Yet More Monster Metrics

Hopefully you recall our simulation work to generate our MonsterMetrics results from a few weeks ago (link). Today you'll see a few iterations on that concept, based on some recurring comments from the discussion here that followed. Things you'll see below:

• Monsters assessed with 8-sided hit dice as a default. Knowledgeable readers will know that I personally run my games still using the 6-sided hit dice for monsters as they appeared in Original D&D (Vol-2; while using 8-sided dice for fighter hit dice, as per Sup-I Greyhawk). Granted that most people use 8-sided dice, it seemed warranted to run an assessment on that more common configuration. This, then mostly matches the stats as in Moldvay B/X or the AD&D Monster Manual. (Notes: While skeletons & zombies were boosted to 1HD and 2HD respectively, I kept other undead as in OD&D/BX, not the +1 HD boost for other undead as in AD&D. Normal men are therein uniquely 1d6; NPC fighters 1d8.) This will give most monsters a bit more power against the men.


• Fighters assessed with advanced equipment. To measure a raw "equivalent hit dice" value (EHD), the initial assessment program kept fighter equipment constant (chain mail, shield, +1 sword), with the emphasis on correct XP awards. Here, for the purpose of balancing encounters, we may also simulate more expected gear for high-level fighters; plate-mail, shield, sword, and a 20%/level chance of boosting any of those by a +1 bonus (swords still start at +1 by default). Counter to the preceding, this may give the men quite a bit more power against the monsters.

Let's see what happens. First, simply switching from d6 monster hit dice to d8's (men still in chain and shield; no added magic per level):

This makes a fairly small difference in most cases. Previously our toughest monster, the Vampire was measured at EHD 36; now it is EHD 39 (in both cases, equal to 4 12th-level Lords). Hill Giants were EHD 8 and are now EHD 9 (previously worth 5 0-level men and now worth 6). New EHD values are given above if this matches how you run your game; but the differences are not great, and I don't see any need to change XP "boosts" (asterisks) as shown previously.

Now, the case of monsters with 8-sided hit dice against fighters more fully equipped (plate, shield, 20%/level to boost any of their armaments):

Now, that's quite a different story. I've removed the appearance of the EHD column, because these measurements are totally not comparable (and I don't want any readers to be confused by that; again, I suggest using this table for balancing encounters but not XP awards). We see that a fully-equipped Lord of the 12th level can fend off much larger numbers of low-level types: 40 orcs, 45 bandits, 65 kobolds or giant rats, etc. One such Lord has about an equal chances to defeat 2 giants or trolls single-handedly; and 2 or 3 Lords may be victorious over a vampire or purple worm. Note that this is still without any extra attacks by the Fighters (which is more fodder for my frowning against AD&D-style mega-attack counts; surely fending off a half-hundred normal men is sufficient, and we need not further boost that by an order of magnitude!). Also: Fighter stats are on average just straight 3d6; if we dialed that upwards due to expected survival bias, the men would be at even more of an advantage.


Finally, let's include the case as in my games where monsters have 6-sided dice, and men have arms and magic as expected above:

Again, the change in monster hit dice from d6 to d8 or back is not very great. The 12th-level Lord is now only worth 44 orcs instead of 40. Numbers against the upper-level monsters are mostly unchanged. Not a big deal either way.

That said: I would highly encourage any DM's playing with post-Greyhawk 8-sided monster hit dice to try switching back to the original, and rolling d6's for hit dice instead. It's so much easier to find, keep, and use a batch of that die type; as we can see here, the effect in battle is practically negligible; and my players have never noticed the difference.

Want to run these assessments according to your own custom parameters? Here's MonsterMetrics v.1.01 which lets you do that. As usual, download and unzip the first file, and from the command line type java -jar MonsterMetrics.zip to get it running. Now, you can add a command-line switch like -b=3 to indicate the base armor type for your fighters (3=plate, 2=chain, 1=lather, 0=none). Also now included is the switch -p=20 to set the percent chance per level for a magic boost to any item (default is zero if none specified). Finally, changing monsters stats requires editing the monsters data file; included below is the alternate file Monsters-d8.csv with 8-sided hit dice for the monsters (rename this as Monsters.csv to get the program to use it as input). Any interesting new discoveries?

