D&D is a game where you spend half your times killing monsters and half your time interacting with the world (adjust proportions to taste). In every edition, the killing-monsters part is very well-defined, mathematically speaking. The interacting-with-the-world part has a few data points here and there: how much do things cost in shops? How many men-at-arms does a level 9 fighter get? for how much can you sell a subdued dragon? At first it all seems like little islands of subsystem in a sea of dm-use-your-judgment, but what would you say if I told you it can all be distilled into a formula THAT ONLY I HAVE DISCOVERED?
You’d rightly tell me that I was going math crazy, like the guy in Pi. So I won’t say that. I’ll instead offer a rule of thumb that can be surprisingly useful, and offers surprisingly coherent results, that you can use when you don’t know how the size of something, how many there are, how much it costs, or any other game-world number.
The Magic Quantity: How Many at What Level?
Every level has a Magic Quantity (and vice versa). It’s meant to answer this question: “If I have one of something at level 1, how may will I have at level x?” The magic quantity for level 1 is 1. The magic quantity for level 30 is 1000.
TRANSLATING LEVEL TO QUANTITY:
Level 1 to 10: quantity = level
Level 11+: quantity = 10 per level above 10
Level 21+: quantity = 100 per level above 20
TRANSLATING QUANTITY TO LEVEL:
10 items or less: level = quantity
11+ items: level = 10 + 1 level per 10 items (round down)
101+ items: level = 20 + 1 level per 100 items (round down)
What do you do with a magic quantity?
You multiply it by things. Gold coins, soldiers, miles of land.
x1000 GP: That’s how much PCs can earn per level.
x1000 GP: That’s the price of a really awesome thing that’s appropriate for a given level (pet monster, castle, airship)
x1 mile: That’s the diameter of the domain PCs can control.
x1 soldier: That’s how many soldiers PCs can defeat singlehanded.
x10 soldiers: That’s how many soldiers PCs can command.
Disadvantages of this system:
Advantages of this system:
I think this rule of thumb is strong enough to be the backbone of several D&D subsystems. Below, I’ll try a couple, and compare my work against existing D&D rules.
TREASURE PER LEVEL
If you multiply the Magic Quantity by 1000 GP to generate treasure by level, a character might get 1000 GP at level 1, 2000 GP at level 2, 20k GP at level 12, 100k at level 20, and 1 million GP at level 30. (Or less. This might be the total treasure the DM puts into the adventures, but no party clears out the whole dungeon.)
This not too terribly far off from the 3e expected Wealth By Level. A WBL character would earn 900 GP as opposed to 1000 at level 1. By level 20, a character using the magic quantity system would have accumulated about 600,000 GP; a 20th level WBL character is expected to have wealth of 760,000.
(For first edition, where GP=XP, wealth by level is irrelevant. You level up as soon as you collect the right amount of money.)
I recently posted a giant list of things for high-level characters to buy. I used the Magic Quantity rule to price the items.
The awesome-things economy is based on the same multiplier as the treasure-by-level economy – x1000 GP – so you can always spend your level’s worth of treasure for one level-appropriate cool thing. This might be a magic item, in campaigns where you can buy magic items; a new spell; or cool stuff like hippogriff eggs, castles, and flying pirate ships. To determine a cool thing’s price, just figure out the level at which you’d expect it to show up in the campaign. For a pet monster or henchman, this is the level of the monster. For instance, if a hippogriff is a level 3, encounter level 3, or 3 HD monster, you could price a hippogriff at 3,000 gp.
How well does this stack against canonical rules? OD&D specifies that a party can sell a subdued ancient red dragon for about 50k GP, so I presume they can buy it for 100k GP. That means that, if a red dragon were for sale, a level 20 character could afford to buy it. Badass! Similarly, in AD&D, hippogriffs are 3 HD monsters whose eggs and fledglings sell for 1000, 2000, or 3000 GP, depending on age.
