Dime-Scale Strength, Damage, and Characters

[GreatWyrmGold]

Shrinking characters down to miniscule size and societies of tiny people are common tropes in fiction, but GURPS doesn't handle them all that well. The system simply lacks resolution at that scale. I've seen an official system for half-levels of Strength, but that didn't particularly help with the granularity of statistics based on strength (ie, HP and damage). I've been brainstorming a way to make a more precise system for a while, and think I've hammered out the details well enough to share it.

It involves finding the statistics which change the most from changing size and are expressed in game terms rather than real-world ones (damage, health, SM) and finding a way to shift them down by a given factor. Since GURPS already has rules for decade-, century-, and millennium-scale damage, I decided that the best place to start would be multiplying the health and damage of these tiny creatures by 10. I call this dime-scale, because the only other idea I had was decimal-scale and that sounds vague.

Part 1: Data

Spoiler:  

I decided to start by figuring out how much dStrength would equal normal levels of Strength. Since magnitude scaling is based on damage first and foremost, the damage dealt by plain old Strength is the main factor in making this system (second only to ease of use).

I tossed some numbers into an Excel spreadsheet, did the math, and got the following chart:
https://image.prntscr.com/image/kLIu...UVNEqcMA-Q.png
Turning the Strength approximations into a graph produced the following approximations:
https://image.prntscr.com/image/ZOhi...pr0Oj2clWg.png
https://image.prntscr.com/image/R7P0...DQ4yUdrJFQ.png
The quick and math-savvy among you will notice that, while those approximations work well, they are very much nonlinear. Thankfully, there is a linear approximation which works well enough (accurate to within ~10 ST) over this range:
https://image.prntscr.com/image/JJwU...VB7j12e_pQ.png
Unfortunately, it's not quite what we need, either. See, the formula is linear, but doesn't intersect the origin. This means that following it strictly puts ST 1 at roughly dST -50. This is, obviously, nothing like what we would want.

My dreams of an elegant mathematical solution effectively shattered, I decided to pick a decent, simple approximation and go with it, deciding that a factor of 5 would do perfectly. In other words, dST 10 would be ST 2 and ST 10 would be dST 50. It lacks the precision I was hoping for, but it works fine. A more precise approximation would be to halve the square of ST to get dST, meaning that ST 10 would be dST 50 and ST 2 would be dST 2, but the assumptions this generates obviously fall apart quickly at low dST values.

Part 2: SM, or Putting Dime-Scale Into Context

Spoiler:  

How big are dime-scale humans? That is, how big would humanoid creatures with dST 10 be?

There are a few ways to figure this out. First would be to cross-reference with other creatures of ST 2; unfortunately, the Basic Set only goes down to 3 (Falcon, SM -4) and 4 (Cat, SM -3); however, these suggest that a dime-human would have an SM around -5.
Alternatively, we could look at Basic Lift. BL at ST 2 is 0.8, 4% that of a ST 10 creature. Strength is roughly proportional to the cross-sectional area of muscles, which is roughly proportional to the square of the length. This suggests heights between ~12 and ~14 inches, which is roughly equal to the lower end of SM -4.
Another possibility is to look at firearms and make sweeping generalizations. For instance, an LMG deals about 24.5 damage per bullet, so a dime-scale LMG would probably be smaller than a derringer (average 3.5 damage per bullet); a normal derringer is 1/60 of the weight of an LMG, suggesting that dime-scale humans should have about 1/60th the weight of normal humans. Similarly, an HMG does about 51.5 damage per bullet, while a snub revolver deals about 5.5 per bullet; the difference in weight is a factor of roughly 1/77th. (While machine guns have additional weight and complexity from needing to fire many bullets rapidly, they also have a comparatively small proportion of weight devoted to necessary details like the grip. For the purposes of this crude approximation, this probably balances out well enough.) This suggests dime-scale humans would be shorter than normal humans by roughly a factor of 4, making them roughly 15-18 inches tall (the upper end of SM -4).

