Wizarding numbers: 24 000

[Mikael Raaterova]

No: HPFGUIDX 83188

To summarize my findings below:

- About 30 percent of Hogwarts students are muggle-borns
- No more than half of the 11-17 years old wizard-borns in the British 
isles attend Hogwarts
- The wizarding population is about 24 000 (bounded at 20-30 000)


Robert Shaw wrote:

>True, but to extrapolate the wizarding population from Hogwarts
>without assuming (in the absence of good evidence) that structure to
>be invariant, you do need to known what the population structure is.

Not completely. We need to know if the yearlings born between, say, 1975 
and 1985 deviate from the mean yearling fraction of the total population, 
and if so, in what direction. Given that Voldemort's reign of terror has 
effects comparable to WWII, I'd expect Hogwarts to be relatively 
underpopulated in Harry's first and second year (because comparatively few 
children would have been born during the bad years), but becoming 
progressively crowded from Harry's third year onwards (baby-boom starting 
nine months after Voldemort's fall). It's not unreasonable to assume that 
the under-represented years and the over-represented years average out to 
something pretty close to the yearling mean fraction. Even if it would 
deviate from the mean, i don't think it would matter much, because that 
error would pale in significance compared to the problems of establishing 
Hogwarts attendance, which might conceivably vary from 100% (every 
wizarding child attends Hogwarts) to 5 % (only a chosen few needs a degree 
in witchcraft and wizardry).

Interestingly enough, the fraction of muggle-borns would put a cap on 
maximum theoretical attendance. We know that 25 % of the wizarding 
population is muggle-born. But how big a fraction of Hogwarts students is 
muggle-born? Erring on the side of caution, I'd say it's maximally 31%, 
probably less. How can I say that? We can calculate this if we know the age 
distribution of muggle-born wizards, which in turn would have to be 
inferred from historical data on live births and assumptions of die-off in 
the wizarding world. UK census web site has a data on live births going 
back 1838, and I used a fairly simple die-off function (I'm not good enough 
at maths or demographics to manage anything more complicated; I'm a 
*sociologist* for crying out loud): 20% of the wizards born between 0 and 
100 years ago are dead (die-off for each year increases linearly by 0,2 % 
per year of age up to 100), and almost 80% of wizards born between 101 and 
164 years ago are dead (die-off increases linearly from 20%+1,26% per year 
of age from 101 up to 164). This probably exaggerates the number of deaths 
in wizarding middle-age, and thus the ratio of 11-17 year-olds (mean 
fraction of total pop within the 11-17 age group compared to mean fraction 
of pop for every year). This model gives a life expectancy of 124 years and 
a mean age of 67. Incidentally, this means that 11-17 year-olds constitute 
5,3% of the muggle-borns, basically equal to the guesstimate 5 % touted by 
Ffred.

I was a bit surprised that the model put the fraction of muggle-borns for 
Hogwarts students at only 31%, since I expected it to be higher (continued 
population increase and all), but i didn't reckon with the effect of the 
enormous numbers of births from the 1870s to WWI, or the declining birth 
rates for the last 30 years.

So, if about 30 % of Hogwarts students are muggle-borns (e.g. 300 people) 
and they constitute 5,3% of the muggle-born wizard population, then the 
muggle-borns should number slightly less than 6 000. Given that 
muggle-borns constitute 25 % of the wizarding population (purportedly a JKR 
fact), wizard-borns would number about 18 000. If wizard-borns have about 
the same age structure as muggle-borns (a constant birth rate for 
wizard-borns in the die-off model makes 11-17 year-olds 5,8% of the 
wizard-born pop), and about half are half-bloods, the 11-17 year-old 
pure-bloods should be *at least* 7,5 % of the wizard-born population, or 1 
350 wizard-borns aged 11-17, of which roughly half thus attends Hogwarts.

Feel free to poke holes in my reasoning. I'm not entirely convinced that my 
attempt holds up to scrutiny, but i don't think i made any glaring errors.


