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Estimating Wizarding Population:

Okay. We’ve got a major disconnect on our hands. In the joint interview which followed the release of HBP, JK Rowling revised her earlier statements that the enrollment of Hogwarts Academy was about 1,000 students, down to about 600.

Unfortunately she also made an unfortunately vague-sounding guess that the entire wizarding population of Great Britain was about 3,000. This flatly does not work either. Nor did she correct, or modify, or contradict either of these statements later, in the course of DHs.

Rowling admits that she is bad at maths. In fact she is so bad at maths (even where they intersect with common sense!) that it is ridiculous. If we want to start from a base that is even remotely plausible, we are just going to have to do the retrofit, from scratch, ourselves. And just try to keep it in something like the same ballpark on one end of the equation.

Because an enrollment of 600 is far too high for a population of 3,000. Certainly if we are talking about an enrollment of only the children between the ages of 11 and 17/18. If we were talking about all the school-aged children from about the age of 6, yes, maybe, that might about work. But not if we only start counting them once they reach the age of 11.

And certainly not if Rowling’s statement that wizards may have much longer life spans than Muggles is to be taken seriously. The statement was made long enough ago that it might reasonably be dismissed as a “cool idea” that she never managed to actually incorporate into the story, but she still made it.

In point of fact, she has scaled what she actually shows us back considerably. There seem to be a fair minority of wizards who live into their 2nd century. But my own extrapolation of an estimated potential wizarding lifespan of 90–120 years seems to be about right.

It is clear that lifespans on the order of that of Griselda Marchbanks (who must be about 135–150) are vanishingly rare, but she did finally bring herself to depict a few of the “Wizards of the Month” on the official site as having comfortably passed their century mark reaching the ages of 110–120. So we cannot simply dismiss the statement altogether.

Although we probably should continue to scale it back. For all of my own calculations I will be working from the basis of a projected wizarding lifespan of about 90-120 years. This corresponds to the presumed “natural” wizarding lifespan, without any additional enhancement by lifestyle modifications or medi-magical procedures which I had been postulating to be the case since this site first went up. Clearly such artificial extensions to a wizard’s life are not available.

However what Rowling has still failed to take into account is that if you have a population which lives, in the main, around 100 years, you still have to have an “age cohort” of individuals in every representative year. And this age cohort will reflect, to at least some extent, the number of individuals who were born in that particular cohort’s birth year.

Assuming relatively constant age cohorts, an enrollment of 600 students will need an annual intake of about 85 students. Ergo; a Hogwarts enrollment of 600 would imply that about 85 magical children are born every year.

If you project a lifespan of about a century the bulk of this age cohort will be supposed to have survived for that century.

That does not add up to a total population of 3,000. It adds up to 8,500.

That’s nearly three times as many.

And if there is a wizarding population of 3,000, then the projected wizarding lifespan is certainly nothing even close to a century. Your whole population either winnows out alarmingly across the board, or the average wizard doesn’t make it to the age of 35.

And no, we cannot factor in the wizarding war. We are trying to calculate the results of natural processes here.

So which of these statements do we throw out?

From what we are shown in the course of the series, it seems improbable that more than half of all the wizards born abruptly start dying off as soon as they leave school.

And an enrollment of 600 in a society in which people live to the ages of 90–120 ought to have a total population of between 8,000 and 9,000. Which would fit what she shows us of their general standard of living.

But to be honest, she has never really shown us a Hogwarts enrollment which would have plausibly “read” as being as high as 600, has she? Not in the day-to-day matters where it counts.

Oh, sure, she occasionally pans the camera over a crowd scene as a background prop, but there are still only 12 subjects taught at the school, and only one professor to teach each subject, and class sizes run to about 20 students per class, and no more than about 6 classes are held in a day. This doesn’t add up to 1000 students. It doesn’t add up to 600, either.

Rowling consistently shows us far fewer students (about half as many) than she claims are actually there, which has finally forced me to simply dismiss any of her statements about the total Hogwarts enrollment.

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To one point, on this subject, I was more inclined to take Rowling’s stated word for the matter over the impression that we are given in the books themselves. But that attempt to dodge the issue no longer works.

