## 2016-03-21

### More Monster Metrics, Pt. 1

The previous series of articles on assessing monster threat levels by way of simulation had, arguably, one weakness -- the simulator was only able to model a One-on-One battle between one fighter and one monster. It then found the level of fighter that gave as close to a 50/50 chance of beating the monster in question, which was correct insofar as it went. However: in statistical inference we might semi-disparagingly call this a mere "point estimate"; it tells us what happens at that one level, but little to nothing about the variance found for matchups at other levels.

So here's the solution to that, and, I think, a much more stable and trustworthy measurement of what I'm calling Equivalent Hit Dice (EHD), which can be used to gauge threat levels and apply simple XP awards without complicated table look-ups (e.g., as in the original system awarding 100 XP per HD). As of version 1.08 of the Arena simulator, I implemented Party-on-Party battles, so that arbitrary numbers of men or monsters could face off against each other and get a view of data on those scenarios.

Before I present the output from that Party-based simulator (that will be next time), a few thoughts on the model of combat that went into it. First: exactly who attacks who? In the AD&D DMG, Gygax gives recommendations which fully abstract the selection, reflecting the fact that his games had removed miniatures from the table by that point:
As with missile fire, it is generally not possible to select a specific opponent in a mass melee. If this is the case, simply use some random number generation to find out which attacks are upon which opponents, remembering that only a certain number of attacks can usually be made upon one opponent... (AD&D DMG, p. 70)

That seemed like a pretty handy model to implement, because it meant that I didn't have to track actual position or movement of any of our simulated combatants. In fact, I went so far as to randomize the target of every separate blow, which was a pretty simple way to parse out multiple attacks (e.g., as for those creatures who can battle multiple opponents). Furthermore, I set a maximum number of attacks against any creature in a round at 6 (again, taking a cue from the hex-based rule in DMG p. 69; and didn't bother to adjust for relative sizes). Note that a side-effect of this is to come close to coincidentally implementing the AD&D rule for Hydras that "up to 4 heads are able to attack the same target simultaneously" (while not going quite so far with the safety bumper, this will reduce the immense number of attacks that made Hydras look so deadly in the prior model against just one target at a time). Another side-effect is that there will possibly be some small bit of bias for mobs of many creatures, as one can possibly take a hit and keeping fighting as other targets take their place (as opposed to a fighter picking one target and attacking until that one goes down from the fight).

The Party-based combat also made it worthwhile to implement a number of special abilities that had to be left out previously, notably area-attacks such as: Breath Weapons, Petrifying Gaze, Manticore Tail Spikes (shot among many opponents), Vampire Summoning, and Dragon Fear. With each of these special attacks I assume that the monster in question automatically gets one "entry attack" usage before melee begins. For example: With Petrifying Gaze (e.g., Basilisks and Medusae), the entire opposing party all have to make initial saves or turn to stone at the outset; thereafter, I assume everyone knows to "avert their gaze", and the melee proceeds with everyone getting −4 to hit the monster, but no further gaze attacks are assessed. Breath Weapons are abstractedly assumed to hit about half the opposing party (meleers on one side?), or a maximum number scaled to the breath area (4 for Chimera, 7 for Gorgons, 14 for Dragons). Fear from Dragons (included as part of the description from Chainmail) was assessed as a D&D morale/loyalty roll; all opponents must roll 2d6 + HD ≥ 6 or else flee before the fight starts.

Discuss these rulings for mass melee: reasonable or unreasonable? Which of the special abilities mentioned above would you guess are the most dangerous?

1. Upon first contact I let the (N)PCs choose their melee targets as long as there is a clear path (so, no blockers on the way). Also, once in melee, I rule that disengaging from melee is particularly hard resulting (depending on circumstances) in a free attack by the opponent and/or may take a full round (prohibiting a swing at another target) and/or requires a dex and/or str check.

The Dragon's breath weapon is very powerful, but since there is a cap on the total amount of victims, I think that the gaze attack (without such a cap) is in the long run the most dangerous one. Especially when coming in multiples, as a higher fraction of the party will be taken out of combat before round 1.

