Obnoxious Nitpicking

Harry Potter Demographics

What We Know

Actually, we know surprisingly little.

We don't even know how many students there are at Hogwarts. See How Many Students Are There At Hogwarts? at the Harry Potter Lexicon for a detailed discussion of the textual evidence as of GOF. It more or less boils down to many indications that there are about ten students per house per year, for a total of 40 incoming students a year, versus a few indications that there are about a thousand students total, which would be about 142 incoming students a year. Also, there are about 12 teachers.

"All children who are not Squibs are sent invitations to attend Hogwarts, but they don't all accept." (See the Harry Potter Lexicon again.) Also, Hogwarts is "the only Wizarding school in Britain for kids eleven and up." (See the HPL academics.)

We do know there are thirteen professional Quidditch teams in Great Britain and Ireland. (See the Harry Potter Lexicon yet again.)

We also know that in 2001, the United Kingdom census reported 58,789,194 people. This excludes non-Northern Ireland. The birth rate was estimated in 2003 at 11.74 births/1000 population. (Demographics of the United Kingdom) England alone had 49,138,831. (List of United Kingdom countries by population)

The population of England at the time of the Norman invasion in 1066 is estimated to have been about 1,100,000. In 1215, it is estimated to have been about 2,500,000. (Wikipedia: Population of England)

Premodern birthrates were significantly higher than birthrates today. I couldn't find any hard data on this in my quick Internet check, but apparently premodern birthrates could get as high as 60/1000 population, maybe even higher.

Extrapolating

Assumptions

In order to extrapolate further about wizarding demographics, we have to make some assumptions about at least one or two of the following:

Is the wizarding birthrate the same as the Muggle birthrate?
Is the wizarding death rate the same as the Muggle death rate?
Has the wizard/Muggle population ratio stayed steady over the last 1000 years, and if not, which way has it swung?
Which figure of Hogwarts student body size is correct?
Just how many wizards choose not to attend Hogwarts?
What was the birth rate in the 11th century, anyway?

Some initial calculations based on simplistic assumptions

Let us suppose that the student body figure which seems more likely from the texts to me, namely the forty new students a year, is correct. Let us also suppose that the number of Muggle-born students is canceled out by the potential students who choose not to attend, and that wizarding infant mortality is negligible, giving us a wizarding birthrate of 40 births/year. Let us assume that the wizarding and Muggle births/population rates are identical. This gives us:

(40 births/year) * (1000 population / 11.74 births) = about 3407

That strikes me as way too small, especially given how many Quidditch teams they have, and how big the Ministry is.

Let us revise the assumptions

Okay, the birth rate has been changing. Even back in the '90s it was more like 12-14/1000 population. These people were born in the late '70s/early '80s. Let's try it again, using 15/1000 population.

(40 births/year) * (1000 population / 15 births) = about 2667

Oops.

Let us revise the revisions

We'll keep 15/1000 population, because it seems more likely. Let's look at the intake of students per year. Maybe significantly more potential wizards do not attend Hogwarts. Since we're short on wizards, let's try assuming a lot more. Let's up the wizarding births/year to 100.

(100 births/year) * (1000 population / 15 births) = about 6667

This is a move in the right direction, at least. However, the small Iowa town where I attended undergraduate school had close to half again as many people. More than that if you count the college students.

Clearly, minor revisions are not doing the trick

There are several obvious targets here. We may be all wrong about how many students are at Hogwarts; the proportion of wizarding families who send their children to Hogwarts might be very small; there may have been a sharp drop in the birthrate due to the first Voldemort war.

This last possibility seems quite reasonable. However, if there were a sharp drop in the birthrate during the war, I would expect to see a sharp rise immediately after the war -- this would be the class two or three years after Harry & co. This rebound to normal levels and beyond ought to be really darn noticeable -- "hey, the first-years outnumber us two or three to one" -- and I don't think it's been mentioned. It isn't out of the question that the wizarding birthrate is just generally lower.

I don't think we have had any indications that relatively few families send their (magically gifted) children to Hogwarts, but I'm not as sure we would have to. We are given that there are no other educational choices in Britain. We're left with going abroad or no formal education. If, as J.K. Rowling has said, all magical children are admitted to Hogwarts, why would they not come?

Too many deaths?
Uneven and frequently questionable education (See essays on HPL academics page.)
Too expensive

This last raises some disturbing possibilities -- perhaps likelihoods.

A Disquieting Possibility (or, Hypothesis One)

Are we only seeing the narrow upper crust of the British wizarding world, those who can afford a formal education, while all the rest are denied even secondary school, their only hope earning enough in a blue-collar trade that maybe their children we be able to go to Hogwarts? A large maybe -- we never heard any mockery of first-generation Hogwarts students, and given the atmosphere of that school, we can be pretty sure there would be mockery.