• MonsterMetrics v.101 (Java ZIP package)
• MonsterMetrics v.101 Source Code
• MonsterMetrics v.101 Java Documentation
• MonsterMetrics v.101 Results Spreadsheet
• MonsterMetrics v1.01 d8 Monsters File (CSV)

Aging Through the Ages

I thought age should speak, and increased years should teach wisdom. How have the rules for aging changed between different editions of D&D? An exercise in meta-aging:

Original D&D (1974)

Staff of Withering: A Staff which adds nothing to hit probability, but when a hit is scored it scores one die of damage and ages the creature struck by ten years. (This is not to say it matures it, but rather it shortens the life span by ten years.) A man struck four times thusly will be doddering, an animal dead of old age, and so on. It will have no aging effect upon Undead, and creatures with very long life spans will also be little harmed. (Vol-2, p. 35)

Here, a pretty sketchy rule. The DM must adjudicate what in-game effect "doddering" represents, as well as what proportion of that effect, if any, applies to individual strikes from the staff?

Advanced D&D (1979)

Gygax gives a more comprehensive treatment near the start of the DMG. A series of five age categories are established for each of the PC races, and ability modifiers are given upon entering any of those age categories (approximately every 20 years for humans). In addition, dice ranges are given for establishing the age of starting characters (for example: d4+15, d4+18, or 2d8+24 respectively for human fighters, thieves, and magic-users). The ability modifiers are as follows; in general, physical abilities go down, while mental abilities go up with advancing age (DMG p. 13):

The staff of withering retains its ability to age by 10 years, and so links into this rule -- as well as other added abilities, like destroying a particular target limb (the same "wither" effect as the new reversed clerical regeneration spell; DMG p. 134). Ghosts can strike targets so as to age them by 10-40 years (MM p. 43). Dragons, of course, always have their unique rule for advancing powers with age.

Advanced D&D, 2nd Edition (1989)

In 2nd Edition AD&D, Zeb Cook presents a table slightly stripped-down from the 1E DMG; age brackets and modifiers are only identified for three categories of Middle Age and above (and those modifiers are identical to 1E). This makes some sense, as there could be some confusion in 1E about whether those modifiers should be applied immediately to all newly-created PCs (esp. the +1 to Strength and Constitution in the first two brackets), or whether an older PC (like a human magic-user, starting out Mature at average age 31) should have modifiers for the younger bracket retroactively applied.

A few other tidbits I should mention here. In the Gygax's 1E Unearthed Arcana (1985), the extra-high level Hierophant Druids gained the abilities of "Extra longevity equal to level as expressed in decades", "Vigorous health, equivalent to being in the prime of life", and "the ability to actually hibernate, suspend animation (same length as longevity  -  no aging)" at levels 16 at 17. These anti-aging abilities are maintained in effectively the same format in 2nd Edition. The staff of withering is, as usual, a copy-and-paste job from 1E; and the ghost attack ability is likewise the same.

D&D 3rd Edition (2000)

The 3rd Edition rules maintain mostly the same model for aging as in 2E (modifiers only at the level of Middle Age and above), with a somewhat expanded array of changes to the ability scores (note that all abilities are affected, and the reductions for physical abilities are more severe):

Like many other "exotic" dangers, the 3E ruleset removes the original aging effect from the staff of withering; it is here transformed into the rod of withering, whose effect is to inflict 1d4 Strength and Constitution damage on the target (may be temporary or permanent, depending on a saving throw). Similarly, Ghosts (now a "template" to be added to other monsters) also have their aging effect removed, replaced by straight points of ability-score damage from a suite of a half-dozen different special attacks. High-level Druids still get their immune-to-aging ability (at 15th level, here referenced as "Timeless Body"), and for the first time, Monks also get the identical ability (at 17th level). This latter addition seems new to 3E; 1E Monks did not have such an ability, and Monks did not appear at all in the 2E core rules (perhaps the addition appeared in some supplement of that era?).

D&D 5th Edition (2014)

Looking through the 5E SRD and Basic Rulebook, I can't find any general rule for aging. Druids and Monks still maintain the "Timeless Body" ability, somewhat downgraded, so perhaps such a rule for the effect of aging does exist (see here). The staff of withering now only does straight hit point damage, with a temporary penalty to ability checks (link).

Let's wash our hands of that and look at the "side branch" of the D&D Basic line through the 1980's (you might want to look back at the OD&D rule off of which this branched):

D&D Expert Rules (1981)

To my knowledge, there are no general rules for aging characters in the Cook/Moldvay rules. The staff of withering is modified to say this:

Staff of Withering: A hit from this item will age the victim 10 years. The effect of old age will be fatal to animals and to most character classes, but elves may ignore the effect up to 200 years of aging. Dwarves may also ignore the first 50 years of aging. This item does not affect the undead.

It seems like the DM still has to adjudicate what counts as "old age", and then declare the victim as killed outright at that point? Harsh, Zeb!

