Estimated populations and revenue by realm size issues

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ahstrongmorse
Adventurer Conqueror King BackerSinister Stone of Sakkara Backer
Joined: 2011-07-13 02:05
Estimated populations and revenue by realm size issues

I've been doing some spreadsheet work, analyzing the tables of estimated realm populations and revenues. I've encountered some problems. I have a potential fix towards the end of this post.
1. There is a general problem because these estimates represent a snapshot of time, but that snapshot is highly unstable. Let's start with a by-the-book prefecture/principality, built from the bottom up by assuming that each patrician rules 20 families, each castellan rules 80 families directly and 4 patricians, and so forth, using the numbers from the table Tiers by Realm Size: it starts out with roughly 60K families, right in the middle of the range for a prefecture, and a net realm income of 50K gold per month--well within the estimate, although further towards the high end than the population figure. I assume throughout that all hexes are "average" land value hexes (6 gp/family); that's probably pessimistic, because why settle low value hexes?, but we can assume that some hexes were higher value when settled or that other hexes were settled for strategic reasons or because of overcrowding or something, so the land value is average.
I then advanced the realm 12 months, month by month, assuming average morale, standard growth rates based on domain populations, and average family loss rates due to disaster. By the end of one peaceful year, the prefecture's population had nearly doubled, to 116K. The prefecture's realm income had only increased by roughly 10%, but some of the lower level dominions had much more dramatic increases in income: the legates' income had gone up by about 150% (to 2.5 times the starting level) and the tribunes' income had grown more than ten-fold.
And that's with starting assumptions that I believe are unreasonably sparsely populated (see point 2, and the sorry fate of the patricians). If we tweak the assumptions slightly--starting each patrician with 35 families (the average for a starting wilderness one-hex dominion) and give each castellan 105 families (assuming that the castellans rule 3 hexes, each with the average for a starting wilderness hex--a low assumption, in my opinion), then our prefecture goes from a still reasonable 76K families at start to a whopping 213K families after one year of peace (well into the overall realm population estimates for an exarchate). And again, that's after one year of growth, with merely average management. Reinvestment of income, a positive Cha modifier, or fortunate choices of land to settle would create substantially higher growth rates. Because the starting assumptions put essentially the entire realm (except the personal domains of the prefect, the palatines, and the legates) in fast-growth parts of the growth curve, populations explode over even one year. And while the income gain at the top is moderate (on my tweaked assumptions, the prefect's personal income still only increases by about 10%), the income gain at the level of tribunes and castellans is huge (my tweaked assumptions increase the tribunes' net income from 278 gp/month at the beginning of the year of peace to 2270 gp/month at the end; castellans go from 68.7 gp/month to 1402 gp/month--and they would grow more if they weren't hitting the population caps for wilderness hexes while not having large enough domains to become borderlands. This also has consequences for level assumptions; by the end of the year, most landowners are still not getting any xp, but 7th level totally average legates are earning 600 xp/month (reaching 8th level in roughly 10 years, 20 if the 1/2 xp rule applies here), and 6th level completely average castellans are getting 600 xp/month (reaching 7th level in roughly 5 years, 10 if the 1/2 xp rule applies). I don't really have a problem with 5 or 10 years of rulership over a prosperous dominion producing a level, but it's strange that it only hits that way for parts of the rank structure--neither the bottom level rulers (assuming the patricians only have one hex) nor the high level rulers advance, only the bottom-mid.