The closest we've seen to poverty in Hogwarts students is the Weasleys. Arthur Weasley has a white-collar government job, and at least in my experience would be considered middle-class no matter how embarrassing his children's secondhand dress robes are. They own a house. Molly Weasley is a housewife -- can afford to be a housewife. This is not the lower class. But when the Weasleys are the most impoverished people in evidence -- where is the actual lower class hiding? Or perhaps, where is it being hid?

I'm not suggesting over half the population is destitute and on the brink of starvation. A society that poor probably couldn't support thirteen Quidditch teams, either. I'm suggesting a society that is starkly stratified and severely resistant to social change. Forget no college -- kids here wouldn't get any schooling at all. I guess I'm just saying that in this scenario, Hermione might be well-advised to save the house-elves for later and look at a broader picture.

But then again

I somehow think that if JKR envisioned a world with such violent class divisions, she would have mentioned it by now.

So maybe we have the number of Hogwarts students all wrong. Let's look at the thousand-student hypothesis, which, recall, gives about 142 incoming students a year. Let's raise the births/year rate to 150.

(150 births/year) * (1000 population / 15 births) = 10,000

That's better. I'm not sure if I'm happy with it, but it no longer looks absurd. Although it's less than a third as many people as there are in the suburb I grew up next to. (The suburb I grew up in is kind of puny.)

Since birth rates have tended to go down as life expectancy goes up, and wizards live longer than Muggles, it's reasonable to posit a lower yearly birth rate. Let's try... 8/1000 population.

(150 births/year) * (1000 population / 8 births) = 18,750

Better yet. Still smaller than many cities, though.

(Incidentally, applying the 8/1000 population birthrate to the 40 births/year model -- let's raise that to 50/year -- gives:

(50 births/year) * (1000 population / 8 births) = 6250

which is better, but not enough better.)

What a Crummy Student-to-Teacher Ratio (or, Hypothesis Two)

The number of teachers is more solid than the number of students, and the number is twelve. This gives a student-to-teacher ratio of:

1000/12 = about 83

I don't think this is acceptable. Or likely. But what do I know, maybe they do all constantly use Time-Turners. Or maybe some of the staff just never come to meals or interact with Harry in any way. But it's still tough on the teachers who have to teach all the students.

Hypothesis One still seems more plausible.

More wild assumptions

Let's now assume that the wizard/Muggle population ratios have stayed constant and try to work out how many students Hogwarts had when it was founded. It was founded about a thousand years prior to the books, which puts it in the late tenth century. /however, the earliest population figures I have are for 1066, over half a century later, so we'll just look at that.

The most simplistic method would be simply to assume the proportion of Hogwarts students to Muggle population stayed constant, and calculate thusly:

(280 students/49,138,831 Muggles) * (1,100,000 Muggles in 1066) = about 6

(1000 students/49,138,831 Muggles) * (1,100,000 Muggles in 1066) = about 22

This would work out to less than one student a year in the first case, or just over three a year in the latter. Either way, not very big. Fortunately, the above assumption is silly; it incorporates not only the assumption that the wizard-to-Muggle population ratio stayed constant, but that the per capita wizarding birthrate stayed constant, when it makes sense that it fell just as the real per capita birthrate did.

Somewhat more rational assumptions

Suppose the wizard/Muggle population ratios have stayed constant and the wizarding per capita birthrates have not. Since Hypothesis One doesn't actually give us a population, we can't do anything with that. With Hypothesis Two, we had 18,750. Let's say the wizarding per capita birthrate, in 1066, was... three times the current one. That would be 24 births/1000 population. Therefore we have a 1066 birthrate of:

(18,750 wizards/49,138,831 Muggles)*(1,100,000 Muggles in 1066)*(24 births/1000 population) = about 10

Ten incoming students a year sounds quite workable.

Regrouping

So, basically, we have two workable hypotheses. The advantage of Hypothesis One is that it does not try to stuff a thousand students into a school apparently designed for 280. The advantage of Hypothesis Two is that it does not posit the existence of an entirely unseen wizarding underclass, which need not exist; there may not be any impoverished wizards. This is a good time to expound:

Hypothesis Three (courtesy my mother)

Why can't the wizarding population be 6250?

Hypothesis Four (courtesy Desist)

JKR isn't a mathematician or historian and doesn't worry about whether this stuff makes sense, you obnoxious nitpicker!

Final Thoughts

Having been thoroughly quashed by my mother and sister, let me leave with a few questions:

Has the wizard-to-Muggle ratio stayed constant? If it's changing, which way do you think it's going?
Are there people who cannot afford to go to Hogwarts? Are there provisions for helping them?
Do wizards grow their own food, harvest/mine/find their own raw materials? If so, they need a bigger population. If not, they must get them from somewhere. Do they trade for it? With what?
The Muggle way of life, quality of life, and lifespan in Britain have changed dramatically in the past thousand years. How much have the wizarding way of life, quality of life, and lifespan changed?
On average, in history, was it more dangerous to be a wizard or a Muggle?

Comments, objections, additional hypotheses? Visit the feedback page.

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