I need help with distance scaling in a homebrew RPG - from "your body" to "the whole planet" in 10 simple steps

Question

Years ago, I developed and play tested a simple RPG system, in which magic-alike powers were driven by 2 parameters, namely Power and Precision.

• With high precision and minimal power you could burn a specific card in a standard 52 cards deck without charring any other card.

• With high power and minimal precision you could easily burn a house, maybe even a village, but with a risk of burning the wrong one.

  There were also specific techniques to be used, but that's besides the point for now.

Scales were non-linear, each step about doubled or tripled what you could do (I intend to post it as a separate review question). The idea behind that was to make characters who allowed themselves to have flaws also be more and more shining with their strength, and to make "balanced" characters objectively worse.

Playtesting was showing that it worked reasonably well, but what we lacked in the magic department was Distance - how far a PC would be able affect things with their spells and minds. What we decided would be OK was the non-linear progression from only being able affect one's own body and the things he touches, to the whole globe. A high Precision, high Distance, minimal Power kit would make a great messenger-type character or seer. Self distance would be good for shapeshifters, touch for healers, etc.

We got this rough sketch we never playtested properly, but it was in storytelling terms and had a big hole in it. I was wondering if / how to turn it into numerical values, like meters or kilometers, preferably with a simple equation and not just arbitrary table.

1. One's own body
2. Touch
3. Immediate area
4. Village
5. Town or City
9. A continent
10. Whole world

Numerical or not, this progression seems totally uneven. I expect and want each step to be bigger than previous one, but I want them to feel natural, to feel "not arbitrary" for the lack of better words. (I am not a native English speaker).

Problem: how to make this progression feel more natural?

By "feel natural" I mean that your average player wouldn't be shocked or taken aback by it. Ideal answer would point to other systems that already solved similar problem, your own playtested homebrew experiences, or design guidelines from a reputable source I could use. Seeing your specific solution, be it table or equation, is less important than the process that lead to it, or one that confirmed it works.

Note: 0 means none whatsoever in this system. 0 power is obvious. 0 control means you can't even decide if it's on or off (basically a death sentence unless other one is 0). 0 on distance means your power cannot reach beyond your imagination, your own mind. A lot of children games teaches a basic mental discipline, so Control 1 is free.

Answer 1

Take a look at Mutants and Masterminds

This is the only RPG with which I have direct experience that measures things in ranks, from physical capability to discrete units of distance/mass/etc., so if you're researching ways to set up a capability system based on ranks, this would be something to look at to inform your game's system.

In particular, you want the Ranks and Measurements section: d20HeroSRD link here

The whole table is likely more granular than you want--it has ranks -5 to 30 (0 being base human standard), but it advances in a very logical manner, roughly doubling with each increase in rank. If you're looking to go from Self to World in 10 steps, you may need something more like an 8x or 10x increase.

(You may also need a more complex equation, as a simple 10x increase from a roughly 'touch' range (e.g., 3 feet) remains pretty close range until rank 6 or so. Other answers already posted have taken a harder look at the specific math.)

I will note that this scale is meant to be used with hard measurements: inches, feet, miles, etc. If you want something more qualitative instead of quantitative (e.g., using settlement sizes/line of sight), you will likely get less value out of this.

The Ranks and Measurements section also denotes using the Measurements table with a character's ability ranks to calculate things like speed or throwing distance. From what you've mentioned of your homebrew system, the three spellcasting stats sound like they are separate, and separately improved, but if you wanted to try and design an inter-relation of the stats, or just play with making Distance be a function of the combined Power and Precision stats, that might also be a place to start.

Answer 2

Well, if we take SI units as what we're using, Earth is \$6.371 * 10^6\ \text m\$ in radius, so about \$1.2 * 10^7\ \text m \$ in diameter or about \$2 * 10^7\ \text m\$ for "half of the circumference"

With that in mind, and having 9 rather than 7 levels of "larger" (taking "own body" as 0, "touch" as 1 m), you'd end up with a multiplier of 6.47 per level for the circumference and 6.16 for the diameter.

If you don't massively care about strict discontinuities at the low end, using \$2*10^{n-3}\$ gives you (with two discontinuities). Without those, "touch" turns to 20 cm (8 inches, give or take) and "own body" to 2 cm (4/5ths of an inch), with the following table keeping "own body" and "touch".

