Divine Favor & City-State Gods

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Thomas Weigel
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Joined: 2012-06-20 11:57
Divine Favor & City-State Gods

This uses these values for spells by rank (which can be summarized as rank×(rank+1)×0.5), and assumes a single patron divinity for the city-state. Some math corrected, thanks to DrPete.

Starting with a city-state with 60,000 rural families and 1,200 urban families, and 2 divine casters per 9 adventuring classes, the city-state has the following divine casters:

level 1: 3,333 who require no spells per day
level 2: 1,333 who require 1 spell point per day each; total 1,333
level 3: 444 who require 2 spell points per day each; total 888
level 4: 222 who require 5 spell points per day each; total 1,110
level 5: 67 who require 8 spell points per day each; total 536
level 6: 22 who require 24 spell points per day each; total 528
level 7: 8 who require 45 spell points per day each; total 360
level 8: 3 who require 59 spell points per day each; total 177
level 9: 1 who require 80 spell points per day each; total 80

Total 5,012 spell points per day. This assumes that special divine abilities (Turn Undead and similar) cost nothing, or close enough to nothing.

Each rural family produces (per Alex) 1 point of divine energy per week, but the average domain only gets 40% of that (4 per 10 families). Let's start with an idealized domain, however, that gets 100%, and say that differences arise from people who worship other gods than the primary patron.

At 100%, the domain is producing 60,000 spell points per week, or 8,571 spell points per day: enough to power the listed divine casters, plus about half again as many.

Old, Incorrect Conclusion: That doesn't mean it's wrong . . . but it creates the interesting assumption that the gods run their churches on a deficit: they offer the amount of power they offer, because most of it goes unused. If a domain's clerics really started casting, the divinity might . . . run out of juice.

New Conclusion: The gods are doing pretty well for themselves. This also means that the primary divinity of a domain can support more than half of the divine casters in the domain.

Tom Hudson
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Joined: 2011-07-24 18:35

Thomas, I think in your math you forgot the 2/9th multiplier you introduced in your text?

60,000 families is 300,000 people.
From Demographics of Leveled Characters on page 235, that's 1/20, or 15,000 characters of 1st level.

If 2/9ths are divine spellcasters, you'll have 3300 at first-level, not fifteen thousand.

This puts the gods at a 50% surplus: they get 60k spell points per week, and their priests consume 40k, leaving a nice tidy profit for feathering their nest on the home demiplane.

(The profit's a bit thinner if you use Player's Companion and have a nontrivial number of Priests or other Divine-4 types instead of Clerics, but that's probably all handwavey.)

Then we have four level 7 clerics, two level 8 clerics, and maybe one at level 9, which is a more tractable count of life-and-limb-restoring types.

Tom Hudson
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Joined: 2011-07-24 18:35

Actually, this math seems to give us a nice upper bound for what fraction of society can be an active divine spellcaster, right?

I didn't account for the 40% multiplier, but isn't that 40% to the primary god, and presumably the other families are followers of other deities? So you have that many divine spellcasters, but only about half of them belong to the primary temple, and the others are spread among whatever other gods get worship.

It's then interesting trying to extend the math to support cults and illegal worship.

Thomas Weigel
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Joined: 2012-06-20 11:57

Yes I did!

Thank you, that's been bugging the back of my brain all week.

DrPete
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Very cool. To me, though, this kind of analysis strongly suggests that clerics should "pay" for their spell casting with a congregation. That, in turn, leads to the question of what they are doing roaming the countryside, and what happens to a cleric far from home. The cleric should at least have a sense that they owe their god for spending its resources on them without getting anything in return.

I think shamans and witches should get their power from sacrifice, rather than believers, or at least a hybrid. Doesn't one of their class descriptions talk about the horrible sacrifices driving away recruits or something? We should get back to great temples filled with bulls and sheep, even for the lawful, I say :)

Alex
The Autarch
Joined: 2011-06-30 18:10

There is a similar analysis in the ever-under-draft Auran Empire setting:

The idea that the gods gain something from worship and sacrifice was implicit in the syncretic Greco-Roman religions. Worship was an act of propitiation, expressed in the formula do ut des (“I give that you might give”): The gods were expected to reward acts of worship with blessings, gifts, victories, and so on.
Do ut des is the basis for the mechanics of divine power detailed in Chapter 7 of ACKS. While the rules discuss divine power in the context of clerical magic, all magic is, in effect, an application of divine power. The difference between arcane and divine magic is that mages use their personal power to manipulate sources immanent within the world, while clerics use their personal power to channel divine sources.
The Cost of Spells
For Judges who, like Pythagoras, believe that numbers constitute the true nature of things, here are the actual costs in divine power to cast each level of spell in ACKS:
1st: 1 / 5 4th: 10 / 50 7th: 28 / 140
2nd: 3 / 15 5th: 15 / 75 8th: 36 / 180
3rd: 6 / 30 6th: 21 / 105 9th: 45 / 220
The number before the slash is how much of his own divine power the spellcaster must expend to channel the spell’s magic, while the number after the slash represents the total divine power consumed to fuel the spell, drawn from the caster’s god or from immanent sources in the environment.
Creating magical items (including the components to cast ritual magic) requires an additional 500 divine power per spell level to transform the materials used into a form which can hold the magic. This extra divine power is sourced from special components, sacrifice, etc.
Divine Power of Creatures
The total amount of divine power possessed by a creature is equal to ten times its XP value. When a creature dies, about 90% of this value rapidly transmigrates; the other 10% remains as a residue within the creature’s blood or organs, which can be harvested as special components for magical research. When a creature is sacrificed, 80% of its divine power passes to the entity worshipped, 10% is retained by the sacrificer for his own ends, and 10% remains residual within its blood and organs. This why XP value = special component value = sacrifice value.
A living creature will generate excess divine power each day equal to 6% of its XP value. For example, a mage with HD 14** (worth 3,800XP) therefore has (3,800 x 6%) about 230 points of divine power available. Casters use some of this to fuel their spells (a 14th level mage’s spells cost about 190 spell points). The rest is dissipated or bequeathed to a god through worship. (As with sacrifice, a cleric that leads a congregant in worship collects 10% while the god collects the rest). Once expended, the creature’s divine power will recharge through food, drink, and sleep – the living body fuels the soul.
Divine Power of Gods
How much divine power do the gods have access to? From ACKS, we know that sacrificing a normal man to a god will yield 5 points of divine power to the sacrificer. Since the sacrificer gets 10% and the god gets 80%, the god must get 40 points to the god. Sacrificing 50 normal men will yield 2,000 points of divine power.
Alternatively, 50 average peasants might yield a cleric 4 points of divine power per week (out of a maximum of 10 – most men aren’t that worshipful!) That means the cleric’s god is getting 36 points of divine power per week from those 50 men (or about 0.7 points per worshipper). Given its global population of about 150 million normal men, the world of Cybele yields around 108 million points of divine power per week.
There are around 2.7 million clerics in Cybele; fueling their spells costs about 80 million divine power per week. That leaves the gods with about 25% of their power available for other purposes. (And of course the gods have more worlds than just Cybele to draw on.)
Apotheosis
How much divine power would a mortal have to accumulate to achieve godhood? It costs 800 divine power to fuel a 14th level cleric for a single day, 5,600 to fuel him for a week. This would require about (800 divine power / .7 divine power per worshipper) 11,420 worshippers. It is thus conceivable that the priest-king of a city-state who persuaded his subjects to worship him could serve as his own god…
That priest-king is not really a god, of course, merely a cleric of his own faith. To be a nigh-almighty being, for example one that could cast wish continuously for seven consecutive days of creation, how many worshippers would be required? A 9th level spell costs a total of 265 divine power. Being able to cast wish every round for a week would cost (265 x 6 rounds/minute x 60 minutes/hour x 24 hours/day x 7 days/week) 16,027,200 divine power per week. That would require (16,027,200 / .7) 22,896,000 worshippers. Any mortal is likely to be struck down before acquiring so many worshippers… though some will still try.

koewn
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ohmygosh you've mathematically tied divine power to HD and population it's sooooo fluffy I'm gonna die.

Seriously, you're killing me. I already have a spreadsheet problem; I'm the guy that also likes doing taxes.

It occurs to me there's a great model for doing ley lines or making astrology actually work in there....crap. You're gonna make me start looking into orbital mechanics and a custom Celestia solar system. I wonder if it'll do a geocentric solar system.

Alex
The Autarch
Joined: 2011-06-30 18:10

Koewn, if you like spreadsheets, you need to see the secret Pythagorean spreadsheets which underly ACKS. Only Thomas W. has seen them and he has never been the same since.