There have been previous discussions on the board about the growth of the Order of Hermes. The general conclusion is that for the setting to make sense the Schism War had to nearly wipe out the Order.
Three days have passed. There're 24 downloads of my spreadsheet. And 5 replies besides my own. Now that's fame.
Also, I've finished skimming through HoH books for hints on magi population and got frustrated. So I'm going to share my pain.
But first, the boring part. I've made several alterations to modifiers in the spreadsheet that seem to be more plausible according to setting background. For those who're interested, they're...
- Starting population is 13+24 - just playing with numbers here.
- "Conversions per mage@age, period" modifier goes up to +0.03 from +0.02. I guess it's implied that more hedge mages were absorbed into the Order during first centuries of its existence than I've supposed before.
- HoH:S, p.101 mentions that addition of Ex Miscellanea doubles the size of the Order. So "events growth@age, period" for 817 goes up to approx. 50.
- "wars, convertions & events deaths" multiplier for 1017 is 4.3 instead of 3. The argument is pretty vague, but... Before Schism House of Diedne was one of the largest - supposing about 1.5 average houses in population - and it was completely wiped out. Tremere, Flambeau, Quaesitores and Ex miscellanea were the most active combatants and lost many mages - let's say 0.5 of average house population. Losses of other 8 houses are much more limited but still significant - let's say 0.1 per house. It means that total losses of population from Schism are about 1.5+40.5+80.1=4.3 average houses (or 92 mages in my estimation). About third of all mages of the Order at the time. I guess it's a large enough number to be seen as threatening the existence of the Order itself, just like it's presented in the setting. For comparison, as far a I know, modern estimates place losses of SPQR during Second Punic war in the range of 25-45% of adult male population (a holy war that defined a national mythology). USSR has lost about a third of its adult male population during WW2 (still a holy patriotic war until this day). So it kinda fits.
- "apprenticeships per mage, period" go down from 1.25 to 1.1 to offset increased absorption of non-hermetic mages into the Order. "No time to teach when you've got to preach." It might also better suit the implied amount of apprentices per mage, I'm not sure.
After these adjustments model again gives about 1090 mages in 1217, though historical population changes slightly.
Now, the frustration bit.
I'm a bit concerned about implied distribution of population in the Order. It seems too small to be believable.
For example, Ex Misc chapter in HoH:S states that there're about 180 mages divided to 8 "big" traditions (Columbiae, Donatores, Orpheuses, etc.), several smaller ones (Koldun, Corrguineach, etc.) and, of course, random mages who had nowhere else to go. Average tradition has "somewhere between 5 and 25 members". These populations are too small to a) call these groups "traditions" from a sociological/antropological point of view, and b) should be very vulnerable from intergenerational reproduction point of view, because loss of each adult/experienced magus would mean losing 5-50% of population of experienced magi within that group. In the real world it's hard to imagine such small social groups that would reproduce for many generations. Especially if they are hindered by Gift-induced quarrels. I have no idea how Order is planning on advancing a magical tradition when one random calamity (say, a lab multibotch with mega-explosion) can wipe significant portion of its population, if not some small tradition in its entirety.
Moreover, when HoH books mentions subgroups of mages from different Houses that have their own culture, historical traditions and whatnot... It's all well and good until one realises that these "traditions" are maintained by groups of no more than 50 people. It's not "culture". It's secret handshake in a local hobby club. It's stated, for example, that Tremere have 14 styles for Certamen. With a population of 92 it's less than 7 people for each "style". When I went on karate practice, our club had about 40 people. And no one tried to say that we had 6 different styles within it. And we didn't even had 50 TeFo combinations, dragons, churches and longevity rituals to occupy our attention with.
Basically, most of the stuff in HoH books is too narrow and specialized to be believable, even within the setting. In a setting with tens of thousands of mages it would seem okay, I guess. But not in Mythic Europe, RAW. A thousand people doesn't even need its own juridical code (not mentioning 13 smaller sub-codes). It's excessive!
...