And I also think that had she really intended to depict a student body of 600 we have been particularly ill-served by the Harry filter. Harry is not a child who takes a great deal of interest in other people. In ideas, events, mysteries, puzzles, yes. Sometimes. He has a keen, if inconsistent, interest in all of these — once they get his attention. But not people. Or not people in general. He does not particularly notice people unless their existence is forced on him, or something about them has caught his attention. If there are really supposed to be 500–600 students at Hogwarts then where Harry is concerned we have simply never had the whole story.

For example; how likely is it that the only 6th year student in Gryffindor House in the year of OotP was Katie Bell? But have we ever, in the first five books, some 2,600+ pages, ever heard of another? Nope. Not until HBP, wherein we were suddenly introduced to Katie’s friend Leanne and year-mate Cormac MacClaggen, because Harry now had to personally deal with them.

Okay then, how likely is it that the only students in the year following Harry in Gryffindor House are Ginny Weasley and Colin Creevy? Really? Who are they? In fact who were the Prefects for their year. Ginny didn’t make the cut, and we never heard that Colin did either. Are there any students at all in the year after Ginny and Colin? Well, yes, there are. Romilda Vail and a whole raft of other girls. But when did we ever get a hint of that? For that matter neither Romilda nor Cormac sound like the kind of kids to keep themselves quietly in the background, but they certainly never before showed up on Harry’s radar until HBP.

Were the only 7th year Gryffindors in OotP Lee Jordan and the members of the Quidditch team? For that mater who was the Gryffindor male Prefect in the Twins’ year? (Clue; it’s not Lee Jordan. Harry would probably have noticed that.) Are we even sure that we know all of the students in Harry’s own year, if it’s five to a dorm, and any others were assigned to a different dormitory? And this is just in Gryffindor House!

If you were only attending to Harry’s impressions, you could be excused for assuming that there are no more than a hundred or so students in the whole school. And yet even Harry is supposedly aware that there are hundreds of students in the stands at a Quidditch game. At one point I believe he even registered that there were a couple of hundred of them in Slytherin green. Which would assume at least 800 total students right there. There is also an inordinately large number of students cited as having attended the Yule Ball in year 4. (About 1200) But none of this is convincing on a day-to-day basis.

No, I’m afraid that our Harry’s-eye-view of the population of Hogwarts is just not good enough, or comprehensive enough to be going on with. Harry is simply too unreliable a witness in this particular subject. We can’t just take his “word” for it. We get no usable picture of the student population from Harry’s PoV. Not if there is a student body of 600.

Let me repeat: Ms Rowling shows us a 7-year school with only ONE instructor of each subject offered (at least until Firenze showed up), dorms which house no more than five boys or girls per house per year, and combined classes with equipment enough to only serve 20 students. Having allegedly trained as a teacher herself, one might have expected her to have a better grip on the logistics than this. And this makes no sense at all when stacked up against 200 people in Slytherin green at a Quidditch match, or close to 1200 students at the Yule Ball.

She knows better than this. It is positively insulting to blithely hand us a school of 600 students wherein there are 12 subjects taught and yet there is still only one teacher for each subject for the whole school, and expect us to accept it.

To teach 600 students, prepare lessons, oversee classes and mark papers, all on your own is not humanly possible even if these are wizards. A teacher in a Muggle secondary school carrying a full course load doesn’t deal with more than a couple of hundred. If that.

And, on that day-to-day level, what she actually shows us is dormitories that house about five for each year (one for boys and one for girls), and combined classes numbering about 20. That does not add up to an enrollment of 600 students over 7 years. Particularly not against a total population of 3,000.

Assuming that the attendance at Hogwarts is reasonably constant; if approximately 600 students represents seven years of the entire wizarding population’s births for all of wizarding Britain and Ireland, then you must get around 85-86 new students each year, which, given that the charmed quill records all magical births in its range, right there tells us the total average annual number of Magical births within Hogwarts territory. If there are any children who do not attend they would be rare. In HBP we were shown some of the sort of maneuvers that are gone through to ensure that any magical child would be enabled to attend Hogwarts.

From Rowling’s statements in the joint interview of July 2005 she seems to be trying to “over think” the problem, and has hit upon the number 600 because wizards are a rare breed, and she claims that a school of 600 would be tiny for all of Great Britain and Ireland.

And it probably would be. But if the total population is around 3,000 it isn’t tiny enough.

Although from any reasonable standpoint, a total population of 3,000 still sounds a great deal too low for their standard of living. At the time, Rowling also compounded the problem by making some comments about the actual number of magical people being filled out by magical beings that look basically human (hags, etc.) but aren’t. Which makes her estimate even more implausible.

