HelgaCon VIII – Vault of the Drow

HelgaCon, the annual mini-convention with my Boston-area friends, was held once again in early April. We rent a house by the seashore on off-season rates and play games all weekend. Actually, the event is now so busy that the house is full and we have overflow attendees staying at a nearby hotel. Pretty cool.

Frequently, this is actually the only time I run D&D games all year long. That's not ideal for someone who blogs weekly about the game, but I'm very grateful for some kind of opportunity to blow the rust off. To some extent, it allows me a greater chance to reflect deeply on the proceedings and how to improve things the next time I play; my house rules have been richly cultivated in the last few years in response.

It's been 6 years now that I've been running the G-D (Giants/Drow) series of adventures annually. Of course, this is Gygax's masterpiece, originally a sequence of tough high-level tournament adventures, the first to be published by TSR back in the day. Many would agree that they constitute the best D&D adventure series of all time -- I might even expand on that, and assert that all by themselves they justify the existence of the D&D game system, as a platform for experiencing this particular campaign. So here we conclude the cycle (I'm unlikely to run Q1 for a few reasons) with module D3, Vault of the Drow. In my opinion, it's the best of the series; Gygax at the pinnacle of his powers, with the richest expression of his gumbo of pulp fantasy a la Vance/Howard/Lieber/Moorcock, et. al., and pieces that only the gaming grandfather could have come up with. (I am not alone in this opinion.)

I've been running these games for a mix of players: some who started with Red Box D&D; younger players who are more familiar with things like Fate and Dread; and complete newcomers who have never used funny-shaped dice before. It's definitely my favorite way to play these days, and it's delightful to get to revisit these adventures through new eyes, as it were. This year I reached a new record number of registrations for the game, with a full table of 10 players ready to bring nemesis to the Drow. And they bring both quantity and quality; their play performance has been getting sharper each year, and they all come very organized and ready to support and reinforce each other (particularly brand-new players), and really bring some serious hurt on my monsters.

Each year,  I've been learning a little better how to fit these sprawling adventures into a tight 4-hour convention block -- and this year I think it finally "clicked". You really have to work on developing and preparing the major set-pieces, the "crown jewels" of the setting in question. For the D1-3 series it's actually pretty straightforward (I say now): each has two lead-in tunnel encounters (say: 1 hour each), and then a major terminal area at the end (estimate: 2 hours). One should almost certainly skip random encounters so as to not miss out on time in the major areas (although there is a loss in both resource-challenge, and texture to the milieu; for example, finding that the major tunnels are patrolled and maintained by Drow, while the secondary passages have more exotic monsters). The G1-3 modules are somewhat more highly coupled (being single sites), and a little trickier to know what to highlight. But one thing I found this year is that it's no bad thing to give lots of detail to earlier important areas, and if you have to improv later areas that you didn't expect players to reach, they don't mind at all.

So it's possible that this was the best game I've ever run in my life; after 30-odd years of kicking at D&D, I finally ran one game that really felt right. Spoilers, of course, follow.