D&D BXCMI (1983)

Frank Mentzer's rules do introduce aging into the D&D Basic line for the first time, but is considerably stripped down. The general rule in the Companion rules only sets a maximum age for characters at which they die, with no age-bracket gradations or modifiers for advancement (DM's Companion, p. 21). Ghosts (and related "haunts") are introduced in this book, and as in 1E AD&D, their strike ages victims 10-40 years; here, unlike the section for the general rule, each 10 years is further said to drain 1 point of Constitution (p. 33). In Mentzer's Expert set, the staff of withering has almost identical language to the Cook Expert rules, except for a rephrased second sentence: "One or two hits will be fatal to most animals and harmful to many humans." (This could be either more or less harsh than per Cook, still requiring DM adjudication.) All of these edits were maintained in the later Allston Rules Cyclopedia (1991).

And one more interesting "tributary" which we could have easily overlooked:

Dragon Magazine (1980)

I keep returning to Gygax's writeup of Robert E. Howard's Conan in Dragon Magazine #36 (April 1980), within the year following the publication of the AD&D Dungeon Master's Guide. In this article Conan is given more detail than any other published D&D character before or since -- in particular, because different profiles were given for Conan at eight different ages of his story. He is also given a very long list of special abilities, skills, and proficiencies; recall that this later became the template for Gygax's Barbarian class description (later published in Dragon and then Unearthed Arcana). Here's the key table from the original Conan article (reposted from the last time I discussed it):

A couple things from this writeup: First, as usual, Gygax freely breaks his own rules on aging published just a few months before; Conan's ability scores vaguely follow the same trend as in the DMG, but the numbers are quite different (more variation in the upward direction in the case of Conan). Secondly, he applies an additional mechanic: Conan gradually loses Fighter and Thief levels as age advances. This is done at the rate of about 1 lost Fighter level per 2 years, and 1 lost Thief level every 5 years, after the category of Middle Age is reached (40+). I find this to be a commendable idea, and the result seems quite satisfying. Gygax writes in the article text:

The drop-off in level in later years is meant to reflect the effects of advancing age, and while hit points might drop off more, skill level would not drop below 9th level—say until 100 years of age, perhaps, and possibly not even then.

An intriguing suggestion!

 

Lankhmar – City of Adventure (1985)

It was later pointed out to me that the writeups for Fafhrd & the Gray Mouser in Lankhmar: City of Adventure (by Nesmith, Niles, and Rolston) use the same mechanic as Gygax showed for Conan, in presenting statistics for the heroes at different ages -- in which levels are low in youth, go up to a peak, and then degrade at older age. This is the only other time I've seen this implemented in official D&D publications. We see the following:

Note that both the pair's levels in Fighter and Thief (and Bard) rise and later degrade, but the Gray Mouser's levels in Magic-User do not degrade (or change in any way) at later stages. This seems to echo the idiom throughout editions that physical abilities diminish, but mental capacities increase with age.

Conclusions

In mainline AD&D, the tradition from Gygax in 1E on was to apply some modifiers to ability scores due to advancing age, but to leave the PC in question otherwise unchanged (with 3E removing the special aging effects from certain monsters and magic items). In the D&D Basic line, things were a little more gentle, with a maximum age established by Mentzer, but no other general rule for effects from the aging. Gygax's take on Conan, with both ability-scores and energy levels lost due to advancing age, might be the most compelling mechanic, but it was not used again in any other published D&D product, aside from the Lankhmar book.

Finally, a summary of the various ability modifiers found in different sources (summed cumulatively over all age categories):

Super Saturday: Alternate Universal Tables

One thing that's always bothered me is how the Marvel Super Heroes Role-Playing Game (FASERIP) has significantly more detail in the space of ability scores from 10-50 than outside that range, creating a "flat spot" there if you make a graph of it. I've suggested a few fixes for that in the past. In addition, I'm always on the lookout for some way to easily convert Marvel Wiki Power Grids to the FASERIP system. But: Any such fix to the FASERIP ability scores would require a new Universal Table, of course.

Here's one option, one that I would be likely to use these days, based on a very simple 1-2-5 series progression (a "Basic" table, if you will). This actually gives exactly 7 ranks from Feeble to Unearthly, the same granularity as Marvel Wiki Power Grids, so in theory you could convert them directly to the fixed ranks as given. (With one caveat: on the Marvel Wiki, "2" indicates "Typical", so we might have to offset it by one place.)

Alternatively, if you want more granularity (an "Advanced" table), you could use the Renard R5-series (ISO 3), which is actually a better match for the "flat spot" from Good to Amazing, although it also introduces new ranks above and below for consistency -- like Anemic (3) on the low end, and Shift H ("Shift Eta", 600) on the high end. In this case if you were looking at the Marvel Wiki Power Grids, a score of 1 would be Feeble/Anemic, 2 would be Poor/Typical, 3 Good/Excellent, and 4-7 would respectively be Remarkable, Incredible, Amazing, and Unearthly (as an initial approximation).