But we will try to keep this in the back of our minds. We have some other factors to consider.

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Frankly I think we may need to dismiss both of Rowling’s statements as stabs in the dark and calculate from the prep work that she tells us that she has actually put into the books, and that we know that she has put into the books — because she has shared some of it with us, and that part of it she has gone on to show us in the books.

Rowling tells us when she sat down to plan out the story, she created 40 individual students in Harry’s year.

And she did. Some years ago in a televised interview called something like ‘Harry Potter and Me’ she showed us a list of their names with various marginal notes.

And by the end of the series we’ve met most (although never quite all) of them. So I think we can absolutely take her at her word on this statement. That statement is true. Those 40 students existed in the story, even if we neverdid met a handful of them face to face.

And, consequently, if we know the Hogwarts enrollment for one year, we ought to be able calculate the total enrollment for 7 years well enough to extrapolate at least a ballpark figure for the total wizarding population that fits what we see. Kind of.

The Hogwarts enrollment estimate is an easy one. It has been out on the web ever since that televised interview (which I think may have been in the year 2000) despite all of her statements otherwise. If there are 40 students in an average year, then there must be approximately 280 students at Hogwarts. This number probably varies by 6–12 in either direction year by year. Harry’s birth cohort, having been born at the very height of VoldWar I may be slightly smaller than average, but the variation is probably well under a dozen.

And just about everything Rowling has ever shown us (rather than told us) about life at Hogwarts, supports this number.

If we calculate a standard birth cohort of 40 with a projected lifespan of 90–120 years you get a total population of 3,600–4,800.

Offset against a Muggle population for Great Britain and Ireland that is now up to around 65,000,000 that doesn’t really look proportionally that far off from Rowling’s estimate of 3,000.

And most wizards don’t actually make it to the age of 90–120. There are a lot of magical illnesses out there that tend to carry them off before they realize their full potential life spans. And besides, magic is dangerous.

There was also a terrorist war going on among them for over 20 years. The current population of human wizards may very well be around 3,000 by now. Although I doubt it. I don’t think the casualties of VoldWar I were anything like as high as the fans would like to make them.

For that matter, it is difficult to imagine a wizarding population of 3,000 managing to survive at all, let alone to survive and enjoy as high a standard of living as is clearly the norm by Harry’s day, but what Rowling actually shows us at Hogwarts supports this projection. Sort of.

We just have to ignore what she keeps trying to say about the matter.

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The most recent adjustment which has been forced upon us is whether one can safely factor in a projected lifespan of some 100+ years. In interviews made around the time of the release of HBP Rowling stated her contention that wizards normally live until some magical ailment carries them off. Which is to say that they rarely die of old age alone.

They do, however, die of accidents and foul play with somewhat alarming frequency, and magical ailments appear to be fairly widespread. An outbreak of dragon pox carried off Abraxus Malfoy at some point recently enough for his grandson to be claiming to remember statements which he is supposed to have made. Given that anything with a “creature-pox” name has all the potential to be a virulent epidemic, it is not impossible to reflect that the same outbreak, or a similar one, may have also removed the Princes, Severus Snape’s maternal grandparents, explaining how he comes to be living in what I suspect to have been their house. Or even the elder Snapes. We have no reason to believe that a Muggle living with witches or wizards would have a significant resistance to all magical maladies. They are both human, after all.

Rowling also informs us that James Potter lost both of his aging parents, quite suddenly, by means of yet another outbreak of a magical ailment which, if the dates of that silly tapestry are to be taken seriously, turns out to have been in 1977. (And excuse me but 57 is not what I would call elderly, even if Rowling does.)

It has also belatedly occurred to me that by splitting off from general human society by 1692, it is rather unlikely that wizards have yet groked the concept of immunization, which was only introduced to England toward the end of the 18th or in the early 19th century. Wizards may be able to treat Muggle diseases very quickly and completely, but it occurs to me that they probably do little or nothing to prevent them.

And most of the wizards whose birth and death dates are known to us (from Rowling’s Wizard of the Month notations, and Famous Wizard Chocolate Frog Cards) seem to have rarely managed to attain an age much past 90. Although, as I say, she is getting better at that. Never mind the example of Griselda Marchbanks who appears to be very old indeed.

Which makes any sort of population projections dicey to say the least.

