Tabletop games can often only handle a narrow range of physical (or other) scales, but for some concepts, widely varying scales are relevant. WEG's old Star Wars d6 used different scales -- so people, speeders, and ships could all come into play -- using one method we'll look at.

Three six-sided dice of different sizes

There are four broad approaches we could take.

I. Linear Scale

This is normally what's used in games, and provides poorly for different scales. The numeric values (like damage capability, say) simply fall in a range of integers, or a susbet of them (for instance, if die size is varied as part of the mechanics then only even values between 2 and 12, plus 20, are permissable).

Die scaling option I

To accomodate very widely varying scales, very different numbers must be used: a human might be scale 1 while a vehicle is scale 1,000. The difficulties should be obvious enough:

  • Only a subset of mechanics can deal well with such figures. Varying die size is ruled out.
  • Even simple mathematical operations becomes annoying for human players: division and multiplication are ruled out, and even subtraction is a hassle.
  • Small numeric differences are important at the low end of the scale, but trivial at the upper end (1+1 versus 1000+1). Nonetheless, all such differences must be kept track of.
  • General inelegance.

II. Discrete (Interchangeable) Levels

The least mathematical solution is to divide the range of possible scales into qualitatively discrete levels, and design mechanics to work well within any of them.

Die scaling option I

This is the route taken in Star Wars d6, with a human scale, a speeder scale, and a ship scale. It's presumed that most of the time, mechanics will operate within a single scale; that is, game elements of the same scale are interacting with one another. This means one (fairly ordinary) set of mechanics can deal with the dynamics of the game, and can do so at any scale. (Of course, very different mechanics could also be used for different scales, but this isn't necessary.)

The rub is interaction between scales: special rules will have to allow conversion. For instance, by multiplying and dividing values, or some other transformation. Alternately, large scales could simply trump small scales, with rare exception (natural 20s, the expenditure of special character points).

There are disadvantages here too:

  • It is only reasonable to use a few different scales. While theoretically any number is possible, as the number goes up, interactions between scales become more numerous, and presumably more cumbersome (since the rules are "optimized" for the "normal" situation of in-scale action).
  • Generally presumes few between-scale interactions, which is really only true in some games. An RPG like Star Wars can uphold that expectation, because each scene has a certain mileu. But in a wargame or other board game, across-scale interaction may be the norm.

IIb. Discrete Levels with Different Mechanics

As above, but multiple, quite different sets of mechanics are used at each scale.

Die scaling option I

The advantage is that each scale has a unique feel, and can model dynamics appropriate to the events happening at that scale. For instance, human-scale combat might be very random and dangerous, and based around traditional modifiers and hit points; while combat at the scale of techno-derigibles would be slow and thoughtful, with complex interactions of special ship powers. The disadvantages:

  • Because players will have to learn distinct systems, only two or three are probably feasible.
  • Each system can only be but so complex, or speed will suffer as players must look up rules more often.
  • As in II, between-scale interactions are still a special case. Worse, a different conversion rule is needed for each pair of scales (with three levels, three sets of conversion rules are needed; with four, six are needed; and so on).

III. Non-Linear Transform (Plus Fudging)

If we defined an ideal set of discrete scales to work with, to cover a large range, they might well be an exponential series: 1-10-100-1000 or 1-2-4-8-16. But humans are not great at manipulating exponentials in their heads. Instead we can provide players a linear scale representing the "virtual" scale. In the above cases we can use the exponent itself: a numeric scale of 4 in the game would represent 10^4 or 2^4.

Die scaling option I

This does pose a challenge mechanically: dice and other common methods are linear variables, not expontents or even products. But consider that in comparing two in-game attributes, it can be seen as division: the odds of one character winning versus another, say. To divide two exponential statistics, one subtracts the exponents:

strength 2 v. strength 7

Represents:

2^7 / 2^2 = 2^5

And can therefore be compared simply:

7 - 2 = 5

This 5 represents odds of 2^5:1 (or 32:1) of winning, which is 97%. We just need a die mechanic that simulates that in its use of the attribute values (or thier difference, 5).

It turns out that counting successes (i.e., 4+ on a d6, or a coin toss) creates about the right odds when players roll dice equal to their attributes: 7d6 wins against 2d6 about 91% of the time, and ties 7%.

These mechanics do not directly come from the "virtual" scales, but work well enough. In this case the virtual scale represented a base of 2; but higher bases, like 10, probably cannot be so easily approximated. And as with any variable-die-rolling methods, high values quickly become cumbersome. A final key element is to interpret values, in in-game terms, exponentially.

IV. Relative Scales

A more radical alternative is to begin with the assumption that very different scales will interact, and be compared, most of the time. Therefore, attributes actually name a scale, rather than a small numerical variation. Because there will be a large number of such scales, they are always compared relatively: i.e., an attribtues never directly gives a certain number of dice to roll; instead, attributes are always transformed in reference to competing attributes.

Die scaling option I

For example, if a spaceship of size 7 fires on one of size 5, neither of these numbers is used: +2 is. And a +2 value can be referenced on a chart to indicate, perhaps, 6d6 are rolled against 1d4.

The disadvantage is that many charts, or many mathematicl operations, will still be required to create effects that expand or shrink as necessary. However, upper and lower bounds make this more feasible: if a size 10 ship attacks a size 1, the 1 is simply a goner, and no further mechanics are really necessary. In generally them, more binary, qualitative results may be preferable -- and make this method better for a "softer" game, with less tangible elements, like heroism and cosmic balance, rather than pounds-per-square inch or hit points remaining.

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