The magic quantity: How to scale everything important in the D&D world

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.

Level 1 to 10: quantity = level
Level 11+: quantity = 10 per level above 10
Level 21+: quantity = 100 per level above 20

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.

Level Quantity
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 10
12 20
13 30
14 40
15 50
16 60
17 70
18 80
19 90
20 100
21 100
22 200
23 300
24 400
25 500
26 600
27 700
28 800
29 900
30 1000

Disadvantages of this system:

  • it’s spiky (it’s linear for 10 levels and then changes by an order of magnitude). Linearity means that, between level 1 and 2, a number is multiplied by x2, while between 8 and 9 it is multiplied by x1.125. Still, this is not new to D&D: this is also how hit points work.
  • There is a weird repeated value at level 10 and 11, and again at 20 and 21.

    Advantages of this system:

  • It’s spiky. It changes the focus of play at what 4e calls heroic, paragon, and epic tiers. Suddenly, around level 12, new possibilities open up.
  • it is easy to learn: It replaces several different charts with a learnable rule. It also generates some convenient short cuts: 10x the number of something is always 10 levels higher.
  • It generates results not out of the realm of plausibility, which I will demonstrate below.

    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.


    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.

  • 3 Responses to “The magic quantity: How to scale everything important in the D&D world”

    1. 1d30 says:

      This is hot stuff. It really lays out what 30th level PCs are like (not just ten levels above where the book’s tables stop) in a better way than very specific rules like the 2.5E PO: High Level Campaigns or the 3E Epic Level Handbook. As a general rule it also provides a guideline for creation of specific rules, which a book of specific rules doesn’t do very well.

      How would you handle renown? It feels like you could just go with 3 miles x MQ, but I think it’s more likely for the King of France to be known in Shanghai than in Siberia. And what happens when you discover a circle of people who have never heard of King Louis, suggesting that his renown spread E/W/N/S and is about to meet in the middle? ROUND EARTH PROOF!

      Here’s a problem though: it takes double XP to get from L2 to L3, etc, up to name level (let’s say 10th). After that you need a fixed amount per level. That means you’re getting a linear progression from levels 10 to 20, at which point the domain progression explodes upward. Couple this with greater inputs of XP from monsters and treasure that are level-appropriate, and you get a really incredible surge. The implication is that the low levels are a thankless struggle, and Name to Epic (10 – 20) is where you really start to enjoy success, but after L21 you just devour the world. Perhaps it takes a L21+ leader to gather a large country together.

      But I have a problem with this, and with the ACKS assumption that all leaders are high level. What about the next generation after the conquerer? There’s no way Napoleon III was anything like 10th level much less 27th.

      I think it would be better if personal territory assumed underlings. You grow until level 10, whereupon you grab a bunch of 5th level mini-barons and rule them instead of ruling all their lands. The ruler becomes hands-off the daily affairs of the land, which has to be directly controlled by L1-L10s. This way it’s possible to have a 12th level King, above a passel of 10th level Dukes, which wach control a horde of L7-L10 underlings who range in importance from local village lord to baron.

    2. paul paul says:

      Interesting response!

      -I don’t usually do anything mechanically with renown. I’d assume that anyone with a level 20 realm is well known across the continent. Even emperors on different continents are little known among any but scholars: only the most famous, like Prester John, are known, and they’re little more than legend.

      Abou the exponential increase of power: I don’t have much experience in first edition campaigns much above name level, but I’ve been operating on the premise that, although the XP tables become linear, it still takes the same number of game sessions to achieve either level 14 or level 20. If levels do start increasing rapidly up there – like one level per session – I think something weird is going on in the campaign. That said, the exponential increase in power above level 20 is intentional. For a 9th level lord, clearing a hex is a good day; for Napoleon, annexing Egypt is a good day.

      About the fact that all leaders are high level: I’ve always though it absurd that every monarch was high level. There’s no reason why a hereditary monarch should be name level. I believe that you need high level to CONQUER a kingdom. Therefore, William the Conqueror is one of the few English monarchs who might be level 23.

      Similarly, Henry the Fifth, who conquered a lot of France, was over level 20 (probably a lot of thief levels gained with Falstaff followed by some fighter levels). There’s no way Henry the SIXTH, a boy king, was level 20+. He might be level 0. (In fact he lost a bunch of France, right?)

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