Which looks better to you?

The Marshal: Utility for Units of Men

In Original D&D, most of the monster listings in Vol-2 are only a single, short paragraph long. But there are two obvious, far more complex outliers that run several pages each: one is Dragons (running about 3½ pages), and the other, the very first monster listed, is Men (spanning about 2½ pages). In each case, part of the complication is that there many sub-types to choose from (for Dragons: the different colors and ages; for Men: various vocations and terrain-types), and each of them also have numerous sub-categorizations, with many details to work out. We dealt with an assessment for Dragons here last week. But personally, I find that one of most complicated things I can be called upon to handle as DM is a spur-of-the-moment, random encounter with a group of Men in the wilderness -- with figures numbering in the hundreds, several different units types, and possibly a dozen or more high-level NPC leaders.

So here's a computer utility to make the generation of groups of D&D Men a bit more manageable, which I call the Marshal. It's written as a Java program which you run on the command-line (and hence should work on any computing platform where you've got Java). Just ask it for a particular unit type of Men, and it outputs the listing for all the various soldier units (footmen, archers, cavalry, etc.), as well as all the high-level Fighter leaders in complete detail (including abilities, hit points, magic arms and armor, and compiled combat statistics).

Here's why this is a bit different from similar tools you've probably seen before: All of the NPC leaders have the entirety of their active careers actually played out in a simulation. This was motivated by the prior Arena project, as noted in the last blog post; we take a group of Men of the indicated size, insert them into the Arena and have them fight a whole career's worth of gladiatorial matches, simply reporting the top performers at the end. The Marshal'd NPCs aren't simply blank slates; they all actually started as 0-level normal men, with abilities rolled 3d6 in order, and had to battle their way to the top, one fight at a time. Those who were lucky in terms of ability scores, hit dice, match selections, and magic arms acquisition, rise to the top. As an example of Darwinian natural selection, the leaders will tend to have higher ability scores, hit points, and magical equipment -- without any arbitrary munging or guesswork by the DM. I find this to produce far more organic and believable results; in theory, we could name and identify every individual man our leaders ever crossed swords with to gain their current positions.

Here's how you can get and run the Marshal: (1) See the bottom of this post. (2) Download and unzip the first file, Marshal.zip into a location of your choosing (this includes the executable Marshal.jar and required data files). (3) Open a command prompt in this location and type java -jar Marshal.jar bandits (or whatever type of Men you need). It will simulate the careers of all the soldiers and leaders involved, and write the results to standard output. Then you can pipe or copy this output to a document of your choosing and easily compile your own "Rogues Gallery" for use at the table (or else keep the program itself handy on a laptop or tablet and run it live during play). Here's an example of the output:

---

D:\Prog\Java\Arena>java -jar Marshal.jar brigands

Brigands, Chaotic, 110 Total

- 60 Light Foot (AC 6, MV 12, HD 1)
- 20 Short Bow (AC 7, MV 12, HD 1)
- 20 Light Horse (AC 6, MV 24, HD 1)
- 10 Medium Horse (AC 4, MV 18, HD 1)

Walther, Human Ftr8 (AC 0, MV 6, HD 8, hp 53, Atk Sword +9 (1d8+1); Str 14, Int 14, Wis 7, Dex 7, Con 17, Cha 10; Plate +1, Shield +2, Sword, Dagger)

Falco, Human Ftr7 (AC 0, MV 6, HD 7, hp 47, Atk Two-handed sword +8 (1d10+1); Str 13, Int 15, Wis 13, Dex 17, Con 13, Cha 15; Plate +1, Two-handed sword, Hammer)

Hugo, Human Ftr5 (AC 0, MV 6, HD 5, hp 27, Atk Morning star +6 (1d8+1); Str 13, Int 13, Wis 10, Dex 16, Con 11, Cha 12; Plate, Shield, Morning star, Dagger)

Friedhelm, Human Ftr4 (AC -2, MV 6, HD 4, hp 15, Atk Morning star +4 (1d8); Str 9, Int 13, Wis 10, Dex 16, Con 13, Cha 10; Plate +1, Shield +1, Morning star, Dagger)

Johannes, Human Ftr4 (AC 3, MV 6, HD 4, hp 27, Atk Halberd +5 (1d10+1); Str 13, Int 14, Wis 11, Dex 10, Con 16, Cha 9; Plate, Halberd, Spear)

Notes: Leaders on heavy barded horses; morale +1.

