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Ponyville Statistical Trivia: Population by dziadek1990 Ponyville Statistical Trivia: Population by dziadek1990

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EqD Article:…
Digibrony's Q&A:…
MLP Conspiracies:…
Thoroughly analyzing "A friend in deed":…
Everything wrong with "Dragonshy":……


EDIT 7th April, 2012: Corrected a large error in mug's size I found.

Time taken: 10 - 16 hours.

The small apparent errors in multiplication are not mistakes; they include multiplied fractions that were not shown earlier due to rounding.

Assuming a population of 3,650, if you walked around Ponyville and managed to meet 100 ponies every day, then after a week you would have a 68.4% chance of meeting at least one of the Mane 6.
You would have to meet at least 1,400 ponies if you wanted for that probability to be bigger than 90%.

Want to give suggestions for the next analysis? Here's the place:…

S1 - S3 screentime analysis:
Pony size and mass estimation:
Life, death, sex, pregnancy and birth:
"20% cooler, 10 seconds flat" meme's thermodynamics calculaton:

Screentime analysis paper fallout:
Binary Mane 6 Picture:
Add a Comment:
TurquoiseThought Featured By Owner Dec 22, 2017  Hobbyist
It's amazing what you can do with math and pixel measurements! Thank you for doing this! This information was usefull for me.

To answer your questions, I say that this presentation was quite glear to me.  Also those little jokes (such as "thanks Twi") were freshing and helped me to keep the focus on the math. (I'm not a math-person myself, I only have a small capability to understand it in some low level.) You asked was there any flaws/good things in you presentation's texts and as an amateur writer (I have been writing actively for 3-4 years now) I can say this:

 There was enough text to understand and it was short enough so that I didn't get bored. It was interesting and (as I said before) clear and understandable. The only tip that I could give to you, is to avoid too long senceteces. Short sentences make it easier to read. This wasn't really a proplem but I'm still saying it so you don't fall on that trap so to speak. I am very aware that in mathematical explanation it is really hard.  (And as you can see, I tend to write long sencetensies myself.) So more like, you would try to make sure that there isn't too many long sentences after another.  Overall, it was very good.
dziadek1990 Featured By Owner Dec 24, 2017  Hobbyist Writer
Thanks. Glad that I could help.
T1mbuk0n3 Featured By Owner Jun 11, 2017
What about all those duplicates? They might've been changelings.
CaptainRiceQuakeFox Featured By Owner Apr 23, 2017  Hobbyist Writer
"Assuming a population of 3,650, if you walked around Ponyville and managed to meet 100 ponies every day, then after a week you would have a 68.4% chance of meeting at least one of the Mane 6."

Actually it would be 100%, because Pinkie Pie would greet you ASAP. ;P

This was a good read though! Probably slightly outdated by statistical info from newer seasons, but still!
bitter-pen Featured By Owner Apr 18, 2017
Very helpful, thank you. :)
dziadek1990 Featured By Owner Apr 21, 2017  Hobbyist Writer
No problemo!
sonicx25976 Featured By Owner Jan 23, 2015
you used so much time to get an estimate of the population of a town in a show targeted towards little girls, using advanced methods of math?! are you fucking kidding me? shouldn't you be curing cancer or something?!
dziadek1990 Featured By Owner Jan 24, 2015  Hobbyist Writer
:) Mathematicians don't cure cancer. Especially mathematicians who have average/below-average grade. I'd just kill someone if you gave me a scalpel.

And that math was not advanced. It was just easy, but time consuming.

If I tried to do advanced math, I would give up soon after I began.
Nakamura-Michi Featured By Owner Jan 13, 2015
My head hurts! But I know more now!
dziadek1990 Featured By Owner Edited Jan 15, 2015  Hobbyist Writer
I'm gonna teach you... and you're gonna LOVE IT! :iconcrazytwiplz:
funestis Featured By Owner Jan 4, 2015
LittleshyFiM brought me here. Exelent job
dziadek1990 Featured By Owner Jan 5, 2015  Hobbyist Writer
Dragonjek Featured By Owner Oct 22, 2014  Hobbyist Writer
I don't think your probability-of-meeting-one-of-the-Mane-Six percentage is right.  Applejack and Fluttershy live outside of town and only come in if they've something to do in Ponyville proper, while Pinkie Pie, Twilight, and Rarity all live in the more densely-populated and heavily-traveled sections of town, and are relatively-to-extremely social.  Considering that they live in the three most iconic buildings in town (which people are generally interested in at least looking at), it seems like it would be a good deal higher than that.