Because while Rowling may be perfectly accurate in stating that wizards can live to more advanced ages than Muggles, it is beginning to look as though a comparatively small number of them actually manage to do it.

And we do not know what that percentage may be.

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The key issue that almost all subsequent speculations on just how the wizarding world actually operates depends upon is the question of just how many wizards and witches actually populate this secluded wizarding world. Because most of the visions as to how these people must manage things hangs upon whether, first, there are enough people to actually do the work that such a service requires, and second, that there be enough revenue to underwrite the living expenses of the people who provide such service. Up to the release of ‘Harry Potter and the Half-Blood Prince’ Rowling made no solid statement on this issue, apart from a comment in one of her early interviews that Hogwarts is not a fee-paying school, although books, materials and uniforms are the responsibility of the students and their families. Ergo; Hogwarts probably amounts to the equivalent of being state-supported. Its running expenses and staff’s salaries paid by some as yet unidentified sector of the wizarding world itself, presumed until further notice, to be the Ministry of Magic, with additional funding via the Board of Governors, although additional private (alumni?) donations are, of course, probably welcome.

Post-HBP, we now know that there is also a special fund for students with severe financial hardships.

Rowling has also stated that there are no wizarding universities, and that if wizarding children are not taught the basics at home they are sent to Muggle primary schools. Clearly general education is not a concern of the Ministry of Magic. The magical training of young witches and wizards, however, is.

Of course, about a year or so after making that last statement, Rowling amplified it with the information that wizarding parents typically do not enroll their children in Muggle schools due to security issues. And that, consequently wizard-born children are all but universally educated at home; typically only Muggle-born wizards are educated in Muggle primary schools.

We have been given at least a few other clues regarding this issue as well. From which we may determine that the wizarding population of Great Britain and Ireland (or, rather, the area within the range of the Hogwarts quill, which covers Great Britain and Ireland) is probably not much more than would support a rather small town. If even that. If the total human magical population of Great Britain and Ireland really doesn’t exceed 3,000, close to half of them could be living in and around Hogsmeade.

My earlier calculations were based upon the statements that Hogwarts, acto all of Rowling interviews in the subject, is the only magical training center in Great Britain. (Otherwise, one might expect most of the Slytherins to be off at Pureblood High or some such place.) And it is the Hogwarts staff which has custody of the charmed Quill which records all magical births in its catchment area.

So. Rowling originally told us that there are about 1000 students in attendance. She has since modified this number to 600, which is still too high to correspond with what she has shown us in the books. This new estimate is taken from the joint interview with the founders of TheLeakyCauldron.com and Mugglenet.com immediately following the release of Harry Potter and the Half-Blood Prince.

I would not count upon this information remaining stable, either. Rowling openly admits that she is weak on the number thing. One of the better descriptions online is that her grasp of numbers is “impressionistic” rather than accurate. This seems a very fair summation.

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We have only been told of two schools of comparable size (and presumably age) to Hogwarts in Europe. There is a great deal of suggestion that there may be other, smaller schools on the continent in addition to Beaubatons and Durmstrang. But we have no indication of how many or what size these might be. In any case, the wizarding population on the continent must be more widely dispersed than it is in Great Britain and Ireland, which are, after all, island nations.

Support for this last hypothesis can be read in the fact that Viktor Krum, from Bulgaria (A Balkan State, sharing boundaries with Greece and Turkey) is a student of Durmstrang, which from its climate and Germanic name one would most likely expect to be located somewhere in the northern part of Europe, possibly on the Baltic Sea, i.e., Scandinavia. This alone strongly suggests that any geographic division between the catchment areas of Beaubatons and Durmstrang is that between Western and Eastern Europe, rather than that between North and South.

However, we have also been told that Muggle-born students are not admitted at Durmstrang, which would tend to suggest that if Muggle-born witches and wizards are not simply left untrained on the Continent, there must be some other school, or schools, which serve them. If the 25% Muggle-born demographic that is the norm in Britain is also the norm in Continental Europe, one might expect such a school, at most, to be about one third the size of Durmstrang.

Or maybe not. We don’t know how many schools may be in wizarding Europe. Only that Durmstrang and Beaubatons are the two closest in size to Hogwarts.

