D&D 3E/3.5 v4: Challenge Ratings pdf (3.5 compatible)

Upper_Krust said:
The fact that you already recognise a flattening of numbers tells you that there will be be no exact formula.

No, it tells me that the core designers recognized that there are different treasure needs for the party at different levels. I can accept multiple expressions that apply to groupings of character levels (1-4, 5-8, 9-12, etc.) or I can also accept a single formula that pushes around the numbers at levels 1-4 a bit.

I seem to recall someone on these boards (was it you CRGreathouse mate?) discovered a formula that was very close to explaining the Wealth progression.

Would love to see it.

The DMG formula can be summarized as:

4 (party size) x 75 (the "base" xp award) x N / 3

So, to scale this formula with XP awarded (and thus with EL), it could be expressed as:

(4/3)(XP)(N).

The trick is finding an expression for the mathematical progression of N (3,6,9,12,16,20,26,34, etc.), to which I have set my sigmanalysist.

Beginning with the increase from 4th to 5th level, the progression of N is approximately 1.3 x (N-1). Depending on when, whether, and how you round off the numbers, you can hit the DMG numbers pretty closely.

Wulf
 

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Wulf Ratbane said:
Beginning with the increase from 4th to 5th level, the progression of N is approximately 1.3 x (N-1). Depending on when, whether, and how you round off the numbers, you can hit the DMG numbers pretty closely.

Yeah, that's how I looked at it. From 7th level on, the formula is roughly

W = 3000 * 1.32 ^ L

where W = wealth and L = level. This gets more accurate as levels increase; by 18th level, it's off by less than 1%.

At epic levels, the progression is quadratic--it can actually be computed exactly with dual formulas for even and odd, though they're off by just a constant. That is, a single formula would be off by a little bit every other number, but the amount would decrease proportionately with levels. (It's not large anywhere.)

At low levels, it's roughly quadratic... 345 L ^ 2 - 400.
 

CRGreathouse said:
Yeah, that's how I looked at it. From 7th level on, the formula is roughly

W = 3000 * 1.32 ^ L

where W = wealth and L = level. This gets more accurate as levels increase; by 18th level, it's off by less than 1%.

That formula's not workin' for me-- even when I correct it to 300 * 1.32 ^ L, which is what I assume you meant...

Wulf
 

Hi Wulf mate! :)

Wulf Ratbane said:
The DMG formula can be summarized as:

4 (party size) x 75 (the "base" xp award) x N / 3

So, to scale this formula with XP awarded (and thus with EL), it could be expressed as:

(4/3)(XP)(N).

The trick is finding an expression for the mathematical progression of N (3,6,9,12,16,20,26,34, etc.), to which I have set my sigmanalysist.

Good luck with that. :D

Wulf Ratbane said:
Beginning with the increase from 4th to 5th level, the progression of N is approximately 1.3 x (N-1). Depending on when, whether, and how you round off the numbers, you can hit the DMG numbers pretty closely.

It all just seems a bit arbitrary to me. :rolleyes:
 

Wulf Ratbane said:
That formula's not workin' for me-- even when I correct it to 300 * 1.32 ^ L, which is what I assume you meant...

Well, it works for me (again, on upper levels -- 7 to 20) just fine. I meant 3000, though.

Here are the numbers my rough system gives:

7 21,000
8 28,000
9 36,000
10 48,000
11 64,000
12 84,000
13 111,000
14 146,000
15 193,000
16 255,000
17 336,000
18 444,000
19 586,000
20 774,000
 

CRGreathouse said:
1 hobgoblin (EL 2): 300 gp (300 each)
8 hobgoblins (EL 8): 1470 gp (184 each)

So when you get more hobgoblins together, they collect less treasure?

First off, a hobgoblin is EL 3 (CR 1.5) . . . Second, eight hobgoblins would thus be EL 9 . . . That means 390 for the single hobgoblin and 1830 for the eight hobgoblins . . . Where do you get the idea that the amount of treasure per hobgoblin matters in the slightest? Treasure scales by EL, not per creature; as such, the amount per creature is a moot point in every conceivable way. This is D&D, not Final Fantasy.

Upper_Krust said:
Hi all! :)

It seems as if we have reached an impasse.

We have three systems for determining treasure, none are perfect, but each have their pros and cons.

The only con in mine is that at higher ELs with wide CR spans, the treasure slants up at the low end and down at the high end; in a campaign, though, this evens out absolutely perfectly.

Basically, the only thing it does it not perfectly follow the wealth formulas; if you base wealth on the treasure gained, every level between two ELs is linear until you reach the next EL. This is not a problem, however, as it still evens out PER EL, which is the basis for challenges and XP anyway, meaning it is perfectly and flawlessly balanced.

EL 21 is Levels 32-39 . . . EL 21 treasure is 117,120 gp . . . This gives more than the average wealth for the bottom end and less at the top end, but unlike the unbalanced results basing results on CR, these even out even using other ELs and give the proper treasure for the XP gained as well.