And of course, most, if not all, of them would show up at the Welcome To Ponyville Pinkie Pie Party you'd get when you arrive, so...
Brother-Malachai Featured By Owner Dec 8, 2015
Yeah, she kinda does that for everypony.  :-0
Lepperb0y Featured By Owner Oct 12, 2014
These stats are amazing, you sure put some great effort into gathering them. Good job! =D
dziadek1990 Featured By Owner Oct 12, 2014  Hobbyist Writer
:) Thanks.
timgil Featured By Owner Apr 9, 2014
1.8 Gallons for 1 mug of cider!? I think you're greatly overestimating the volume of those mugs. It looks like it is meant to be equivalent to about a pint, your estimate is over 14 times that!
The one mug per pony is certainly not a hard and fast rule, so for all we know the average could be 3 mugs of cider per pony or even more.
Measuring by pixels doesn't work well when objects are different distances from the camera. The mug is at least 1 1/2 feet closer to the camera than Applebloom's head, and the barrels are several feet behind Mac in the other shot.
The other method seemed to be very slightly more sound, but given the incredible variance between your estimated population sizes, it seems ultimately to produce no reliable data either.

I appreciate what you tried to do here, but in the end I'm afraid the result is so imprecise and varying that no usable data can pulled from this study.
dziadek1990 Featured By Owner Apr 10, 2014  Hobbyist Writer
Note: ponies' heads are WAY bigger than humans'. Even though the mug seems average-sized if compared to human's head, it isn't.

And about the shrinkage-of-objects-due-to-distance, yeah, I know.

It can be anyways slightly corrected by using 1.1 or 0.9 multipliers on various values calculated in sub-steps, or by less half-assed distance shrinkage calculations.

Also I could've used calculus for estimating volumes better, and created better models which take customer imigration into account (and various other stuff people suggested to me), but after some point the slight increase in accuracy is no longer worth the time spent improving the analysis... plus it stops being fun, and fun was the sole reason why I did the analysis.

Btw.: If you plan to use the perspective in whatever future analyses you will be doing, know that the animators screwed up the size shrinkage for bigger distances - I checked the math. Short distance shrinkage is probably fine though.
LizzysMind Featured By Owner Mar 25, 2014  Hobbyist Digital Artist
I love this
favmir Featured By Owner Mar 11, 2014  Hobbyist
Came here from one of those "Everything Wrong With~ " videos.
Loving this. haha ;)
dziadek1990 Featured By Owner Mar 13, 2014  Hobbyist Writer
Thanks. :)
dziadek1990 Featured By Owner Mar 13, 2014  Hobbyist Writer
Be aware though: I wanted to create this ASAP before laziness stopped me, so it is half-assed a lot.

The info here isn't TOO inaccurate, but I know that if I put more effort/research into it, it would be better.

...and neater. Some of the methods I used here really show how lazy I was and the reasult looks ugly to me.
alexgieg Featured By Owner Mar 4, 2014  Hobbyist Writer
Very interesting! Thanks for taking the time to do all this!

There's one problem with your analysis in regards to ponies life expectancy.

Winter Wrap Up (S1E11) establishes that Ponyville has existed for centuries, hence 200 years minimum, but probably 300 or more, and Family Appreciation Day (S2E12) plus another episode I don't remember now both establish that Granny Smith was one of the village's founders. Also, other still living old members of the Apple clan that appear in the show are referred to as childhood friends of Granny Smith, hence in her same age bracket, showing she isn't an exceptional case.

Those details put the life expectancy of ponies (earth ponies at least, since we don't have information for unicorns and pegasi) in the range of 200 to 350 years, with a bias towards the later number. And given that Ponyville has a strong earth pony majority, having been founded by them an all, we can well assume that to be the average life expectancy for the whole village.

I'm not well versed in the math techniques you used, so I don't think I'd be able to redo them for your statistics, but it'd be amazingly interesting to see at which conclusions you'd arrive by taking this longer life expectancy into account instead of basing them on the human average!
dziadek1990 Featured By Owner Mar 13, 2014  Hobbyist Writer
I wanted to just MAKE the analysis ASAP so I that laziness/procrastination would not have nough time to stop me, hence I didn't do enough research. ;)


Twice longer life duration would make the population:
- Approximately 2 times larger, if ponies lived longer during their "looks old" stage of life,
- Approximately 2 times smaller, if they lived longer during their "looks young" stage of life,

Reason: I made the assumption that all ponies present were relatively young and, based on the age distribution, I calculated how many ponies were NOT present, so if young-looking ponies constitute as a large fraction of population, then the number older off-screen ponies decreases.