2. The populations are so low that the patricians' dominions, on average, fail. By the book, the average patrician has 20 families. At a 25% growth rate for a dominion under 100 families, they gain 5 families per month. But a disaster claims d10 families per month, with exploding 10s; about 6. The average patrician's estate by the book dwindles over time to 0. 24 families is around the breakeven point--at that point, the expected increase in population is balanced by the expected decrease. At the 35 families that a typical wilderness hex would start with, explosive growth is expected--within 11 months, the population reaches the maximum 125 families for one hex. (If the patrician rules more than one hex, then the population continues exploding.) The poor patricians in the standard assumptions of the book are also poor in another way. I assume they're all ruling single-hex dominions of wilderness; the population is far too low for even a single borderland hex (as noted, it's low for a starting wilderness hex). At that point, they can't afford to pay the upkeep on their 30,000 gp castle (the smallest fortification allowed by the rules to protect a hex of wilderness). The prefect does fine, well within the table's range of income. But the patrician ruling 20 families in the wilderness is paying 96 gold per month for the privilege of seeing his hopes destroyed as fire and flood kill off his peasantry. (The castellans start off similarly badly, losing 99 gold per month assuming a 3 hex domain, but at least over time the castellans' estates become profitable--wildly so, in fact.) With the tweak of assuming 35 families, the patricians still do badly at first, but it's more in the way of an investment. The patricians start breaking even around month 5 or 6; by the end of the year, the patricians are getting a stable 187 gp/month, nearly double the top of the Tiers by Realm Size estimate.
All of this is related to: 3. Where is civilization? A prefecture is a pretty big place; even with pretty small estimates for domain sizes (one hex for patricians, 3 for castellans, 4 for tribunes, 10 for legates, and 16 for palatines, a prefecture contains in the ball park of 1500 hexes. Out of those 1500 hexes, you might expect a large area of sparsely settled wilderness, with a moderate amount of borderlands, and then a good chunk, smaller than the others but still substantial, of civilization. Or you might expect most of that to be borderlands, with a fringe of wilderness and maybe 20% civilization. Well, you'd be wrong. Based on the population figures, the prefecture has exactly 16 hexes of civilization (the prefects' domain), 0 hexes of borderlands, and about 1500 hexes of wilderness. The population estimates are so low that you just can't get borderlands or civilization. It's a little strange that the palatines typically have a large village of around 2200 people in each of them, despite being in the wilderness, but there you go.
4. How do cities fit in to the domain system? The prefecture has one large town of maybe 7000 people. Is that part of the prefect's domain (which has about 7800 people, making the large town essentially the prefect's whole domain)? What about a year later, when the prefecture of 116,000 families implies that the large town has grown to be a city of maybe 14000 people, making the city 1.5 times as populous as the prefect's entire domain? Are we assuming that cities are independent charter cities, not beholden to the local lord? (And what size are their armies?) Is that in addition to the prefect's personal domain's population?
5. Why are there so many lords giving large amounts of land to their vassals when they could administer it directly perfectly well? Why would a castellan with only 3 hexes of personal domain give 4 vassals one hex each? For that matter, why doesn't a tribune ruling roughly 32 hexes consolidate that into a single domain of 16 and one vassal of 16? That would then allow it to grow from wilderness to borderlands. There is a partial answer in the math: with really sparsely populated hexes, a castellan can increase his income by pushing rule of some of those hexes to vassals, because they will have to pay the whole bill for their castle's upkeep, but still pass on 20% of their gross income to the castellan. Basically, because the patricians lose money, the castellan gains (or loses less at first). But as the population grows, that slightly bizarre situation reverses, and the castellan looking to maximize his wealth wants to seize his vassals' lands. To be sure, that happened with some regularity in medieval times, but...
6. Should hexes be able to advance from wilderness to borderlands to civilized without being part of a domain of 16 hexes? It makes sense that you can't civilize a single hex surrounded on all sides by wilderness. But it doesn't make much sense that the tribunal of Whatzit, consisting of 32 hexes all at the maximum population of 125 families, never contains any borderlands territory, because no single domain consists of 16 hexes of max population domain.