---

I've tried to keep the output as brief as possible, to make it immediately readable and playable in a live game (granted that there's already so many moving parts, and these groups of Men are likely to show up by random rolls without any advance preparation by the DM). Keeping that in mind, here are some things that it simplifies or won't do (yet):

• The various heterogeneous-composition units (e.g., light foot, short bow, etc.) are rounded to blocks of 10 for readability and possible utility in a 1:10 scale mass wargame. For very small groups, some of the heavier unit types may not appear (see previously here). 
• You are guaranteed to get at least as many leaders of the top level as dictated in the OD&D text. Levels below that may not perfectly match up with the official rules, because of natural variation in the Arena simulator. For example: By the Vol-2 rules, the group of Brigands above should have one leader of 8th-9th level (which they do), two fighters of 5th-6th level (where they got one 5th and one 7th), and three fighters of 4th level (where in this case they only have two). Personally, I prefer this bit of organic variation and unpredictability; but as you can see, the results are naturally very close to the book rule anyway. 
• These fighters all have one 8-sided hit die per level up to 9th, and then add +3 hit points for any levels after that (which you're pretty unlikely to see here). So, the output is fundamentally compatible with Original D&D (using Sup-I for hits), or any of the Basic D&D line (like Moldvay/Cook B/X, Mentzer BXCMI, Allston Rules Cyclopedia, etc.)
• The only magic items included are those with a straight bonus-to-hit. I think this makes it easier to use at a glance, and were the only indicated items for Fighters which would make any difference in the career-simulator, anyway. If you want to go through and add more exotic types (like: intelligent swords, etc.), you can roll for that manually. The items shown were developed by rolling a 5% chance at each level-up to get an added point on any piece of equipment.
• Armor will be fixed for a particular type of Men (e.g., plate for Bandit leaders, chain for Nomads, etc.); primary melee weapons are randomized among the obvious options (which I wanted for some variety); while missile weapons are not included (which I usually find are not important for leaders anyway). Technically, the OD&D rules specify that leaders of Men will only have magic "Armor, Shield, Sword". If you want to enforce that last stricture, use the switch -s on the command line, and then everyone will be armed with Swords.
• Spellcasters, who have a chance of occasionally showing up for groups of size 200+, are outside the scope of this program, as they really don't fit into the model of simulating careers through man-to-man martial combat (also, they tend to be more variable by campaign in terms of identity, spell list, etc.; and are really quite rare in any case). You'll have to roll those members on your own, or make use of a separate single-character simulator (one possibility is here, although it doesn't naturally produce higher ability scores).
• Boats for the Buccaneers and Pirates are also not specified. Personally, I go through and select  a Longship or Sailed Warship for about every 75 Men, assigning the top leaders as the captain of each.

And more command-line options to consider:

• If you know how many Men you want in advance, just append that to the command, for example: java -jar Marshal.jar cavemen 50 gives you exactly 50 Cavemen. This also allows you to generate higher-than-normal group sizes (beyond the normal range of 30-300), although it might take a while to generate all the leaders, and as a side-effect some may come out at a higher level (I've seen 10th-14th level on occasion doing this).
• If you want to include my OED House Rule Fighter Feats, then the command switch -f will add one every 4 levels (first published in Fight On #9, and detailed here; includes things like exceptional Strength, Weapon Specialization, Two-Weapon-Fighting, Tracking, multiple attacks, etc.).
• If you want to force all the leaders strictly to have swords as in the Vol-2 text, then the switch -s does that (as noted above). 
• If instead of the default XP-award rule in OD&D Vol-1 (100 XP per hit die), you want to use the alternate XP table from Sup-I/BX (included in data file XPTable.csv), then the switch -x does that. You're unlikely to see much difference from that in this program (maybe marginally longer to generate the leaders).

Also, a Java source code archive and documentation are available if you want to dig into that (normal users can just ignore everything except the first link below). Hope this adds to your game, enjoy!

• Marshal executable package (ZIP)
• Marshal source code archive (GPL license)
• Marshal Java code documentation

A Frightful Simulator Symmetry

Let's say you take our Arena simulator (see previous posts here), and run the most generic model possible. Generate 10,000 men of 0-level, ability scores 3d6-across-the-board, dress them in plate, shield, and sword, and then pair them off to fight. Award XP according to the simple Vol-1 system (i.e., 100 XP for a 1 HD enemy; with a ×4 multiplier for presumed treasure awards), and if they level up, apply a 5% chance that any of their equipment gets a magic boost by 1 pip. Refill the list with new recruits and repeat, say, 500 times. Here's the level distribution that results from that simulation:

But consider the leaders specified for groups of Men in OD&D Vol-2; recall that it asserts for Bandits and likewise all other types of Men:

BANDITS: Although Bandits are normal men, they will have leaders who are supernormal fighters, magical types or clerical types. For every 30 bandits there will be one 4th level Fighting-Man; for every 50 bandits there will be in addition one 5th or 6th level fighter (die 1-3 = 5th level, die 4-6 = 6th level); for every 100 bandits there will be in addition one 8th or 9th level fighter (die 1-3 = 8th, die 4-6 = 9th).

