Wednesday, 8 April 2015

Sizing Things Up

By way of explanation: This blog mostly consists of extracts from my homebrew system Explore, but they should mostly be applicable to any other system which is vaguely OSR related due to a shared heritage. Explore is a traditional role playing game of exploration / adventure / intrigue in a world of swords / sorcery / monsters. The rules have been iteratively developed and refined through the fire of play testing (I have very critical players!) in an attempt to make them as simple as they can be without losing their vital essence.

I've previously given a system of heights and weights of humans, which leads to the obvious question of heights and weights of other races. Here below is a unified system of measures and related bonuses, which in particular can be applied to the heights and weights of non-humans. My desire to find such a system has it's origin in the observation that it's very tricky to work out a consistent set of such bonuses, and I always find myself querying these bonuses in other systems, so such a system makes it much easier for me! As usual you can adapt this to other systems.

By "unified system of measures" I mean I’d like the same system for working out what damage penalty a Halfling gets compared to a human, and for working out what damage bonus a giant wolf gets compared to a standard wolf, and in fact for working out what damage bonus a statue made out of stone might get, or what bonus a ballista might give compared to a crossbow. And it’s got to give sensible answers. And it’s got to be simple.

Firstly I borrow from a popular idea for simplifying encumbrance - precise weight is not important (the earliest reference I know of this is Delta's weighing things in stones), and apply this to all measures. (So everything is measured to the nearest rank)

Secondly I continue the principle from my open dice system that +1 always means the same percentage increase. (So there is a fixed ratio increase between ranks)

Thirdly I link the different measures and bonus system, so that if you increase the height of a creature by one rank, you also make it +1 weight and +1 damage and +1 strength.

Let's start with weights:

Weights are given in pounds, and every two categories the weight doubles:

1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24, 32, 45, 64, 90, 125, 180 etc.

Things will only ever be given a weight from that list.

How much does a Giant weigh?
If a 6’ human weighs 180lbs, how much should a 12’ giant of the same build weigh?

You might expect it to go up 2^3 = 8 times, but the general consensus appears to be that weight goes up at a power of 2.5, so 2^2.5 = 5.7 = approx 6 times. In our system of weights this means a size of +5 ranks, which is a weight of 1000lbs. Hence for +1/-1 in weight rank to match +1/-1 in height rank, the height ranks must double every +5.

Addendum - see Squaring The Cube for a discussion of this rule.

Heights are given in feet and inches, and every five categories the height doubles:

3', 3'6'', 4', 4'6'', 5',
6', 7', 8', 9', 10', 12’, 

Again heights of things are only ever given from this list.

Note that characters have more precise heights and weights, but that's purely for flavour.

Inanimate objects
Surprisingly this rate of increase also works for inanimate man-made non-solid objects such as clothing or tables. As a table gets larger you have to make the legs thicker, so they go up by more than the square of the size, but they don’t need to be made as much thicker, so they don’t go up by as much as the cube of the size. Hence a giant’s sword (like the giant) is twice as long, and is six times as heavy.

How strong is a Giant?
The height bonus for a Giant of +5 translates into a +5 damage bonus purely because of their size (they will probably get another +3 for being strongly built for a total of +8), which seems reasonable.

Am I dense?
If you increase the density of a weapon (keeping it the same weight), then it concentrates the force and hence the damage. For density we keep with the same +2 categories = double the density (This is so that +1 density has to be accompanied by -1 size or +1 weight).

Densities are given in pounds per square foot, and every two categories the weight doubles:

50, 75, 100, 150, 200, 300 etc.

For example, Animals are 50 lb/sq foot (as is water, ice, and wood), Stone is 150 lb/sq foot.
Note that for simplicity we assume that density and strength of a material are the same, which means we have to include a slight fudge - there is an ad-hoc rule where a human punch is less deadly which would not apply for example to a stone one.
So, how about a human-size statue made out of stone?

How strong is a Statue?
Stone has +3 density compared to flesh, but the statue is the same size so it is also +3 weight. So the statue is 6' tall, 150  lb/sq foot (+3), weighs 500 lb (+3) and is +6 damage.

Speed versus Size
Now the speed of an animal is more affected by their build than their size; small animals tend to scurry and large animals tend to plod. So I'm having Halflings and Giants move at the same speed as humans. Similarly I'm having their maximum speed they can throw things to be the same (Giants can just throw heavier items - they can throw a small boulder as far as I can throw a tennis ball).

A range of values
So what about range? How does throwing something faster and further affect damage?
If a giant hits me with a sword he gets +5 damage, and so if he throws a spear at me you’d also want +5 damage.
The spear's +5 damage comes not from increased speed / range, instead it comes from the +5 weight.
We're going to assume that the damage comes from increased Kinetic Energy, thus it is proportional to the velocity squared, thus proportional to the range.
So if +5 range gives the same bonus as +5 weight, range doubles every other rank, like weight.

Range / Drop
Ranges and drops are given in feet, and every two categories the weight doubles:

10', 15', 20', 30', 40', 60', 80', 120', 160', 240', 320', 480', 640', 960'

(Drops have the same maths as Ranges, so they use the same ranks).

So that's enough explanation for now. In the next post I'll cover in the next post examples of how to use this quickly for many different purposes.

No comments:

Post a Comment