Enough criticisms; are there any solutions?
I would suggest that some of this can be solved by looking at this at a hex level, instead. A wilderness hex becomes a borderland hex when it (a) has a population of 125 families and (b) the surrounding six hexes have an average population of 125 families or more. A borderlands hex becomes a civilized hex when it (a) has a population of 250 families and (b) the surrounding six hexes have an average population of 250 families or more. We assume that all hexes in a domain have the same population (except for urban centers?), except when population limits are at work; so a 6 hex domain of wilderness with a population of 600 means each hex has 100 families, but a 6 hex domain with 5 hexes of wilderness and 1 hex of borderlands and a population of 800 families means 5 hexes with 125 families (the maximum for wilderness hexes) and one borderlands hex with a population of 175 families.
Likewise, if we define realm sizes more in terms of hexes than in terms of dominions, we'll produce larger realms at each level, but with more reasonable population dynamics. So patricians will rule dominions of roughly 1 to 8 hexes, with roughly 35 families per hex (perhaps they should have 55 or 60 families per hex, so they can break even or make a small monthly profit). Castellans will typically rule dominions of 9 to 12 hexes, with roughly 70 families per hex, plus an average of 4 patrician vassals. Tribunes would then rule dominions of 13-16 hexes, with roughly 130 families per hex (tribunes' dominions, at the center of substantial realms, are typically borderlands, not wilderness), plus 4 castellan vassals. Legates would rule 16 hexes, with roughly 260 families per hex (civilization), surrounded by their 4 tribune vassals. We could then build the realm size table by building these from the ground up: start with an average patrician ruling 4.5 hexes and 157.5 families (or 270 families on the 60 family assumption), then calculate a castellan ruling 10.5 hexes directly and 4 patrician vassals, and so forth. The result will be a much higher population at each level of the chart, but a more consistent set of assumptions about social organization. And if we want to, we can run numbers for smaller and larger realms at each tier to get the ranges instead of the prototypical averages. Those averages will overlap--a large palatinate will be bigger than a small prefecture, and maybe even than a tiny exarchate--but that's historically accurate and interesting. And the numbers will be more consistent with mixes of population density that make sense for settled territory, instead of assuming that the average prefecture is mostly empty wilderness. If it's actually mostly empty wilderness, I doubt that there's any prefecture to speak of--it's probably mostly random small governments with only token (if that) allegiance to higher authority. To the extent that this makes dominions ahistorically large for a given title (i.e. Dukes are ruling territory that is in fact comparable to historical monarchs), we can weed out some of the titles--I haven't cross compared these numbers to actual historical numbers.
That doesn't solve the stability over time issue, although it helps--if the castellans have populations in their domains of 700, then they're getting a base population increase of 1% per month, not the explosive growth of 25% per month, and even the patricians with 157 or 250 families (depending on assumptions) are down a category or two from the 25% per month category. We can then impute in some other stabilizing factors--monster attacks, war, and other factors that aren't included purely in the per month population growth and loss calculations, and we can simply assume population stability in the absence of PC type activity. (In other words, if we assume that a PC patrician would need to go on one adventure a month to stop orc attacks, slavers, undead outbreaks, and other things from reducing population growth to flat replacement, then we can assume that on average NPC ruled domains without PC activity have flat population growth. This also provides some information about the appropriate threat levels for dominions to face on average--they need to face an average mix of threats that keeps growth at 0 unless you affirmatively go out and deal with the threats beyond what the average NPC ruler would do.) Add in those assumptions, and we can treat the realm calculations as relatively stable over time, which is important because it means that we don't need to be recalculating a PC's realm from the ground up every month in order to accurately reflect change over time.

