GURPS Scale

Introduction

Fundamentally, GURPS is designed for characters operating on a human power scale, and works pretty well within that regime. Outside of that regime, it doesn't work so well. Some of this is just an issue of point costs, but there's just no way you could run something like GURPS Insects using standard values, it's too low resolution, and larger scales can still be a hassle.

There is, of course, a fairly obvious option for dealing with this: just change the meaning of ST, HP, DR, and so on, so a character with all abilities at default is an average character for the setting. As long as you aren't planning on crossovers with other settings (including using creatures from other settings) this might be all you need. If you are, though, it gets a little more complicated.

Common Scales to Adjust

There are several things that can be useful to scale in a game:

• • Damage Scale(DS): what a single hit point, point of DR, or point of damage means. GURPS has already introduced the concepts of D-scale, C-scale, and M-scale for damage (those are somewhat unfortunate names for those who are used to metric terminology, which would probably use da-, h-, and k- for those scales, while d- would be 1/10, c- would be 1/100, m- would be 1/1,000, and M- would be 1,000,000).

  • Hex Scale (HS): for mapped combat, the size of a hex on the map. Assume anything that talks about yards is really talking about hexes, so you can move a single hex as part of a step, move your Speed in hexes as a move, and so on. This includes calculations of size modifier.

  • Mass Scale (MS): replaces 'pounds' in calculations of lifting, mass affected by powers, and so on.

  • Turn Scale (TS): the length of a single combat turn. This is already used to some extent in vehicular and spaceship combat, but there is no particular reason it can't be extended to other creatures.

Derived Scales

There are other scales that are not normally adjusted, but are rather ways of describing the interactions between the scales above. They are as follows:

• • Collision(CS): What multiplier to use in the collisions rule on B430; 0.01 in default scale. Equal to 0.01*HS*MS^(1/3)/(DS*TS). This assumes that a hp scaling that doesn't match mass scaling means massless hp.

  • Gravity(GS): When using the falling rules on B431, multiply distance by FS to determine fall speed. If you need fall time, it is equal to computed fall speed / (10 * FS). FS is equal to (local gravity in Gs)*TS^2 / HS.

  • Object Toughness(OTS): how many hp an object should have (in units of DS), as compared to an object of similar relative size in default scale. Equal to HS^(1/3)/DS. Also gives the DR of barriers with the same relative thickness.

  • Object Weight(OWS): how much an object should weigh (in units of MS), as compared to an object of similar relative size in default scale. Equal to (local gravity in Gs)*HS^3/MS.

Sample Common Scaling

World of Props Scale

World of props scaling occurs on a movie set, so the giant rocks are made of styrofoam or paper-mache, walls are made of thin plywood or even paper, weapons and armor are made of wood or plastic, and so on.

Basic Cinematic Scaling

In the days before CGI, if you wanted to make a giant monster movie, you dressed your actors up in rubber suits, built a bunch of toy houses, and started filming. You mostly avoided having the monsters and the normal humans on the same screen at the same time, and when you did it probably looked bad. This is by far the easiest type of scale to use in a game, because almost everything works normally. You can't really match the way it works in films, as the filmmakers often varied the size of the creature between scenes (King Kong was 18-60' fall, Godzilla used both x25 and x50 sets), but you can come reasonably close.

What this means is that a giant monster moves about the same way as a human. It also means that if a giant monster, say, picks up a giant rock and throws it at another giant monster, it's going to have the same arc and flight time on screen as

The simplest scaling is, of course, hex scale; it's obvious that it matches the size of the monsters, so if Godzilla is at 25x, the hex scale is 25 yards.

The next simplest is turn scaling: at fixed acceleration, the time taken to perform any given action scales with the square root of distance. While we don't immediately know the acceleration from muscles, the acceleration of gravity doesn't change meaningfully with size, and controls the speed of actions such as walking; since the speed of other giant monster actions, in compared to the speed of walking, looks normal, we can probably assume that acceleration from muscles is also the same, and the general turn length is multiplied by the square root of linear scale. Note that this still means giant monsters are very fast -- if Godzilla is a 25 yard hex scale and 5s turn scale, with a basic speed of 5, his move is (25 yards)*(5 move)/(5s), or 25 yards per second, or 50 mph.

Mass scaling is slightly more difficult, because we don't actually know how dense giant monsters are, though in the simple case of a giant sized human, it's just (size scale)^3 -- mass obviously scales with the cube of height, and as we noted above, giant monster acceleration seems to be about normal for their mass, so available force is linear in mass. Of course, giant monsters are usually dealing with prop scenery so lifting things that aren't giant monsters is easier.