1. Own body (or 0.02 m, 2 cm, ~1 inch)
2. Touch (or 0.2 m, 20 cm, ~8 inches)
3. Up to 2 metres (medium-sized group / small room)
4. Up to 20 metres (large hall / building)
5. Up to 200 metres (neighbourhood / complex / large building)
6. Up to 2 km (village / city block / palace grounds)
7. Up to 20 km (city)
8. Up to 200 km (province)
9. Up to 2 000 km (country)
10. Up to 20 000 km (planet)

As for how I ended up with this, I started with the premise that multiple systems already use a logarithmic (or exponential, depending on your point of view) scale. GURPS distance penalties are on an approximately sixth-root-of-10 per extra step, many human sensory organs are essentially logarithmic on incoming stimulus (hearing for sure, 10x sound power is perceived as about 3 times as loud; I believe also sight). This also matches the "roughly doubles or triples" (base somewhere between 2 and 3, rather than 10, though) that the existing system already has for power and precision.

From there, it was mostly an exercise in number-fitting. If ~10 levels is "about right", and the largest number is "world", fitting something to distance on the planetary surface and taking Earth as a suitable model world, it was mostly a case of playing around with the exponential base, trying to balance on the one hand "easy to work with" and on the other "fits the asked-for design".

If we instead had gone with "doubles", we would have had 27 levels, and with "triples", we would have had 18 levels (or, with only 10 levels, a MUCh smaller world).

Answer 3

Square Cube Law

When we increase the range os a spell by a simple value, we increase its area of effect by the square and the volume of effect by the cube. Or rather:

$$R$$ $$A=\pi R^2$$ $$V=\frac 4 3 \pi R^3$$

Energy density is defined as energy per volume. So our power scale should follow the Volumetric scaling, not a linear one. From one step to the next, you increase the energy needed by the third potence.

Self

A typical human body has about a weight of 100 kilos if we are rather broad. A human body also has a density of 1 ton per cubic meter, so a human is 1/10th of a cubic meter or \$1 \times 10^{-1}\ \text m^3\$. That's, if condensed into a sphere, one of about 30 cm radius. $$\frac V \pi \frac 3 4=R^3$$ $$R=0.287 \text{ meters}$$

Planet

Mother earth has a volume of \$1.08 \times 10^{21}\ \text m^3\$.

Scaling the difference

We want to stretch between \$1 \times 10^{-1}\ \text m^3\$ and \$1.08 \times 10^{21}\ \text m^3\$ in 10 steps. That's -1, 0 and 1 to 21, so 23 numerals for the exponent to scale the volume. Let's try to get a nice progression, with a factor 1 in front.

1. \$10^{-1}\ \text m^3\$ - That's the volume of our human, so self
2. \$10^{0}\ \text m^3 = 1\ \text m^3\$ - a 1x1x1 meter cube, or anything you can easily touch with one arm.
3. \$10^{1}\ \text m^3 = 10\ \text m^3\$ - Anything within 1.3 meters, or about 2 steps
4. \$10^{3}\ \text m^3\$ - Anything within 6.2 meters - about a small building or large room
5. \$10^{6}\ \text m^3\$ - Anything within 62 meters - or almost a Manhattan city block (technically that'd be 80.5 meters)
6. \$10^{9}\ \text m^3\$ - Anythign within 620 meters - about 8 blocks or a city quarter or village
7. \$10^{12}\ \text m^3\$ - Anything within 6.2 kilometers - or if you'd stand in the center of Manhatten, almost the whole of the peninsula. So let's round that to Town.
8. \$10^{15}\ \text m^3\$ - Anything within 62 kilometers - or about the size of an average county or shire or halfway to space
9. \$10^{18}\ \text m^3\$ - Anything within 620 kilometers - or whatever is within an about a single European country if you are centered in it.
10. \$10^{21}\ \text m^3\$ - Anything within 6203 kilometers - or a sphere as big as earth centered around you. This sphere encompasses a whole continent. Yes, it means you affect less than half the planet, and only a small fraction of the distance to the moon, but this compromise keeps the scaling somewhat nicely.