Beedo
Beedo's picture
Patreon SupporterLairs And Encounters BackerBarbarian Conquerors of Kanahu ContributorACKS Heroic Fantasy Handbook Contributor
Joined: 2011-07-12 13:55

I noticed that the lowly lord didn't break even as well; my assumption was that the higher levels might subsidize those wilderness frontiers (in the case of NPCs), but PCs would need plunder and free followers to get over the hump.

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

ALEX: Ahstronghorse, first off, I have to cheer your highly detailed work here. For what it’s worth, I have all these spreadsheets (they are how I created the data in the first place), so if it would be easier to work from those rather than try to reverse-engineer them, let me know.
1. There is a general problem because these estimates represent a snapshot of time, but that snapshot is highly unstable. Let's start with a by-the-book prefecture/principality, built from the bottom up by assuming that each patrician rules 20 families, each castellan rules 80 families directly and 4 patricians, and so forth, using the numbers from the table Tiers by Realm Size: it starts out with roughly 60K families, right in the middle of the range for a prefecture, and a net realm income of 50K gold per month--well within the estimate, although further towards the high end than the population figure. I assume throughout that all hexes are "average" land value hexes (6 gp/family); that's probably pessimistic, because why settle low value hexes?, but we can assume that some hexes were higher value when settled or that other hexes were settled for strategic reasons or because of overcrowding or something, so the land value is average.
I then advanced the realm 12 months, month by month, assuming average morale, standard growth rates based on domain populations, and average family loss rates due to disaster. By the end of one peaceful year, the prefecture's population had nearly doubled, to 116K. The prefecture's realm income had only increased by roughly 10%, but some of the lower level dominions had much more dramatic increases in income: the legates' income had gone up by about 150% (to 2.5 times the starting level) and the tribunes' income had grown more than ten-fold.
ALEX: This is true, but the growth rates for the smaller domains aren’t meant to apply to NPC domains that a PC isn’t actively running. NPC domains just use the estimates. Throughout most of ancient and medieval history, population growth was very low, flat in many years, and downright negative in others. The population growth rates for PC domains in part assume immigration due to the PC’s reputation for awesomeness.
And that's with starting assumptions that I believe are unreasonably sparsely populated (see point 2, and the sorry fate of the patricians). If we tweak the assumptions slightly--starting each patrician with 35 families (the average for a starting wilderness one-hex dominion) and give each castellan 105 families (assuming that the castellans rule 3 hexes, each with the average for a starting wilderness hex--a low assumption, in my opinion), then our prefecture goes from a still reasonable 76K families at start to a whopping 213K families after one year of peace (well into the overall realm population estimates for an exarchate). And again, that's after one year of growth, with merely average management. Reinvestment of income, a positive Cha modifier, or fortunate choices of land to settle would create substantially higher growth rates. Because the starting assumptions put essentially the entire realm (except the personal domains of the prefect, the palatines, and the legates) in fast-growth parts of the growth curve, populations explode over even one year. And while the income gain at the top is moderate (on my tweaked assumptions, the prefect's personal income still only increases by about 10%), the income gain at the level of tribunes and castellans is huge (my tweaked assumptions increase the tribunes' net income from 278 gp/month at the beginning of the year of peace to 2270 gp/month at the end; castellans go from 68.7 gp/month to 1402 gp/month--and they would grow more if they weren't hitting the population caps for wilderness hexes while not having large enough domains to become borderlands. This also has consequences for level assumptions; by the end of the year, most landowners are still not getting any xp, but 7th level totally average legates are earning 600 xp/month (reaching 8th level in roughly 10 years, 20 if the 1/2 xp rule applies here), and 6th level completely average castellans are getting 600 xp/month (reaching 7th level in roughly 5 years, 10 if the 1/2 xp rule applies). I don't really have a problem with 5 or 10 years of rulership over a prosperous dominion producing a level, but it's strange that it only hits that way for parts of the rank structure--neither the bottom level rulers (assuming the patricians only have one hex) nor the high level rulers advance, only the bottom-mid.