From the 1e DMG, it’s hard to tell how much it costs to build a typical castle – the construction menu is complicated – but I priced a four-tower castle of a couple thousand square feet at around 20,000 GP, which would make it suitable for level 12. Sure.
Let’s say we use the magic quantity for the diameter, in miles, of a PC’s area of control: 1 mile at level 1, up to 1000 at level 30. That means that a level 1 character will find enemy monsters 20 minutes from his house, while a level 30 character can control an area about the size of Europe.
How well does this stack against canonical rules? We’ll sanity-check this against the only D&D data we have for determining characters’ areas of control: the rules for PCs building strongholds at name level. At level 10, when an OD&D fighter is clearing five-mile hexes for his stronghold, a Magic Quantity character can control a ten-mile-diameter area (about four hexes). OD&D specifies that a character can control land up to 20 miles distant from a single stronghold: that’s a diameter of 40 miles, and, according to the magic quantity rule, would require a level-14 character. This is plausible for the level of a character who has maxed out his stronghold. For it to grow any further, a character will need to become a monarch or other ruler of vassals.
If you want to be a serious big-time king, you need to conquer an area the size of England. It’s about 300 miles from the north of England to the south, making England a level-23 realm. (France is level 27.)
How many soldiers (or, more strictly, level 1 creatures) can a character expect to beat? Using the magic quantity for this might, or might not, match with actual combats run in different D&D editions. It’s hard to say for sure, because D&D doesn’t handle battles against 100 opponents very well. It’s also inexact because it varies a lot by class and situation: a flying wizard can lay waste to legions while the rogue is better away from the battlefield. The numbers are reasonably plausible, though: A level 1 character can beat one soldier (sure, PCs are better than NPCS). A fifth-level fighter can defeat 5 soldiers, a 15th-level fighter 50, and a 25th-level fighter 500.
How well does this stack against canonical rules? I think it works reasonably well up to level 10, especially if you use the fighter as your yardstick. High-level PCs don’t engage in melee with dozens of orcs, so let’s turn away from D&D, towards literature, and see if we’re capturing the right feel for battlefield might.
For an example of a paragon-level fighter – over level 10 – I usually think of Inigo Montoya, one of the best duelists in the world, who helpfully comments that, even at his best, he could not defeat 60 men. If he could defeat 50, that would put him at a very plausible level 15. For over-the-top epic heroes, one of the best is mythical Irish warrior Cú Chulainn. When he’s singlehandedly defending Ulster from the army of Connacht, he flips out and kills “one hundred, then two hundred, then three hundred, then four hundred, then five hundred, where he stopped” – making him a level 25 barbarian. Archbishop Turpin, one of Gygax’s inspirations for the cleric class, supposedly killed 400 Saracens in a battle, which means he’s a level 24 cleric.
Now that that’s set in stone, we can settle an old debate! What level are the Lord of the Rings characters? At the Battle of the Hornburg, Gimli kills 42 enemies to Legolas’s 41, so both characters are level 14. That’s settled!!
Let’s say that a PC war leader usually has access to a number of level-one troops equal to 10 x the Magic Quantity. Thus, a fighter might command 10 troops at level 1 (as a sergeant), 100 troops at level 10 (as a lord), 1000 troops at level 20 (as a king), and 10,000 troops at level 30 (as an emperor). 100 at level 10 is in line with the followers granted to 10th-level fighters in the 1e DMG, and 10,000 is a realistic historical size for a medieval army from a powerful (non-points-of-light) country like France. (The largest late-medieval armies are larger than the ones generated by these rules, but human populations are probably smaller in a fantasy world shared with a hundred hostile species.)
How well does this stack against canonical rules? A level 9 AD&D fighter collects between 60 and 120 troops – 90 average. In OD&D, every group of 30 bandits has a 4th level leader, 50 bandits have a 5th or 6th level leader, and 100 bandits have an 8th or 9th level leader.
I’ll go more into this later: for instance, I think you could put the troop guidelines together to make a decent mass combat system.