This also strongly suggests that the Hogwarts quill may be unique. The student body of these two leading European schools is clearly not determined by such methods. Nor are they likely to be administered by such a conveniently “state-supported” principle of inclusion. A moment’s reflection will remind us that if, unlike Hogwarts, their student body routinely draws from multiple nations and the jurisdictions of several European Ministries, they cannot be managed by such a simple all-inclusive selection process as that of Hogwarts which is supported and to some degree overseen and administered by the British Ministry of Magic. It could very well be that Beaubatons, as well as Durmstrang are both effectively schools for the elite, within the magical community. This would go some way towards explaining the initial haughtiness of the Beaubatons guests as well.

At this point we cannot simply make a blanket statement as to there being X many additional European schools of Magic that we have been given no information on. But the indication seems to be that Great Britain and Ireland, being island populations, may have a more highly concentrated level of magical traits within the general (mundane) population, resulting in a higher number of magical births, per capita than on the Continent. With the Hogwarts Quill in the equation, the British Ministry certainly may be able to keep more accurate records of what the magical population of those islands actually is.

As to attempting to make a general estimate of a worldwide wizarding population, it stands to reason that an estimated number of wizards could be extrapolated by determining what fractional percentage Great Britain and Ireland’s possible 3,250 magicals (a general ballpark estimate chosen strictly for convenience. It is within the general parameters, and the numbers come out even.) is of the total recorded mundane population of those nations, and to apply that percentage to the total worldwide population.

To make such an estimate, we will have to agree to be resigned to assuming that the result of such calculations will almost certainly result in a miscount, possibly a considerable miscount. We cannot automatically assume as high a ratio of wizards to Muggles worldwide as can be found in Great Britain. Which itself may be an overestimate due to the uncertainly over the length of the average, rather than the extrapolated potential wizarding lifespan. At this point we have absolutely no canon support for believing that the per capita representation of wizards to Muggles is necessarily as high on the Continent as it appears to be in Great Britain.

Note: This “high” ratio is relative only. According to the internet, the combined Real World population of Great Britain and Ireland is now estimated at something around 65 million. Of which, in the Potterverse, only some 10 or so births per year are Muggle-born magicals. It is at this point uncertain what percentage of the 20-so estimated annual halfblood magical births would be recorded in the mundane birth records. It is also only assumed that the 10 or so purebloods born inside the secluded wizarding world may not also appear in the mundane census. In point of fact, they very likely may.

Given the growing evidence to suggest that for all their apparent ignorance of Muggles, and Muggle culture, the majority of wizards actually live out in the world among them, the assumption that their births go unrecorded becomes an untenable hypothesis. We cannot resolve this conflict with the information at our disposal at this time.

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A further complication is added by the existence of the Hogwarts quill. It really does seem likely that this particular magical artifact is unique and that due to its existence the wizarding census of Britain and Ireland is a good deal more accurate than those of Continental Europe. Even if only due to the opportunities for mistakes due to the difficulty of sharing data over the jurisdictions of multiple Ministries. In the absence of something like the Hogwarts quill, it seems very probable that there are Muggle-born magical births which go unrecorded there and such children are only identified, if at all, when they have public magical breakthroughs strong enough to be detected by whatever means of monitoring for magical activity (if any) are utilized by the different European Ministries.

But I could be wrong in this supposition. It is entirely possible that it is the Continental Ministries who possess such quills, rather than the schools.

I suspect that if the proportion of Muggle-born magicals to the total population seen at Hogwarts (25%) is anything even close to a worldwide estimate, then areas with large mundane populations might generate a higher number of magical births as well. It is difficult to factor how much more thinly spread the sources of magical traits in the general population might be over large geographic areas, however, and how this dispersion would affect the number of magical births.

Which may be why Rowling says there is no wizarding university. The wizarding population in Europe is not quite high enough to really support one yet.

Plus, the logistics of the matter do not indicate that such an institution would be performing a function that offers an adequate return for the resources necessary to operate it. If we estimate that even as many as one out of every 3 Hogwarts NEWT students would choose to continue their education into something comparable to a conventional 3-year university, that would only give this hypothetical institution a British student body of under 50. Such a low number of students would severely limit the number of instructors such an institution could afford to retain, which would limit the number of subjects that would be available for study. Which would further reduce the number of students who would seek such instruction.

Which at the very least would suggest that if such a university is ever founded, it will almost certainly be multi-national, serving several countries across the European Union.

