### Author Topic: Drow and math  (Read 2879 times)

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#### Pariah

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##### Drow and math
« on: May 20, 2014, 04:22:57 PM »
Alright, I'm trying to figure out if the Drow as written could survive.  Because huge math equations make me cry a little I decided that the best way to do this is brute force with perl.  So, after 6 hours writing a script I finally have something that doesn't suck, now it's onto finding actual numbers to base the estimates off of.

Where I'm at now:

Basing the Drow directly off of the Elf entry in the 3.5 SRD I have them living to age 300 (where they suffer a 100% mortality rate because I can't be bothered to make them older, they can't breed at that point anyway so it's moot.)  The SRD has Human middle age at 35 and Elven middle age at 175, a couple of fermi estimates later I get Human breeding age of 14.7 and a Elf one of 73.5.

Because Drow are Evil and kill each other like it's going out of style only half of all drow born will make it to the age of 74.  Because at this point I'm just doing raw estimates I'm going to give them a flat mortality rate of 0.932312147% a year.

Fertility wise I'm putting them at a birth rate that in humans would produce 1.9 children/family (6.33...%/yr).

What I found in this Extremely guessimate based simulation is that a mortality rate of 0.932312147% and a fertility rate of 6.3% gives them a stable population.

Now is where you all come in, I want any piece of information regarding Drow fertility and survival rates people can think of.  I've never read the Drizzt books, which I'm sure has something somewhere in them regarding how likely it is for Drow to reach adulthood, and when adulthood is for that matter.  Currently the only hard information I have comes from the Drow of the Underdark, pg 24.

Quote
The drow are notably more fertile than are their surface-dwelling cousins.  They become pregnant more easily and have a slightly shorter gestation period.
This information is less than helpful seeing as I haven't found any information regarding the rate of pregnancy in surface elves, nor their gestation period.
Quote
Perhaps spurred on by these hostile circumstances, drow children develop much faster than other elves -- almost as swiftly as humans, in fact -- often beginning schooling as early as age eight or ten.
This implies that drow reach adulthood sooner than elves, but it doesn't outright state it.
Quote
Once they have reached adolescence (at about age 20, by wich time over a thrid of them have been murdered or sacrificed.)
This is actually useful, kinda.  Adolescence implies the beginning of puberty.  In humans (F) puberty begins at 10-11 while (M) is 11-12 ending at (F) 15-17 // (M) 16-17.  For the sake of argument I'll just multiply all these numbers by 2 to get a guess for the Drow of 32 for sexual maturity.  Do they start having kids at this point is another question, though that one is extremely cultural and I doubt there's any information on it in the splatbooks.

On that note, I NEED INFORMATION!!!!!  Please
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

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##### Re: Drow and math
« Reply #1 on: May 20, 2014, 07:24:11 PM »

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#### Pariah

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##### Re: Drow and math
« Reply #2 on: May 22, 2014, 08:28:10 PM »
And that looks like the best I'm getting.  I can find no real "official" information regarding the Drow, but most of that seems to be pulled from the DotUD book I quoted earlier, so now I have for information:

Children _at least_ once every hundred years, which sounds helpful until you realize the same could be said about humans.  On the other end you could say that Drow can have children at least once every other year and it'd be just as useless.  That's like trying to determine a human reproductive rate off of "Humans are capable of producing at least one and up to eight children every nine months.  While it is not a common practice, they've also been known to eat their young."

On their lifespan, "Drow live for several hundred years."  At this point I'm starting to hate the English language, which defines several as a number greater than two but less than many.  How much is 'many' you ask.  Why good sir, it is a large number of something...  FRACK!  Because Mrs Do'Urden lived to be 600 I'm just going to call that the new cap.

And now my own personal favorite: "Drow remain viable until the last few years."   Viable of doing what?  Left to the reader's imagination apparently, because it just goes on to say that if you're no longer viable you're gonna get kill.  I'm going to interpret this as negligible senescence, mainly because it gives the Drow the ability to keep producing more Drow until the point when they finally shuffle out of the simulation.

Stupid fantasy writers, stupid lack of scale.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #3 on: May 23, 2014, 12:53:07 AM »
I decided to take a different tact.  I'm going to start with their surface dwelling kin.  AND I'm going to use numbers for a nominally first world country, the USA.