So, 4th level fighters appear in a ratio of 1/30 = 0.03; 5th-6th level fighters in the ratio 1/50 = 0.02; and 8th-9th level fighters in the ratio 1/100 = 0.01. Let's compare that to the numbers that fall out of our Arena simulator above:

At the first step and the last step, the results match surprisingly, almost supernaturally, well. At the middle step the simulator asserts there should be about twice as many 5th-6th level fighters combined, as compared to the book rule. But nonetheless the book ratios constitute a basically reasonable distribution, and our simulator generates roundly the same kind of population. (Remember that this is not the same as the population of adventurers exploring underworld dungeons, which is exponentially more dangerous.)

This, then, motivates the development of another software tool that you'll see here on Monday.

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!

• MonsterMetrics (Java ZIP package)
• MonsterMetrics Source Code (GPL license)
• MonsterMetrics Java Documentation
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Monster Details

Two tidbits in relation to Monday's post:

Dragon Breath

Here's my thinking about figuring out how many people get hit by dragon breath in an abstracted combat. The first thing I thought of was: what percent of an arc around a dragon can its cone-shaped breath hit? For red dragons, the fire is a cone 9" by 3" in size. Here's a slice of half that area:

Since this half-area is a right triangle, it's easy to figure out the angle involved: about 9.5 degrees -- so the whole red-dragon cone is about 19 degrees, say 20 degrees for convenience sake. So that means if the red dragon was pivoting its head outward like a random turret it would only cover 1/18 of the surrounding disc, or 1/18 of an opposing party, at a time. That seemed far too little, so I looked for another approach.

The idea I thought then, was this; a smart party would want to spread out as much as possible on the dragon, but the dragon's body is long, so effectively you'll have half of the fighters on one side, and half lined up on the other side (optimally to the attacker's view). Assume the dragon can crane it's neck around and shoot a blast just scraping one side of itself without hurting itself. We know from physical testing that a red dragon cone can hit up to 14 figures in a sparse formation (link). So the conclusion was to rule that a red dragon's breath can hit half of the opposing party, to a maximum of 14 figures. The same rule was used for gorgons and chimeras, with a little math on the smaller areas to give a different maximum figure number (7 for gorgons, 4 for chimera).

Giant Melee

Initially I was surprised by some of the result from Monday, by how few low-level fighters it took to match up against fairly high-level monsters. For example: The table says it only takes 4 1st-level fighters (in chain & shield with a sword and +1 bonus) to be evenly matched against a Hill Giant (with 8 hit dice and a double-damage attack). So as a double-check I sat down and manually scratched out a case study.

• Giant average damage/round: 7 × 0.65 = 4.55. This gives about a 50/50 chance of the giant killing a man per round; if the fighter's hit points are 4 or below he's dead, if hit points are above 4 (on d8) he lives another round. That is: expect to kill a man every other round.
• Fighters average damage/round: 5.5 × 0.35 = 1.925. Say on average that each fighter tags the giant for about 2 hit points each round.
• Giant average hit points are 3.5 × 8 =  28 (OD&D d6 dice, as always).

 Case 1: Giant kills no one with initial rock-throw. By melee round:

1. Giant kills 0; 4 fighters do 8 hp damage; giant at 20 hp.
2. Giant kills 1; 3 fighters do 6 hp; giant at 14 hp.
3. Giant kills 0; 3 fighters do 6 hp; giant at 8 hp.
4. Giant kills 1; 2 fighters do 4 hp; giant at 4 hp.
5. Giant kills 0; 2 fighters do 4 hp; giant dead, fighters win.

Case 2: Giant kills one man with initial rock-throw. By melee round:

1. Giant kills 0; 3 fighters do 6 hp damage; giant at 22 hp.
2. Giant kills 1; 2 fighters do 4 hp damage; giant at 18 hp.
3. Giant kills 0; 2 fighters do 4 hp damage; giant at 14 hp. 
4. Giant kills 1; 1 fighter does 2 hp damage; giant at 12 hp. 
5. Giant kills 0; 1 fighter does 2 hp damage; giant at 10 hp. 
6. Giant kills 1; 0 fighters left, giant wins.