The Proceedings

• Among their choices for approach tunnels, the party chose the trapped "garden path" (see also: back cover of the color version of the module). The lead invisible scout was detected, charmed, and drained of a level before the rest of the party could engage. But the party was immediately suspicious of the paradise-seeming cave, and using a sword of detect evil proved the case. Wregan the elf hid in the "trees" only to find the illusion disappear around him and instead be was covered with a wave of giant rats. Melee between party, demon, vampire, and waves of bats was fast and furious. The bats and rats were fireballed, the monsters were put down, the temporarily defeated vampire turned to gas a drifted out of sight, and the party moved to put as much distance between him and them as possible.
• Entering the Vault proper, the adventurers first sent a flying wizard to scout the tops of the cliffs on either side as a precaution. Finding nothing but fungus and crystal-strewn open tableland, they cast a sphere of invisibility which covered the entire party and marched down the road forward. Coming to a three-way fork, they took the upward path, coming to the Black Tower. 
• Using their magical stealth, a few of the group's strongest fighters and wizard scouted out the open gate to the tower. Finding a sizable group of Drow guards, the wizard Ezniak let loose an ice storm that filled the first guardroom, felling many of the lesser Drow. The chief jumped up to close and bar the door, but the party's magically giant-strengthened fighters, Boris and Hedron, charged forward one after the other, breaking open the door, smashing the table inside to splinters, and battling the High Bailiff to a standstill. More Drow poured down the stairs while other PCs ran into the tower until the whole first floor was a confused wall-to-wall melee. The main problem was the High Bailiff's extraordinary AC, defending with enchanted sword and dagger. The player of one of the pregenerated PC's, randomly named Atol Daggerbreaker, asked: "Can I try to break his dagger?"; to which the answer seemed like it had to be "yes". So with his warhammer he smashed the magic dagger, and then the sword, and then the High Bailiff finally got the beat-down. 
• Meanwhile outside, a more cautious Jurden the Red Wizard chose to levitate to the top of the tower, thinking it would be abandoned; however he appeared over the battlement right in line with a guard manning a ballista-sized crossbow. "I go down! Down!" cried the player. "Too late, he fires!" I said gleefully. My roll: a natural 1. Saving throw vs. fumble: failed. Result from the critical chart: entangled with weapon; so the bolt snagged the dark elf's belt and he was shot off the roof, Wilhem-screaming (link) to earth.
• Inside, a wall of fire up the tower stairs fried most of the remaining Drow guards. One was charmed and gave the party useful information about travel and customs in the Vault, and the way to the High Priestess of all Drow. A chest containing an invaluable set of green cloaks were procured, which would thereafter allow travel in the Vault with being accosted by Drow patrols; and also a set of weird eye-cusps, and a letter of passage from some entity named "Eclavdra". The wizard Zaki Azeem chose the opportunity to cast animate dead on the fallen dark elves, raising ten zombies under his command, which were also outfit with green cloaks. So enlarged, the group moved on from the tower into the larger expanse of the Vault.
• Here I described the party's further travel in the Vault, entering into the debauched city of Erenhei-Cinlu, and the disturbing practices of the people therein. The group was allowed over the flying bridge to the plateau of the noble families, and directly passed on to the very Egg of Lolth. (This was a sequence which I intentionally planned to accelerate, but I think I gave just enough narration to get an overall sense of the setting; all random encounters and even the Lesser Temple were skipped.)
• The party entered the terrifying, demon-carved, web-shrouded Great Fane of Lolth. On the first floor, the group marched directly through the foyer to the Great Temple Area. The figure of Lolth herself rose before them! So the party launched a vicious barrage of offensive magic: an ice storm, fireball, hold monster, and more (a total of 68 points of damage), all to seeming no effect! (Or was she held?) Fighters slashed, and the party wizard cast fly, spiraling up around her to investigate. (Eerily,  the players perfectly recreated the Jeff Dee illustration of the scene.) Once the ruse was discovered, the dwarven fighter/thief Bellinus noted the weird mural in the rear, but the rest of the party was cautious, and chose to move in a different direction.
• The web-like stairs up were chosen: and the group was ambushed by a giant black widow spider the size of a small horse. Boris was bitten but made his saving throw against the extra-deadly poison, and then with the rest of the party's help he slew the creature.
• On the second level, four Drow guardswomen surprised the party and let loose poisoned bolts. The PCs responded smartly with Ezniak using a ring of human control to charm the whole group, ending the combat, and forcing their agreement to lead the way upward to the High Priestess.
• Up another three levels to the topmost floor of the temple's pagoda. But the High Priestess was warned by a secret alarm, and an opening flame strike instantly fried all the charmed Drow and the zombie troop leading the way. With the priestess casting spells from an unseen location (through a high peephole on the wall), the PCs pushed into luxurious lounge area with jewel-studded spider-tapestries. A word of power and the tapestries transformed into another 8 gargantuan spiders, scuttling forth with more murderous venom! Fighters struck and dodged, Atol tried to smash through the very wall with his hammer to get at their tormentor, and a few spiders were hemmed in with a wall of fire and magic missiles. Then the infamous Zaki Azeem declared that he was dropping a cloudkill to cover the whole room. The whole table groaned, thinking they'd died to friendly fire, and I turned to the Book of Spells thinking the same thing. But it turned out this was a brilliant ploy; all of the party was too high-level to be affected, while the giant spiders all died to the poison gas. Brilliant. (And the same would be true in any standard edition of the game.)
• Then the High Priestess used her sinister demon staff to conjure a Vrock demon on the party! The response in this case was: a suggestion spell to "protect us". I tried to find some loophole on why this wouldn't work on a demon, but couldn't find any (nor could I after the fact) -- failing both magic resistance and saving throw, the demon stood rooted to the spot, neither attacking for the PCs nor hindering them. The crew then bashed down the High Priestess' inner door and engaged her in melee. She fought back with blindness spells and a magical +5 mace; only a few members of the party could make contact with her back to a corner, and with her AC of -9 (!) the party was almost entirely unable to land blows -- it looked like she might alone turn the tide against them. And then Jurdan nailed her with a feeblemind spell, and failing her saves she was reduced to a drooling incompetent. The players all cheered lustily and finished her off en masse.
• The party gathered what treasure they could from the queenly riches around them. The secondary priestess was met running up the stairs, and another charm spell turned her too to the party's side. Inquiring as to a way to escape the Fane (one of the victory conditions I'd set for the group), she revealed the hidden tunnel far below in the cellar. Leading them there, the group quickly worked its way back down the stair, along the hidden tunnel, and into the wharf cavern with underground-river going galleys, scores of ghoul and ghast sailors, and much-needed stacks of supplies. One galley was loaded up, and the party sailed off into the darkness on a demon-headed ship surrounded by Drow priestesses and slavering ghouls. 