What is more, the wizarding world, unlike our own, does not have such a surplus of newly-qualified young people that it needs to establish such artificial standards as the demand for advanced degrees in order to delay their entry into the workforce. The standard within the wizarding world at present appears to be to accept candidates into a number of specialized training programs and then to train them in the specific requirements for their chosen profession, directly.

For that matter, since we have already been directly told in the text that at NEWT-level a Professor can refuse to accept you into their class if your performance on the OWLs was substandard, it seems quite likely that the last two years at Hogwarts already constitutes the equivalent of an undergraduate degree.

As the total wizarding population of Europe continues to increase, it is possible that there will be a (small, international) University in their future within the next several generations. But there is no need for us to go there right at the moment.

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So: first to calculate the percentage of magicals to mundanes within Great Britain and Ireland and apply the findings to the known worldwide Muggle population, and try to get some idea of just how bad the situation really is:

These estimates, again, are based on the Rowling interviews which have stated that Hogwarts is the only magical training Academy in Great Britain and Ireland, and the calculation above that there are currently just under 300 Hogwarts students (estimate adjusted for common sense). Consequently, apart from those hypothetical Muggle-borns whose parents do not permit them to attend, the wizarding kids whose parents send them overseas to Beaubatons or Durmstrang, or those hypothetical rare cases who, due to some overriding (health?) consideration continued to be educated at home, those 300 or so kids represent all the wizards and witches who were born over a 7-year period, and are, ergo, a representative 7-year slice of the total wizarding population of Great Britain and Ireland.

At the other end of this equation, we have an overall Muggle population estimate of about 65 million.

What we need to remember is that these are the estimates for Great Britain and Ireland. We have a number of clues in canon that the political boundaries between Muggle Europe and wizarding Europe no longer exactly correspond with one another and that in wizarding Europe, whose establishment predates the uprising of 1916, Ireland never split off from the UK.

Taking the 65 million figure as a base, approximately 3,250 wizards would come in at 0.005% of the total population at a rough (very rough) estimate. That is: five thousandths of one percent.

65,000,000=100%
6,500,000=10%
650,000=1%
65,000=0.1%
6,500=0.01%
3,250=0.005%

(Now you see what I mean by having chosen to use numbers that come out even.)

Therefore, if we apply this formula to a current overall estimated world population which, according to the wikipedia online encyclopedia just tipped the 65 billion point in February of 2006, we can project a ballpark estimated worldwide wizarding population of 325,000. Which is probably highly inaccurate. I very much doubt that thinly populated areas produce as high a percentage of magical births as heavily populated ones, and much of the world is not all that heavily populated. It is extraordinarily convenient for our purposes that the worldwide numbers fall out to being almost exactly 100 times that of Great Britain and Ireland, but this really is a coincidence, and largely a result of rounding off.

So, even ignoring the unknown attrition rate, and its attendant miscount; we can only project a worldwide wizarding population of under half a million. Trying to resolve an overcount could reduce this by as much as a third.

It should also be noted that some of this population may consist of as yet unidentified Muggle-borns, and that part of it will be spread very thinly over a large geographic area, making it more difficult to identify, contact and train, rather than collected into organized enclaves within mundane settlements. Indeed, much of sub-Saharan Africa’s magical population appears to operate openly on a tribal level, out among it’s Muggle neighbors, as may well be the case in some other geographic locations with an appreciable number of aboriginal peoples.

It also seems clear that the although the worldwide wizarding population is probably at the highest point that it has ever been, it is dangerously low when compared to the non-wizarding human population. And, that the increase in Muggle population and Muggle longevity over the 19th and 20th centuries may well be crowding the wizards out. More to the point, the wizarding population may be even more dangerously low when compared to that of other presumably highly efficient magical races, such as the Goblins. Unless Goblin birthrates are significantly lower than human birthrates. Of which we have been given no indication whatsoever.

Which renders the pureblood fanatics’ ongoing debate over whether or not Muggle-born magicals should really be given the right to be admitted into the wizarding world into exactly the sort of a piece of monumental stupidity and short-sightedness that it appears to be to the reader.

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The second part of this exercise is to estimate the magical birthrate in comparison to the mundane birthrate, and to try to determine the Muggle-born birthrate within the mundane birthrate.

These calculations are going to be even more abstract, arbitrary and inexact. They are also probably completely hosed since I have begun to suspect that the numbers I was able to find for Ireland are actually only the numbers for Ulster. But I’m going to leave it as is. They will at least give us a rough estimate. And it does not affect the calculations above.