The scaling here is clearly logarithmic, with two distinct areas: the "short" ranges (steps 1-3) and then the Magnitude steps from 4 to 10. This allows to differentiate better on the low end, and then proceeds into a smooth large scale, offering useful intermediate steps.

Why this scale?!

So, why did I choose this scale, which focusses on the low end?

First of all: game usability & realism

Most spells that a typical player character could or should use need to be in distances that are within sight or useable in what accounts for typical combat ranges. These paradigms are fit up to somewhere between steps 6 and 7, depending on the weapons involved - a typical military rifle is useful all within step 6, while modern artillery would go up to 7.

The typical engagement distances of armies over time are rather short, so a focus on the short end for spells is best to model typical spells and have a difference in ranges available that allows separating between short and medium range combat spells. Some examples:

• Spear infantry was limited at 15 feet or about 4.5 meters. That's Range step 4.
• Archery in the middle ages was used at ranges of about below 300 meters, so inside the range step 6.
• modern infantry combat doesn't go further than 500 meters usually, and in urban areas is often quoted to be below 50 meters even. Artillery, especially naval one, can stretch that.
  • in fact, the typical engagement range in WW1 was 50 to 250 meters
  • in WW2, the typical long engagement range for tanks was 500 to 800 meters while infantry fought well shorter at below 300 meters. The longest tank hit recorded was 2.5 kilometers... on a stationary target.
  • the longest ever navel artillery hit was 24 kilometers, which makes that the absolute maximum distance we can assume any engagement will happen unless missiles or drones are involved. That is a third of range step 8.
  • Drones are generally used on the same side of the planet to keep latency short by reflecting signals of one satellite only. This is pretty much Range step 10.
  • Modern ICBMs have ranges that are double the range of our step 10 - 12000 to 16000 km. They can hit literally any target on the planet but spend hours in flight. We are in the same order of magnitude though, so that's just a little adjustment of factor 2 or something if you really want to have spells that far

Magic-propagation speed calculation

The scale also has the benefit of being roughly multiples of 60. So it can be used to quickly calculate speeds from the distances. Say our fireball with range step 5 takes 60 seconds to get to that far point, and for math sake, we round to the closest 10. 60 meters/60 seconds means it travels at 1 meter a second, or rather sluggishly and can be dodged. If the range was step 6, that's 600 meters/60 seconds, so in the area of 10 meters a second - Olympic runner speeds! And if it takes step 6 but only takes 6 seconds, we are at 100 meters per second, that's the speed of a longbow arrow or about half the speed of a slow bullet or a quarter of a heavy arquebus.

Look over the plate: other systems

Let me pull out GURPS. GURPS is notorious for cramming everything in spreadsheets. Including this list for range increments from 3rd edition, and I bold roughly equivalent distances to our distances above:

• 1/10" - 1/5" - 1/3" - 1/2" - 2/3" - 1" - 1.5" - 2" - 3" - 6" - 12" - 1.5' - 2' - 1yd - 1.5yd - 2yd - 3yd - 4.5yd 7yd 10yd 15yd 20yd 30yd 45yd 70yd 100yd 150yd 200yd 300yd 450yd - 700yd - 1000yd - 1500yd - 2000yd - 3000yd - 4500yd - 7000yd/4 mi (~6 km) - 10000yd - 10mi - 15mi - 20mi [~30 km] - 200mi - 2000mi - 20000mi - 200000mi

Those are horrible fine segments, and the modifier progression in that thing goes from -15 to +49 with 0 on the 2-foot step. But for the far distances (where GURPS goes with half my proposed distances but adds another increment in the end), the distances I propose show up, making them at least useable for a simulatoric standpoint.

The picture of putting the focus on the engagement ranges of combat however shows itself in various Fantasy RPGs:

In my decade-and-half of being the GM for various The Dark Eye groups, the longest engagement range ever wanted was 550 meters from the weapon used - a heavy trebuchet. Most TDE spells have a range well below 100 meters, even there are very few spells that have a range of as far as the eye can see or continent. I only know of one instance where such a spell was used in combat at distances further than about 100 meters - and it was aimed at a target the size of a house. Any spell that I witnessed to be used at a longer range was either a communication or clairvoyance spell. In this I am not counting any trans-planar spell: the distance to hell is one step through the invocation/banishment pentagram. As a result of the costs and targeting needed, most combat magic in this system is actually pretty close to mundane ranged weapons when it comes to their ranges, even though the efficiency/impact of the spells can be much higher.