ALEX: To use the oft-quoted phrase, “that’s a feature, not a bug.” Bottom-mid rulers are where most player characters enter the dominion game, and the rules are structured to allow for those domains to experience the most growth the most quickly. At 500 families, they become harder to grow, because you are gaining 1% of 500 while losing an average of 10 families per month, so to get from 500 to 1000 you have to do agricultural investment. At 1000 families you hit a stable point, as you gain about what you lose.
2. The populations are so low that the patricians' dominions, on average, fail. By the book, the average patrician has 20 families. At a 25% growth rate for a dominion under 100 families, they gain 5 families per month. But a disaster claims d10 families per month, with exploding 10s; about 6. The average patrician's estate by the book dwindles over time to 0. 24 families is around the breakeven point--at that point, the expected increase in population is balanced by the expected decrease. At the 35 families that a typical wilderness hex would start with, explosive growth is expected--within 11 months, the population reaches the maximum 125 families for one hex. (If the patrician rules more than one hex, then the population continues exploding.) The poor patricians in the standard assumptions of the book are also poor in another way. I assume they're all ruling single-hex dominions of wilderness; the population is far too low for even a single borderland hex (as noted, it's low for a starting wilderness hex). At that point, they can't afford to pay the upkeep on their 30,000 gp castle (the smallest fortification allowed by the rules to protect a hex of wilderness). The prefect does fine, well within the table's range of income. But the patrician ruling 20 families in the wilderness is paying 96 gold per month for the privilege of seeing his hopes destroyed as fire and flood kill off his peasantry. (The castellans start off similarly badly, losing 99 gold per month assuming a 3 hex domain, but at least over time the castellans' estates become profitable--wildly so, in fact.) With the tweak of assuming 35 families, the patricians still do badly at first, but it's more in the way of an investment. The patricians start breaking even around month 5 or 6; by the end of the year, the patricians are getting a stable 187 gp/month, nearly double the top of the Tiers by Realm Size estimate.
ALEX: The mathematical backend of the system actually uses a minimum domain size of 1 square mile, not 1 6-mile hex. The 6-mile hex minimum was put there simply because that’s the scale we assume the GM is mapping at. Mathematically, patricians rule civilized domains that are 1.95 square miles in size, or about 1/16th of a 6-mile hex. That puts their minimum stronghold size at 1,000gp – basically the stone townhouse listed under civilian structures. I assumed they’d probably have slightly nicer homes than that, at about 5,000gp. Thus a 20-family patrician earns an average of (12 gp/month x 20 families) 240 gp, and faces costs of (10%x240 + 20%x240 + 2x20 + 25) 137gp, giving him a net income of (240-137=103) 100gp per month, as shown on the chart. Likewise, if you want to be accurate, for domains of less than 1 hex/100 families, you should roll 1d10 and on a 10 the domain loses 1 family. Based on how many people have been wanting to have “mini domains” for their low level PCs I had been planning to re-write some sections to explain how to adjudicate these micro-domains for PCs, but hadn’t gotten to it yet.
All of this is related to: 3. Where is civilization? A prefecture is a pretty big place; even with pretty small estimates for domain sizes (one hex for patricians, 3 for castellans, 4 for tribunes, 10 for legates, and 16 for palatines, a prefecture contains in the ball park of 1500 hexes. Out of those 1500 hexes, you might expect a large area of sparsely settled wilderness, with a moderate amount of borderlands, and then a good chunk, smaller than the others but still substantial, of civilization. Or you might expect most of that to be borderlands, with a fringe of wilderness and maybe 20% civilization. Well, you'd be wrong. Based on the population figures, the prefecture has exactly 16 hexes of civilization (the prefects' domain), 0 hexes of borderlands, and about 1500 hexes of wilderness. The population estimates are so low that you just can't get borderlands or civilization. It's a little strange that the palatines typically have a large village of around 2200 people in each of them, despite being in the wilderness, but there you go.
ALEX: Patricians have domains of less than 1 hex. Castellans have domains of 1 hex. Tribune domains are 2-3 hexes. Legate domains are 15 hexes. Palatine domains are 96 hexes. Prefectures are 600 hexes. (This is all about to be published in v19 of the rules… somewhat frustrated I didn’t get that out before this conversation.)
4. How do cities fit in to the domain system? The prefecture has one large town of maybe 7000 people. Is that part of the prefect's domain (which has about 7800 people, making the large town essentially the prefect's whole domain)? What about a year later, when the prefecture of 116,000 families implies that the large town has grown to be a city of maybe 14000 people, making the city 1.5 times as populous as the prefect's entire domain? Are we assuming that cities are independent charter cities, not beholden to the local lord? (And what size are their armies?) Is that in addition to the prefect's personal domain's population?