>As an aside, much of that increase is actually due to immigration.
>How do wizards deal with that?
>
>The Hogwarts' quill records the names of wizards born within range,
>but Indian muggle-borns whose parents have just immigrated will not
>be listed.

And will thus not get a magical education nor become wizards. Hence they 
won't affect the wizarding population.


>English muggle-borns whose families emigrate to the US when they're
>five will cause similar problems

If the US wizards use a similar system they won't get an education there 
either.


>Does the Ministry hunt down immigrant muggle-borns, and notify
>other countries of emigrants, or do the muggle-borns in such families
>slip through the cracks?

Why would the MoM care about non-listed magical muggle-born children? If 
the Hogwarts quill don't register them, they don't exist.


>If the ministry lost track of many muggle borns during the
>mass muggle migrations of the last centuries this could have
>a significant impact on wizarding demographics.

Possibly. Migration don't affect the muggle population in any dramatic way, 
and given the rarity of magical births to muggles, the possible changes, in 
absolute numbers, to the wizarding population of a few years of abnormal 
fluctuations due to migration are entirely negligible.


I claimed:
> > Changes in muggle numbers have to be *huge* to affect the number of
> > muggle-born wizards.

Robert Shaw replied
>The change may be huge, but since the muggle population is also
>huge this cancels out.
>
>A 5% change in muggle numbers will produce a 5% change in
>muggle-born numbers, to a first approximation.

To take Robert's last point first, a 5% change in muggle numbers will 
produce a comparably *smaller* change in the numbers of muggle-borns, given 
the longevity of wizards, muggle-born or otherwise.

As to the first point, I need to clarify myself. I *should have* said 
"Changes in muggle numbers have to be really, really huge to affect the 
number of *wizards*" (i.e. not only muggle-born wizards. This makes a 
difference, see below.


> >If we ignore post-OWL dropouts, then 36
> > muggle-borns enter Hogwarts per year (in present years), if 25 % of
> > students are muggle-borns.
>
>So, e.g, a 5% increase in the muggle population means 2 extra
>muggle borns, and the percentage increases to 26%. A 15%
>increase would push the percentage to 28% and so on
>(though its not actually proportional)

But 14 (2 per year) extra muggle-borns mean next to nothing in terms of the 
entire wizarding population, and not much even to the Hogwarts population; 
it's an increase by 1,4% in 7 years. Also, if we take into account that a 
change in muggle numbers is at least a third smaller for the muggle-borns, 
it only adds one muggle-born per year. Conversely, the same logic goes for 
reductions in muggle birth rates.


Robert, replying to me;
> > If you don't accept a fairly stable wizarding population, you'll have
> > to posit that they have had periods of low mortality and high
> > fertility followed either by cataclysmic extermination events or
> > equal periods of population decline. I think you'll have trouble
> > finding causes for such changes.
>
>The problem is that we know the muggle population has had
>major fluctations, which must have some impact on the
>wizarding population.

Yes, but every change in muggle numbers goes through two reduction-filters. 
1) Muggle-borns live vastly longer than muggles, so effect of changes are 
reduced. 2) Effects are reduced even more due to the fact that muggle-borns 
constitute only a minority of wizards. A 10-year freak birth dearth among 
muggles may give dramatic effects in muggle society, but is only a mild 
echo in the wizarding world.


>I'll accept fairly stable, but not static, and you need static
>to extrapolate from Hogwarts.

I'm not after exact numbers, so "fairly stable" is enough for me.


>Going by the student population of Hogwarts alone, we can deduce
>the wizarding population with an error of perhaps plus or minus 50%
>(not good enough to base any conclusions on)

If we look at muggle birth numbers (actually, UK birth numbers) over the 
last hundred years, the *maximum* fluctuation for *any* consecutive 
seven-year period deviates from the mean by only 20 % (this including 
effects of migration, to boot). Assuming that wizard birth numbers vary as 
much, my estimate of wizarding numbers of about 24 000 is bounded at 20 or 
30 000 (assuming my die-off model is reasonably accurate).


Whew. If you managed to wade through this delusional demographic debate to 
the bitter end, you have my deepest respect.

/ Mikael