Pathfinder 1e and D&D 3.5 have only very few spells that have ranges that are longer than half a kilometer (those exceptions are generally clairvoyance, communication, or translocation spells). Most combat spells are even limited to less than about 100 meters. Generally, magic can be (and is) treated as just another type of ranged weapon in Pathfinder, even if area-effect spells are common.

Shadowrun also fortifies this experience: Shadowrun imposes no range limit but the (optically redirectable) line of sight (and ability to see its target) of the caster. However, in the last 12 years of playing Shadowrun the longest spell directly cast by any caster I witnessed was about 250 meters using binoculars, and most spells were flung even below 50 meters. In fact, I remember only very few casts of spells further than 50 meters, unless a spirit sent on a mission was involved. As far as I witnessed, even as magic in this system is allowed to be super-long-range, generally it was used at ranges where close-combat weapons are used - and often as a replacement for such.

Mage the Ascension uses one of the magic disciplines as the limiter for distances in its rather freeform magic system, on a success scale: you need 1 to target something that you can see, 2 allows you to reach a very familiar place (like you home) no matter how distant, 3 a familiar place (your buddy's home), 4 gets you to a place you have been once (like the capitol), 5 can get you somewhere you have only been described or seen on a photo and 6 gets you anywhere on earth you can imagine, even if you have no idea what is there. But yes, Mage is a really poor limiter in magic ranges, as it is very free in casting magic (and only clobbers you over the head with paradox for it).

Answer 4

I think a radius from a point would make sense here, because you can have both distance and area in mind.

1. One's own body - radius 0m

2. Touch - 2.5m radius (for medium size creatures)

3. Immediate area - 10m radius (a round figure around the minimal average distance it takes to pull a pistol and fire a first shot successfully at an incoming knife attacker - 7m)

4. Village - 100m radius. I didn't try too hard to understand this study but I think the average size of a village (rounded for easy application) is about 5 Hectare for about 50000 people. I might be way off so check yourself (wtf is 7 log population...). I think that 100m radius (about 3 Hectare) is ok for a small village. I'd note that an arrow flies about double that, 200m so you need to decide if you want a good log transition or usability in game.

5. City - 1Km radius. Including farmland outside of it.

6. Region - 10Km radius. Enough room for a few cities and villages.

7. Kingdom - 100Km radius. Keeping with round numbers and smaller than real life examples.

8. Empire - 1000Km Radius. Area of Europe is about 10M Km^2 which gives less than 2000Km radius. For simplification I'd say 1000Km radius would make a good distance for an empire in a smaller than earth world. An empire would have several kingdoms in it and should be continent size.

9. World - 5000Km radius for simplification. The real radius of the world is 6371Km.

Answer 5

Here's my suggestion for distances:

As a preface, rather than a mathematical equation that calculates how far away you can reach, I took inspiration from how Ars Magika does ranges.

In Ars Magica, there are only a handful of distances, Personal, Touch, Eye (you have to maintain deliberate eye contact with the target for the duration of the casting), Voice (the distance your voice carries, estimated at about 15 paces for a normal speaking volume, or about 50 paces for shouting), Sight (anything you can directly see), and lastly, Arcane Connection (anywhere you have an arcane connection too, distance is immaterial).

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Ranges 1-5 are the Basic Distances. They'll be the most commonly used, and most players won't have a reason to bring their skill higher than 5. These should all be fairly straightforward to understand. You should expect to see these get used in most any regular fight, since incredible range isn't typically necessary.