Back to that Hogwarts enrollment: we have an annual intake of some 40 students. Rowling has further stated that the percentage breakdown comes to 25% Muggle-born students, 25% purebloods and the remaining 50% halfbloods. Or 10:10:20.

Given that literal halfbloods may still be comparatively rare, we may assume that most of the “halfbloods” referred to here are the descendants of Muggle-born magicals. According to Rowling’s statements it seems evident that she does not envision any significant differences in birthrate between purebloods and halfbloods. In order to eliminate the maximum confusion from any considerations over pureblood/halfblood as opposed to muggleborn parentage we will concentrate on determining the birthrate among pureblood families and use that as our base estimate for the magical birthrate.

Crude birthrates are generally estimated by the number of births per 1000 population. However, to do so for the whole wizarding population may introduce a slight distortion due to the allegedly longer projected life spans of wizards. Muggle birthrates are based upon a population with a theoretical age range of 0-100 years, which for all practical purposes abruptly diminishes and all but disappears after the age of 85-90. The total wizarding population, with its theoretical age range of 0-120 years (diminishing and disappearing after the age of around 95-105 in practice) would skew the results just a little.

What I propose is to limit these calculations to the general segment of the wizarding population which is of the same approximate age range (0-80) as that of the effective mundane population base. While this may be eliminating a handful of wizards over the age of 80 who may be married to witches still of childbearing age, it is still a better representation of the wizarding world’s effective breeding population, which is what this exercise is all about.

Calculating from an annual birth cohort of 40, the total population (not counting attrition) between the ages of 0 and 80 would come to 3,400. Divided by 4 to determine the numbers of purebloods within this population we reach a total of 850.

Well, that introduces a slight snag. We do not have a base example of 1,000 from which to calculate.

We do however already know that the average number of births among purebloods per year is about 10, since it roughly matches that of Muggle-born magical births. In order to determine the birth rate per 1000 population, we need to extrapolate the number up. So if there are roughly 10 births a year within a population of 850 that comes to 1 birth for each 85 individuals represented within the population. Which, scaling the population up to 1,000 individuals gives us a total 0f 11.764 births, or roughly about a dozen a year.

Is this in fact lower than the birthrate of Muggles? Well, yes, as a matter of fact, it is. But not as much lower as we might have suspected.

Of course that varies by the year.

In 1975, back when the Marauders were in their 4th year (acto Rowling), the crude birthrate for the British Isles was 17 per 1000. That of the UK alone, 12.5.

In 1980, the year of Harry’s birth, the combined crude birthrate for the UK and Ireland was 17.7 births per 1000. That of the UK alone was 13.5.

By 1990, the year before Harry started Hogwarts, this crude birthrate for both had dropped to 14.5 per 1000, but that of the UK alone was 13.9. The Irish birthrate, on the other hand had dropped from 21.9 the decade earlier to 15.1. (As I say, this may turn out to be only the Ulster birthrate.)

As of November (i.e., incomplete data for the year) 2004 the crude birthrate for the UK and Ireland stood at 12.7 per 1000, that of the UK alone, 10.9.

The pureblood birthrate of approximately 12 per 1000 is not really all that much off from that of the UK, although it appears to not reflect the higher birthrates earlier shown in for Ireland, despite the fact that these numbers are bound to include pureblood Irish wizards.

****

As to the magical birthrate within the mundane birthrate, which is to say, the Muggle-born birthrate as a percentage of the mundane birthrate: this requires a whole different set of calculations. And here we are seriously hampered by the uncertainty of whether or not pureblood and halfblood births are recorded in the mundane census, as well as the widely fluctuating actual birth numbers on a year-to-year basis over the 20th century. These have varied as widely as a high of 1,126,800 births recorded in the year 1920 to a low of 657,000 in 1977. Nor have I been able to find a readily available listing of what the actual birth numbers were for my example dates above (1975, 1980 & 1990). It is most unlikely that the Muggle-born births remain a steady 10 per year regardless of the fluctuating trends of the Muggle birthrate. It is far more likely that they have fluctuated just as widely as the total birth numbers have.

It should be noted that it has been at the point that the first children born when the Muggle birth rates were at their highest (the 1920s and the “baby boom” of the 1960s) were of an age to begin showing up at Hogwarts that the pureblood supremacist movements have been depicted as becoming most strident. This, at least, is completely understandable.