ALEX: The cities are assumed to be independent charter cities.
5. Why are there so many lords giving large amounts of land to their vassals when they could administer it directly perfectly well? Why would a castellan with only 3 hexes of personal domain give 4 vassals one hex each? For that matter, why doesn't a tribune ruling roughly 32 hexes consolidate that into a single domain of 16 and one vassal of 16? That would then allow it to grow from wilderness to borderlands. There is a partial answer in the math: with really sparsely populated hexes, a castellan can increase his income by pushing rule of some of those hexes to vassals, because they will have to pay the whole bill for their castle's upkeep, but still pass on 20% of their gross income to the castellan. Basically, because the patricians lose money, the castellan gains (or loses less at first). But as the population grows, that slightly bizarre situation reverses, and the castellan looking to maximize his wealth wants to seize his vassals' lands. To be sure, that happened with some regularity in medieval times, but...
ALEX: Historically, it was because widely dispersed threats required widely dispersed management. The ability to project power was quite limited, and the desire to do so even less so (do you think most lords want to constantly be riding around through the woods to deal with bandits plaguing a hamlet 4 – 8 hexes away?) This is why England had 10,000 domains, with a manorial lord for each one, with an average of one castle ever 6 miles! Since ACKS largely assumes that people act as they did historically, I built the Tiers with that in mind. Economically, centralization has always and everywhere benefited the upper tier ruler, but most of the time it simply hasn’t been possible or even desirable.
6. Should hexes be able to advance from wilderness to borderlands to civilized without being part of a domain of 16 hexes? It makes sense that you can't civilize a single hex surrounded on all sides by wilderness. But it doesn't make much sense that the tribunal of Whatzit, consisting of 32 hexes all at the maximum population of 125 families, never contains any borderlands territory, because no single domain consists of 16 hexes of max population domain.
ALEX: I don’t think I understand your question. But on the macro level, the presence of cities is what really determines what’s civilized and what’s borderlands. Most area within a kingdom, for instance, will be civilized, just on the basis of proximity to cities. You can easily see this for yourself. A kingdom of 600,000 (Southern Argolle, for instance), will cover an area of 68 24-mile hexes, or roughly 8x8 24-mile hexes. There will be 6 cities within the kingdom, and everything within 50 miles (1 24-mile hex plus the next 24-mile hex) will be civilized. A quick sketch on hex paper gives about 40 civilized and 28 borderland hexes. The rules for becoming civilized through population growth are just there to allow for civilized elven homesteads, frontier domains that grow into powerhouses, and so on.
Enough criticisms; are there any solutions? I would suggest that some of this can be solved by looking at this at a hex level, instead. A wilderness hex becomes a borderland hex when it (a) has a population of 125 families and (b) the surrounding six hexes have an average population of 125 families or more. A borderlands hex becomes a civilized hex when it (a) has a population of 250 families and (b) the surrounding six hexes have an average population of 250 families or more. We assume that all hexes in a domain have the same population (except for urban centers?), except when population limits are at work; so a 6 hex domain of wilderness with a population of 600 means each hex has 100 families, but a 6 hex domain with 5 hexes of wilderness and 1 hex of borderlands and a population of 800 families means 5 hexes with 125 families (the maximum for wilderness hexes) and one borderlands hex with a population of 175 families.
ALEX: I don’t think I follow what you are trying to achieve.
Likewise, if we define realm sizes more in terms of hexes than in terms of dominions, we'll produce larger realms at each level, but with more reasonable population dynamics. So patricians will rule dominions of roughly 1 to 8 hexes, with roughly 35 families per hex (perhaps they should have 55 or 60 families per hex, so they can break even or make a small monthly profit). Castellans will typically rule dominions of 9 to 12 hexes, with roughly 70 families per hex, plus an average of 4 patrician vassals. Tribunes would then rule dominions of 13-16 hexes, with roughly 130 families per hex (tribunes' dominions, at the center of substantial realms, are typically borderlands, not wilderness), plus 4 castellan vassals. Legates would rule 16 hexes, with roughly 260 families per hex (civilization), surrounded by their 4 tribune vassals. We could then build the realm size table by building these from the ground up: start with an average patrician ruling 4.5 hexes and 157.5 families (or 270 families on the 60 family