1. Self Only affects the caster This range would be used exclusively for buff spells, since it can be reasonably expected that you wouldn't normally want to cast a harmful effect on yourself. In D&D, this would be spells like Shield.
2. Touch These effects of spells using this range can be transferred to another target, but you have to physically make contact with them. May be able to be channeled through a held weapon such as a sword, depending on the spell This is the first range at which your spells can directly affect other things. A spell to enhance your swords cutting edge, a spell to mend the wounds of an injured ally, really any number of possibilities are available, as long as the person casting the spell doesn't mind being up close and personal with their magic. Will see probably equal use of buffs and offensive magic. At this range, (and to draw a comparison to D&D again) you should expect to see spells like Shocking Grasp or Enhance Ability. You may see a smidgen of utility here, such as a spell to open a locked door, or to turn something invisible.
3. Toss The distance a normal person could throw an object that's suitably designed to be thrown, like a baseball or frisbee. Somewhere in the range of 240 feet/80 meters. Your first ranged magic, this will see heavy use by offensive spells, and also likely the first range where utility spells will show up. Short range teleportation (like Misty Step), control spells (Charm [X] or Hold Person) and a slew of damaging spells. You'll also start to see illusion magic pop up more, since making an illusory distraction on top of yourself tends to be less effective than making one that's on the other side of the market square.
4. Propel The distance you might see from something getting launched by a trebuchet/catapult. Roughly 1/4 mile/400 meters. This category is going to be almost completely dominated by damage spells, like Fireball and Magic Missile, but will also see a smattering of utility, such as Dimension Door.
5. Sight If you can see it clearly, you can target it. On a flat open prairie, it should typically be something along the lines of 3 miles/5 kilometers due to horizon curvature _{(assuming a planet of roughly Earth size)}. Normal sight range only, no scrying shenanigans. (Optionally, a good vantage point, such as the peak of a mountain may improve this distance.) This will be dominated less by offensive spells and much more by utility. D&D doesn't really have much in this range category, and most things that are are pure utility, but then again, D&D is very combat centric. This would be things like Storm of Vengeance, Alter Weather, and Mirage Arcana. All of these cover very large areas, but only one is a true offensive spell.

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Ranges 6, 7, and 8 are less a set distance, and more related to circumstances and actual location. For example, being able to target the spell anywhere on Asia is farther than doing the same on Australia, even though both are continents, or targeting within the Amazon Rainforest would have a greater range that targeting within the Mohave Desert, even though both are defined Regions.

I think it's important to note here that doing anything on the scale you reach in these categories will have significant story impact. Almost all spells that occupy these tiers of distance will impact your campaign, most of them could even warp your campaign purely from being accessible by people. Players and NPCs will almost certainly behave differently if they know one or the other can target with spells them from the entire other side of a continent, or devastate entire forests.

Almost all spells using one of these range categories will be used for utility magic. All of them will certainly be used for teleportation and scrying spells, and depending on if your game is combat light, that may be all they get used for. In fact, outside of Teleportation, Sending, and Scrying, there aren't many other spells that would use this type of range. Certainly each of these categories could be used for offensive spells, you probably won't see it much. In my experience, players who can hit things at these sorts of ranges tend to not need to engage in combat anymore, since they can assassinate any enemy they know of as soon as they learn of them, or else immediately leave a combat with ultra-long-range teleportation. This may be useful for offensive spells that don't deal damage, such as mind control spells, if the spell requires that the target remains within the spells range to be able to maintain control.

6. Road Anywhere that's within a days travel on foot for a normal person, somewhere in the range of 25 miles/40 KM. (optionally, Swampy or mountainous terrain may impede this range, while a particularly urban expanse may improve it, as a flavor aspect)
7. Region An entire geographical region: An entire mountain range or forest, a river an all its tributaries, a single canyon, etc. This can vary widely based on how large a region is
8. Continent Anything on the same geographical continent that the caster is on

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Lastly, we have the Big Deal™ distances. A size or distance this large will almost definitely impact the story in a significant way, regardless of the effect used. Similar to ranges 6, 7, and 8, these are going to see heavy use as with utility effects, and not so much the damage effects. An additional note, most campaigns (although this is dependent on setting) tend to take place within the same continent, so really, these are probably superfluous. There are basically no spells in D&D, Ars Magica, or really any other game I can think of that have spells that can reach this far that aren't specifically teleportation or telephone spells.

9. Sun Everything on one side of the planet. Everywhere that it's daytime, the northern hemisphere, etc.
10. World Nowhere is safe, your reach extends to anywhere on the planet

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Bonus range:

11. To the Moon, Alice! You can target anywhere on any extraplanetary body, assuming you have the means to know such a place exists.