Neutral_Zone and I got into a pretty neat discussion about average levels in Faerun.
I debated the point that NPC's should average 1st lvl
Neutral_Zone debated that they should be higher because of the higher level characters in Faerun and the High Magic setting
So we decided to let the math speak. I went ahead and did up some numbers here to figure it out. Neutral_Zone said he'd do the same. Here's my take
We decided to take the city of Waterdeep's population as a kind of representation of the population of Faerun. Of course this isn't completely accurate but the high population of Waterdeep helps get a larger group to use for calculation. Race and exact class is a bit irrelevant for this, class is only needed to separate our numbers for calculation.
I'm working with the population of Waterdeep as per the FRCS pg 178 (not the regional population, the city population)
And the numbers for most of it comes from the 3.5 DMG pg 139
First we need to define some variables for this. Here is mine:
A = Percentage of Fill
B = Class Level
C = Total population to be filled
D = Number of different classes in a group
X = Average roll on die for class level
Y = Highest Level per class
Z = Number of NPC's with class levels per class
N = NPC's per class level shared
So first we need to figure out the highest level for each class according to the population of a Metropolis. You are to roll a die check and add 12 to the result for the highest level of each class in the city. This includes all standard PHB classes and NPC classes like Commoner, Expert, Adept, Aristocrat, and Warrior.
So this equation... and for simplicities sake I'm going to only follow the Adept for this post because that is way too many numbers to write. However the process is the same for all of them really.
12 + X = Y
This gives us the value for Y which we need. The Adept is defined as '1d6 + Community Modifier (12 for Metropolis) * 4 (because Metropolis population)'. So the average number rolled on a 1d6 is 3.5. This is of course because
1+2+3+4+5+6 = 21/6 = 3.5
So plugging in 3.5 for X we have
12 + 3.5 = 15.5
YAY! We have a value for Y. The highest level Adept on average in the city of Waterdeep is a 15.5th lvl character. Of course you can't be 1/2 a level, but for math's sake we'll leave it as is because we want as true of a value as we can get.
Now that we have a value for Y, we need to take the next step. After this you have to take half of your highest level NPC's level for your next group, and double that over the previous number for number of NPC's with that level.
For our Adept that means...
Y/2 = Z
Plug in Y and we get
15.5/2 = 7.75
We know our next highest level adepts are level 7.75. Now we double the number of NPC's from the previous level to 2, since there was only 1 Adept, and we have
Adept 15.5 lvl = 1
Adept 7.75 lvl = 2
Adept 3.875 lvl = 4
Adept 1.9375 lvl =8
Adept .96875 lvl = 16
I went ahead and did the math for the rest of the levels. We are stopping at .96875 because rounded to the nearest ones place gives us 1, which is the lowest possible level for anything. (Hit Dice, BTW, are not included in this calculation because all standard PHB races have no extra Hit Die).
So now we have how many NPC's are of each level of the Adept in the city of Waterdeep. But we're not done. You see cities as large as Waterdeep are Metropolises and the DMG requires that you roll four times to determine the highest level NPC's. It seems our lonely Adept had a graduating class with him
Since we're taking averages here, no need to really roll out new numbers or anything, just multiply by four.
Adept 15.5 lvl = 4
Adept 7.75 lvl = 8
Adept 3.875 lvl = 16
Adept 1.9375 lvl = 32
Adept .96875 lvl = 64
That gives us the total number of Adepts in Waterdeep of each level.
Now you should go through the process of the other 15 classes... I did but I'm not writing it. So nanny nanny boo boo stick your head in doo doo.
So now we have the total number of NPC's and their respective levels. So what we need to figure out now is the total amount of levels of every citizen in waterdeep as per their class. Sounds tough, but easier than you think.
For one many of the classes use the same die roll for their highest level. Since we're working with averages that means they are identical so we can group them together for some ease. For example our Adept class has the same average number of NPC's for every level that the Bard, Cleric, and Druid have (1d6+12*2) so we can merely multiply the number of total NPC's by the number of classes that share the same die roll to get our total.
Z * 4 = N
So the new 'Group' which is Adept, Bard, Cleric and Druid is
15.5 = 16
7.75 = 32
3.875 = 64
1.9375 = 128
0.96875 = 256
Now you would go through each class and group them, do the same math and come up with your totals.
Now we need to add up each of the numbers of NPC's in each group to determine a total number of NPC's this set represents. That means going through each N variable and adding them together. 16 + 32 + 64 + 128 + 256 = 496
So there are 496 Total NPC's amongst the Adepts, Bards, Clerics, and Druids in the city of Waterdeep. Do the same for the other groups and add the total together. I got 1,364 total NPC's.
Now the population of Waterdeep is 132,661 as per the FRCS, so that's no where near the same. But this system is designed to tell us about a small population of a metropolis, not the whole one. The rest are filled in with 1st level commoners and other npc classes.
So...
132,661 - 1,364 = 131,297 NPC's we need to fill.
These NPC's are to be divided amongst the NPC classes all at lvl 1.
So basically...
A/100 * C
Commoners are 91%, Warriors 5%, Experts 3%, Rest are equally divided between Aristocrat and Adept, all lvl 1
91/100 * 131,297 = 119480.27
5/100 * 131,297 = 6564.85
3/100 * 131,297 = 3938.91
1/100 * 131,297 = 1312.97/2 = 656.485/2
So adding all together...
131,297 = Good, did that right
So in order to find out average level of all citizens of Waterdeep we have to first figure out how many levels are in Waterdeep total.
So we have to add all the levels together. Luckily, as stated before, several of the classes have the same levels so it makes the math a little easier once you group them by results. Example Fighter and Rogue. All you have to due to determine the total number of levels that Fighters and Rogues take up is to figure out one, then divide that number by two.
(N * B) / D =
So for our Adept, Bard, Cleric, Druid group we have
(15.5 * 16) /4 = 62
Now of course really all levels of the grouped classes will calculate out to be the same number because we halved them all earlier. So each will turn out 62 levels. There are 5 different levels, so 62*5 is 310. So between all the Adepts, Bards, Clerics, and Druids in Waterdeep there are 310 Class levels. Now do the same for each group.
So the total levels of all classes we calculated prior to the fill is 5,090 total levels.
Since all the fill NPC's are 1st lvl, we have to add that to 5,090
131,297 + 5,090 = 136,687
There are a total of 136,687 levels amongst the populous of Waterdeep.
Alright, so now we can get an average. Out of 132,661 citizens in Waterdeep there are a total amount of levels of 136,687, so..
.
136,687 / 132,661 = 1.0303480299409773784307369912785
Which rounded to the nearest ones place, cause you can't be lvl 1 1/2,
Level 1.
However, interestingly, the total levels of those previously calculated NPC's did effect the outcome higher than I thought at a .03 over 1, so there ya go.
Now someone might say... "What about Halaster, or Khelben or Piergeiron".
Let's face fact. You can subtract every special NPC from the books that lives in Waterdeep from the population of 1st level filler commoners and add their levels in and *STILL* not really even hit barely a bump in there. IMHO High magic really is irrelevant to average level. I mean just cause there are more mages and magic is more available doesn't mean that wizards are going to be higher level. And even if your average wizard is Level 3 instead of Level 1, it won't make that large of a difference to the average of the world.
However... this means that according to the math there is a 22.5 (23rd) level commoner strutting his stuff around Waterdeep. And he might have help from a pair of 11.25 (11th) level commoners. Be wary 5th level adventurers, or you might bite off more than you can chew against that farmer!