You could interleave the 2nd case so that the fighters get initiative on the giant (attack first in each round); they still lose, although it's a closer match, the giant having only 4 hp at the end. But in short the result does check out; the giant-vs-four-veterans matchup has about a 50/50 chance of going either way, depending on whether the giant strikes with its initial rock attack or not.

More Monster Metrics, Pt. 3

Last time I posted a table of improved EHD values (link), which takes into account simulated battles between mass groups monsters and fighters across arbitrary levels. Here I'd like to focus on the monsters at the extreme limit of power levels in D&D, where in some places we have clarified our vision, and in others the model may break down a bit or open up other questions.

Single XP Bumps Predominant: The majority of D&D monsters assessed here have either one, or none, exceptional XP awards warranted. That is: almost no monsters are worth more than double their base HD value (the level at which I've indicated a Cook/Moldvay-style "asterisk" for an added XP increment). There are three exceptions: Medusae, Basilisks, and Vampires, which we'll discuss further below.

Big Brutes at Risk to Many Men: Some monsters which in the prior "point estimate" model had exceedingly high values are now seen to be surprisingly vulnerable to moderate-sized groups of normal men. For example: In the first version,the most dangerous creatures were Hydras and Purple Worms; the former was balanced against a single Fighter of up to 44th level (due to its many-headed attacks); and the latter was favored over any single Fighter of arbitrary level (due to its unavoidable Swallowing ability). Looking at the Party-based output, we see that these types are evenly matched by only 10 or 12 Fighters of the 1st level (with chain, shield, and +1 swords). And hence their EHD scores are now 18 and 33 -- not infinite, but rather at the more standard double-HD level.

The reason for this is clear; both these types have abilities in the "high-level killer" category (many attacks, and save-or-die-on-hits), that are not immensely useful against masses of lower-level men (no area attacks). Also, both of these "giant worm" types have pretty low ACs -- 5 and 6, equivalent to chain -- allowing pretty much anyone to reliably hit them. Note: This model doesn't even give the men extra attacks due to monster size. Even limited to the standard 6 melee attacks per round, 1st-level Fighters vs. chain (needing 14+ to hit, that is, 7/20 = 35% to hit) have an expected damage output of 6 × 0.35 × 5.5 = 11.55 points per round. That is, they'll probably be killing about 3 hit dice/heads per round, and even a 10 or 15 HD creature won't last more than 4 or 5 rounds on average.

On the one hand, we might consider this to be a letdown (even our biggest monsters are underdogs to groups of 10 or 20 normal men, say). But on the other hand, this gives us additional motivating material for our campaign world: abominations like these have good reason to remain lurking in the underworld -- they can't afford to appear in the open where organized groups of men can oppose them. Open terrain is strategically advantageous to large numbers of weaker creatures; while maze-y defenses are advantageous to less numerous, but individually more powerful monsters (think: "tank blocks the doorway"). This would be even more pronounced if ranged attacks were modeled, which they are not in this simulator.

Medusae and Basilisks: The Medusa is the only monster shown with two asterisks (HD 4 and EHD 13); and the Basilisk is the only monster with three (HD 6 and EHD 24). Why is that? Simple: They're the only monsters in the list with both low-level and high-level-killer abilities. They both start every combat with a Petrification gaze attack (assumed unavoidable here), and against low-level opponents, a great many of them will fail saving throws and be out of the fight. But if this fails and/or they confront higher-level opponents, then they can still melee with save-or-die effects on every hit, round-after-round (for the Medusa deadly poison; for the Basilisk petrification). This complementary nature of their deadly special abilities makes them two of only three cases where it's really justified to give an XP award for each ability separately.

Note that in the prior one-on-one assessment about a month ago I overlooked the fact that Basilisks in OD&D get petrification for both gaze and touch, which is maintained as the rule throughout the Basic D&D line (Holmes Basic, Cook Expert, Mentzer BX, and Allston Rules Cyclopedia). In the AD&D line, the touch petrification was stripped out, making the basilisk a much weaker opponent due to the removal of that single key word (1E, 2E, 3E, etc.). If I take out the touch ability for the Basilisk and run it through the system here, it gets measured at only EHD 10 -- that is, petrify-by-touch more than doubles its value, as compared to Basilisks with only gaze attacks, according to this model.

Vampire Terrors: So you may have observed that the highest-rated monster in the current evaluation (last in the list) is the Vampire, the only other monster with more than one asterisk -- base HD 8, EHD 36, more than 4 times difference (and so given an unprecedented 4 asterisks here). We've mentioned before that they have an almost comically large number of special abilities -- Flying, Magic-To-Hit, Energy Drain, Regeneration, Charming, Summoning, and Polymorph. If you look into my monster data file, the Vampire special abilities are more than twice as long as any other, literally scrolling off the width of the screen.

