free backstab at the start, if appropriate. I'd guess they would be less valuable than FM on the whole for this combat simulation. MUs could be given an appropriate proportion of combat spells, then maybe model how many they have left as a flat distribution and let them fire off every turn when they aren't hit. Might work for fireball and lightning and sleep like your dragon breath models. It won't really handle the more subtle spells, so I don't know if the coding effort is worth it.

1. It would be an enormous amount of coding work. :-) Then you have even more interpretive calls to make; e.g., I let MU's cast spells even in rounds the do get hit.

5. Magic is hard, but spells like magic missile, fireball, and lighting bolt could be modeled. Basically the damaging spells. Also spells like sleep or charm could be modeled by if the creature fails the save it has lost the encounter. Some spells are handy like levitate, but trying to reflect its benefit would be difficult.

1. That's certainly the initial approach, I'd take (time permitting), I agree!

2. Levitate and Fly in a fight to the death are basically just a binary condition:

if ( Ceiling High Enough & No Enemy Archers )
Win
else
Wasted Round

In similar conditions, Hold and Sleep would, as you say, be equivalent to killing any creature that failed its save. Charm would be the tricky one; they weakened it in later editions, but according to the LBBs charmed creatures will even fight for you!

Wall of Fire/Ice could just be modeled as dealing 1 die of damage to each enemy (or two to those with vulnerability to it), since using the circular configuration means they MUST pass through it in order to attack the wizard at all. Perfect for dealing with swarms of weenies; on average, it should weed out close to one-third of a large group of 1st-level fighters!

6. Although I would really like to see the effects of magic and other abilities, I appreciate the 'simplicity' of the current approach. FMs can be implemented in a more or less unambiguous way and in my opinion this is a big plus over other refined approaches.

I understand that there are caveats with this approach. For instance: an orc and an orc with 100% magic resistance, will both have the same EHD rating with in the current simulation environment.

So, yes, party configuration matters (a lot) but the aim of the exercise is to determine some metric for 'dangerousness' and I think that the current take is both clean and (relatively) simple.

That said, I restate that I would love to see magic in the simulations!

1. Right about the magic defenses; fortunately they're quite rare. But there was the one case of the Ochre Jelly that had to get entirely removed because they're only hittable by special methods.

7. "Our results show that this effectively impossible; interactions of complicated powers are, as we see again and again, fundamentally irreducible, and trying to use a simple formula or table will be essentially broken."

While this may be inconvenient for those of us driven to systematization, I actually think it's the desired result, as it makes for a much richer game and game world.

While I keenly await any additional analysis you do of how mixed parties and a broader range of player abilities affect the results, I actually expect fewer surprises there; although you could probably find quite a few models where particular lower-level spell provides a dramatic advantage over a higher-level spell.

1. Excellent observation!