Monday, January 25, 2010

Matters of Scale

The root of our game is historically-based. "Besides providing you with an exciting and enjoyable battle game, we hope that these rules will interest the wargamer sufficiently to start him on the pursuit of the history of the Middle Ages. Such study will at least enrich the life of the new historian, and perhaps it will even contribute to the study of history itself." (Chainmail, p. 8). It's eminently clear that the author of Chainmail's basic, historical mass-combat game paid attention to simulating realistic scales of men, distance, and time. Continuing in that tradition, let's think about what games are possible at different scales, if we apply the same precision to our research and foundations.

We can begin by taking certain real-world measurements as our limiting factors; the speed and size of men in an army, the time it takes to make one attack or bowshot, the size of the miniature figures we might use, etc. Then we can select a certain figure scale and deductively reason out what that implies for the scales of distance, time, movement, bowfire, etc. (Note that all of this can be based on real-world data, with the sole exception of areas of magical effects, which are not considered here).

Here are my starting assumptions: Men in a line take up approximately 3 linear feet; they advance in a "quick march" gait at about 4 mph. A longbow effectively fires some 200-plus yards maximum outdoors (200 feet indoors), and it takes about 10 seconds on average to fire an arrow or make one potentially damaging melee attack. Finally, the standard miniature figure that we use is 28mm tall with a 20mm (3/4 inch) square base.

Evidence for each of these base assumptions is linked above, and we'll leave aside any further discussion on those for now. Certainly, each of these items will have some wiggle room and potentially individual debate on the specifics, but I don't think anyone can much argue for an order-of-magnitude change (double or half) of the figures given.

1:1 Figure Scale

Let's consider the case where 1 figure = 1 man (i.e., man-to-man combat). Since the figure is representational, we should use an equivalent distance scale of 1 inch = 5 feet (6 ft man/ 28 mm fig * 25 mm/inch = 5 ft/inch). Since attacks should also be resolved on a one-for-one level (i.e., one damaging blow or arrow shot per attack) use a time scale of 1 turn = 10 seconds (see attack rate assumption above).

At this point we'll compute second-order quatities, such as movement and bowfire. An unencumbered man at the "quick march" speed will move 12" per turn (4 mph * 5280 ft/mi / 3600 sec per hr * 10 sec/turn / 5 ft per inch = 12 inches/turn). Assuming action indoors, then we'll have a maximum 40" longbow shot (200 feet/ 5 ft per inch = 40 inches).

Now, here's a side note considering the movement rate above. Conveniently, since at every scale level we'll multiply the distance and time each by the same number (or at least approximately so), movement rate will be the same in inches for all scale levels. And it's doubly convenient because, of course, the 12" movement rate is in fact that specified as the base movement rate for men in classic D&D. In other words, it's accurate to use the D&D-specified movement rates (in inches) at any scale whatsoever.

Advantages of the 1:1 Scale: (1) Easiest to use with representational miniature figures (figure scale matches distance scale, so figures take up the appropriate amount of space in each dimension). (2) Every turn represents the opportunity for one single, simulated attack.

1:2 Figure Scale

This scale may be unheard of, but bear with me for a second. If 1 figure = 2 men, then we can basically double the distance & time as specified above. Distance will be 1 inch = 10 feet and, for time, 1 turn = 20 seconds. Movement will be the same as for all scales (12" per turn), and indoors we'll have an approximately 20" longbow shot (200 feet/ 10 ft per inch = 20 inches). While notable disadvantages are the awkward figure scale and need to resolve two discrete attacks per turn (e.g., similar to AD&D's 2/turn rate of arrow fire), there would be some notable advantages:

Advantages of 1:2 Scale: (1) Easiest to use mentally without representational figures (distance scale inches match the standard dungeon mapping at 1-square-per-10-feet). (2) Missile fire ranges in inches match those found in the D&D rulebooks.

1:10 Figure Scale

Let 1 figure = 10 men. Looking at the shape of our square-based figures, it doesn't make sense to assume that we have ten men in a single line; more reasonable is to have 2 ranks of 5 men each. Therefore, the distance scale here is most accurately set at 1 inch = 20 feet. (5 men/fig * 3 ft/man / 0.75 inch base per fig = 20 feet/inch). Since this is a multiplication of x4 over the root 1:1 scale, we should multiply time by the same amount; so you could say 1 turn = 40 seconds, but just to maintain a round number I prefer 1 turn = 30 seconds and call it "close enough".

Movement is again at the same fixed rate of 12" per turn (4 mph * 5280 ft/mi / 3600 sec per hr * 40 sec/turn / 20 ft per inch = 12 inches/turn). Assuming action is now outdoors, we'll have a 30" longbow shot (200 yds * 3 ft/yd / 20 ft per inch = 30 inches).