Findings

• As noted above, choosing to spend preparation time on selected highlights of the adventure really paid off. (And note that Gygax adventures are generally pretty open-ended with demands for DM expansions, with D3 surely the pinnacle of those.) I created illustrations of the outside of the Black Tower and the Great Fane which set the scenes well (above); and also floor maps of the inside of the Black Tower, thinking that was a likely necessary battle to have (in fact, the module text comes close to fully describing the layout; was there a map that was cut for space?). I skipped all random encounters which turned out to be the right thing to do. Based on prior games (which were always short on time), I really did not expect the group to make it all the way to the High Priestess of the Fane, so at that point I was flipping through the book in an ad-hoc fashion trying to interpret her defenses there. The players actually took great joy in my discomfort when I blurted out this fact. (But possibly on a future run I might plan that final encounter out a bit more.)
• Module D3 has some of Gygax's most fantastic descriptive text, but it is tangled up with rules information and material the players should not know -- recall that this is before the invention of "boxed text" which would set the scene for players as they enter a new area. Again, concentrating on the highlight areas, I drafted a page of my own effective "boxed text" for the outer encounter areas: the Garden Path, the Vault, the Black Tower, and the entry to the Egg of Lolth. I surely wouldn't do it for every room, but being able to edit out the essence of Gygax's flowery descriptions, and setting each encounter zone by sharing most of his words with the players, felt right. I think it would be a shame to play through D3 and not get to encounter his descriptive language here. 
• In particular, Paul S. noted after using the "weird cinnabar eye cusps" to see clearly in the Vault, and thus viewing its "true splendor... [as] a dark fairyland", how reminiscent this was of the mystical lenses in Jack Vance's story of Cugel the Clever, "Eyes of the Overworld" (link). Asked Paul, "Is what I'm seeing now the real thing, or just a fraudulent illusion? That's creepy!". It's one of those great observations that I smacked my head for being blind to in advance (no pun intended), and wish I'd thought to play up ahead of time.
• Nowadays I am ready to use miniatures in the game, almost only if the players request it for clarity. (This happened in another game last year and it worked out pretty well.) I actually created and brought simple scale battlemaps of the first floor of the Black Tower, and also the "Gatehouse" encounter (outer hex Q²49), but neither of them were used. 
• A lot of Gygax's creations from this era of Advanced D&D have an overwhelming number of special abilities (Drow, Demons, Kuo-Toa, etc.; their descriptions run several pages each) that even I can't keep track of during fast-paced play. So I make the decision to streamline those, too, and try to pick around 3, at most 5, abilities to highlight during play. A few of the Drow minor abilities get snipped out as I do this, but this too feels like a correct decision.
• A possibly more legalistic issue to Drow powers is that if you play them by strict AD&D rules, then they would inherit the powers from other elves in the Player's Handbook; in particular, 90% resistance to sleep and charm spells. But that resistance doesn't show up anywhere in the OD&D rules that I'm using (even Supplement-I, Greyhawk), and so that's a power that the Drow here do not have. The players in my game relied quite heavily in more than one place for charm spells against certain Drow, to gain information and guidance; whereas technically as published that would likely not be possible. Truthfully, I didn't mind either the pacing pickup or reduction in wall-of-powers to track. But was the AD&D elf resistance to charm specifically an invention to prevent this stratagem in D1-3? Also, it's fortunate for the players in this regard that the description for Drow says they know the "common tongue", in addition to various underground races (and honestly I didn't even think to consider any language barrier for them during play).
• On the other hand, all Drow did have both boosted saving throws and magic resistance being checked -- and yet they seemed to routinely fail both every time I checked them. Generally the players in this game had great rolls working in their favor (making almost all their saves), and terrible rolls on the part of my monsters (failing almost all their saves and resistance checks). So certainly that was a helping hand on this particular mission.
• My Book of Spells finally feels "right". Everything that happens with magical effects feels correct, efficient, quick, and necessary; never skewed or irritating to the proceedings.
• Keep in mind that at high levels, long-lasting invisibility is both very powerful and widely available (via spells, rings, cloaks, invisibility spheres, etc.). Part of my preparations for high-level is to always consider the interaction of invisible scouts into each area and whether and how they might be discovered, etc. (among the first details in any area description; see back in my D1 game when I was caught flat-footed at the need for that).
• My expectation was that this would be final appearance of this group of pregenerated PCs and this campaign sequence, and I wouldn't mind ending on a high note in this way (there was a heartwarming round of applause from the players at the end of the game). But at the end there was more than one request to continuing playing with them somehow. One inquiry was to actually go back and re-play module G3 from a few years ago (link): that's probably the most physically brutal adventure in the series, and the players were short-handed, so they got mercilessly pasted in that adventure. Another possibility, I think, is to start expanding to other locations in Gygax's underworld; as the PC's ended sailing on the waters of the Pitchy Flow, it seems like a pretty clear opening to adventures in the realms of the Mind Flayers, Kuo-Toa, Sunless Sea, etc. But that's the end of the Gygax-penned adventures for now!

Dungeons & Demographics, Pt. 3

In the last installment, we noted that OD&D text descriptions for leader distributions (read: NPC levels) are totally different than what emerges from a simulation of actually playing out games against the dungeon encounter tables (read: PC levels). But: We did see that if we alter rolls on the OD&D encounter tables in the simulation to the reduced level of 1d6-4, then we do get a population that is passingly similar to the described NPC distribution. Here I'd like to use those simulations to come up with an evidence-based system for generating high-level character ability scores and hit points.

One important thing I noticed in an earlier, partial analysis of ability scores and hit points (link) is that these improved high-level distributions are still bell-shaped. That is: You would not want to use a method like "roll d6's, minimum 3", because that causes a pileup of scores on the low end (e.g.: 3), which is to say, generates a right-skewed distribution. (For example, the "minimum score" method that Gygax uses for hit points in AD&D Unearthed Arcana, p. 74, is contra-indicated.) 

What I came up for a simple dice-rolling method for such heightened, generally bell-shaped scores is to roll two dice of some type and add a fixed bonus, such that the maximum result is still 18. Consider these dice to be our toolset for this purpose: 3d6 (Expected value 10.5), 2d6+6 (E = 13), 2d4+10 (E = 15), and 2d3+12 (E = 16). Now we look at the average scores for our population generated by the Arena program (with an encounter roll modifier of -4), and try to find the best fit at each level:

I've batched up the levels into groups of about 3 at a time for convenience. At higher levels, the picture is pretty clear; scores in each of Strength, Dexterity, and Constitution trend upward as only the fittest characters survive to higher levels, as we would expect. In the 2nd-4th level tier, characters have an average of 13 across each of these abilities, arguing for a roll of 2d6+6 in three abilities of the player's choice. For levels 5th-7th, it looks like one ability is about 15 (2d4+10), and the two others 13 (2d6+6). For levels of 8th and above you have at least two scores at 15; in this case I'll take a bit of artistic license and use one 2d3+12, one 2d4+10, and two 2d6+6 scores. Not too bad.

But now let's focus on the slightly troublesome 1st level. Whereas the 0-level clearly depicts the straight 3d6-roll for newly generated normal men (average about 10.5), characters surviving to 1st level do evidence about a 1-point advantage across each of Strength, Dexterity and Constitution (average about 11.5). The problem is, using the dice "tools" above, none of the abilities quite reach halfway to the 2d6+6 roll method (mean of 10.5 and 13 = 11.75). But if we pool the overall improvement in all three scores, then we get a value a bit over 3 (3.2). So to reflect that basic trend, I'm going to give 1st-level characters in my games a boost of about 3 points by selecting one single ability -- likely their prime requisite -- and rolling 2d6+6. (This replaces my old house rule of rolling all 3d6 and then swapping two of the player's choice.)

In summary, here's my new evidence-based house rule for rolling ability scores:

• Level 0: Roll all abilities 3d6 in order. 
• Level 1: Roll one selected ability 2d6+6, others 3d6.
• Levels 2-4: Roll three selected abilities 2d6+6, others 3d6.
• Levels 5-7: Roll one ability 2d4+10, two 2d6+6, others 3d6.
• Levels 8+: Roll one 2d3+12, one 2d4+10, two 2d6+6, and two 3d6.