Oh, yes. "It's magic, I'm not gonna explain shit."
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Of course the terms "culture" and "tradition" have different meaning than in sociology books. Here it's more like a family or clan that teaches to its sons. Probably many of them went extinct indeed (and they aren't probably even mentioned in the books) and those that survived got a good share of luck.
It's a "custom" then.
And I've botched example with certamen - 14 styles are practiced in the Order as a whole, not only by Tremere. So it's about 75 practitioners per style on average in 1220, not 7. The point still stands, I guess.
I think it is a very interesting exercise.
The population growth does need a cap, as you say, when it reaches the carrying capacity. You explore the vis supplies, another could be simply the availability of gifted individuals in the population. This, however, would complexify the model a lot, I think, needing information on historic / semi-historic human populations, as well as the ratio of gifted individuals. Allso, as the population of the Order goes up, the amount of good potential appremtices decreases, presentimg the dilemma of a suboptimal apprentice.
So far, the factoid I have taken away from this is the idea that there were only about 300 magi during the Schism War, and about 100 of those died.
Those numbers fit Demographer's estimates. Interesting.
I that's actually the key to understand, or at least to re-interpret, the setting: most "traditions" are, indeed, very small affairs. It's kinda of like the Sith Lords, where "there are always two" - often the tradition indeed has only two, or a very few, practitioners per generation. Until the rise of the modern Order, magic was rare, and even with the new explosion in magi's population the traditions are still small. This also means that there are a lot of "failed" traditions, so-called "Ancient Magic" that no one practices anymore.
at 10°/°° gifted children, only in France you would get around 160.000 (Provence and Normandy tribunal with 16 000000 people around 1220)... I don't see how you can get only a thousand mages in an Order who pretend to be very strong in Europe.
Actually we decided my husband and I to multiply all number by 10 : with 10.000 the Order can start to be fearful. And also, when you see all schools and secrets within Houses... there are much to few mages on a so big territory (10 000 000 sqkm).
Even using 1°/°° having the gift, we get a much bigger number than the one given in the book.
I should use demographic indicator to calculate, I will do some day when I'll have time.
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I think you are overestimating the population of Europe at the time. You probably just misread the number, because the population of France at the time was 16 millions, not 16 billions.
Wikipedia (not the most reliable of source, but still) mentions an estimated population of Europe peaking at 100 million in the 10th-13th century.
With 1 Gifted for every 10,000 person, that would leave only a Gifted population of 10,000.
Many of those Gifted would still be unsuitable to become Hermetic apprentices for various reasons -- like having been recruited by a lesser tradition, or being killed due to a mundane's reaction to the Gift.
I corrected my mistake, sorry, but I was confused between billion and million... as I am Frenchspeaking, I guess you forgive me
Even with 1 gifted for 10.000, that would give 1600 only in France as you said...
On let's say 100.000.000 as you said, it would be 10000 gifted children... so as mages live around 150years and have around 2 apprentices, you can count without problem around 10.000 mages of the Order, which would be 1 mage on 1000 people in Europe... and would make of the Order a really major Order.
1000 people is less than Royal families in Europe...
In sundered eagle 7 years in the Theban tribunal, there is around 13 to 20 new apprentices (it is 1 on 10.000 have the gift and 1 on 100 has something magic)
So it is 2 a years, only in the theban tribunal... I don't see how you arrive only a 1000 thousands mages after 500-600 years
Counting on 100 hermetic age, there is more than 200 magicians in Theban Tribunal
if you just take 200 (which is very few) by tribunal it would give 2600, already more than the number given.
Three datapoints that might be of interest.
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Ars Magica explicitly states that you should expect something around 120 years of life after gauntlet for the typical magus before death/twilight/whatever. Granted, there are magi who live longer, but canonically "very few" do, and there are also a few who don't make it to that mark due to early deaths etc. So, just assume a lifespan of 120 years after gauntlet for every magus; meaning that if a population is stable, and has e.g. 2 new magi who are "born" each year (and thus 2 old magi who die), there are 240 magi in that population.