assumption), then calculate a castellan ruling 10.5 hexes directly and 4 patrician vassals, and so forth. The result will be a much higher population at each level of the chart, but a more consistent set of assumptions about social organization. And if we want to, we can run numbers for smaller and larger realms at each tier to get the ranges instead of the prototypical averages. Those averages will overlap--a large palatinate will be bigger than a small prefecture, and maybe even than a tiny exarchate--but that's historically accurate and interesting. And the numbers will be more consistent with mixes of population density that make sense for settled territory, instead of assuming that the average prefecture is mostly empty wilderness. If it's actually mostly empty wilderness, I doubt that there's any prefecture to speak of--it's probably mostly random small governments with only token (if that) allegiance to higher authority. To the extent that this makes dominions ahistorically large for a given title (i.e. Dukes are ruling territory that is in fact comparable to historical monarchs), we can weed out some of the titles--I haven't cross compared these numbers to actual historical numbers.
ALEX: That would make the rulers a-historically wealthy and powerful…
That doesn't solve the stability over time issue, although it helps--if the castellans have populations in their domains of 700, then they're getting a base population increase of 1% per month, not the explosive growth of 25% per month, and even the patricians with 157 or 250 families (depending on assumptions) are down a category or two from the 25% per month category. We can then impute in some other stabilizing factors--monster attacks, war, and other factors that aren't included purely in the per month population growth and loss calculations, and we can simply assume population stability in the absence of PC type activity. (In other words, if we assume that a PC patrician would need to go on one adventure a month to stop orc attacks, slavers, undead outbreaks, and other things from reducing population growth to flat replacement, then we can assume that on average NPC ruled domains without PC activity have flat population growth. This also provides some information about the appropriate threat levels for dominions to face on average--they need to face an average mix of threats that keeps growth at 0 unless you affirmatively go out and deal with the threats beyond what the average NPC ruler would do.) Add in those assumptions, and we can treat the realm calculations as relatively stable over time, which is important because it means that we don't need to be recalculating a PC's realm from the ground up every month in order to accurately reflect change over time.
ALEX: I hadn’t assumed anyone would care so much as to worry about it with this detail, but since you’ve brought it up I can certainly address the rules. As a deep simulationist, I totally get the desire to have mechanical game rules that function equally as mechanically for NPC domains as they do for PC domains. That said, it’s a bit hard to square realistic growth rates with population increase during a reasonably playable campaign length. To address this problem, I’ve come up with the following:
1. Populations increase by 1d10 per 1,000 and decrease by 1d10 per 1,000, per month. 10s explode both ways. Growth is essentially zero (flat). For domains of 100 or less, growth is +1 on a roll of 10 on the high die, -1 on a roll of 10 on the other die, and roll again on 10.
2. Populations increase at the listed rate under Growing the Domain only if the ruler is an active adventurer. If the ruler has never been an adventurer (i.e. he inherited it), growth is never at the listed rates. If a month passes without the adventurer adventuring, his growth rate vanishes. This represents the added immigration an up-and-coming ruler gets when he attracts fame and reknown for adventuring.

Bargle
Joined: 2011-07-21 00:39

Speaking of historical england, has anyone done the math on jrr Martins westeros in the game of thrones? I think 1" is 100 leagues and I know he's pretty big into war-game miniatures and whatnot. Do the starks really have that high a density of castles and vassal lords as you describe England as having? Historicity is one thing, but I'm not sure I want to trip past a hedge knights keep every hex in a "game". Or do I? I don't know!

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

Just finished updating the v19 rules to create a "zero equilibrium" for NPC domains, with +1d10/-1d10 population growth. PC adventurer domains (and NPC domains ruled by adventuring types) have additional growth opportunities. Also added the rules for mini-domains.
I think this is actually a really elegant solution, so I'm glad we went through this exercise.

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

Bargle - I have no idea how well Westeros would work using ACKS, but I'd love to know!

Duskreign
Joined: 2011-08-10 17:22

V19 already? I haven't even seen v18 yet! LOL

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

v18 is an internal build. You can find most of the changes in v18 in the thread entitled v17 Rules Addenda.