Some of these abilities aren't modeled at all in my simulator: like Flying and Polymorph. The Magic-To-Hit is a non-issue, too, because I assume that all Fighters at this level have at least a +1 magic sword (so as to prevent infinite-loop-combats in the simulator, basically). The Charm ability is put in play, but I assume that only works against a single opponent at the start of combat. Regeneration is always potent, of course (and yet something that one might forget about Vampires). Energy Drain of 2 levels is here adjudicated with no saving throw, and also punitively reducing current hit points by the same amount that are lost from max hit points in the level drain. Still, that's been found to not increase risk within a single fight by very much (the same ruling barely gives any benefit to Wights, Wraiths, or Spectres).

The power that really turbo-charges Vampires in this assessment is their Summoning ability -- something that could not be modeled in the prior version that did one-on-one combats only. And here we get into an adjudication debate, because the statistics for their summoned helpers, and how they function in combat, weren't even specified at all within Original D&D. The description for Vampires says simply: "Vampires can command help by calling to them from 10 to 100 rats or bats or from 3 to 18 wolves." Gygax in the AD&D Monster Manual specified that the former was for dungeon settings only, the latter for wilderness encounters. Cook in the D&D Expert rules gave additional options of 5-20 giant rats or 2-8 dire wolves (perhaps to make the fight easier to run?).

The assessment I've done here was run using only the 3-18 wolves option, with statistics taken from the Monster Manual: AC 7, MV 18, HD 2+2, Attacks 1 bite, Damage 1d6 (this is also in line with D&D Swords & Spells p. 18, even though OD&D Vol-2 parenthetically suggested only 1 HD for wolves on p. 20). Note that with an average of about 10 wolves summoned, this obviously accounts for about 2 × 10 = 20 Hit Dice worth of value. Adding this to the prior solo value for Vampires (15) gives 20 + 15 = 35, almost perfectly accounting for the change to EHD 36 seen here. The addition of 10 Wolves adds nearly a Hydra-level of extra attacks against any opponents -- and even better, serve to shield the Vampire from attacks, because of the DMG-style adjudication that melee combatants must roll for targets randomly. (Or on a tabletop with miniatures: the supra-intelligent Vampire should place the Wolves so as to surround, cut off, and block any opponents.)

It gets even worse if we think about what happens if the Vampire summons around 50 or so Rats to his cause in the dungeon. First, what kind of Rats are these? We have at least two pieces of evidence that they are normal, not giant rats; (1) Cook's separate listing for a smaller number of giant rats, and (2) Gygax's inclusion of ordinary rats in the Monster Manual II (in addition, we will see that the end result is frightening enough as-is with just the normal type). In that latter tome, EGG laid out ordinary rat statistics like this: AC 7, MV 15, HD ¼, Attacks 1 bite, Damage 1 point. If anything, I think that the HD listed is too high (1-2 hp, that is, as robust as one third of all normal men; but in our simulator it makes no difference, since all the Fighters do at least 2 points of damage on a hit anyway).

In this case, running the Vampire-With-Rats figure through the existing simulator outputs a result of EHD 47, almost 6 times the base HD value, worth about 5 asterisks of award points. But a few reasons we shouldn't trust this value: First and foremost, it seems less reasonable to say that ordinary rats can block attacks against the controlling Vampire (which occurs by default in the simulator). Certainly as DM I'd rule that a PC can wade through the mass of rats and attack (or shoot) the Vampire if one so wishes. Secondly, the simulator assumes that the entirety of the monster party must be cut down one at a time before the other side achieves victory; and I'd probably say that having come to blows and defeated the controlling Vampire first, the ordinary rats would all scurry away (not stay and fight to their individual deaths). But on the other hand: I would probably give more than the default 6 attacks per opponent to the rats in question; and having a whole bunch of rats swarming all over your whole PC party (magic-users and thieves included), scoring some points of damage every round, is itself pretty distressing. (If I adjust the code in the program so Fighters can direct all their attacks on the Vampire, and controlled animals scatter after his defeat, then Vampire-With-Rats drops back down to EHD 15, and Vampire-With-Wolves goes down to EHD 25; the difference being in the animals' individual damage output before the Vampire goes down.)


Does that level of danger from Medusae, Basilisks, and Vampires seem reasonable to you? Have you remembered to make the most of the Vampire's Summoning ability the last time you used one? (I know I probably didn't.)

Tombs Too Tough to Touch

For those upset that Gygax's classic Tomb of Horrors is too scary:

Credit to Erik Garland, via Facebook.