1. Your engagement rule is pretty reasonable, and the free attack on retreat is by-the-book as I read (I'm one of the few people who don't do that).

Good guess on the "most dangerous special attack". :-)

2. On the topic of multiple attacks, the hydra head limitation actually makes a great deal of sense in the context of hex-based combat - the hydra can only attack with one head in each of the two frontal and two flank hexes, and isn't flexible enough to reach around to the two rear hexes. In any case, with randomized targets against a whole party, a hydra making more than four attacks against a particular target is really an edge case, only happening often when the strongest hydras face off against small parties.

The amount of targets hit by the dragon's breath may be a bit high, but it's probably fair since you're only letting the dragon use it once instead of three times.

The morale thing for dragons gets a little hinky because of the fact that PCs never have to take morale tests. Also, are you including any of the traditional morale modifiers, e.g., +1 for Lawful creatures and -1 for Chaotic ones? Undead as a category should be altogether immune to dragon fear, as well as to poison. Speaking of morale, are you including morale tests when 25% or 50% of a force is defeated? That was always a major part of game balance when adventuring parties fought against large bands of enemy humanoids.

1. Interesting point about morale (which of course is a super gray zone any way you slice it); I'm not using any modifiers except what I wrote above (HD), which is likely to only effect low-level NPCs anyway (you're actually immune as of 4th level with the reaction-based mechanic above). I'm not otherwise implementing morale for groups in the simulator; while that could make a difference, in some sense the exercise is "how really powerful is everyone", which could then provide a better knowledge gauge about when you should run away (I suppose).

To be clear, the Dragons here do still get 3 breath weapon attacks, because the book rule says they can still choose to do that when they're in melee. The only things that get the one-time limitation before melee are: Hurl Rocks, Tail Spikes, Gaze Attacks, and Fear.

2. If possible, then, I might suggest simulating the opening breath attack and subsequent breath attacks as different attack forms, the former occurring once at the start of the battle and the latter occurring at most twice during the battle. I say this mainly because I find (from experience playing in map grids) that while a dragon can often get a well-aimed breath in while the PCs approach, during the thick of the battle it's nigh impossible to catch more than two PCs in a breath unless they're exceptionally numerous. The one exception is green dragons; the square cloud is devastating in close quarters. For all the rest, though, neither straight lines nor acute cones are especially conducive to hitting several targets that are spread out around you. With those sorts of areas of effect, I find that you can generally only hit one enemy if you don't move, and two or absolute max three if you reposition yourself to get the most advantageous angle - possibly braving several attacks of opportunity to do so, depending on edition.

Though you're not currently running any morale checks other than dragon fear, I would still be interested in the future possibility of simulating the effect of undead immunities in monster vs. monster combat. Like, how big of a horde of skeletons does it take to kill a cornered dragon? How does a mummy fare against a giant scorpion? That sort of thing.

3. How big are your parties, generally? I suppose one thing in the model here is that all the fighters are melee specialists, so they need to be in close contact with dragon. That rationalizes a bit more the likely hit the half on one side with a cone breath?

4. In my main campaign, there's technically a max of a dozen, but 7 or 8 is the norm - I get 5 or 6 players, a couple of whom run henchmen as well as their PCs. Generally 4 or 5 of those characters will be in melee with a huge enemy like a dragon.

5. Assuming the whole party is in melee and attacks of opportunity don't exist, though, then yeah - getting half of them sounds reasonable. Hell, a green dragon could probably hit the entire party.

6. Good for you having big party size!

3. It feels like Gorgons underground represent a huge breath weapon threat. Save or die, the gas fills the whole area.

Fear causing people to run themselves off cliffs or separating the party so the dragon can approach the runners as 1:1 fights could easily be the worst if all that were implemented.

Charm is really tough vs. multiple opponents, because each charmed target both removes an enemy and adds an ally. A Charm gaze that everyone must save against (instead of a Charm ability you have to target on someone) would probably wipe PCs the most regularly.

