Commonality of Enchanters
 

In the setting in question, magic is a relatively new thing, about a hundred years old. The setting uses ritual magics with the core skill being "Deeper Astrology," which has the prerequisites of Astronomy and Occultism. The Enchant spell has a prerequisite count of zero, and the special prerequisite of "Must Have at Least One Point in each of ten other Colleges." Planetary, zodiacal and decanic modifiers apply and sorcery is a legitimate profession (generally speaking), so it's not too hard for even an inept mage to get enough bonuses to have an effective skill of 15+ with the needed spells.

The big change is that Slow and Sure enchantment is vastly faster: An enchanter can put as much energy into an object in an hour as that enchanter can recover in that same hour. At the lower end, that's 6 energy per hour per enchanter; at the upper limit, that's 30 energy per hour per enchanter. However, they can't use powerstones, called in this setting starstones.

One in 375 men has Magery, and four in 375 women (I wanted 1 mage in 150 people average and a skewed sex ratio). The setting is an alternative history that diverged in 1660. It's currently TL 5, early industrial; the Vaucanson lathe was invented thirty years ago.

Given all the above, how common would you expect enchanters to be?

Re: Commonality of Enchanters
 

Learning 10 colleges of magic is arguably equivalent to becoming an MD. There are about 1 million MD in the US population of about 300 million, so 1 MD per 300 people. I wouldn't expect enchanters to be more common than that.

Becoming an MD requires exceptional intelligence and discipline. It's possible that not everyone who can work magic has the drive and discipline to learn multiple colleges of magic to become an enchanter. If only 1 in 300 mages have the drive to become enchanters, I'd expect there to be 1 enchanter per 45,000 people. I wouldn't expect the number to be much worse than that.

The final result is a question of world building. If 1 in 300 people is an enchanter, enchantments are going to be extremely common and every no-name village is going to have an enchanter. If 1 in 45,000 people is an enchanter, only the largest cities are going to have an enchanter, much less multiple enchanters.

I'd probably split the difference, and put it at 1 enchanter per 5,000 or 10,000 people. Every medium sized town has an enchanter, and major cities have several. Large capitals such as Paris have enough enchanters to possibly have a guild to discourage additional entrants into the market.

Re: Commonality of Enchanters
 

Far LESS common than that. If only one person in 150 was genetically capable of being a medical doctor, you wouldn't get one MD per 300; you'd be damn lucky to get one per three thousand.

And if Enchant retains the requirement of Magery/2, you've sliced the pool that much thinner. Then toss in the various caveats: how many mages of that capability are casting spells-for-hire? They're not enchanting for a living. How many are court wizards? They're not enchanting for a living. How many are pure researchers, or professors at the magical academy, or just retired coots puttering around in their gardens and using lightning to zap voles and rabbits? They're not enchanting for a living. (Come to that, how many are adventurers? They're not enchanting for a living either.)

Too many discussions about the density of mages just assume that everyone capable of doing X is doing X. Far too few recognize that it means that those doing X are not doing Y, Z, Q, or any other letter.

Re: Commonality of Enchanters
 

It doesn't. Enchanting without the usual prerequisites only makes a spell more difficult, as per the rules in Thaumatology, p. 73.

Re: Commonality of Enchanters
 

You probably also need to filter for the social system - again, using the MD example, fi you're born in the ghetto you're going to struggle to get that training you need to qualify (it's not impossible - I can think of one globally famous example - just damned difficult).
Likewise, in a traditional feudal setting a potential enchanter born to a family of illiterate serfs ... or, for that matter, as the eldest son of a feudal magnate ... is going to need some special stars to get themselves into wizard school.

...and a medieval population is going to be small. IIRC England got up to about 7 million before the Black Death hit ... and took a long time to get back there. Suddenly the number of practicing enchanters looks very small indeed.

And for a further fly in the ointment ... I would suggest training to be a wizard probably has a higher fatality rate than medical school...