A side note here: From the observation that each figure represents two ranks, we can conclude that a missile-armed figure will make twice as many attacks as a melee figure in the same span of time (just as in Chainmail). The reason isn't that the bows themselves fire more rapidly, but rather that as one rank of melee troops makes immediate contact with an enemy, twice as many ranks of missile troops may be casting arrows.

Advantages of the 1:10 Scale: (1) Individual "special characters" of around 10 HD can potentially be represented as single figures. (2) Constructions such as castles & ships can be made to scale and still have space to physically contain the miniature figures we use. (3) There is a remarkable, elegant mechanic for mass-combat resolution at the scale of 1 turn = 3 rounds of D&D (which this margin is too narrow to contain, and so must wait for a future presentation).

1:20 Figure Scale

Assume that 1 figure = 20 men. Like the preceding, to make sense of our square figures we must assume multiple ranks of men, in this case say 3 ranks of about 7 men each. Therefore, the preferred distance scale here can calculated to be close to 1 inch = 30 feet (7 men/fig * 3 ft/man / 0.75 inch per fig = 28 feet/inch). Since this is a multiplication of x6 over the root scale, time should be similarly multiplied, i.e., 1 turn = 60 seconds. (In other words, 1 inch = 10 yards and 1 turn = 1 minute.) Movement is the same as at any other scale, while bowfire will have a 20" longbow shot (200 yds * 3 ft/yd / 30 ft per inch = 20 inches).

You'll notice that all of these measurements precisely correlate with those found in the basic Chainmail game(!). One thing that doesn't quite match up is the rate of missile fire; since we here assume that figures are 3 ranks deep, archery figures should have an attack rate 3 times that of melee troops. While Chainmail only has a rate-of-fire of 2/turn, the later Swords & Spells game did increase this number to 3/turn as we would desire here.

Advantages of the 1:20 Scale: (1) Figure, distance, and time scales are exactly as specified in the original Chainmail game. (2) Movement and missile fire ranges in inches are also exactly as specified in Chainmail and classic D&D.

Conclusions

Any of these hypothetical game scales have significant good reasons for using them. It's interesting that with some reasonable base assumptions and arithmetic, what results for the top-level scale is absolutely identical to the Chainmail system for figures, distance, time, movement, and ranges. The original system was clearly not a fantastic accident, but very carefully designed; and our other scales can be thought of as smooth interpolations of this same system. It's also interesting that if we use miniatures for man-to-man combat, 1" = 5 ft is preferred, but with imagined combat and no miniatures, then 1" = 10 ft seems more efficient to use mentally. Granted that the designers of original D&D fundamentally stopped using miniatures, then it's no surprise that the latter scale came to be embedded in the core texts. The one thing that I continue to be highly critical of is the holdover of the 1 turn = 1 minute scale from Chainmail into D&D man-to-man combat; if figure and distance scales change, then the time scale really should do so as well.

17 comments:

  1. Why does the time-scale change with the figure scale? Chain Mail always uses a one minute round, as does OD&D, regardless of scale.

    The point about shooting rates seems a bit misplaced to me. In the ordinary shooting rules for Chain Mail two ranks of figures may shoot, which means two ranks of bows or two ranks of crossbows. Further, the movement rules attached to those weapons absolutely contradicts the hypothesis that bows are not being shot at an increased rate.

    In terms of frontage, you are assuming close order deployment (3' frontage per figure), but at 1:1 scale you say each figure occupies 5'. Is this the reason you started looking towards 1:2 scale?

    I think that 1:10 probably assumes deployment of two ranks of five men, as you say, but 1:10 scale probably assumes two ranks of ten men, as that would be a true "doubling" of scale. Interestingly, Gygax mentions the problem of depth relative to miniatures in the DMG in a different context.

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  2. "Further, the movement rules attached to those weapons absolutely contradicts the hypothesis that bows are not being shot at an increased rate."

    Definitely not, read my post again. There is no need for an individual bow to fire twice as fast as an individual sword; the observation that a single figure is itself two lines deep suffices to explain the twice-as-many-attacks-from-a-missile-figure rate.

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  3. Definitely not, read my post again. There is no need for an individual bow to fire twice as fast as an individual sword; the observation that a single figure is itself two lines deep suffices to explain the twice-as-many-attacks-from-a-missile-figure rate

    Nothing to do with sword, but with crossbows. If a bow shoots twice and a crossbow shoots once, it cannot be the case that two ranks of bows are assumed, rather than they have twice the shooting rate. Indeed, bows shoot once in the movement phase and once in the melee phase, but crossbows shoot in either or (see p. 11 of CM).

    One could possibly argue that more bowman can shoot than crossbowman, but this ignores that two ranks of missile troops can shoot in all cases. So, whether you have one rank of figures representing two ranks of men, or two ranks of figures representing four ranks of men only half of the ranks would be assumed to shoot under your paradigm [i.e. unrelated to the number of ranks that can shoot, only the total number of ranks].