NOTE: I now know more about statistics than when I wrote this analysis, and even THEN I was aware that I half-assed it a LOT. But still, the info given here IS better than merely trying to guess the town's population. :)
timgil Featured By Owner Apr 9, 2014
I'm not so sure. 
The population of Ponyville is roughly = 326 ponies, with the maximum data set at 1260 min at 37
Or is between 3100 and 4300 ponies
Honestly I think a reasonable guess might be more reliable than these two wildly different numbers, especially when both methods had such glaring flaws as these.
dziadek1990 Featured By Owner Apr 10, 2014  Hobbyist Writer
Notice: in the first method of estimation I specifically said that the numbers I came up with were lower bounds of the values. And I meant the VERY lowest, as in "this number or infinitely bigger". No info about upper bounds.
dziadek1990 Featured By Owner Apr 10, 2014  Hobbyist Writer
Plus, since the show's creators don't specifically plan the population size for the town, and just want the town to look not empty (or empty when the episode's scenario demands that), then using different estimation methods WILL almost always give VERY different results.

They would be only similiar if the creators wanted to be realistic, or if we were analyzing an actual town.

Some people simply counted the number of houses visible in the theme song (plus estimated the number of houses off-screen), multiplied the number by 4 or a bit less/more (ie. assumed number of ponies living in each house), and ended up with various values below 1000.
dziadek1990 Featured By Owner Apr 10, 2014  Hobbyist Writer
The first formula for estimating population depended a lot on the value of the number C, which could be any value between those given in the table and 0 (due to many same-looking ponies and our uncertainity whether the same-looking pony is the same pony we marked earlier).

A non-zero number divided by ~0 can be arbitrarily high, so the first method of estimation could imply values of ~300 (or ~4 times higher, if I included the age distribution), or values many orders of magnitude higher.

That is why I said in the analysis that the first method wasn't good in this problem.
LevelHeadedBrony Featured By Owner Dec 26, 2013  Hobbyist Traditional Artist
The cider way is actually a very clever method of estimating the population. Game Theory on Youtube does similar stuff sometimes.
Mister46 Featured By Owner Nov 23, 2013
Why assume the barrels are cylinders? Adding the bowed-out sides could potentially add a bunch more volume. Maybe not, but I think it's worth just checking to be sure, since it would be a pretty simple integral to get the volume (could make the sides of the barrels sin curves probably). I'm assuming you know some calculus if you're enough of a math nerd to make a math paper about mlp.

Great work anyway! I'd always felt that ponyville would have between a few hundred and a few thousand ponies in it.
dziadek1990 Featured By Owner Nov 23, 2013  Hobbyist Writer
And thanks. :)
dziadek1990 Featured By Owner Nov 23, 2013  Hobbyist Writer
Because I round the results in the end, which would erase that additional gained accuracy. And you can see that the range of the estimation is approximately 1000 ponies wide. I just wanted to give the general idea of the scale of Ponyville.
baxil Featured By Owner Oct 23, 2013
Cider mugs hold almost *2 gallons* of alcohol?!  For being roughly human-sized, those ponies can sure put away their drinks …

dziadek1990 Featured By Owner Oct 23, 2013  Hobbyist Writer
I wonder how ANYTHING fits in their bodies. They have clearly no problem stomaching one or more of those mugs in one go. Bladders alone would take a considerable volume of their abdominal cavity.

How much place is there left for stomach, liver, guts, lungs and other stuff? Their torsos are fairly small.
BugflyTk Featured By Owner Oct 1, 2013  Hobbyist General Artist
You sir, are a math genius. I don't think I could ever contribute so much time to a project like this.
dziadek1990 Featured By Owner Oct 1, 2013  Hobbyist Writer
:) When you compare the time I spent on this to how much I have to study on the uni, you'd find this project a lot less impressive.

I am overall a lazy person. Explosions of motivation like this, I have once or twice a year, max - hence my grades are below average.
yoshiegg64 Featured By Owner Aug 24, 2013
Congratulations this was mentioned in "(Parody) Everything Wrong With Dragonshy in 4 Minutes or Less"…

dziadek1990 Featured By Owner Aug 25, 2013  Hobbyist Writer
Wilson8787 Featured By Owner Apr 23, 2013
This is just...incredible!:iconbravoplz:
Caerdwyn Featured By Owner Apr 23, 2013
Consider the Ponyville hospital maternity ward (an absolute minimum of 7 beds, all of which were occupied, which we saw at 00:00:22 of Baby Cakes... but various camera angles imply about 10). What population can we infer?