Hit Points: Note that in the table above, average hit points at each level are truncated, not rounded (average hit points at 0-level are really 3.5, at 1st level about 6.5, etc.) The best method to generate higher-level hit points is to simply re-roll any dice that come up 1 or 2. (Or equivalently: roll a die of one size less and add 2.) From a purely technically standpoint you wouldn't want to do this for the very last level (the character has not proven survivability through that level yet), but for practical purposes I don't want to split that hair in my house rules, nor have to remember about it.

Final Thoughts: While we've developed this system looking at the "NPC" population at the -4 encounter die level, the truth is, any other close modifier generates about the same ability scores and hit points upon surviving to higher levels. So I'm comfortable using this system for generating scores for both high-level PCs and NPCs. It's conceivable that future refinements of the Arena simulator program might change things here, but my expectation is that the method will remain pretty stable going into the future.

Dungeons & Demographics, Pt. 2

In the last installment, we noted that throughout all three volumes of OD&D, depictions of groups of men assert that there will be a leader of about Name level for every 100 or so normal men-at-arms. We can get fairly close to this distribution by a (surprisingly) simple divide-by-two method from each level, starting at 0-level, which is equivalent to an exponential function with a decay rate of about k = -ln(2) ≈ -0.70.

Now let's go back to our Arena simulator (link1, link2), which runs combats for a several thousand dueling fighters as per slightly smoothed-out classic D&D rules, and compare. For this investigation I've done a few things. One: I've modified the simulator to start the combatants at 0-level (Normal Man), with a 1,000-XP requirement to reach 1st (Veteran). Two: I'll only look at the Man-vs-Monster duels, following the Monster Determination and Level of Monster Matrix in OD&D Vol-3, p. 10. Three: I'll end the analysis at character level 9 (Lord), because after that point the XP charts switch to a linear progression, which would not be following the same regression function as the levels up to that point. With a constantly-refreshed population of 10,000 fighters, after 200 cycles of combat this is what we get:

That table tells a scary story! Practically no one survives past the 3rd level. In this case, one lucky soul is still alive at 8th level. But there are no characters of Name level or higher in this population. Only 1 in 20 of this population is above the 0-level. While the OD&D description for Men says that every 50th man is 4th or 5th level, there are no such lieutenants or subalterns in existence in this group.

Keep in mind that this simulation is actually more forgiving than by-the-book OD&D, because I didn't implement any special abilities: no monsters with poison, paralysis, petrification, spells, blood drain, energy drain, charming, hit only by magic, etc. If we had included those surely the death toll would be even higher. Also: There's no aging-out, so that 8th-level survivor might be effectively a hundred years old or more. Let's compare the two populations side-by-side: on the left, the text descriptions that I'll call the "OD&D NPC Demographics", and on the right, the output of the Arena combat simulation using Vol-3 monster encounters, which I'll call the "OD&D PC Demographics".

Major conclusion: These populations are not playing the same game. They're not even remotely close; it's hopeless to even think about harmonizing them as-is. While the NPC population has a regressed level decay rate of about k = -0.60, the PC survivors from the Vol-3 monster encounters have a decay rate of almost twice that, over k = -1.00. Obviously if the first population has about 1-in-100 Name level leaders, and the second has none, then they are essentially contradictory.

This is not tremendously unique news, because we've pointed out in the past that the OD&D Vol-3 wandering monster tables are really far too tough (1st level characters have a 1-in-6 chance per encounter of a 4th-level monster like wraiths, gargoyles, lycanthropes, etc.) All later editions toned down those tables -- especially Gygax in AD&D, who arguably made the tables in the DMG too easy.

How can we interpret this for D&D? Perhaps we can best assert that, whatever the exact encounter tables, our PC's are playing "the most dangerous game", a much riskier and more desperate gamble in the dungeons and wilderness, where they might quickly win fame and fortune, but is most likely to end in hideous death. On the other hand, we can propose that our NPCs are following some entirely distinct path: a slower and steadier progression in experience among the army legions, guild halls, and colleges of magic. This latter progression is not so likely to result in death, but characters of a given level are likely to be much older than PC's of the same level. PC's will be gaining levels in just a year or so that NPC's take an entire life's career to obtain. We are reminded of Gygax's note on experience from AD&D DMG p. 85:

Note:  Players who balk at equating gold pieces to experience points should be gently but firmly reminded that in a game certain compromises must be made. While it is more "realistic" for clerics to study holy writings, pray, chant, practice self-discipline, etc. to gain experience, it would not make a playable game roll along. Similarly, fighters should be exercising, riding, smiting pelts, tilting at the lists, and engaging in weapons practice of various sorts to gain real expertise (experience); magic-users should be deciphering old scrolls, searching  ancient  tomes,  experimenting alchemically, and  so  forth; while thieves should spend their off-hours honing their skills, "casing" various buildings, watching potential victims, and carefully planning their next "job". All very realistic but conducive to non-game boredom!

Now, let's think about exactly how how far we'd have to bend the encounter tables in Vol-3 to create a PC population that resembles the distribution of the NPC population. What I usually do here as a zero-degree house rule is to modify the d6 on those tables (which determine level of encounter) by some subtracted number (minimum 1 in all cases). For example: with a -1 modifier the 0- or 1st-level characters cannot ever run into 4th-level monsters, at least. This modification bottoms out at a level of -5, which is equivalent to simply always taking a roll of "1" on those tables. Let's re-run the Arena simulator, again with 0-level entrant to the Arena, for each of those modified levels:

The best fit to our NPC population is the "Mod -4" table (most but not all encounters being at the minimum level possible on those Vol-3 tables), with a decay rate of k = -0.58. We might say that this much safer game is equivalent to what the NPCs in our campaign world are playing at.

As I've said before, in my own games I do modify the rolls on those encounter tables downward in a fashion similar to this. On the one hand, I wouldn't actually use the -4 modifier; that's both too repetitive and doesn't honor the higher-variance game that the PC's have chosen. At the moment I'm splitting the difference in half: applying a -2 modifier to those encounter level rolls, and it's feeling about right. The encounters now only ever vary from the PC/dungeon level by a maximum of ±1 level; but on a 6-level monster level scale as in OD&D, that still covers half of all the monsters in the book.

