Monday, June 27, 2016

Gygax Module Stats, Part 3

More of Gygax's module encounters assessed statistically; this time from the era of his "campaign" style modules. On the one hand, these were all published later than his "tournament" modules; but on the other hand, most were quite likely conceived and played at some earlier point during his Greyhawk campaign.

Gygax Module Encounter Stats 2

Now, this list looks short because I've left out those modules that don't really include any true "dungeon" area. Modules EX1, EX2, and WG6 are all "exceptional" modules which occur in some freaky side-dimension, and are predominantly outdoor/wilderness adventures in a strange new environment. (Each maps out a small mansion or cave complex, but these are either unkeyed or have just a single principal monster, so they are not representative of a standard dungeon exploration.) T1-4 and WG4 are much more canonical examples of Gygax's ideas for a true dungeon; and of course B2 is his contribution to the D&D basic set, with its dozen separate cave lairs for introducing new players to the idiom of the game -- so these are the ones assessed above. Statistics for T2 include only the dungeon areas, not the extra-planar "nodes" which are left principally for the DM to fill in (although the suggestions work out to about 40% areas with monsters, and about 10% with a trick/gate area).

Aside from the tournament/campaign axis, a second way to categorize Gygax's modules appears to us: whether the dungeon is organized/disorganized as a single community. Several of Gygax's modules present a stronghold run by a single racial type (most often "giant-types", i.e., humanoids); in these places, nearly every room serves a purpose, like a real-world institution or military base, and the number of "empty" boundary areas, and possibly "tricks/traps", will be small. These would certainly include the famous G1-3 and D1-3 sequences; B2 often looks like that, especially from the perspective of any single cave system; and WG4's uppermost and T2's lowest levels function like that. In contrast, other modules are more heterogeneous "ruins"-style dungeons, where a more random assortment of monsters have taken up posts and watch against each other; empty areas and traps may be more likely here -- and possibly this is the better match for the initial conception of the sprawling underworld "dungeon". Examples of this second case would be the S-series, EX1-2, WG6, T1, and levels 1-3 of module T2.

Having considered all of Gygax's modules at one go, let's reflect on some of his major tropes:
  • Watch Posts: Single guard watching approach through peephole.
  • Guard Rooms (multiple): Guards with negligible treasure.
  • Leader's Room (single): Leader with major treasure. 
  • Storage Rooms: "Empty" rooms with food, drink, supplies, arms, etc.
  • Prisoners: Cells with slaves/prisoners; mix of potentially helpful and harmful captives.
  • Kitchen/Dining Hall (esp. in giant-type organized areas). 
  • Random Beasts: Animal-type beasts with small hidden/forgotten/swallowed treasure.
  • Secret Treasure Room (occasional).
  • Strange Decorations (occasional, otherwise empty). 
  • Bandits in Upper Corner Structure (in dungeons of DMG, T1, T2). 
  • Crypts with Ghouls (DMG, T1, T2, suggested in WG4). 
  • Weird Temple Area (B2, G1, G3, S1, D2, D3, T2, WG4). 
  • Hidden Prison of Deity (D3, T2, WG4). 
  • Optional Expansion Area (often caved-in, clearance at DM's option; B2, G1-3, D1-3 underworld map, T2 wilderness & nodes, S4 river course, DMG dungeon caverns, etc.): A person could spend a whole career just expanding and filling in these areas!
  • Secret Exit Tunnels.

So in broad strokes, can we discern anything of the "standard population" of a Gygaxian adventure module? Looking at the statistics for more "normal" dungeon areas like B2, T1-2, and WG4 may give us a pretty good idea (see also: G1, D2-3). If we somewhat take the average of those statistics, and say possibly that I should have counted more "pocket change" monsters in the "monsters only" category, then for every 6 encounter areas we get something like this: 2 Monsters, 1 Monster with Treasure (major), 1 Treasure Only, 1 Trick/Trap, and 1 Empty.

Investigating the canonical B2 module, we see this highlighted, because every organized giant-type (humanoid) cave lair falls into the same approximate pattern (this includes caves A-D, F, H, and J). After initial entry (possibly with watch post or trap), there are about a half-dozen areas. And these areas tend to include: 2 Guard Rooms, 1 Chief's Chamber, 1 Common Chamber, 1 Storage Room, and 1 Special (possibly a slave pen, torture chamber, secret room, armory, or garbage pit). Or look at the partially-keyed Orc's Lair in module S4: every fighting "group" is split into exactly 3 chambers; generally 2 Guard-type positions, followed by the Leader/Chief's lair, and every cave being occupied for some purpose (none are empty). We might very well call this Gygax's "Rule of Three".