Upper_Krust said:
1. Treasure determined by Challenge Rating: 90 x CR x (CR+1) + 30.

2. Treasure determined by Encounter Level (by Anubis): ((Lowest Wealth of EL+1) - Lowest Wealth of EL) x 0.3 ÷ # of Levels with that EL band

Is that right Anubis mate?

Not exactly. It's specific for the first 20 ELs, but from EL 21+, it's based on a range of CRs. Again:

Well, after doing some checking, my proposal doesn't really work very well at all. At low levels, it totally bombs due to the huge jumps in EL at the initial levels. I guess relative treasure don't work after all!

Anyway, I've been thinking very hard about this, and I think I have come up with a solution. The ONLY possible bad thing about the solution is that wealth gained during gaming would not exactly match wealth from the tables at certain points. Then again, I don't know a single campaign where those tables are followed to the number, so the differences are within acceptable limits. All things considered, it all balances out in the end because although you get more treasure at the low end of a particular EL, you get less treasure at the high end of the same EL. All in all it's the ONLY solution that works at ALL levels.

Indeed, you must give out treasure PER EL (as you guessed at one point), and have a specific level of treasure for each EL. This of course would normally give us the problem of giving more treasure to higher level characters within the same EL, right? WRONG. By taking the average needed for every level within a given EL, you get an average amount of treasure per encounter within that EL.

In order to do this, though, you must change things at ALL levels, not just epic levels. I present to you the following chart:

Code:
EL     Treasure Value     Treasure Level
==================================================
1                 210                  1
2                 300                  1 (+90 gp)
3                 390                  1 (+180 gp)
4                 480                  1 (+270 gp)
5                 570                  2
6                 840                  3
7               1,110                  4
8               1,470                  5
9               1,830                  6
10              2,730                  7
11              3,810                  8
12              5,070                  9
13              7,320                 11
14             10,920                 12
15             15,240                 14
16             20,280                 15
17             29,280                 16
18             43,680                 18
19             60,960                 19
20             81,120                 20
21            117,120

For every value that is within the parameters of the DMG, I went ahead and assigned a Treasure Level from the DMG. The first column is the EL of the encounter. The second column is what the value of a treasure from such an encounter should be in order to keep PCs with wealth parameters. The third column gives us the Treasure Level from the DMG to use that matches those values, as per p.170 of the DMG. Five Treasure Levels will of course never be used, but that's okay. Each Treasure Level indicated gives an average of the indicated amount of treasure and thus keeps PCs within wealth guidelines. Over Treasure Level 20, it is of course up to the DM to assign treasure that is worth a total of about the given value, as per the suggestions in the ELH about not randomly generating epic treasure.

The numbers in the second column were obtained through a method similar to the one I gave you before for obtaining treasure values per level. The formula seems more complex, but it actually isn't and this is unfortunately the only way to get accurate treasure numbers. It's no more complicated than your entire CR system. The formula is as follows:

{ [ (calculated wealth for first level of next EL) - (calculated wealth for bottom level of current EL) ] *4 } / 13 1/3 / (number of levels in current EL)

That looks even more intimidating than before, of course, and likely needs explanation. What it means is subtract the wealth of the bottom level of the current EL from the wealth of the bottom level of the next EL up (because that's how much wealth should be accumulated through that particular EL), multiply the result by 4, and then divided it by 13 1/3. Then finish it up by dividing the result by the number of levels within the current EL. Remember that by the system, 13 1/3 encounters is the technical norm, and that is where I got the number of course. Of course there is an even easier way to get the following numbers, which I will get to later. Now it is time for an example to explain. The following is how you get the value of an EL 21 treasure:

EL 21 = Levels 32-39
EL 22 = Levels 40-47

PC Level 40 (bottom level of EL 22) Wealth: 6,400,000
PC Level 32 (bottom level of EL 21) Wealth: 3,276,800

For this formula, it has been shown to me that the functions of * 4 and / 13-1/3 are much more easily expressed with a single function of * .3

6,400,000 - 3,276,800 = 3,123,200
3,123,200 * .3 = 936,960

936,960 / 8 (number of levels within EL 21) = 117,120

As I said, PERFECT. This finally fixes the problems with wealth and treasure, assuming you use the wealth formula that has been settled upon. I know this is a bit complex, but then again, it's 255% necessary. You changed the way to CR/EL system works, which breaks the current treasure system by default because it was run based around the old CR/EL system. As such, there were bound to be complications when wealth was changed, and as such, treasure needed to be changed right along with it.

Anyway, problem solved.

Okay, not exactly perfect, but still far more accurate than all other systems unless anyone can prove otherwise.

Upper_Krust said:
3. Treasure determined by Experience Points: EXP x ((EXP+300) ÷ 1000) + 30

If we use Method #1 we get conflicting results when EL is a variable.
If we use Method #2 we get conflicting results when the # of monsters is a variable.