If you scale a 5'8"/150 lb man (average ST 10 in GURPS) to 50 meters, computed weight is about 1,800 tons; the actual claim from the studio is 20,000 tons. The latter is fairly implausible due to Godzilla's apparent ability to swim, though he's bulky enough for a weight of 3-4,000 tons to be believable.

Finally we get damage scaling, which runs into a problem. On the one hand, GURPS normally expects something N times bigger to have N times more hit points, so a 25x larger humanoid has 25x more hit points. On the other hand, our giant monsters aren't just bigger than human, they also move a whole bunch faster; even if we assume any extra hit points are massless, a collision at 5x the speed does 5x the damage, for a total of 125x more damage. This causes destructive power to rise much faster than size -- specifically, it rises with (size scale)^1.5.

There are a couple of reasons to choose the larger value. One is consistency with how ST works -- lift varies with the square of ST, HP are linear in lift, and we already established that the mass scaling is (size)^3. Another is collisions: we want a giant monster moving at 5 giant monster hexes per giant monster turn, with 10 giant monster hit points, to to (5 x 10)/100 giant monster damage dice. Finally, well, most giant monster movies in fact use extremely flimsy scenery, specifically to make the giant monsters look more impressive. Frankly, even with 1250 ST and DR 250 or so, Godzilla isn't all that impressive compared to tanks.

World of Props

, it seems plausible that a

If we were to scale a 5'8"/150 lb man ('average' ST 10 according to B18) to 50 meters we get a weight of about 1,800 tons.

, but simple geometry says if we take the weight of a 6' version of the monster and multiply by (scale^3) we get the final weight. If we assume a 6' Godzilla is 300 lb, a 50 meter version would be about 3,000 tons. Note that this differs substantially from the studio's claim of 50 meters and 20,000 tons

The amount of time it takes to do gravity-assisted actions such as falling, including the falling involved in normal walking or running, is proportional

Basic cinematic scaling, obviously, increases hex scale to match the size of the monsters,

Basic cinematic scaling works as follows:

• • Damage Scale: while mostly limited by

  • Hex Scale: SM, obviously

  • Mass Scale: SMx3. Note that this is not the same as

To give an example, in a fantasy game it is plausible to choose ST 20/DX 10 over ST 10/DX 15; while both will give some good abilities, it's not obvious that one is glaringly superior to the other. On the other hand, in a Giant Monsters game, choosing ST 1010/DX 10 over ST 1000/DX 15 is not so plausible; a 1% increase in damage/hp and 2% increase in carrying capacity is not worth 5 points of skill. There are several ways around this, but one very easy method is to rescale the game so ST 10 is now an average giant monster, instead of an average human. At that point, we are choosing between ST 10(GM)/DX 15 and ST 20(GM)/DX 10, which we would expect to be just as balanced as human version.

By itself, this isn't a particularly deep observation

By itself, this isn't a particularly deep observation. However, a game at a different scale really does behave in somewhat different ways, and these are worth discussing, as are ways of resolving interactions between characters at different scales. The remainder of this article will go into greater details.

The Scale Chart

T

Damage Scale (100/level if positive; -100*(linear scale-1) if negative).

Damage scale determines the basic meaning of a hit point; D-scale is scale +6, C-scale is scale +12, M-scale is scale +18. When converting between scales, damage is multiplied by linear scale for (attack scale-target scale), or DR is divided by the same amount (this is usually only needed is several defenses, at different scales, are involved, but also applies to afflictions). All fractional values are rounded down. In addition, afflictions add (target scale-attack scale) to the initial resistance roll. Collisions use the damage (hp) scale of the colliding creature. Special modifiers:

• • Attacks Only: -40%. Damage scale applies to attacks but not defenses.

  • Defense Only: -40%. Damage scale applies to defenses but not attacks. If you have this limitation, you may also apply the Limited modifiers from the DR power.

  • Limited: Powers Only: -ST%; applies to a maximum of 6 levels.

Distance Scale (

Types of Scale

There are actually many different types of scaling a game could engage in; however, this article will focus on only four of them: damage scale, distance scale, mass scale, and time scale, plus a few combined or computed scales. They have functions as follows:

• • Damage Scale: 100*scale (if positive); -100*(linear scale-1), if negative. Normally Always On.

  • A game's damage scale determines what a hit point means; D-scale is scale +6, C-scale is scale +12, M-scale is scale +18. When converting between two scales:

    • Multiply damage resistance by linear scale for (target scale-attack scale). This is not considered armor piercing, and is not affected by hardening.

    • Multiply injury by linear scale for (attack scale-target scale). Less than 0.5 damage becomes 0.

    • If defenses at different scales are not involved, the above two steps may be combined by multiplying damage done by linear scale for (attack scale-target scale) before applying DR.

    • Damage scale applies to all your personal abilities, including ST, though note that it multiplies your actual damage, not your ST score; your swing damage at ST 10 (scale +2) is 2d, not 3d+2. If you want super-attacks without super-ST, buy your basic ST down until its scaled value is appropriate.