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House Guernicus in HoH:TL is reported as having about 1 apprentice every 8 magi. With apprenticeship lasting 15 years=120 years/8, that means that the population of house Guernicus is currently stable: every 15 years 1/8th of the House dies off, and is replaced by former apprentices.
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The thebes tribunal assigns some 12-20 apprentices every 7 years. Let's say 14, meaning an average of 2 new magi per year. Then, if this "recruitment rate" stays at that level (and the tribunal is neither a net importer or a net exporter of magi), the tribunal's hermetic population tends to some 240 magi. I'd say it's probably half of that, and growing, which is not that unreasonable - some big conflict can easily wipe out a century of slow growth. Plus, I'd say that Thebes probably exports a smallish fraction of its magi towards the fringes of Mythic Europe like the Novgorod, the Levant etc.
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In terms of the growth curve there are 2 issues:1) how many Gifted people are in Europe, and 2) what percentage of them are Hermetic.
The Hermetic magi grew quickly early on because they had a small percentage of the Gifted practitioners and were able to recruit relatively quickly. As the percentage they represent grows, there is also less room for growth, and the growth curve starts to flatten out a bit.
Note that it is a population of 10,000 Gifted for Europe, not 10,000 Gifted children.
That includes all of the magical, faerie and infernal traditions which find the Gift valuable. Given the average lifespan at the time, this means about 200 Gifted children being born every year. Or about 1,000 Gifted youths between age 5-15, which is suitable to become an Hermetic apprentice.
From these, many would be snatched by other traditions which also value the Gift. Some would have the Gentle Gift and never be found.
You also need to take into account the major investment in time that taking an apprentice represents. The master basically spends almost 4 years of his life training a single apprentice. Only in the last few years does the benefit of having an apprentice begins to outweight the investment in time -- provided the master spends a significant amount of time in the lab, where having an apprentice can speed things off.
All that being considered, I think that the average number of apprentices trained by a magus over his life would be around 2 or 3. That limits the growth rate of the Order. And as Fafnir mentioned, any big conflict (like the Schism War) can wipe out several decades of growth. Smaller conflicts (likes the Tremere Sundering, the Tytalus Infernal Purge and more recently the sack of Constatinople) can destroy severeal years' worth of growth.
That being said, if you want the Order to be much larger in your saga, go for it! Just realize that the more magi there are, the more pressure there will be for them to affect the development of Europe. If 1,000 magi can for the most part remain hidden and have subtle influence in the course of history, 10,000 represents such a large power that they would literally have the power to take control of Europe. It will make for a very different setting. 
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So, I found this thread four years later. I think it's very interesting and the conclusions are sensible, namely that Magi train apprentices fairly infrequently and that the Schism war set back Order growth by about a century.
I was trying to figure a heuristic about apprenticeship rate for my own purposes and I came up with the following back-of-the-envelope calculation.
Unlike the original poster I divide time in 15-year increments, not 50-year increments, because 15 years is the duration of an apprenticeship. So in the 450 years fr 767 to 1117 he gets nine periods and I get 30 "generations". But the population growth dynamics should come up to roughly the same.
We're told there were 12 founders in 767 and there are about 1200 Magi in 1220 so that's a 100-fold increase in 30 "generations" of 15 years. There were 13 founders if you count Trianoma but one house is wiped out in the Schism War. So it kinda washes out for my purposes. The calculation is not all that precise anyway.
A 100-fold increase in 30 generations is a 10-fold increase in 15 generations. This is very very close to a 1/6 increase per generation. That is, (1 + 1/6)^15 ~ 10, so let's use that.
Mage mortality is maybe 1/10 per 15-year "generation". So the rate of apprenticeship has to compensate for that. 1/5-1/6=1/30 is too little, 1/4-1/6=1/12 is about right for the mortality rate, 1/3-1/6=1/6 is too high. So pick 1/4 for the average apprenticeship rate.