No we don't. What conflicting results? Treasure has NEVER been given "per creature". Not in the core rules (3 or 3.5) and not in any previous versions of these rules. Only the lame CR treasure rules ever gave treasure per creature. My system gives treasure PER ENCOUNTER, as it should be and is perfectly balanced to be.

Upper_Krust said:
If we use Method #3 we get conflicting results when (PC) CR is a variable...though according to Wulf this isn't actually a flaw.

Personally I think we may (?) have to go with two methods: Fixed (as per Method #1) and Relative (as per Method #3).

Anubis method (#2) is somewhere in between both of these.

I am curious to hear what the rest of you think on the matter before I make any decisions?

Like I said, I would like someone to point out any flaws in my system. That creature example was a totally lame (and futile) attempt because the point is balancing treasure with XP gains, meaning the number of creatures is moot.
 
Last edited:

Cheiromancer said:
Can you assign treasure based on the 4-person party for which something is a moderate challenge?

The level of the party can be plugged into 90*level*(level+1)+30 to get the standard value of an encounter of that level.

For example, if you have a first level party (standard point buy), their total CR is 8, making it EL 13, but then subtract 4 (4 members in the party) and the actual EL is 9. A moderate encounter for them is four less than their EL, so EL 5.

If a first level party is going to accumulate 2800 gp over 13.333 moderate encounters, each such encounter has to be worth 210 gp, so that's what an EL 5 is worth.

An EL 16 encounter is an appropriate encounter for an EL 20 party. For example 4 13th level characters (standard point buy) have a total CR of 56 or an EL of 24. Subtract 4 because the party has 4 members, and the LE is 20. Perfect!

The treasure for a moderate encounter for 13th level party of 4 is 16,410 gp. So that is what an EL 16 encounter should be worth.

And so on.

I'm sure that if I were clever I could make a spreadsheet that will calculate these values. But first, do you see anything wrong with this procedure?

[edit]
Ok. Calculating from the equations (instead of the charts) I get a slightly different set of values. But this is what the described method yields for expected treasure for an encounter of a given EL:

EL. . . . . Treasure (gp)
1. . . . . . 30
2. . . . . .50.25058026
3. . . . . . 82.72077939
4. . . . . . 133.1970865
5. . . . . . 210
6. . . . . . 325.0596018
7. . . . . . 495.4415588
8. . . . . . 745.5110554
9. . . . . .1110
10. . . . . 1638.352968
11. . . . . 2400.883118
12. . . . . 3497.489641
13. . . . . 5070
14. . . . . 7319.640996
15. . . . . 10531.76624
16. . . . . 15110.8494
17. . . . . 21630
18. . . . . 30901.02223
19. . . . . 44073.53247
20. . . . . 62775.17928
21. . . . . 89310
22. . . . . 126939.0054
23. . . . . 180277.0649
24. . . . . 255854.2805
25. . . . . 362910
26. . . . . 514515.8547
27. . . . .729164.1299
28. . . . .1033014.249
29. . . . .1463070
30. . . . .2071673.085
etc.

The gp value is given by the treasure formula with 2^((EL-1)/4) in place of the level.

So have I misunderstood how to calculate a moderate encounter for a level 1 party? If there are 4 of them and they have the standard array, I get a moderate encounter to be an EL 5.

Is this right?
 

Hi Cheiromancer mate! :)

Cheiromancer said:
So have I misunderstood how to calculate a moderate encounter for a level 1 party? If there are 4 of them and they have the standard array, I get a moderate encounter to be an EL 5.

Is this right?

The difference between Anubis Table and your table is that you modify Treasure based around PC Ability Scores and Anubis doesn't...I think. :D
 

Treasure, what else

Hi all! :)

I think part of the problem we are facing is that in this system EXP derived from EL is relative; not fixed (as with the core rules).

As such, even though its the clumsiest of the three methods, I think we are going to have to use a variation of Anubis/Cheiromancers ideas for Treasure by EL.

Personally I think a fixed Treasure result gives the best results.

I must admit though I still don't understand Cheiromancers equation for determining Treasure - can you explain that to me mate with an example?
 

Upper_Krust said:
I must admit though I still don't understand Cheiromancers equation for determining Treasure - can you explain that to me mate with an example?

I think his method is determining Wealth by Level, not Treasure per Encounter.

Anubis is on the right track, but I would tie my solution to XP awarded instead of directly to EL. GP should parallel XP awarded; I think the equation goes fuzzy in the DMG because they are actually assuming a loss of some accumulated wealth, from level to level, in terms of expendable resources.

FYI, I outsourced the problem to the finest minds in Bangalore, graduates of IIT, and am waiting to hear back. So if a solution can't be found, it won't be for a lack of trying. ;)

Wulf
 

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