Further research required: Propose a system for assessing the XP gains by NPC characters, who are pursuing safer and more "professional" advancement than the dungeon-delving PCs.

Next time: A comprehensive system for establishing high-level character ability scores.

Arena v1.05 Java Source Code (with 0-level support)

Dungeons & Demographics, Pt. 1

If we look at the Original D&D source material, and take up the many clues there that normal men are 0-level (even the standard men-at-arms, soldiers, brigands, pirates, etc.), then we also see several points of data as to the distribution of higher-level leaders and fighters.

In Vol-1, we see that when Clerics achieve the name level of Patriarch (8th) and build a stronghold, then they attract faithful soldiers numbering from 50-300 (p. 7):

In Vol-2, at the start of the lengthy entry for different types of Men, we read that groups of 100-300 such men will be led by an 8th or 9th level fighter, as well as numerous lower-level leaders (p. 5):

In Vol-3, in the section on the Wilderness and the various types of Castles to be encountered there, we are told that all of the castle rulers are either Name level or one less (so in the range of levels 8-11), and have from 30-180 normal men-at-arms, in addition to a small number of other heroes or monsters to assist them (p.16):

So the general commonality to all of these descriptions is this: any body of normal Men numbering at least a few hundred seem to have a Name level character leading them. The consistency of this proportion across passages in all the different booklets gives some confidence as to the sensibility meant to be taken in the stock OD&D campaign.

Now let's look more closely at the distribution given for Bandits (shared by all other types of Men), with its additional detail regarding the mid-level heroes and leaders (4th-6th level and so forth). If we wish to fit a regression curve to this data, then clearly the model to use is an exponential function of the form f(x) = a∙e^(kx), where our k will be negative and referred to as the "decay rate" (link). This will produce a proportional reduction at each level from whatever constant we start with for 0-level normal men. In theory, we could achieve a closer fit (less error) to our data via a power curve of form f(x) = a∙x^k (with negative k), but that has the unfortunate implication of an infinite number of normal men (that is, asymptotic at level 0), which is clearly not what we perceive for our campaign world. Note that we will only carry out this analysis to around name level, because after that point the X.P. charts switch from a geometric progression to linear, and so we could not expect to extrapolate the same function from one piece to the other.

Here we take a starting population of 10,000 normal men-at-arms and compute the expected number of 4th, 5th, 6th, 8th, and 9th level fighters as specified by the Vol-2 paragraph above, and then perform the regression to the best fit exponential function. (We could pick any other fixed number to start with, and it wouldn't change the output parameters in any way.) The result is the following:

That's a pretty close fit with the decay rate k = -0.60 (providing a coefficient of determination of R^2 = 0.89, that is, the regression accounts for 89% of the variation from the mean between the data points), but in trying to balance the large number of high-level data points, we've missed the starting point at 0-level by almost exactly half. Let's temporarily ignore the high-level leaders at level 8th and 9th and focus only on the initial dropoff at the data points up to the 6th level:

That's a much nicer fit; it comes very close to the first data point at level 0, and has an improved R^2 = 0.98, for nearly 100% agreement. This argues that taking a decay rate of around k = -0.80 will be a much better match, at least for the first few levels of our distribution.

Now, the funny thing to me is that this exponential fit comes close to simply halving the number of men at each level, from 0-level on up (a nearly trivial model that I've pooh-poohed in the past, looking at AD&D specifications). If you do divide the number of men by two at each level, that's precisely equivalent to an exponential function with a decay rate of k = -0.69, say -0.70 for convenience (more precisely: -ln(2)), or just halfway between the two analyses carried out above. Here's a table and comparative charts with which you can compare the two models:

 

Either of these models do about as good at fitting to the Vol-2 Bandits specification as we'll get. They are a bit high in the numbers specified at levels 4-6 (by about double), and a bit low in the numbers specified for levels 8-9 (by about half).

In conclusion: The sensibility expressed by Gygax for number and levels for leaders of groups of men in the OD&D campaign (in several different places) is surprisingly close to a simple divide-by-2 at each level method. We can fine-tune this with some other nearby exponential function, but the result will not be an order of magnitude difference. (Download an ODS spreadsheet for the work if you like: here.)

In Part 2, we'll compare these results to the distribution of characters (starting at level 0) who survive encounters with the Vol-3 "Monster Determination and Level of Monster Matrix".

Joe Nuttall's Blog

I just had the opportunity to discover Joe Nuttall's OSR-themed blog, "Explore: Beneath & Beyond". He just started it last month, but he posts on some novel rules alternatives that you may be interested in.  Plus he has a PhD in mathematics and investigates things like the distribution curves for his mechanics, so I'll be keeping an eye on it. A random sampling from his first few posts:

• Open Dice
• Height and Weight from Stats
• Roll for initiative! (initiative by in-contact subsets)

Compositions of Men

In Original D&D Vol-2, Monsters & Treasure, the first and most detailed monster description is for: Men. I find that running groups of men in the wilderness is potentially harrowing to manage, because each group comes in several different categories of composition (a certain percentage of footmen, some archers, some cavalry, etc.), as well as an array of different high-level leader types (each potentially with special abilities and unique magic items).

The number appearing for groups of Men is given as 30-300, which I think most of us generate by rolling 3d10×10. But technically this is contradicted by the example on p. 6:

Note that the number 183 is not a multiple of 10, so it could not actually be generated by the dice above. Did Gygax intend for us to be rolling 30d10 for this purpose? If so, then that would make for an extremely narrow distribution of values; 99% of the results would be between 125 and 205. (See Torben Mogensen's TROLL calculator here, with entry "sum 30d10": link). So let's assume that we don't literally take that approach. But the following paragraph may be even more troublesome:

Notice that the percentages given don't add up to 100% (40+25+25+20 = 110), so some fix is obviously necessary here. In AD&D, Gygax makes the composition percentages add up to 100% (MM p. 66), but in doing so he expands the number of distinct troop categories from 4 to 7, almost doubling the amount juggling that the DM has to do in these encounters (and he also increases the number of types of high-level leaders). Fortunately, if we batch up those AD&D types into superset categories, then we get the following: 50% Light Foot, 20% Archers, 20% Light Horse, and 10% Medium Horse; those numbers are workable as corrections to Vol-2, and they're conveniently all multiples of ten, so let's assume that we use them in OD&D.