Unfortunately, without specific numbers, if we are forced to work from an abstract, using the approximate population numbers above (65,000,000) we just end up with a mathematical “proof” of the hypothesis above; that the Muggle-born birthrate as a percentage of the mundane birthrate, is generally the same percentage as of the magical population within the mundane population, which is a clear distortion, since it does not take account of a possibly undocumented birthrate within the wizarding world. Nor are we necessarily working from the correct numbers from the Muggle end of the equation.

It can, however, give us a broad estimate of the number of magical births to mundane births, but I would hate to have to answer for this estimate’s accuracy. In any case:

Starting from a base of 63,000,000 (2003 figure. Let’s try to make the birthrate stats roughly current to the most recent crude population number), we divide by 1000. Giving us 63,000. At a birth rate of 12.8 per 1000 this would imply some 806,400 births for that year (which I will not claim was actually the case. Maybe it was in the Potterverse). Of this 806,400, approximately 10 can be estimated to have been Muggle-born magical births. Dividing 806,400 by 10 we get a rough estimate that there was approximately one magical birth for every 80,640 mundane births. Or, round that down to 80,500 for convenience.

(If all 40 of the annual wizarding births regardless of blood status are recorded in the official census, this ratio drops to one magical to 20,160 mundane births. But I am not using those figures in this reckoning.)

Either of which seems so statistically insignificant that I’m not going to even try to figure the percentage. Particularly given the built-in inaccuracy.

But, as I say; I’d hate to be held to it for anything beyond an approximation. The following essay on ‘The Rise of the Mudbloods’ is also pretty approximate, but it sheds a bit more light on a few more assumptions that the fandom has been harboring.

And my recent realization of the probability that half to 9/10ths of the wizarding population almost certainly lives out among Muggles anyway (which was largely confirmed in DHs) and that their births are probably recorded right along with those of Muggles makes me just throw up my hands in despair.

This particular essay is not going to get any further modification from this point. The issue has just too many variables for me.

I’m not a mathematician either, you know.

****

For a more professional viewpoint on wizarding life spans, however, I append the following which was posted in 2003, or early 2004, in reply to a discussion of the above on one of my listgroups regarding the hypothetical 200-year lifespan generally used for convenience in calculating estimated population at that time. Although the conclusions were based on an outdated interpretation of the Potterverse, the information is still of interest and some of it may still be applicable. To wit:

"Emerging from lurk mode for the first time, I suppose I should introduce myself. I’m a professional biologist, nearing retirement, a university museum curator working in areas of taxonomy, zoogeography, and pertinent to this post, ecology.

It’s possible to fine this estimate a bit by using normal human age pyramids (see F.F. Darling, 1951, The ecological approach to the social sciences, _American Scientist_, 39: 244-254 for the grungy details; E.P Odum, _Fundamentals of Ecology, 3rd ed, p.179 repeats the graphs.) Assuming the normal convex mortality curve and an age pyramid stretched to accommodate a maximum age of 200 the population essentiality vanishes beyond about 160 yr. More importantly, the age classes will each constitute about 1/2 the same class in the normal pyramid, with a maximum age of 100 and an effective vanishing point of 85-90. In this "stretched" pyramid, the age classes below age 20 will make up about 10 percent of the total population.

We have as given that the age class between 11 and 17 is approximately 600, whether Hogwarts actually accommodates them all, or whether JKR misspoke and it is actually a smaller school, educating the elite of that 600, as implied by class sizes shown in the book.

Each age class below age 20 will then contain 1/2 of 1% of the total population, and the 1000 secondary school students make up 7 x 0.5 or 3.5% of the total wizarding population, yielding a total population (1000/3.5 x 100) of about 17,143.

Varying our assumptions, in the unlikely situation that we have an increasing population, we would have a current total population of 15-16,000. Making the more likely assumption of a decreasing population, we would get a current population of as much as 20,000 but with a birth rate disastrously less than the death rate.

What we have seen of family structure suggests that we might have a situation with corporate families much like Stuart England, with marriages determined almost exclusively by the heads of the extended families. In this case, of course, the existence of a very different marriage system in the Muggle society in which the wizarding population is embedded is going to produce lots of lovely tensions. (Lovely from the viewpoint of authors, that is, it’d be Hell for the participants.)"

Will Pratt