In regards to the T2 module, when we first presented publication statistics in Part 1 here, there was some debate or question about whether that adventure should really be counted as a work of Gygax's or Frank Mentzer's (see the comments there). I'm incredibly indebted to Jonathan Miller for providing links and previous personal communications with Gygax on the subject: indeed, Gygax wrote "Just FYI, that is my version of the adventure. Mentzer simply fleshed out the considerable body of preliminary work I had done but could not find time to finish.", and there are numerous pieces of evidence that Gygax had copious notes and had run playtests of the Temple around the era when T1 was published. The statistics in the chart above provide yet another piece of confirmatory evidence that T2 really was largely the work of Gygax: the stocking proportions per area are almost identical between T1 and T2. (Contrast this situation with Q1, which all evidence points to being the wholesale work of David Sutherland, and not Gygax.)

Now compare the ratio we're finding here to that suggested in OD&D Vol-3 from 1974 (2-in-6 with any monster, 1-in-6 of the rest with treasure; so about half empty). Or Gygax's 1976 Dungeon Geomorphs product (2-in-6 empty, 2-in-6 monsters, 1-in-6 trick/traps, 1-in-6 monsters and treasure by DM selection [so no suggestion of treasure-only areas]). Or his 1977 Monster & Treasure Assortment product (weirdly, even more empty: recommending only 20% with any monsters, or close to 1-in-6, and no comment on any other 5-in-6 contents). Or the 1979 DMG Random Dungeon Generation (12-in-20 empty, 2-in-20 monster only, 3-in-20 monster & treasure, 1-in-20 special, 1-in-20 trick/trap, 1-in-20 treasure only). These all suggest many more empty areas than Gygax actually put in his published adventures, unless we look solely to his sprawling S3 map with its many unkeyed/blank areas (or, alternatively, a locale like Rob Kuntz's WG5).

So having observed this, an exceedingly easy critique to make is now this: We should probably not methodically ape what Gygax did in his adventure modules. Yet as we key our own dungeons, I think it is useful to expand the frame of what can be a workable design. Having most of the areas with some content, and very few "empty" areas (and even those not actually devoid of furnishings) seems to have done a pretty good job for Gygax of hitting the adventuring "sweet spot" of published modules.

But a final, concluding question: Is that even doable for us mere mortals? One thing I must say in retrospect is that Gygax's output during this period was truly monumental. Between running TSR as a company, promoting its products, writing the AD&D hardcover books, and original drafts of all of these adventure modules (etc.) in about a 5-year span from 1975-1980; I'm really staggered at how he accomplished all of that. Just looking at the module materials here: They are big, extensive, richly detailed, deeply considered. Many encounter areas have brand-new items or monsters just for a single room, or a dozen random novel effects, and frequently the text may run for several pages for a single chamber (esp.: see S3, T2). Even just reading it, trying to digest it, consideration of running it in a game can be an intimidating experience. (But perhaps Pascal's "I have made this longer than usual because I have not had time to make it shorter" might be appropriate here.) An altogether towering body of work.

Friday, June 24, 2016

Atatl Mechanics

Speaking of the D-series module (in which the Drow use just such a weapon), here's a fascinating look at the mechanics of the atlatl:

Hat tip to Jonathan Songe Scott.

Monday, June 20, 2016

Gygax Module Stats, Part 2

Continuing from last week, here's a rough breakdown of the encounter areas in Gygax's published modules from the era of tournament origins (first appearing in conventions from 1975-1978). A few notes: This only includes dungeon areas, not wilderness or other adventuring locales. The categorizations given here are of course roughly subjective, and are discussed in detail further below. Again I try to present them in approximate chronological order of creation.

Gygax Module Encounter Areas 1

In the table above, the column marked "Empty" counts any room lacking a monster, trap, or treasure; but they are almost never literally bare. Most often this will be a fully-stocked storage chamber, supply room, armory, or at least some arcane decoration which foreshadows what is yet to come. Perhaps the closest one gets to a truly empty area are the galleries under clearance in the dungeon of G1, with only a few giant tools present. Contrast this with Rob Kuntz's WG5 module (1972-1973 design), which really does have many totally unkeyed/blank rooms on the map, with no defined contents whatsoever.

Initially I intended "Monster" to be a creature with zero treasure, in contrast to the "Monster & Treasure" entry. But midway through the assessment, I realized there was a bit of a problem; a common Gygax trope was to have some boundary guards with very small amounts of treasure (say, 1d6 or 2d6 sp or gp, something like that), and then a leader's chamber with a more sizable haul (hundreds or thousands of gold pieces). So later on I tried to put the "pocket change" bearing monsters in the first monster column, and the "major haul" monsters in the second; but this was extremely subjective, and I'm not sure that I always got it right (in retrospect, ideally I'd have some cutoff threshold for each dungeon based on adventuring level; perhaps someone else can improve on that). Again, contrast to Kuntz's WG5; most of the monsters there really have zero treasure.