Both SM -5 and SM -4 would work well. I'm inclined to go with SM -5, if only because bird-sized humans should probably be stronger than birds rather than weaker (due to birds needing to be specialized for flight above all else).

TL;DR: Dime-scale humans would be SM -5 or SM -4—that is, somewhere between almost a foot and a foot and a half.

Part 3: Playing with Dime-Scale Creatures

Spoiler:  

Luckily for us, GURPS handles changes in size pretty simply. Nearly all statistics will be the same for dime-scale characters as for normal ones; Strength and related attributes need to change, of course, but essentially everything else can remain the same.
In a campaign with both dime-scale and normal PCs, point costs for Strength, HP, and Basic Lift will need to be adjusted. First, the character gets -8 to ST for -80 points. Modifying dST costs 20% the normal amount—that is, 2 character points per point of dST. dHP (or unmodified Damage Reduction) can be bought at a rate of one character point for two HP or two for five. Lifting dST can be bought at one level for one point, two levels for two points, or five levels for three points. Striking dST costs one character point per level. Campaigns with only dime-scale PCs should charge for dST and related traits as if it were normal-scale ST.
These traits can be recorded as either their dime-scale values (e.g, "dST 12) or as fractional normal-scale values (e.g, ST 2.4). Resolution should generally be carried out using normal values.

Beyond that, the rules for handling dime-scale creatures are are largely the same as for decade-, century-, and millennium-scale combat. For situations when larger creatures attack smaller ones with their physical bodies, there is also the option of converting their ST into dST and figuring damage from there. For instance, a human kicking a dime-scale creature would have dST 50. This would deal 5d+2 damage to the hapless little creature.

If using dime-scale rules alongside decade-scale ones, it is highly recommended that you make a clear standard notation distinguishing the two! I recommend using lowercase d's for dime-scale values and uppercase D's for decade-scale values.

If running a dime-scale campaign, it is highly advised that you rewrite existing animal statistics into their dime-scale equivalents.

Part 4: Cent and Miniscule Scales

Spoiler:  

Why not go a step further? After all, the decade-scale damage system is escalated by century- and millennium-scale damage.

Cent-scale creatures have 1/25th the Strength of normal creatures, deal 1% the damage, and have a "default SM" of either -8 or -10—that is, 1.5 or 3 inches tall. (SM -9 is an acceptable compromise, if that's what you want.) Miniscule-scale creatures have 1/125th the Strength, 0.1% damage, and have a default SM of -12 or -15 (0.7 or 0.25 inches tall). This puts them roughly on the scale of small rodents and insects, respectively.

It is not recommended that a campaign include cent- or miniscule-scale PCs alongside normal-scale ones, or miniscule-scale PCs alongside dime-scale ones. Character points are not granular enough to handle such very small differences in Strength, Hit Points, and so on. If you want to play a mouse-sized PC in a normal campaign, use dime-scale rules and give them a low dST. Similarly, to play a bug-sized character in a dime-scale campaign, use cent-scale rules. Those who want to play a bug-sized character in a normal-scale campaign are advised to make them at least as strong and tough as mice, and to build them on the dime scale.

If you want to use these guidelines to play even smaller creatures—SM -16 or -20, 0.15 or 0.03 inches tall—you're on your own for naming that scale. And speaking of names, yes, I know that dimes are smaller than one-cent pieces (at least in the US).

Appendix: Metric Conversions for Specified Sizes

Spoiler:  

I like the Metric System, and a lot of fractional-inch modifiers just aren't helpful for me.

BL-based approximations suggest a height between 30 and 35 centimeters. Firearm-based ones suggest a height between 40 and 45 centimeters. Dime-scale humans would be somewhere between 20 and 45 centimeters tall, depending in part on if you go with SM -4 or SM -5.

Cent-scale humanoids would be 4 or 7.5 centimeters tall. Miniscule-scale ones would be 6 or 17.5 mm tall. Even smaller ones would be 0.75 or 3.75 mm tall.

How does it look? Did I mess up the math badly, or miss an obvious way to simplify things? Are there any other mechanics I'd have to tweak?