This means that in every 15-year period one out of every four Magi is training an apprentice. Or that a given Magus will train an apprentice every 60 years on average. And they live about 180 years on average after apprenticeship.
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don;t forget this simulation
also has data for ages at death and a host of other things...
This is apparently more up to date:
Bob
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I do think a malthusian analysis of the growth of the order demographics makes sense, and it is probably a factor in old tribunals. However, I think there's a few things you can't realistically take into account:
- While it is convenient to look at history to evolve your game, I just don't think it makes any sense to project a demographic curve up until the 20th century, assuming the evolution of the world to be similar to our own, the ratio of gifted to remain the same throughout the centuries, and the vis sources not to vary at all, with the order of hermes still existing as it is in the 20th century. In my mind, you either have to adopt an approach that is similar to the world of darkness: e.g. technocracy with magic slowly fading from the world, and a drop in the number of gifted OR completely revise the history of mankind past a certain point to preserve the mythic feeling (e.g. no scientific revolution - make it a magical revolution, at which point magical auras would increase, not decrease);
- I don't think Europe's sources are anywhere near fully tapped by the order of hermes (although the old tribunals may think otherwise). Some of those are untapped, controlled by faerie courts, controlled by hedge wizards. They will be found and annexed. How many sources are unknown simply because the closest covenant is 200 miles away? How many more covenants can be created in the wilderness to benefit from such untapped sources?
- The order is in my mind on the crux of vastly increasing its vis production. It really shouldn't be too hard to start breeding magical creature lineages to the point where you're able to cull their number to get a yearly vis source. If vis gets scarce, covenants will focus more of their time on such projects. Also, if vis production becomes really tight and such projects can't keep up with demand, the likely reaction is mainstreaming mysteries like Philosophic Alchemy which would basically result in every magus in the order getting a personal vis source to fuel his projects, whose yearly production increases with age (e.g. no worries about scarcity at all - ever).
- While ancient sites might get swallowed up by the Dominion and get pushed into regios if you follow RL urbanization, there is another phenomena that should play in the Order's favor - e.g. the strengthening of auras over time in most major covenant sites. This may in fact end up creating vis sources that did not exist before through slow warping or even lab story events.
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We are actually doing this in my current game and I even broke it down when someone asked about our vis sources. Animals are not the only source of this however, since there is also plants and some objects you can look for.
The only animal breeding for vis we are doing is a pond full of magic carp. We do have a bunch of other animals which have vis, but they are mostly our hermetic cats (we have a mix of white lineage and black lineage).
However we have been transplanting vis producing trees to the point where we actually have several small groves of them. They are a fairly stable and easy to gather vis source. We also have grow truffles of virtue. Sacrificing one every year causes all the plants in our covenant to grow better, as well as having the effect of causing them to grow on each level of the regio.
We have been experimenting with other plants such as flowers, but have not had much success. The most luck we have had is a few of my characters rose bushes produce crystal/glass roses, with the occasional one having vis.
For vis producing objects/locations, you can get some idea from Hermetic Projects and Transforming Mystic Europe. Most of these are not possible to move to your covenant, though there are a few that can be.
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Specific lineages of magical cats (of Virtue) that have been breed by the OoH since its founding. There are three lineages: the black (descendants of Jerbiton’s familiar), the white (descendants of Mercere's familiar), and the Tortoiseshell (descendants of Celtic wizards familiars, actually two lines that split during the Schism War).
If you want more details on them, they are in RoP:M, page 70. They are a nice addition to any long standing Covenant, tracing back their origins to the founding of the Order.
Our group is currently searching for a few other animals of virtue. Specifically horses, dogs, and bees. We have stables and kennels setup, though not in use since horses were not very useful until about 30 years ago in-game. That was when the whole invent portal/Mercere freakout story line happened. It has been "on the list" but very low priority since then. We do have a whole bunch of bee hives scattered throughout our Covenant, though most heavily on the first level.
A few cattle of virtue to round out our cattle herd would be nice as well. We do have a few ravens of virtue, descendants of those collected when some of our Magi were looking for familiars.
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