The "Treasure" column represents halfway significant treasure with no monster guarding it, but is still often hidden, trapped, and/or dangerous to procure in some way. In the "Trick/Trap" column I counted things like actual traps, secret exits, penned-in captives (with a mixed of helpful and hurtful figures), possible allies, random magical effects, teleporting areas, aquatic travel challenges, etc.

Looking at the individual modules: S1 is of course infamous for being almost entirely trick/trap based, and it clearly shows up as an outlier in that sense above. S4 is a bit of a hack-fest; the lower level in particular is almost comical for every room, one after the other, being uniformly a huge monster with an equally huge treasure (somewhere I think I read Gygax saying he wrote this in a single weekend, and frankly, I think it shows; which is not to say that it's bad or something that I could replicate). G1-3 are of course the giant strongholds, organized and run in a coherent fashion for that purpose. G1 gives the appearance of more "empty" rooms, by virtue of its always-in-session celebratory feast (leaving many barracks and bedchambers devoid of occupants). D1-3 here only count the major encounter areas, not the minor encounters leading up the the main "dungeons" (arguably the out-areas function similar to a wilderness overland journey).

What I left for the end here: Module S3 deserves its own dissertation, as it is a wild, dense, and elaborately baroque one-of-a-kind adventure; it has the largest, most sprawling map of any of Gygax's modules, and any given area is liable to have a dozen crazy, new unique features just to liven up a particular room. At the same time, it is the only module in the list that reflects a particular old-school design sensibility: it has hundreds of rooms and areas which are actually unkeyed and blank on the map itself (although they are given a general guideline of having "jumbled furniture or rotting goods... inanimate skeletons..."). Meanwhile, levels II, V, and most of IV are enormous open areas, which made for a huge dilemma on my part about what to count as an "encounter area" (statistics above actually do count all of the separate empty rooms in S3; perhaps that was ill-advised).

Here's a design element that shows up in a few of these early modules that is not used later on: Re-using a particular key code for a very large number of small, similar monster lairs (S3 for its vegepygmy rooms and dangerous flora, S4 in the gnome lair, D1 for troglodyte caves, and D2 for Kuo-Toan pilgrim apartments). Which made a significant assessment coding problem: Should I count each of these minor rooms as a separate encounter area? Ultimately, I did count each one separately for S3, but did not count each separately for D1-2. (At least in D2, it would have added 45 rooms with monsters and 7 empty rooms.) I apologize for that discrepancy.

Now I wonder: Did anyone ever successfully run the S3 module? Just looking at the insane density of its maps and text (to say nothing of its special mechanics and illustration booklet, even a unique full-color insert!) leaves me trembling with fear at the prospect.

Friday, June 17, 2016

Snakes and Ladders

The surprisingly deep meaning of the non-mechanic of Snakes & Ladders (video):

Hat tip to Existentialist Comics.

Monday, June 13, 2016

Gygax Module Stats, Part 1

My  never-ending aggravation: How the dungeon-design parameters throughout classic D&D are at dire odds with the adventures that actually got published. As part of that ongoing saga, here's an attempt at assessing all of Gygax's D&D adventure modules while at TSR. Today, a look at the publication format. Modules are referenced here by their alphanumeric code (see Acaeum's Module Index if you're not intimately familiar with them already).

Gygax Module Publication Stats

In the table above, I've taken my best stab at ordering Gygax's published adventures in chronological order of writing, but the truth is that's an immensely murky, possibly intractable problem. Clearly most or all of these adventures were initially drafted and run for tournaments or his personal campaign, years prior to their mass-market publication, so it's really possible that they could have been crafted in almost any order, irrespective of their publication/copyright dates. But here are some broad observations:

The first wave of published modules are all designated as having been created for D&D tournaments in the era of 1975-1978; this would initially be the various S-modules, then G1-3, and then D1-3. Publication dates follow fairly closely from these tournaments, either the same year or seemingly a few years later. An interesting case is the famed G1-3 adventure used at Origins IV in 1978; the Dragon issue #19 from October 1978 had a players' memoir of the tournament, and editorial sidebars made sure to promote the modules then on-sale: "The setting for round one is available from TSR... it costs $4.49". (Note the 1978 monochrome printing has a cover starburst correctly saying "Official D&D Tournament Module used at ORIGINS '78", while the 1981 color printing for some reason incorrectly indicates "Origins 79 Tournament Module").

Somewhat unexpectedly, it is the earliest modules in the S-series that had some of the most elaborate production values. S1 and S3 include lengthy supplemental booklets of illustrations to show to players at given encounters. S4 had a supplemental booklet of many new monsters, not all included in the adventure; effectively a proto-Monster Manual II for a few years. No later productions ever rose to those heights of production value ever again. S3 in particular is a wild extravagance; it detailed the largest adventuring locale, and greatest total page count, of any Gygax adventure except for his very last one, T1-4 (as well as the most new items and new monsters, excepting S4's special monster booklet). Acaeum notes that G1 was published somewhat earlier in 1978 than S1, and that earlier ziplocked versions of S4 from the 1976 tournament have been traded on Ebay.