One other sticking point remains when I seek to use groups of Men in my game. Even if you roll 3d10×10 (so the total number is a multiple of ten), and use those corrected and simplified percentages, the resulting categories are likely not multiples of ten. For example: 180 bandits would give 90 Light Foot, 36 Archers, 36 Light Horse, and 18 Medium Horse. Personally, I would prefer these cardinalities to also be multiples of ten, so as to make it easier to announce, manage, remember -- and switch to 1:10 mass warfare as in Book of War if that seems convenient. We could do this by rounding to the nearest ten, but then in some cases the total number would be different (for example: rounding and summing the example in this paragraph would give 190 bandits). So that then argues for hand-correcting the values, adding or subtracting some men in the higher-valued categories to always give the right total.

Below, I've done that for OD&D across all the types of Men indicated with sub-compositions there: Bandits (and Brigands), Buccaneers (and Pirates), and Nomads (Desert and Steppe). Of course, you could just note the percent corrections above and hand-tune any force to taste on the fly -- so in all probability you don't really want or need this as a separate handout. But I did it, so just in case you do, here it is (click here for PDF):

The Case for Level Zero

What evidence is there in classic version of D&D for the status level-0 characters? This could be important for a few reasons: (1) It would make a difference in the statistics for mass-combat armies, whether the basic troop type was level-0 or level-1 or something else; and (2) It could provide justification for common 1st-level boosts (as in ability scores or hit points), under the statistical survivability analysis that we've done via the Arena simulation program (link).

Original D&D

In Original D&D, 1st-level characters are distinguished from Normal Men in at least three ways.

1. Starting-level fighters are given the level title "Veteran", implying that some significant action had to take place prior to reaching the 0-XP level (Vol-1, p. 16).
2. Veterans are given Hit Dice of "1+1" (that is: 1d6+1; Vol-1, p. 17), whereas normal men such as Bandits, et. al., are given "Hit Dice: 1 die/man" (that is: 1d6 with no addition; Vol-2, p. 6). 
3. Veterans are also given fighting capability in the Chainmail-based system of "Man + 1", while normal men would presumably be simply "Man" (with no bonus; Vol-1, p. 17). 

That said, in the d20-based "Alternative Combat System" combat and saving throw tables, there is no distinction in abilities; a footnote reads, "Normal men equal 1st level fighters" (Vol-1, p. 19). But other than that, we see that even in the earliest work there was a clear distinction drawn between 1st-level fighters and other Normal Men (even those who appear in large armed groups, making a living via combat and raiding, with high-level leadership, as per the Vol-2 listing for Men such as bandits, brigands, pirates, etc.).

D&D Sup-I: Greyhawk

Here's a puzzle: what hit dice do Normal Men have under D&D Supplement-I, Greyhawk, using the alternate hit dice rule (p. 10: e.g, d8's for fighter levels)? The text says, "Use of this system is highly recommended, but if it is used all monsters should be based on the 8-sided die system." Does this include Normal Men, or merely every other being in the monster listing? If the former, then they are here equal to 1st-level fighters and unique compared to any other ruleset (see below); but if the latter then they have just become less strong than Orcs, for example.

Personally, I think this switch to d8-dice for monster hits was one of the major, early missteps in the evolution of D&D. So much simpler to roll batches of d6's for this purpose, and I see no compelling need for expert fighter dice to match monster dice. 

Swords & Spells

Gygax's Swords & Spells supplement for mass warfare in Original D&D appears to have the first actual use of the phrase "0 level". The combat tables for average damage per figure, unlike the OD&D core books, have a separate row for level "0", with the footnote: "0 Level is normal man-type (i.e., 1 die or less, and not able to progress upwards in levels.)" (p. 25). The two-page spread of weapon-based combat tables in Appendix A are in fact entirely based on Level 0 combatants (p. 31-32), with modifiers for other levels applied from a prior page (p. 27).

These rules include different "Troop Classifications" in six tiers: Peasants, Levies, Regulars, Elite, Guards, and the combination Elite Guards. The latter are quite rare: "As a rule, guards should be limited to 10% of an army, and elite guards would surround the personage of the commander only, for example" (p. 5). But the following all-italic paragraph establishes that any 1st-level fighters qualify for this special category: "NOTE: Scale figures representing human/humanoid (and highly intelligent) creatures of 1st level or above or with 1+1 hit dice are always considered as having elite guard status. For example, the following types of troops are classified as elite guard status: Veterans (1st level fighters), Elves, Hobgoblins..." (p. 6). This status gives bonuses to formation, movement, morale, and melee. So in summary: 1st level is shown to be something very special indeed.

Advanced D&D

In Gygax's AD&D, there are even more copious distinctions made between 1st-level characters and those less than that. The Player's Handbook states, "It is important to keep in mind that most humans and demi-humans are '0 level'." (p. 106). The Dungeon Master's Guide notes in the section on hiring mercenary soldiers, "Note that regular soldiers are 0 level men-at-arms with 4-7 hit points each" (p. 30: again highlighting that even trained career combatants are 0-level by default; see also class followers on p. 16). The combat and saving throw tables here give a separate, reduced column for level 0 fighters (p. 74, 79). A footnote reads, "Dwarves, elves and gnomes are never lower than 1st  level (unlike halflings and humans, which may be of 0 level)" (p. 74: possibly correcting PHB p. 106 above). A table on the campaign's "Typical Inhabitants" specifies combat ability of "0 level", or even as low as -1 to -3 from that mark for sedentary types, with hit points ranging from 1-3 to 2-7 (p. 88). Of peasant revolts it is noted, "Troops will be 0 level" (p. 94). For energy draining by undead, the stated rule is: "If this brings the character below 1st level of experience, then the individual is a 0 level person never capable of gaining experience again. If a 0 level individual is drained an energy level, he or she is dead (possibly to become an undead monster)" (p. 119). City and merchant guards are also 0 level (p. 191-192).