USA National Vital Statistics Report (May 8 2013)
Elves
Death Rate under 40: 0.01146% / year
Corresponding to ages 5-10 in Americans
Death Rate over 40: .11% / year
Corresponding to ages 30-35 in Americans
It also corresponds to an Elven half-life of around 629.75 years.  Because I'm lazy and don't want to go through the effort of changing code too much, I'm just going to continue saying that everyone dies at the age of 600, just like their Drowish cousins.

Because the surface elves are a peace loving peoples, and have access to modern healing magic, I feel like these numbers shouldn't be that far off, as far as that goes.

All the numbers correlate to a starting population of 1000 elves, over 1000 years.

Birth Rate: 0.5% chance / year
1751 1673
1619 1603
1666 1678
1420 1683
1969 1551

0.0662% annual growth rate

Birth Rate: 1%
24325 22248
22296 22202
21896 21284
19484 21538
22549 23780

2.1181% annual growth rate

So assuming the yearly fatality rates are accurate, Elven birth rates are most likely closer .5% chance a year, seeing as a 2.11 growth rate is about the same as Sudan and a couple other high growth rate 3rd world nations.  It also jives with the description of the Elven race as a kin to pandas, namely not willing to screw to save their species.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #4 on: May 23, 2014, 02:15:33 AM »
I think I finally figured it out.  Violent crime rates, assuming every violent crime corresponds to a Drow dying.

Detroit, Michigan - 2,122.9 per 100,000 (#1 in the nation)
Buffalo, New York - 1,288.7 per 100,000 (#10 in the nation)
Minneapolis, Minnesota - 992.2 per 100,000 (#20 in the nation)
Wichita, Kansas - 742.5 per 100,000 (#30 in the nation)
Phoenix, Arizona  - 636.7 per 100,000 (#40 in the nation)

Convert all of them to a death rate we get 2.1229% / year under the age of 20, which gives us 65% surviving to the age of 20.  The next 20 years you face a 1.2887% chance of dying a year, so on and so forth.  A falling death rate as you get older and more able to play the "I'm a murderous Drow" game.  With every age grouping being twice as long as the one before it the Drow should only need to have a kid once every 33 years for as long as they're still alive.  Testing is needed, but will be done tomorrow.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #5 on: May 23, 2014, 04:12:30 AM »
Actually I couldn't sleep.  Current vital statistics:

\$ChildDeath =  .978771; #You chance, each year, of living to see your next birthday.
\$TeenDeath =   .987113;
\$MiddleAgeDeath = .992575;
\$SenescenceDeath = .993633; #half-life of ~108.5 years.
\$SexRatio =    .5; #chance of being female.
\$BirthRate =   .036; #your chance, each year of having a brat.
\$StartingPopulation = 1000;
\$EndifUnder = 1;
\$EndifOver = 32000;

and running it 10 times for either 10,000 years, or until the population reaches one of the set points gives us this:

Year: 29167
Total Population: 32039
Growth Rate: 0.106418212363287%
Year: 26391
Total Population: 32003
Growth Rate: 0.117475654579213%
Year: 31760
Total Population: 32006
Growth Rate: 0.0976259445843829%
Year: 40867
Total Population: 32039
Growth Rate: 0.0759512565150366%
Year: 30601
Total Population: 32008
Growth Rate: 0.101330021894709%
Year: 27090
Total Population: 32014
Growth Rate: 0.114485049833887%
Year: 29421
Total Population: 32001
Growth Rate: 0.105370313721491%
Year: 36650
Total Population: 32002
Growth Rate: 0.0845893587994543%
Year: 34917
Total Population: 32013
Growth Rate: 0.0888191998167082%
Year: 29355
Total Population: 32014
Growth Rate: 0.1056515074093%

So yeah, assuming your chances of dying each year as a Drow are about the same as being mugged in Detroit, Buffalo, Minneapolis, Wichita, and Phoenix and you have a kid once every 28 years on average, you can have a sustainable population.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Gossamer

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##### Re: Drow and math
« Reply #6 on: May 23, 2014, 05:35:33 AM »
I didn't think I could add much to this because it was a while since I read the books. But you can't cap the life-span at 600. At least not the natural one.

http://forgottenrealms.wikia.com/wiki/Yvonnel_Baenre

Quote
Matron Baenre had lost much of the beauty she possessed while young to a combination of factors, including several uses of zin-carla. At the end of her life she looked haggard, with a patchwork of wrinkles across her face. Possessing an unusual vibrancy she was capable of pregnancy till her late 1900s.

She lived to be 2043yrs old, and she only died because she was killed.

http://forgottenrealms.wikia.com/wiki/Drow

Quote
Drow have lifespans far beyond that of humans and comparable with the rest of the elves, although usually somewhat longer. This is, of course, presuming the drow doesn't meet a premature and violent end, as many often do, but those that survive the trials of their society and the horrors of the Underdark can live for centuries,[3] sometimes as long as 1000 years or more.
« Last Edit: May 23, 2014, 12:11:47 PM by Gossamer »
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#### Pariah

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##### Re: Drow and math
« Reply #7 on: May 23, 2014, 11:39:58 AM »
Grrrr.....   I could add another 400 years onto the end of the end of the code, but the only thing that really matters for the sake of the survival of the Drow as a species in this case is actually when they are no longer able to breed.  Even assuming they can breed until the age of 3,000 I'm still only losing 2.3900306% of the populace by cutting it at 600.

Continuing it until the age of 1000 gives us a survival rate of 0.1856975% and IF I continued the simulation out to the age of 2000 about 0.0003125% of the Drow populace would survive to be shuffled of the script do to my laziness.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #8 on: May 23, 2014, 11:43:37 AM »
And after writing all that and then clicking the link of one child of Mrs Baenre, I'm going to have to do just that.

Quote
Berg'inyon Baenre (alternately spelt Bergynion), the youngest son to Yvonnel ... He is Drizzt Do'Urden's rival in the academy

It's not kind enough to give us a death date, but Drizzt was born in 1297 DR, while Yvonnel was born in -685 DR.  Assuming her son is within 10 years of Drizzt age wise, that means she was fertile up until the end...  1400 more years of Drowdom, here I come.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #9 on: May 23, 2014, 11:04:02 PM »
Having added the next 1400 years to the simulation we get the following numbers.  I'm currently running 3.5% after doing 3.6, and I really feel like there should be an equation for these kinds of things.  Most of the stuff I found for figuring out the demographics of a fantasy species was basically "Well, you take the idealized demographics I made up on the spot for Middle Ages type populations (or possibly based off of the Doomsday Book) and then just directly correlate them to your fantasy race, adjusting for stuff."  At this point I'm positive I'm putting too much effort into this, but I no longer care.  I /WILL/ figure out how often the Drow need to have babies.  Then I'll work on kobolds.  Or goblins.  Or some other race that lives less than 100 years.

Quote from: 03.5% chance/year of being a mother
Year: 59260
Total Population: 32004
Aged Out: 54
Growth Rate: 0.0523185960175498
Year: 50555
Total Population: 32020
Aged Out: 28
Growth Rate: 0.0613589160320443
Year: 40523
Total Population: 32007
Aged Out: 31
Growth Rate: 0.0765170397058461
Year: 51986
Total Population: 32021
Aged Out: 36
Growth Rate: 0.0596718347247336
Year: 38186
Total Population: 32026
Aged Out: 27
Growth Rate: 0.0812496726548997
Year: 48209
Total Population: 32017
Aged Out: 40
Growth Rate: 0.0643386089734282
Year: 49310
Total Population: 32009
Aged Out: 39
Growth Rate: 0.0628858243763942
Year: 73672
Total Population: 32000
Aged Out: 41
Growth Rate: 0.0420784015636877
Year: 40103
Total Population: 32019
Aged Out: 42
Growth Rate: 0.0773483280552577
Year: 56638
Total Population: 32009
Aged Out: 25
Growth Rate: 0.0547494614922843

Quote from: 03.6% chance/year of being a mother
Year: 16251
Total Population: 32012
Aged Out: 11
Growth Rate: 0.190831333456403
Year: 14788
Total Population: 32008
Aged Out: 6
Growth Rate: 0.209683527184203
Year: 16167
Total Population: 32005
Aged Out: 9
Growth Rate: 0.191779550937094
Year: 12379
Total Population: 32007
Aged Out: 7
Growth Rate: 0.250480652718313
Year: 13425
Total Population: 32000
Aged Out: 3
Growth Rate: 0.230912476722533
Year: 15378
Total Population: 32008
Aged Out: 10
Growth Rate: 0.201638704642996
Year: 13094
Total Population: 32070
Aged Out: 5
Growth Rate: 0.237284252329311
Year: 14898
Total Population: 32019
Aged Out: 8
Growth Rate: 0.208209155591355
Year: 13905
Total Population: 32010
Aged Out: 11
Growth Rate: 0.223013304566703
Year: 13381
Total Population: 32000
Aged Out: 5
Growth Rate: 0.231671773410059

Quote from: 03.7% chance/year of being a mother
Year: 8494
Total Population: 32025
Aged Out: 4
Growth Rate: 0.365257829055804
Year: 9242
Total Population: 32013
Aged Out: 7
Growth Rate: 0.335565894827959
Year: 8315
Total Population: 32032
Aged Out: 3
Growth Rate: 0.373205051112447
Year: 7894
Total Population: 32003
Aged Out: 2
Growth Rate: 0.392741322523436
Year: 7468
Total Population: 32040
Aged Out: 3
Growth Rate: 0.415640064274237
Year: 7918
Total Population: 32001
Aged Out: 2
Growth Rate: 0.39152563778732
Year: 7967
Total Population: 32039
Aged Out: 2
Growth Rate: 0.389594577632735
Year: 7925
Total Population: 32005
Aged Out: 6
Growth Rate: 0.391230283911672
Year: 8233
Total Population: 32036
Aged Out: 3
Growth Rate: 0.37697072755982

They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station

#### Pariah

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##### Re: Drow and math
« Reply #10 on: May 24, 2014, 12:55:06 AM »
Ran into this: http://www.gf9.com/hobby.aspx?art_id=3660 when I was looking into whether or not Drow are known for all out civil war or if they just rely on their constant state of cold war to keep their population in check and I decided that since I now have a way to actually test their statement, I might as well give it a go.  In this run through, the birth rate is 3.5% and any Drow over the age of 140 has a .11% chance a year of dying.

Quote
Year: 1259
Total Population: 32106
Aged Out: 0
Growth Rate: 2.47069102462272
Year: 1223
Total Population: 32079
Aged Out: 0
Growth Rate: 2.54121013900245
Year: 1198
Total Population: 32083
Aged Out: 0
Growth Rate: 2.59457429048414
Year: 1203
Total Population: 32045
Aged Out: 0
Growth Rate: 2.58063175394846
Year: 1223
Total Population: 32034
Aged Out: 0
Growth Rate: 2.53753066230581
Year: 1248
Total Population: 32010
Aged Out: 0
Growth Rate: 2.48477564102564
Year: 1260
Total Population: 32025
Aged Out: 0
Growth Rate: 2.46230158730159
Year: 1228
Total Population: 32092
Aged Out: 0
Growth Rate: 2.53192182410423
Year: 1215
Total Population: 32002
Aged Out: 0
Growth Rate: 2.5516049382716
Year: 1223
Total Population: 32065
Aged Out: 0
Growth Rate: 2.54006541291905

And the answer is yes.  With a 2.5% annual growth rate, the rule of 72 gives us ~29 years between population doublings.  A century of relative peace would octuple the Drow population.  Granted almost all of that growth would be under the age of 120, and it'd be such a shame losing so many so young in the bloodiest Surface-Underdark war in history...  Who am I kidding, it'd be a freaking barrel of laughs.    I feel like there's an adventure in there.  The spymaster for the Elven nation of Green-trees-and-flowers approaches the party, "Our dark cousins have been acting funny.  For the past 30 years or so there's been maybe a tenth of the wanton slaughter that we normally associate with them.  Could you, you know, go check it out?  I mean, it'd be nice to think that they've finally started abandoning their evil ways, but the fact that they still seem to be worshipping Lloth tends to imply otherwise..."  At which point the party would only need to fight an entire nation composed of level 1-3 fighters, wizards, and clerics.

And back to searching.
They were immediately and absolutely recognizable as adventurers... They were hardy and dangerous, lawless, stripped of allegiance or morality, living off their wits, stealing and killing, hiring themselves out to whoever and whatever came. They were inspired by dubious virtues.  China Mieville - Perdido Street Station