Later published adventurers are not noted as originating from tournament play, and instead generally express being rooted in Gygax's original Greyhawk campaign setting. Allusions to the EX1-2 and WG6 adventures are made in the past tense in the 1979 Dungeon Master's Guide (see p. 112), even though the weren't published until the 1983-1985 time period. Likewise, the 1979 print of T1 references the Greyhawk T2 campaign in the past tense, yet the latter was also not published until 1985.

None of these later works have the elaborate supplemental illustration or new monster packets. Usually they include at most a handful of new monsters, spells, and/or magic items -- almost all of which were subsequently folded into the Unearthed Arcana and Monster Manual II rulebooks. More of the later works tend to have extensive wilderness adventuring components: e.g., B2, WG4, EX1-2, and WG6 have very sizable outdoor components (in fact, WG6 is effectively nothing but a wilderness scenario). T1-4 has a suggestive overland map, but it is not keyed. In contrast, of the early modules, only S4 has an outdoor adventure, and that is noted expressly as not having been part of the original tournament.

It's interesting that each of the S- and WG-series have something of an "interloper"; both those series are written by Gygax except for a single entry by someone else. Specifically: S2's famous dungeon-crawl by Lawrence Schick, and the WG5 entry by Robert Kuntz (with Gygax listed as second author, but the work is clearly Kuntz's). WG5 is particularly interesting, in that it seems to be a throwback to a much earlier style of dungeon design; in the Introduction Kuntz writes that the dungeon was originally designed in the years 1972-1973, giving it conceivably the earliest birthdate of the bunch; it has many empty, unkeyed rooms, few (almost all new) monsters, and very little treasure. (In contrast to Gygax's work, none of these new monsters were folded into later AD&D hardcover rulebooks.) Likewise, the Q1 module was authored by David Sutherland, with Gygax listed as secondary author, perhaps mostly for marketing purposes. None of these modules S1, Q1, or WG5 are included in the statistics here.

Have any scraps of knowledge that would alter the attempted timeline given above? Tell us!

Friday, June 10, 2016

Monday, June 6, 2016

Ballistae and Bell-Shapes

Got in a debate on StackExchange about whether Chainmail's "Fire Optional" rule for catapults (and hence fireballs?) was reasonably realistic or not. Then I realized that the chart that rule generates, so clear in my head, has never appeared on this blog. So let's consider some real-world evidence first.

Strohm, Luke S. "An Introduction to the Sources of Delivery Error for Direct-Fire Ballistic Projectiles". Army Research Laboratory. July 2013. (Link.)

2.2 Normal (Gaussian) Distributions
For direct-fire ballistic projectiles, it is common to assume that error sources and the shot distributions they produce can be characterized by normal (Gaussian) distributions. Normal distributions are defined by a mean (μ) and standard deviation (σ, SD), which produce a bell curve that is unique to the distribution. The mean is the average of the distribution, while the SD quantifies the spread or precision of the distribution. For a one-dimensional normal distribution, approximately 68% of the distribution is within one SD of the mean (+/–) and 95% within two SDs (figure 2).

... In two dimensions, target impact distributions follow a bivariate normal distribution, meaning that the impact locations vary normally in two directions—in this case the horizontal and vertical directions of the target plane.

(Note that the bivariate normal model is the same as I've used in various archery simulations on this site.) Consider also the empirical test of shotgun shell spread presented here: Lowry, Ed. "Properties of Shotshell Patterns". American Rifleman. 1990. (Link.)

Now let's reflect on the rule as written in Chainmail for "Fire Optional"scatter:
Fire Optional: Roll two different colored dice. One color is for an over-shoot and the other is for an under-shoot. To decide which number of use you take the higher of the two. Miss is in inches, shown by dice spots. If they tie then the rock lands at the specified range. This method is simple but effective.
Taking the higher of the two dice biases the scatter towards the high end of the range. This is shown as "Chainmail Fire Option A" below. Note that the resulting probability distribution is distinctly anti-Guassian; it is impossible for a shot to land exactly 1" away from the target; and generally speaking, it's simply total lunacy, some kind of Lovecraftian non-Euclidean physics:

But if we change one critical word to make the rule instead "take the lower of the two" dice, then this mechanic, while still very simple, does in fact generate a quasi-bell-shaped distribution as suggested by the American Rifleman and Army Research Laboratory publications above (shown as "Chainmail Fire Option B" below). It seems patently obvious that this is the better rule: