Lack of Scale Considered Harmful

The first and biggest mistake in the foundation of D&D was not specifying any units of scale in the Chainmail Man-to-Man Combat rules.

In general, specifying units of scale (for figures, time, and distance) was usually among the very first things stated in traditional wargames, often before the actual start of the rules themselves. For a specific example, these are given in the third paragraph of the Chainmail mass-combat rules, preceded only by a statement on what the Middle Ages were, and what size and brand of miniatures are recommended (p. 8). These Chainmail mass-combat rules came with a respectable pedigree of playtests, refinement, and editorial corrections; in the second paragraph, they reference the prior "LGTSA Medieval Miniatures Rules... the rules have been thoroughly play-tested over a period of many months..." (p. 8). Jon Peterson in Playing at the World tells us, "The LGTSA medieval miniatures rules resulted from Gygax's expansion of Jeff Perren's original four-page ruleset..." (p. 30), published in Domesday Book #5 (July 1970). Also, "The core system of Chainmail adheres closely to the earlier LGTSA rules; for example, the movement and missile combat system charts are copied verbatim..." (p. 40). Furthermore, these rules themselves were influenced by older systems such as those of Tony Bath, etc. (p. 31). As a result of this legacy of a wargame refined by diverse hands, we find that the scales of time and distance, movement and missiles, found in LGTSA/Chainmail mass-combat are fundamentally reasonable and match well with real-world data. 

But with the publication of Chainmail, we also get a new 3-page section on Man-to-Man Combat which, relatively speaking, appears to come out of nowhere. It does not claim to come with a history of playtesting, appears relatively slapdash, and is likely the conceptual work of a single author (Gygax?). Notably, while one figure now represents one man, there are no specifications given for time or distance units on the table; it seems to have not even been considered at all. Broadly speaking, these rules try to "cheat" the issue by silently assuming that the mechanics for mass-combat can be used without alteration in man-to-man combat ("Generally speaking, the rules for 1:20 scale apply to man-to-man missile fire...", p. 25) and so forth.

Now, there are some things in the world for which, when we "zoom in" on them, the characteristics appear the same as when we "zoom out"; the technical term for this is "scale invariance" (for example: fractals). You can almost get away with the assume-everything-is-the-same approach for movement (if distance and time are changed in proportion), and melee combat. But it's precisely with missile combat where the problems and contradictions spring into plain sight -- ranged combat is distinctly not "scale invariant".

Here are two of the top absurd positions that this oversight forced Gygax to defend constantly in later a years as a result of this initial oversight: (1) That man-to-man combat took place at the same 1-minute action cycle as Chainmail, and that therefore only one sling or crossbow-shot could be made per minute, etc.; and (2) That effective missile ranges were at the same 10-yards-per-tabletop-inch scale, such that it was feasible to shoot an individual man at 210 yards outdoors with a longbow, which is patently ridiculous. (See OD&D Vol-3 p. 8 and 17; AD&D PHB p. 39).

Of course, a claim is made that the distance scale shortens to 1" = 10 feet in the indoor/underworld environment (OD&D Vol-3, p. 8). As a result of this, magic spells likewise grow and shrink depending on whether they are used indoors or outdoors. In Dragon #15 Gygax writes what seems to be a correction and apology on the issue after Len Lakofka points out the problem here. Gygax calls the existing result "ridiculous" and that "the blame for the possible ignorance of player and Dungeon Master alike rests squarely on my shoulders" (read the article and my past analysis on it here). This altered rule, that magic ranges change indoors-to-outdoors, but areas-of-effect do not,  then gets incorporated into the AD&D PHB (p. 39), in a rather screechy all-caps passage, below:

For purposes of the game distances are basically one-third with respect to spell and missile range from outdoors to indoors/underground situations. Thus most ranges are shown as inches by means of the symbol ", i.e. 1", etc. Outdoors, 1" equals 10 yards. Indoors 1" equals 10 feet. Such a ratio is justifiable, to some extent, regardless of game considerations.

Actual effective range of an arrow shot from a longbow is around 210 yards maximum, in clear light and open terrain. Underground, with little light and low ceilings overhead, a bowshot of 210 feet is about maximum. Archery implies arching arrows. Slings are in this category as are hurled darts and javelins, all arching in flight to achieve distance. Crossbows are a notable exception, but under the visibility conditions of a dungeon setting, a yards to feet conversion is not unreasonable.

Magic and spells are, most certainly, devices of the game. In order to make them fit the constrictions of the underground labyrinth, a one for three reduction is necessary. It would be folly, after all, to try to have such as effective attack modes if feet were not converted to yards outdoors, where visibility, movement, and conventional weapons attack ranges are based on actual fact. (See MOVEMENT.)

Distance scale and areas of effect for spells (and missiles) are designed to fit the game. The tripling of range outdoors is reasonable, as it allows for recreation of actual ranges for hurled javelins, arrows fired from longbows, or whatever. In order to keep magic spells on a par, their range is also tripled. IT IS IMPERATIVE THAT OUTDOOR SCALE BE USED FOR RANGE ONLY, NEVER FOR SPELL AREA OF EFFECT (which is kept at 1" = 10') UNLESS A FIGURE RATIO OF 1:10 OR 1:20 (1 casting equals 10 or 20 actual creatures or things in most cases) IS USED, AND CONSTRUCTIONS SUCH AS BUILDINGS, CASTLES, WALLS, ETC. ARE SCALED TO FIGURES RATHER THAN TO GROUND SCALE. Note that the foregoing assumes that a ground scale of 1" to 10 yards is used.

Now, a couple things to note about this passage. One: a cursory justification for the feet-to-yards conversion is made for missiles ("little light and low ceilings overhead"). Two: absolutely no justification is attempted for the expansion of magic spell ranges; it is purely a matter of raw game balance ("devices of the game... designed to fit the game"). In fact, to my knowledge, Gygax never attempted any in-world explanation or rationalization for this phenomenon. (You can of course make up your own: Do magic energies follow ballistic trajectories and get limited by ceiling height? Is every underworld locale uniformly imbued by dark counter-energies that reduce magic effects? Not to say that any such claim is in any rules text.) Ultimately Gygax hangs his hat on, "It would be folly, after all, to try to have such [magic] as effective attack modes if feet were not converted to yards outdoors, where visibility, movement, and conventional weapons attack ranges are based on actual fact." But this ignores the actual actual fact that shooting an individual man at 210 yards with a longbow is sheer lunacy in the first place.

Here's the thing that occurred to me a few days ago, and that I'm embarrassed at how many years it took me to observe: The whole notion of indoors-versus-outdoors is a false path and a distraction. The real issue is whether the action is at mass-scale or man-to-man-scale. Which again, is the original error, the essential oversight in the new section of Chainmail.

Let's look at some data. There's a notable real-world circumstance in our favor; modern archery competitions in the United Kingdom have the exact distinction that we're looking for here. There's standard target archery, at a fairly close range, with a target passingly close to the size of man; and separately, clout archery at a distance near the limit of a classic longbow, with a relatively huge target area (fundamentally simulating shooting at an army). Specifically: standard target sizes are 122 cm in diameter (approximately 4 feet, or 2 foot radius). Clout archery for adult men is held at 180 yards range, with a target area 12 feet in radius, and a central "clout" (bullseye) of 18 inches radius (that is, about the size of the entire short-range target, or roughly a single man's area).

Here are results for the Yorkshire Archery 2018 Clout tournament. For more, here are results from the National Clout Championships of 2016. Here's a data analysis by myself (ODS spreadsheet) of the latter tournament for the Gentleman's Longbow event . Some results of that analysis (N = 30, discounting last two outliers with only one point between them): The average hit rate on the 12-foot radius target at 180 yards was just 42% (ranging from 11% for the bottom-performers, to 83% for the winner). The average hit rate on the central bullseye/clout -- about the size of a man (assuming a totally immobile, defenseless one) -- was only 1%!. (Even the winner himself only scored a 1% hit rate on the centermost target; the two runners-up scored 6% and 8% bullseye rates, but these may be considered pure luck since their overall accuracy was not as good as the winner's, and in any event represent the equivalent of natural-20's for these almost-England's-best-archers).

The central lesson here is that it can be effectively impossible to hit a target in man-to-man combat at long range (1% vs. the central clout), while being completely feasible against a larger area/group of men (42% vs. the larger target, roughly the same chance D&D gives a 1st-level man to hit an unarmored opponent). If we take the small 18 inch = 1.5 foot radius as roughly the area of a single man, then the larger 12-foot target is equivalent to some 64 men in formation ((π(12)^2)/(π(1.5)^2) = 64). If we were to double the target radius again, to 24-feet and some 256 men, then this would be a 90%-something shot, nearly unmissable (using ArcherySim on GitHub). For emphasis: With a longbow at around 200 yards, hitting an individual man is a 1% shot or less, while hitting an army is a 99% shot or more. The cases are exact binary opposites. Note that Chainmail mass-combat had no rules or penalties for missile range, and we find this to be completely reasonable; but keeping the same or a minimal range penalty for man-to-man combat is, as Gygax would say, "ridiculous".

Some conclusions: One, the maximum effective range for man-to-man missile combat should be set at around 40 yards; this is especially true for a target that is mobile and defending itself (note that the real-world data above assumes a completely immobile, defenseless, unarmored target; hit rates should obviously be lower if that is not the case). This is true whether indoors or outdoors. Note that the legacy of this glitch has led to ranged attacks never being close to right in any edition of D&D. Over 40 years later, and in 5E D&D (from what I can tell), a 1st level fighter shooting a longbow at a mobile, active single man at maximum range of 200 yards still has a 42% chance to hit (AC 10 with +2 attack bonus, i.e., target 8 on 20, with disadvantage); coincidentally exactly the same rate that the UK's champion clout competitors actually have against an immobile, barn-sized target. That's twisted.

Two, in classic D&D, there should have been greater care taken in specifying scales, and distinguishing between the man-to-man and mass-combat situations; the two are not equatable. A random example: In D&D Vol-3, the Aerial Combat and Naval Combat sections seem to be closely related; they refer to each other in places, stipulate the same playing area, turn sequence, and written orders (compare p. 25 and p. 30), etc. But in truth, Aerial Combat is intended for man-to-man scale (each figure a single creature), whereas Naval Combat is intended for mass-scale (each ship model carrying tens or hundreds of men; missile fire as per Chainmail mass rules on p. 30, etc.; at least until a boarding action occurs and then we are directed to switch maps and rulesets to the man-to-man basis on p. 31). These are very different situations, requiring different distance and time units, tabletop missile ranges, turning radii (another characteristic that is definitely not scale invariant), etc., and this qualification should have been highlighted in the original rules.

Three, by Gygax's logic in the PHB, we should also calibrate the range and effect of magic spells on the reduced basis for game-balance purposes ("It would be folly... [for magic to contradict] where visibility, movement, and conventional weapons attack ranges are based on actual fact"). Again, irrespective of being indoors or outdoors; that is not a relevant distinction. Note that once this physical reality of the magic spell range is set by man-to-man scale, it implies that apparent range and usefulness in the mass-scale context is much reduced. Example: In Gygax's later Swords & Spells mass combat rules, spell ranges in inches are copied verbatim from the D&D rules, and hence have extraordinarily long-range effects on the battlefield (e.g., 24" for a fireball, i.e., 240 yards). Reversing the reasoning, we now consider that if the spell range was fixed at 40 yards, as per man-to-man missile fire, then on the mass-scale battlefield a fireball would only be usable at 4" or something like that. That's a fairly major change (perhaps in Book of War?), but upon reflection, it may be a better simulation of magic effects as seen in pulp literature and similar traditions. Some of the higher-level spells meant to influence large areas outdoors might prove troublesome, however.

To wrap this up, we look at a quote from Gygax in The Strategic Review, Vol. 2, No. 2 (April 1976), in his article "The Dungeons & Dragons Magic System" (p. 3), that some of us have been considering recently:

Magic in CHAINMAIL was fairly brief, and because it was limited to the concept of table top miniatures battles, there was no problem in devising and handling this new and very potent factor in the game. The same cannot be said of D & D. While miniatures battles on the table top were conceived as a part of the overall game system, the major factor was always envisioned as the underworld adventure, while the wilderness trek assumed a secondary role, various other aspects took a third place, and only then were miniatures battles considered.

This is somewhere between a strange thing to say and a ghastly oversight (that underworld adventures came first in the calibration of D&D magic, and miniatures battles a distant fourth), because in terms of time and distance, exactly the opposite is the case. The mass-combat miniature scales were carefully figured, and the underworld scales simply taken by theft of the same and without any real consideration. Even in the SR 2.2 article quoted above the issue continues to entirely escape Gygax's attention (the topic being only a defense of the Vancian memorization and daily-limit conceits). If only some assistant had been able to point that out at the earliest date.

Edit 9/1/18:  Around the time I was writing this, Jon Peterson had a new post about some of the prior systems that fed into Chainmail man-to-man combat. It doesn't exactly address my main criticism here, but it's quite interesting to know about for its own sake. Thanks to Jon for pointing this out to me.

Edit 9/20/18: Geez, I may be stuck in a fugue on this issue.


  1. Amazing research as always.
    I think we talked about his before, but in my homebrew weapons are stated out exclusively for man to man, with long range/mass combat being the special rule.
    3e had an interesting approach with the range increment penalty, but then they still used inflated distances (plus being one of those fiddly rules, being overlooked)
    All this talk of scale, I will just throw in my wish that the hobby has gone with 1" = 1 yard/meter back in the day. I think it would have made a number of things better.

    1. Good thoughts, and thanks for the compliment. I agree that founding the system on man-to-man scale (for real) would have been best. Any well-considered scale for man-to-man at the foundation would have been better than just leaving it hazily unstated; so many shenanigans were a result of that.

  2. Both Fireball and Lightning bolt have a very different range mechanic in the Beyond This Point be Dragons mss.

    "Fireball: Has radius of 20 feet, and in a confined space it will elongate accordingly. A Fireball is thrown by the Magic-User, and the accuracy will vary with the distance of the intended target.
    Targets within 50 feet can be hit with 99% accuracy, at 55 feet 95% accuracy, and the accuracy decreases at 5% per every 10 feet."

    I don't know if this is in the original GD&D draft, but it seems clear that somebody - either Gygax or Arneson or Mark Bufkin, was considering the range problem as far back as 1973.

    1. It's an interesting note. One thing that struck about BTPBD is that it mostly gives distances in fixed feet, although scale inches pops up unpredictably in places (monster moves, light spell). That former may have been better for a game sans minis, although it's different than either Gygax's OD&D or AD&D.

      Also I just noticed that BTPBD missile fire table (Table 30) which is nuts! Basically automatic hit at any range for long/crossbow vs. unarmored man, with the numbers from Chainmail used as automatic kill results. Holy moley. (Would bear on my post that went up today, but that mechanic wasn't on display in either Chainmail or any edition of D&D. Granted fixed yards in that BTPBD table, we'd really just have to reject it as lunacy for man-to-man combat.)

  3. Reeeal late to the party on this one; first off I love the blog, it’s been super helpful for me as a DM and designer. Second, I think it’s important to note that when Gygax and Perrin wrote Chainmail, they weren’t trying to take the world by storm. I think the same goes for DnD. Before it’s phenomenal explosion, Gygax was writing games for friends and acquaintances in a relatively small region of the Midwest. So I think any issues with scale were probably handled at the table. The introduction to Chainmail says that the rules are “guide lines around which you form a game that suits you. It is always a good idea to amend the rules to allow for historical precedence or common sense — follow the spirit of the rules rather than the letter.”

    I really think that’s why you have so many discrepancies pop up early on. It was some friends writing for each other, not for us! Yes, we should always try our best to produce a clean product if we mean to sell it, but I don’t think any of us when we write and publish something expect the level of scrutiny DnD and Gygax have gotten over the years.

    1. Thanks for the kind words! It's good to be generous to our creative forefathers. :-) I'm somewhat reminded of an essay I saw saying that while Euler made a big mistake in setting pi to only half a circle's circumference (in other papers he used a quarter, or a full circle), we should be thankful that he was too busy to really think it through. I can partly see the point. I do think when EGG got to AD&D, he was a bit too conservative in defending those glitches, and would have been better served at that point in fixing them instead. Cool to think about.

  4. I’d agree with that, from what I’ve seen. I think it was probably a mix of personality, whatever was going on in his life at the time, and probably years of people arguing with him and asking him for answers. Men back then weren’t trained or really allowed to admit they were wrong, socially. And is nerds sometimes have a complex about other nerds telling us their idea is better. Just imagine if you invented the whole genre and now some teenagers were like, “hey old man, you missed a spot!!!” I’d probably get a bit salty too! Haha!