  • Distance Scale:

  • A game's distance scale determines the size of a hex. Conversion is slightly more complex:

    • Multiply Move, Range, and Reach by (character scale)/(game scale).

    • Multiply Radius of Area Effects by (character scale)/(game scale).

    • Explosion splash damage is divided by range * 3 * (game scale/character scale), but never exceeds 1/3 of the base damage. Thus, a x5 scale giant does 1/3 explosion damage out to 5 hexes, and beyond that divides by (range*0.6).

    • A character whose personal scale is larger than the game's scale cancels out range penalties equal to the range penalty for (character scale/game scale)*2 hexes; this cannot reduce range penalty below zero. Thus, a giant with x5 scale cancels out a -4 range penalty (equal to the range modifier for 10 hexes range); at a 15 yard range (-5) he only has a -1 penalty.

    • A character whose personal scale is smaller than the game's scale has extra range penalties equal to the range penalty for (game scale/character scale)*2 hexes; these penalties are reduced by 2 at 1 hex range, 4 at 0 hex range. Thus, a pixie with x0.1 scale suffers an extra range penalty of -6, which becomes -4 at 1 hex, -2 at 0 hexes.

  • Mass Scale:

  • A game's mass scale determines the basic unit of weight:

    • Multiply BL by (character scale)

    • Multiply mass affected by powers by (character scale)

    • For scales greater than 1, add 2*the size modifier for (scale/2) to ST for quick contests.

    • For scales smaller than 1, subtract 2*the size modifier for (2/scale) from ST for quick contests.

  • Time Scale:

  • A game's time scale determines the basic turn length for characters.

    • A character whose time scale is shorter than the game scale may act (game scale/character scale) times per turn.

    • A character whose time scale is longer than the game scale may act (character scale/game scale) times per turn.

    • For simplicity, multiple attacks can be resolved with a single roll. Treat as an autofire attack with a recoil of 1 and an attack bonus of 1+(SM for number of attacks); e.g. 10 attacks are resolved as one attack at +5.

There are also several combined types of scale:

• • Power Scale (xN)

    • Grants Damage Scale (xN)

    • Grants Mass Scale (xN^2)

  • Size Scale (xN)

    • Grants Damage Scale (xN)

    • Grants Distance Scale (xN)

    • Grants Mass Scale (xN^2)

    • Grants Time Scale (xN)

    • Increases SM of character, with all associated effects.

  • Growth (Super)

Point Cost for Scale

GURPS doesn't generally use scaling for damage, though it does for a number of other effects, such as distance (x10 for a -6 modifier). Using existing rules, you can get roughly 10x damage and durability with injury tolerance (damage reduction) +6, cosmic (no minimum damage) [225] and striking ST +6, super-effort (+400%) [150] for a total cost of 375, though a power scaling of x10 will affect powers that aren't modified by those abilities. In the end, I decided that 100 points per step on the range/speed chart is appealing.

; a power scaling of x10 will apply to a few effects that those abilities don't modify

In the end, I decided on a logarithmic cost for beneficial scaling (500 points for x10 damage, for example) and a linear cost for detrimental scaling (this makes detrimental scaling extremely inefficient; it's usually better to just buy lower levels of scaled powers, unless you have no scaled powers). To cut down on magic numbers, I chose to not have an exact number per step on the range/speed chart, instead using the logarithm of the value. Final costs are as follows:

There are a number of possible combined scales, which have a point value somewhat lower than the sum of their parts, usually because there are some semi-redundant effects.

Use this cost for Damage or Turn Length scaling. Hex Size scaling is

In the end, I decided on a scale for damage that x10 damage was worth 500 points; to cut down on magic numbers, the cost for intermediate levels are slightly tweaked. 10x mass is

a character has a range penalty of zero out to a distance of (character scale/game scale)*2 hexes, and beyond that each step on the range/speed chart is its normal -1. Thus, a x5 scale character has no range penalty out to 10 yards, at 15 yards has a -1, and so on.

, multiply move, reach, and so on by (character scale)/(game scale).

• • Damage: exactly what it sounds like, and already something GURPS takes advantage of. Can be split into offensive and defensive, if desired.

  • Hex Size: how big are hexes. Not something GURPS does very often.

  • Mass: the amount of weight that can be lifted or affected by powers.

  • Turn Length: how often characters act.

There are several methods around this, but one obvious answer is to rescale the game so your average giant monster has ST 10. At that point we get to compare ST 20(GM)/DX 10 to ST 10(GM)/DX 15, and we have exactly the balance we had when we started out. The rest of this article will cover two issues: playing in exotic scales, and handling exotic scales in a way that's compatible with a generic game.