    I started another thread about this over in the OD&D Chain Mail forum if you are interested.

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  4. Definitely not.

    A multitude of individual sword or bow attacks are required to make up one mass-combat figure's attack roll. Since the archer figure has more men actively firing, it achieves this number twice during a turn, while the sword figure only achieves it once.

    For crossbows, the half-speed counteracts the twice-as-many-firing, therefore resulting in one mass roll per turn. Faster individual bows are not necessary to generate these reults.

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  5. I have no idea how you are coming to this conclusion. Let us say you have 20 men shooting a bow in two ranks and you make 2 rolls, whilst you have 20 men shooting a crossbow in two ranks where you make 1 roll. You are arguing what here? That there are more bows being shot, or that the multiple rolls represent more effective shooting?

    The reason this does not work conceptually for Chain Mail is that if you then have two ranks of figures, so 40 in four ranks of 10, the rear rank can shoot as per the rules. It is illogical to assume that only the first and third rank of crossbowmen can shoot, but not the third, so we must conclude that all ranks shoot, whatever the formation.

    With that in mind, we need only look as far as how crossbows work versus heavy crossbows. Crossbows shoot every turn, and heavy crossbows shoot every other turn. If that is not representative of rate of shooting, then I will eat my hat.

    With that in mind, how can bows, which shoot twice per round when stationary not be shooting at twice the rate of crossbows, when we know that more powerful attacks,a s with the heavy crossbow, are represented by adding one to the roll?

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  6. Individual bows are shooting at the same rate as swords are attacking. Individual crossbows are shooting half as often as either of those. Now think through the implications of a 2x5 formation.

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  7. I am still not following you here. What am I supposed to be thinking through? As you point out in your initial paragraph, there is some level of historical simulation in Chain Mail; crossbows shooting at half the rate of bows in ranks of 2x5 or 2x10, 4x5 or 4x10 both fits the historical evidence relative to the game and makes for a perfectly reasonable abstraction.

    Are you making an argument, perhaps, that only the front rank of melee combatants are actually fighting in a given turn? That because 10 swords are attacking, 20 bows are shooting? I do not think those things can be related the way you are imagining, since melee attacks are not a case of 10 men fighting, next 10, or whatever. The die roll represents the strength of the unit engaged, everybody fights.

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  8. Precisely. "The reason isn't that the bows themselves fire more rapidly, but rather that as one rank of melee troops makes immediate contact with an enemy, twice as many ranks of missile troops may be casting arrows."

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  9. I do not think that is a tenable conclusion, although I see what you are driving at; presumably you are here treating Light Foot as Unarmoured, Heavy Foot as Half Armoured, and Armoured Foot as Fully Armoured.

    The missile troops are equivalent to Light Foot in this scheme, in that the total casualties they are able to inflict is of the order 3:2:1, which is to say 3 for every 6 against light foot, 2 for every 6 against heavy foot and 1 for every 6 against armoured foot, per volley, two volleys being equivalent to the casualties potentially inflicted by light foot against those foot types.

    It seems to me, however, that this fails to appreciate the fact that the same number of heavy horse (that is to say 6 figures) is capable of inflicting up to 24 casualties on light foot (or perhaps 30 during a charge), and thus must be attacking at four to five times the rate of the bowmen in that instance.

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  10. Mathhew: I'm not considering troop types or any game's specfic combat tables here, just rate-of-attacks only.

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  11. Then you realise that bows cannot have the same attack rate as swords, figuratively speaking, since swords have an attack rate dependent on type and circumstances? You might get as few as 1 die per four men, or as many as 5 dice per 1 man, and thus the ability to inflict from 0-100 casualties with 20 men in melee per round, but only ever 0-20 with bows and 0-10 with crossbows.

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  12. Chainmail's combat resolution tables are not part of this discussion.

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  13. Now you have lost me. ;)

    So, what are you driving at here? That bow shooting rates should be the same as the number of melee attacks made in a mass scale combat system based on OD&D in order to give a nod towards historical simulation? Or are bows only employed once per round in your OD&D campaign? Will only the first two ranks be able to shoot in this system?

    I do not think it really matters too much, but if the mass combat game is intended to be OD&D on a mass scale, it should probably follow the same rules.

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  14. Yes, bows are only employed once per round in my OD&D campaign.

    Recap of reasons: (1) Matches my real-life research on attack rates, (2) Is the correct scaling down of a mass figure that fires arrows at twice the rate of sword attacks, and (3) Is simpler and more elegant to resolve.

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  15. Right you are; so what is the shooting rate at 1:10 and 1:20 scale? 3 per round (30 seconds), and 6 per round (60 seconds) respectively? (per volley).

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  16. Yes, for individual bows.

    In my own 1:10 mass-combat game, to tell it briefly, every 15 individual attacks become one mass die roll. So each mass archery figure is again making 2 rolls per turn.

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