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Sunday, September 4, 2011

Pellatarrum: Broken River 2A

Broken River
Part 2A: In-Depth Explanation of the Math and Charts
by Mike (Rhishisikk) Kochis


Background
As I was going over My Runelord Ponies (My Little Ponies with Pathfinder elements) [Editor's Note: Mike, this is totally awesome and you need to tell me everything about it as soon as is possible], Erin brought to my attention that most people didn't understand the charts. Well, I don't like the charts – but I use them. So, things to know:
  1. Just because the charts say 12 level one experts doesn't mean Broken River HAS to have them; it just means that given the way I'm dividing the XP, that is how many the town could have. Think of it as a book of "class coupons" that you turn in as you make your NPCs rather than a mandate. Also, try to leave a few open for the person using your product. People have their own important NPCs, after all, and may even (gasp) be inspired by your work to improve upon it.

  2. I have to set these upper limits to avoid "Gygax City" syndrome. Notice how I constantly tell the reader not to rush into development? These are mistakes that I, myself, have rushed headlong into. So I attempt to squash the reader's impulses, and explain why that's a bad idea.

  3. I forget which world-builder article it was, but it suggested that only one in ten first level adventurers survived to second level, and only half as many to each level after that. So if a temple had a 9th level cleric, there would be two 8th level clerics, four 7th level clerics, eight 6th level clerics, and so on. This leads to – too many clerics to fit into the daggum temple. So my methods start at the bottom and work their way up.

  4. I always presume that no more than half the XP "carries upward". For those of you familiar with calculus (If you were, than those charts were a breeze, and you're just reading this for grins. Yes, you're very smart; if you eat a cookie every time you're smart, you'll die of complications caused by being grossly overweight.), this is the limit of 1/(2x) as x approaches infinity, which means (theoretically) we will use 100% of our XP. In practice, we've seen how it leaves bookoodles of XP for us to play with.

Basic Chart Terms
So let's take a look at our commoner chart:

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
562
0
562
0
0
1250
2
281
1
281
281
281
969
3
140
3
43
129
410
840
4
70
6
12
72
482
768
5
35
10
3
30
512
738
6
17
15
1
15
527
723

Level is the level of NPC that we are dealing with.

Base Number is the maximum amout of XP (in thousands) which we are willing to expend at that level for this class.

KXP Each is the amount from the player's handbook for a player to reach the experience level in the leftmost column. Note that we are using the FAST advancement track, and that I have rounded levels 2 and 3 to the nearest thousand XP.

Actual Number is the maximum number of persons we can have at that level. As noted earlier, we don't actually use every slot provided. This number is found by dividing Base Number by kXP Each. This number is rounded down at the halfway point, except for the highest level, which always has a minimum of one individual.

KXP Expended is how much XP we actually spent on NPCs of that level, multiplying Actual Number by kXP Each.

Total kXP Expended is just adding up all the values in the kXP Expended column. This helps us double check our math.

KXP Remaining is just what it sounds like; our total kXP minus the Total kXP Expended. This helps us move between stages – commoner to NPC classes; NPC classes to PC classes; other transitions.


So, now that we have our ground rules and our chart, let's go ahead...

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1








We start with the empty chart, above. We know that half the XP in Broken River is going to be going to the commoners, so we start there. With 1250 population, there are 1250 kXP. Half of this amount is 625 kXP, which becomes our base number:

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625







Everyone "knows" that first level is 0 XP. Notice in the charts for NPC and PC classes, we actually apply an EL+1 modifier, so our 1st level characters with non-commoner class levels actually cost us 1kXP each.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0






So there's no reason we can't have all 625 level one commoners.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625





And with 625x0 = 0, we don't actually use any of our precious XP on just commoners.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2








Remember that each level, we cut the available kXP in half:

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312







We are using the fast track for XP, so second level requires 1kXP:

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312
1






So again, no reason we can't have hordes of exceptional commoners who have reached level 2.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312
1
312





But this does actually cost us XP.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312
1
312
312
312
938
3








Now is where things start narrowing down from both ends, not just XP available. This gives us a believable logarithmic-style curve, where higher level characters become increasingly rare.

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312
1
312
312
312
938
3
156
3
52




Notice that? A total of one sixth, not one half, of the previous level.


So filling out the chart gives us the following:

Level
Base Number
kXP each
Actual Number
kXP expended
Total kXP expended
kXP remaining
1
625
0
625
0
0
1250
2
312
1
312
312
312
938
3
156
3
52
156
468
782
4
78
6
13
78
546
704
5
39
10
4
40
586
664
6
19
15
1
15
601
649


Yes, we expend forty of 39 kXP at level 5; likewise, at level 6 we don't use all our XP. At level 6, we stop; we've found our highest level NPC of this class.

I hope that this helps to explain how the charts work (and yes, I realize that some of the values are different than those originally posted; hope the math errors weren't what was confusing y'all...)


[Math errors? Oh dammit. I just thought I was being innumerate again. Dear readers, I promise you that henceforth, Mike shall be required to show his work or else be flogged with licorice whips.]

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