In the Monster Manual section on Men, the first thing stated is, "Normal men have from 1-6 hit points each." (p. 66), and this is reiterated in the following entries "Hit Dice: 1-6 hit points" for Bandits (Brigands), Buccaneers (Pirates), Dervishes (Nomads), Merchants, and Pilgrims. So in this regard the hit points are identical to those for Men in OD&D Vol-2 (actually downgraded for Dervishes), and it argues that the likely intent in OD&D Sup-I was also to maintain them at the level of 1d6 hits, less than 1st-level fighters or 1-hit-die monsters.

The DMG also has the following statement in the section on henchmen (p. 35):

Number of Prospective Henchmen: Human and half-orc characters suitable for level advancement are found at a ratio of 1 in 100. Other races have an incidence of 1 in 50. However, as most of these characters will be other than low level adventurers and already in a situation they are satisfied with  -  and humans more so than other races, unless the development of the area is primarily other than human - about 1 in 1,000 population will be interested in offers of employment as a henchman. NOTE: This figure must be adjusted by the DM according to the locale, for if  it  is an active adventuring area, the incidence of prospective henchmen might be as great as 1 in 200, while if it  is  a settled and staid area, incidence might be as low as 1 in 5,000.

Note the opening line, "Human and half-orc characters suitable for level advancement are found at a ratio of 1 in 100." If taken at face value, then this could have interesting demographic implications; however, it seems to broadly contradict the fact elsewhere that for about every 100 normal men, there is at least one leader of 8th-10th level, along with a host of other lower-level fighters (see Men: Bandits in the Monster Manual p. 66 and other places). And surely the claim that "Other races have an incidence of 1 in 50 [for level advancement]" is in even starker contrast with the footnote on DMG p. 74 that "Dwarves, elves and gnomes are never lower than 1st  level". So coming up with some synthesized interpretation for these different statements seems very challenging; they seem as though if coming from completely different campaign systems. And yet -- there is no doubt that level 0 men are the norm; the only question is what their relative frequency is (high or extremely high).

Unearthed Arcana

In the AD&D Unearthed Arcana work, Gygax implements a mechanic for gaining XP and advancing through 0-levels in two places: for the Cavalier and the Magic-User. For the former (p. 14):

A cavalier character must be of proper social class, and is usually of noble or aristocratic origin. Only those characters of Upper Class  social status may immediately enter into the cavalier class. Those of lower social standing are generally excluded from becoming cavaliers, but certain members of lower social classes may be so honored. Such a character must be sponsored by a higher authority  of  greater status, and begins first as a 0-level Horseman (a retainer for a Knight), then a 0-level Lancer, and finally becomes a 1st-level Armiger of the cavalier class. The 0-level Horseman starts at -1500  experience points and has 1d4 + 1 initial hit points. The Horseman becomes a Lancer at  -500 experience points and gains another d4 roll for cumulative hit points. The Lancer becomes a 1st-level cavalier at 0 experience points, and gains another d4 in hit points. In contrast, a character whose social standing qualifies him or her for immediate entrance into the cavalier class begins as a 1st-level Armiger with 1d10 + 3 hit points. The character’s hit-point bonus for high constitution (if applicable) is first received at either Horseman or Armiger level, and is then applied to each additional hit die from second level on as normal. The special abilities of the cavalier class are only gained when the character attains Armiger status.

These statistics appear likewise in the class table for cavaliers (p. 15). For the Magic-User, 0-levels are the mechanic by which one can use Cantrips even before the character can cast a 1st-level spell (p. 45):

Cantrips are the magic spells learned and used by apprentice magic-users and illusionists during their long, rigorous, and tedious training for the craft of magic-use. An aspiring magic-user or illusionist may use 1 cantrip per day as a 0-level neophyte (-2000 x.p. to -1001 x.p.), 2 cantrips per day as a 0-level initiate  (-1000  to -501), and 3 cantrips per day as a 0-level apprentice (-500 to -1). Cantrips must be memorized just as higher-level spells are.

So these below-zero-XP rules are broadly consistent in their application. In each case there are actually more than one 0-level in question (two for the cavalier; three for the magic-user). Somewhat oddly in my view, the increasing XP-per level is reversed for the 0-levels; the earliest levels actually require more XP, and the level closest to 0 the least (in both cases, just 500 XP to get to 1st level from the immediate predecessor).

(Side note: Post-Gygax, there was an AD&D-branded Greyhawk hardcover book with an appendix on running 0-level characters. However, those rules do not use standard XP, instead using a totally different AP point-buy system instead -- e.g., get an AP point and use it to boost an ability or buy a skill by one point -- and so we need not consider it further here.)

Holmes D&D

While the status of "0-level/normal men" is fairly consistent throughout all the Gygaxian works, the Basic D&D line veers off in another direction -- one which has caused a few mistakes and incorrect recollections on my part in the past. First, J. Eric Holmes started to dispose of them. Under "Non-Play Characters", he writes: "Generally, only the lowest level of character types can be hired, i.e. first level" (p. 8); that is, he seemed to collapse the distinction between 0-level hirelings and 1st-level henchmen in mainline D&D. Secondly, at the start of the monster list, he writes "Monsters' hit dice are 8-sided", and then three lines later in the lead-off Bandit entry, they get "Hit Dice: 1" (p. 22). So it's hard to read that in any way other than giving Bandits a full 1d8 hit points; a conceivable reading of Supplement-I Greyhawk (see above), but definitely at odds with the listing in the AD&D Monster Manual. On the other hand, the combat tables do include a row for "Normal Man" (p. 18) which didn't exist pre-Swords & Spells, but other than that I can't find reference or use of the term.