Demihumans with resistances to these are a whole lot more valuable than human combatants.

1. I love these predictions! A couple things that might not be what you expected:

- I did compare the Gorgon's breath to Dragon breath for details -- cone-shaped as in AD&D -- so it hits about half of the people around it by my take. But wow I love that fill-the-cave imagery.

- Because of the haziness of the Fear in OD&D, I'm applying a bonus for HD (as above) that makes you immune once you're 4th level.

- I totally wrestled with whether Vampire Charm is against one or many people. I actually came down on the only-one side, because the vampire "looking into their eyes" seems the inverse of the medusa's "those who look into its eyes", say. Maybe I'm reading too much into that (or I've got images from movies in my head).

Do you actually apply Charm on a mass basis in your game, etc.?

2. I think where he's going with the fill-the-cave idea is along the lines of the AD&D iron golem's poison gas. Specifically, that it will linger in an enclosed area lacking proper ventilation.

3. Yes Daniel on treating gasses as volume-filling unless the effect specifically says otherwise. Although I stick with durations unless magical or otherwise significant wind blows it away.

I agree about Vampire Charm, but undead like Liches and Mummies should cause fear to everyone who views them - again, I'm coming at this from a 1E perspective so that probably isn't represented in LBB. Regardless, doesn't it seem strange that a lot of monsters cause area-effect Fear but not area-effect Charm?

I had a Naga with a One-Charm-Per-Target-Per-Day thing, but she had to use the ability on one person per round. It's possible that mass fear is acceptable but mass charm is just too powerful! The only place I can remember mass Charm happening is an 8th level M-U spell with a total limit on victims' hit dice equal to double M-U level. A monster that could Charm all onlookers simultaneously would be pretty gnarly.

4. Right, I don't mind the existing standard for charm vs. fear effects too much. Somehow it feels like fear is a repellant, while charm is an injection-of-will (more difficult, and hence requires more focus?). So the fact that the standard spells roll in that direction (charm person/monster vs. 1, fear vs. an area) seems to set a precedent.

However, it did force me to think that through initially about whether I was happy with it on implementing the vampires. There's at least a little bit of haziness there.

5. There is precedent for vampires having to charm people individually. Just look at Dracula - he only charms Renfield, Lucy, and Mina when he's alone with them. If there's more than one person present, he stays away and bides his time. If he had an AoE charm ability, he could have just charmed Mina's father, Mina, Lucy, and John all at once when he first met them and then the movie would be over.

6. That's exactly what I have running in my mind, too.

4. EDH is the HD of the opposing fighter that has a (roughly) 50/50 chance to the defeat the monster, right? I was wondering how this probability changes as function of the fighter's HD, the function p(HD) if you like (not to be confused with PhD, although you might want use one of those to plot the functions :)

It would give an indication of the threat level for an encounter above/under the HD of the fighter.

I would guess that monsters with identical EDH's will have different curves, depending on how the impact of their special abilities scales with the fighter's HD.

Similarly, what are the curves of fighter vs. fighter? From these curves you may glean some insight how much stronger a lvl x character is than a lvl y. How much stronger is a 3HD fighter than a 2HD one? And what HD should a fighter have to defeat a 6HD fighter with the same odds? 7HD (1HD difference), 9HD (same ratio as 3/2), or something else entirely?

1. EDH is the HD of the opposing fighter that has a (roughly) 50/50 chance to the defeat the monster, right?

A: It was that in the prior articles. Starting next week, EHD becomes a weighted average of number of HD of opponents needed to beat someone (the average taken over levels 1-12).

I would guess that monsters with identical EDH's will have different curves, depending on how the impact of their special abilities scales with the fighter's HD.

You win the D&D Statistics Award for today! Totally nailed that. One of our primary conclusions was that the D&D 3E formula that doubling monster numbers always increases challenge by +2 steps is very broken in exactly that way.

5. :%s/EDH/EHD/g

6. Funny - I may be one of the few people left in the world who plays the randomization of melee attacks BTB, so I guess I agree with your rulings there. ;)