1. The Ponyville hospital is a regional hospital. It serves an area that includes not only Ponyville, but the nearby rural areas (Everfree Forest outskirts, Sweet Apple Acres, etc.)
2. Ponies live 25,000 days or so, and have a negligible infant mortality rate and accidental death rate. Utopia etc. unless you're Applejack, in which case your parents are semi-officially dead.
3. There are at most an average of 1.1 births per pony. Otherwise we'd be neck-deep in ponies after 1000+ famine-free years. Utopia, etc. Also, consider what few families we have actually seen. Cakes=2 children, Apples=3 children, Pies=3 children, Rarity's family=2 children, Twilight's family=2 children. Scootaloo is a free-range child.
4. The average occupancy of the maternity ward is no more than 75% (running it at higher would be very irresponsible) That would give us 10 beds in the maternity ward, since we saw 7 foals.
5. The average stay of a newborn is 10 days.

Okay, here we go. Statisticians, shoot me down.

1. A foal spends 10/25000 = 1/2500 = .0004 of his/her/its life in the maternity ward.
2. Therefore 1/2500 of the population is in the maternity ward.
3. Therefore, if there are 7 foals, there are 7 * 2500 = 17,500 ponies in the region the Ponyville hospital serves.

The only thing I can think of that would throw this off and reduce Ponyville population is one (or more) of:

1. Death rate is higher. Doesn't anywhere close to fit the feel of the show though.
2. Young couples flock to Ponyville, creating a local "baby boom" and a disproportionate work load at the maternity ward.
3. Hospitals are VERY rare, and that hospital serves a much larger area. Ain't buying that, though. Doesn't fit anything else we've seen about the show.
4. Long stays in the maternity ward.

And we expand the population if:

1. There are a lot of unmarried ponies.
2. There are a lot of non-child-producing couples. No I do not want to hear anyone's opinion on that, either way. Shut up.
3. Stable population overall (birth rate = death rate)
4. Home births are anything more than vanishingly rare.

So. I'm going to claim 20,000 ponies in the Ponyville region.

The main question is how much of that 20,000 population lives in Ponyville itself. But that is the subject of another unnecessarily-long comment.
timgil Featured By Owner Apr 10, 2014
It is impossible to accurately extrapolate such data from a single data point, namely how many newborns were in the maternity ward on that particular day. There is no way to know if that number was average, unusually high, or unusually low. Another thing to take into account is the possibility of a mating season. It could very well be that most foals are born around one short time of year, while the rest of the year the maternity ward is usually empty.
Despite these objections, your methodology does seem more sound than those used in the article however.
Scary-Scott Featured By Owner Apr 23, 2013
Okay, that is tiny at least to me.
Where I live the population is 15,200 and I consider that to be a small town.

Ponyville is what I would call a blink and it's gone town, as in if you blink while driving by on the freeway your gonna miss it.
Furboz Featured By Owner Apr 23, 2013  Professional Digital Artist
Im sorry but I believe that you are forgeting a very important fact about Ponyville...

I'll try to get this short

Ponyville its just a town and outskirts... a small town. If you count the houses at the beginning of the show there are around 60 to 70 building in ponyville (not all are for living ofcourse) So if you divide the population (the lowest of your calculation) 3100/70 equals 44.something ponies per house... And that would be ridiculous...

What IF... Not all the ponies that went for a mug of apple cider are from ponyville... What if they came from all over equestria to get a taste of the spectacular cider... That would make sense...

So I'll stay with the 350 to 400 ponies population, Thats more "logical"
RandomnessKing Featured By Owner Mar 9, 2013
now we need a way to estimate for canterlot
Vengir2 Featured By Owner Jan 10, 2013
No no, brawo dziadziuniu, nie sądziłem dotąd, że to w ogóle można oszacować.
dziadek1990 Featured By Owner Jan 10, 2013  Hobbyist Writer

:P W porównaniu z czym się męczę na studiach, to jest absurdalnie proste - jedynie zbieranie danych jest czasochłonne.

No i pozostaje fakt że przy tej analizie stosowałem po części improwizowane metody. Gdyby mnie oceniali profesorowie, to by pewnie za to trójkę mi dali, bo można do takich badań jeszcze precyzyjniej podejść.
DeathAlchemist94 Featured By Owner Oct 2, 2012  Hobbyist General Artist
dziadek1990 Featured By Owner Oct 2, 2012  Hobbyist Writer
I think you meant:
:icontwilightinsaneplz: Math! Muhahahahaha! Math! Math!! MAAATTTHHH!!!
DeathAlchemist94 Featured By Owner Oct 2, 2012  Hobbyist General Artist
nah. I stand by what I said.
dziadek1990 Featured By Owner Oct 3, 2012  Hobbyist Writer
Oh, come on, join the Math Side... we have cookies!
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