Edit: Zenopus Archives has pointed out on his site that in Holmes' original manuscript submitted to TSR, his combat and saving throw tables did not include any separate row for "Normal Man". Rather, they were inserted in an editorial pass by Gygax himself before publication of the final product. But apparently Gygax did not pick up on those more subtle areas where the concept was submerged (hirelings and hit dice). Thanks to Zenopus for that analysis (links: one, two).

Moldvay/Cook D&D

The Moldvay Basic and Cook Expert D&D rules take this a step further, by attempting to make almost every man in an adventure a member of some class. Now, Moldvay does state that, "A retainer may be of any level (0, 1, 2, 3, or higher) and of any class (normal man or a character class)" (p. B21), and he does include rows for "Normal Man" in the combat and save tables (p. B26-27). But that level is used mostly for minor non-human monsters (e.g., bats, rats, centipedes, insect swarms, goblins, kobolds, and mules). The Bandits which previously represented the canonical normal men are here declared to be "NPC thieves" who save as "Thief: 1" (p. B30); but while 1st-level thieves get 1d4 hit points, once again the monster entry simply says "Hit Dice: 1" -- which means 1d8 by the rules of the monster section -- so these seem out-of-joint. Also, a new monster type of "Noble" is given, and for these, "In the D&D BASIC rules, a noble will always be a 3rd level fighter. However, the DM may choose to make a noble any class and level... A noble will always be accompanied by a squire (a 2nd level fighter). A noble might also be accompanied by as many as 10 retainers or hirelings (usually 1st level fighters)" (p. B39-40).

Edit: Thanks to JB in the comments for noticing that I'd overlooked a dedicated monster entry for the unclassed "Normal Human" (p. B40); I missed this because it's the only place in this or any other ruleset where the descriptor is other than "Normal Man". The stat block gives them 1d4 hit points. The description says this: "Most humans are 'normal' humans, though people with certain professions (such as merchant, soldier, lord, scout, and so forth) help in some adventures"; my reading is that those "certain professions" are all classed by default (c.f., "Noble" above and all the soldiers in any B/X adventure). Finally, Moldvay gives a unique rule for advancement, far more generous than Gygax: "As soon as a human gets experience points through an adventure, that person must choose a character class."

In the Cook Expert rules, the only place the phrase "0 level" or "normal man" appears is in the matching combat/save tables, the rules for the legacy potions of heroism and control human, and the stats for seamen and the normal hawk. Mercenaries are not explicated one way or another (p. X22). However, in the catch-all monster entry for Men, they are all given a full 1 Hit Die and saves as "Fighter: 1"; including all of the types of Brigands, Buccaneers, Pirates, Dervishes, Merchants, and Nomads (p. X35) -- very much at variance with the OD&D and AD&D game lines. Likewise, all of the adventures in the X-series of modules specified base soldiers in any army as being universally at least 1st-level fighters: see modules X4, X5, the comprehensive army rosters for all of the Known World in module X10, and so forth.

Conclusions

While there is some attraction to the simplicity of the Cook/Moldvay method (all soldiers are at least 1st-level fighters), I do think that the core D&D system makes the most sense if we interpret things in the sense of OD&D/AD&D with a "0-level/normal man" class prior to 1st-level characters. This justifies 1st-level fighters having the title "Veteran", their improved attack/defense capability, the status that trainee wizards might have prior to casting their first spell, etc.

As usual, I frown upon special-case discontinuities such as that "0 Level is... not able to progress upwards in levels" (per Swords & Spells). In this sense, I look favorably upon Gygax's addition in Unearthed Arcana of some kind of rules for pre-1st-level experience progression. Even if we never expect to use that during gameplay for PC's, it gives us something to hang our hat on for the purpose of campaign-wide NPC demographics, and how the matriculation from 0-level to 1st-level might occur. (And even for active play, I've had at least one player in the last year take over an NPC lantern boy who started racking up a surprising number of kills and a developed persona -- moreso than his original dead PC -- and surely that should be rewarded.)

Here's what I think I would do for the unwashed masses in my "Original Edition Delta" games: Start at 0-level. Roll 3d6 in order for abilities. Roll 1d6 for hit points. Earn 1,000 XP to get to first level. On achieving 1st level, add 1 hp if becoming a fighter, or subtract 1 hp if a becoming wizard (minimum 1 hp before Constitution bonus). A slight wrinkle here is that 1st-level fighter graduates in this way could only have 2-7 hit points, but that actually matches the Original D&D Vol-1 text, and is on average the same as a 1d8 roll.

Note that I veer off from Gygax a bit here in the exact XP needed to graduate from 0-level. For both the cavalier and magic-user, he set the level immediately before 1st at 500 XP; although in both cases, there were other "negative" levels that one needed to progress through initially.  Looking at the standard geometric XP tables, with fighters starting at a 2,000 XP step for 1st level, the clear extrapolation is that the level before that should be 1,000 XP (i.e., half). In addition: under certain other demographic assumptions, having a 500 XP step may actually produce a greater number of 1st-level types than normal men, a result that we should certainly avoid.

A few notes for Book of War: statistically, these distinctions are all below the level of granularity recognized in that game. For example, say a target is wearing chain & shield (AC 4 in any edition above). If the attacker is 0-level, with d6 damage, against a d8 hit die, then the chance to score a kill with one hit is 11%; but if the attacker is 1st-level, with d8 damage, against a d6 hit die, then the chance is 21%. Any other permutation is somewhere within these bounds; but using the BOW d6-mechanic, all of these round off to the same 1-in-6 chance to score a kill (16.6...%). So that's why it's really nice that BOW is a statistically accurate representation of whichever edition of the game you normally play with, regardless of these small details; and at all times I can thus assume that common 1 HD human soldiers are, for simplicity, effectively the same as common 1 HD orcs (at least in reasonable lighting).

So we do like giving the 0-levels a chance to be heroes someday. But what implications does this have for campaign demographics or 1st-level abilities and hit points, having survived the 0-level to get there? More on that next time.