Re: Commonality of Enchanters
 

The absolute lowest point investment to become an Enchanter is [13], for [1] each in Astronomy, Deeper Astrology, Occultism, and each of ten Colleges. In a formal education setting, someone focused entirely on becoming an Enchanter is investing 3600 hours. At 8 hours a day and 25 days a month, that's 200 hours a month, for a total of 13 months of dedicated study. Modern colleges don't go that intense (fewer than 25 days a month and less than 8 hours a day, typically, as well as a few months off), but I think you could achieve that in the amount of time needed for an Associate's Degree (2 years). The Physician template in Bio-Tech has [35] invested in medical skills, nearly 3x as much as the Enchanter requires, and this is on top of having noticeably high intellect (IQ 13). Granted, I think doctors normally take around twice that amount of time (12 years rather than the 6 implied by the above), but a big part of that is that they don't have the option of only learning medical skills in college.

So, with the barrier to becoming an Enchanter (provided you have Magery, of course) being much lower than that of becoming a doctor, you'll have more mages become Enchanters than you have average people becoming doctors. Well, assuming comparable levels of access to such advanced education - at TL 5, fewer people are going to have the option of going to the equivalent of a community college or trade school than here in TL 8. You'd have to weigh the factors involved, but you're almost certainly going to see more than 1 in 300 mages being Enchanters.

Re: Commonality of Enchanters
 

Emphasis mine, and still missing the point. There are, by the OP's numbers, 0.0066% of the people who are capable of enchanting, versus 100% of people genetically capable of becoming doctors. Does becoming a doctor take 150 times as long as becoming an enchanter? I agree that more than one mage in 300 will become an enchanter in just about any milieu or setting. But it sure as hell isn't two mages out of three.

Re: Commonality of Enchanters
 

The point I was responding to was the one about having only around 1 in 300 mages as enchanters, based on 1 in 300 Americans being doctors. The fact the required investment to be an enchanter is much less than the required investment to be a doctor means that, of those individuals who can be enchanters (that is, of the mages), you're likely to see much more than 1 in 300 becoming enchanters.

Also, that physician template I was looking at had IQ 13 - the majority of the population would require much more investment. If we assume effective IQ 13 for medicine (which could be due to having IQ 13, having IQ 9-12 and some amount of a relevant Talent, etc) is just above 1 Standard Deviation, that means only around 16% (roughly 1 in 6) of the population would qualify and the rest would need to work a good deal more to become doctors (although to be fair, some of those 16% would have an easier time than the IQ 13 individual). Thus, one could argue that, of those who can become doctors in the amount of time implied by the template, the number who do so is closer to 1 in 50.

Of course, this does assume that only having [1] in each of the relevant skills is sufficient to become a professional enchanter, and also assumes that all mages have full-fat Magery. If you need more investment than that (OP implies not - "it's not too hard for even an inept mage to get enough bonuses to have an effective skill of 15+ with the needed spells" - but I may be overestimating how effective a bare-minimum enchanter would be), or if many mages have a more Limited form that doesn't allow them to use 10 or more Colleges, then you're going to see it being more rare. I doubt it would be less common than 1 in 50 mages (and thus roughly 1 in 7,500 of the total population, as around 1 in 150 are mages), but I may be mistaken.

Re: Commonality of Enchanters
 

I literally addressed that point in the next paragraph: "If only 1 in 300 mages have the drive to become enchanters, I'd expect there to be 1 enchanter per 45,000 people. I wouldn't expect the number to be much worse than that."

I also disagree with Varyon's point that learning Enchantment is no worse than an AA degree. Having the determination to sit in a classroom and closely follow a lecture, 4 hours/day and 50 weeks/year, is not normal.

But I do think if you combine the two points you get more mages that can potentially be enchanters, but you're still looking at a handful of mages out of a hundred. Which is what I closed my response with: "I'd probably split the difference, and put it at 1 enchanter per 5,000 or 10,000 people."

Re: Commonality of Enchanters
 

Most mages in this setting only learn a few colleges. Healing is nearly universal due to the immense utility of Recover Energy, and the other most common are Knowledge, Protection & Warning, Communication & Empathy, and Light & Darkness.