Character Wealth by Level Formula? [Archive] - Wizards Community

Character Wealth by Level Formula? [Archive] - Wizards Community

Post/Author/DateTime Post
NiteCyper
02-11-07, 12:18 AM So is there a formula for character wealth by level? Formula, not table. It's not in the SRD so it'd help to have a formula. The formula for XP required for a certain level is the level times half the level minus 0.5 times one-thousand. X*(X/2-0.5)*1000.

According to Lordspecineff from the chat, DragonChild declares it simply came out of WotC's arse. I think I may have to agree.
Light_Colonel
02-11-07, 12:26 AM I think it is not in the SRD for legal reasons and I think those reasons prohibit you from posting the table here. I am not quite sure though, just giving you a warning that you may wanna ask a WizO.
pukunui
02-11-07, 12:56 AM I think it is not in the SRD for legal reasons and I think those reasons prohibit you from posting the table here. I am not quite sure though, just giving you a warning that you may wanna ask a WizO.
It is indeed against the Code of Conduct to post the character wealth by level info from the DMG. NiteCyper, you're going to want to remove that info from your post.
Bob Loblaw
02-11-07, 01:09 AM Your formula is incorrect for all levels, save one. Looks like the table is a violation.
ShadowDragon8685
02-11-07, 01:10 AM Up until level 7, this holds true:

450*x*y, where X is the level you're attaining, and y is the previous level. After that this formula falls behind, but I'm certain it's some formula, probably a simple one. Maybe a Logarythmic? I dunno, I can't quite figure it - it's been a semester since I took college algebra, and we barely covered this stuff.

As for levels, it's not too hard.

It's 1000*X+Y, where Y is the amount of XP required to get to the previous level. This may not seem useful, but if you have to (and you have a TI-83 or 89), you can just plug in (1000*1)+(1000*2)+(1000*3), etcetera, until you reach the level before the level you're to attain.
NiteCyper
02-11-07, 01:28 AM Your formula is incorrect for all levels, save one. Looks like the table is a violation.Are you mixing up my XP formula for my character wealth by level formula that I have no statement for? 20*(20/2-0.5=)9.5*1000 = 190,000 XP. That is the XP requirement for level 20. I don't see how it is wrong.Up until level 7, this holds true:

450*x*y, where X is the level you're attaining, and y is the previous level. After that this formula falls behind, but I'm certain it's some formula, probably a simple one. Maybe a Logarythmic? I dunno, I can't quite figure it - it's been a semester since I took college algebra, and we barely covered this stuff.

As for levels, it's not too hard.

It's 1000*X+Y, where Y is the amount of XP required to get to the previous level. This may not seem useful, but if you have to (and you have a TI-83 or 89), you can just plug in (1000*1)+(1000*2)+(1000*3), etcetera, until you reach the level before the level you're to attain. I don't know if you're talking about XP or Wealth, but I assume wealth. I don't know because the poster previous seems to be talking about XP. I think. :S Yeah, it does get screw once you hit level 7.
BlueFlames
02-11-07, 01:40 AM I've tried crunching the numbers on the wealth-by-level table a few times before, and I'm reasonably sure it's just an ugly piece-wise function. You might get something that works for three or four levels, but you'll have to work out another formula for the next three or four levels. If I had to guess, I'd say this was done for the purely mercenary reason of preventing anyone without a DMG from being able to extrapolate the whole table from knowledge of just a few data points.
pukunui
02-11-07, 01:53 AM You know, someone around here has got a link to formulas for everything (including wealth by level) in their sig, but I can't for the life of me remember who that is ...

Have you tried googling something like "character wealth by level formula"?
Tyler Do'Urden
02-11-07, 02:13 AM The formula for XP required for a certain level is the level times half the level minus 0.5 times one-thousand. X*(X/2-0.5)*1000.
It's actually simpler than that. The XP required to reach level n is n x n-1 x 500. 10th level would be 10 x 9 x 500, which is 45,000 and matches the table.

There's no elegant formula for character wealth by level that I've been able to discern. It's not something you need very often. As a player, you really only need it once: at character creation. As a DM, you only really need it when you're checking how far ahead or behind the curve your PCs are, and since you probably need the DMG open for item prices, you may as well just keep a finger on page 135.
Bob Loblaw
02-11-07, 09:09 AM Are you mixing up my XP formula for my character wealth by level formula that I have no statement for? 20*(20/2-0.5=)9.5*1000 = 190,000 XP. That is the XP requirement for level 20. I don't see how it is wrong.

I was, sorry. You skipped topics mid paragraph and I didn't notice.

I put the numbers into Excel, made a graph, and came up with this formula (I hope everyone likes it):

Y= Gold Pieces
X= Level

y = 0.08x^6 - 4.2123x^5 + 96.452x^4 - 1075.1x^3 + 6515.4x^2 - 16716x + 15808

It's also not prefect. It requires some unreasonable rounding and still can't hit every level correctly even though the R^2 value is 1.

I doubt there is an actual formula for the table.
ridiculous
02-11-07, 10:50 AM Actually mathematically speaking the curve MUST be representable by a function, but it might be an ugly one.

The one posted by Bob Loblaw actually works quite well, past level 3 it scores within 5% if the table value, often within less than 1%. Considering this table is nothing more than a guideline, it would actually work, but it is not something you will calculate in your head while creating an NPC on the fly.

I can come up with relatively simple formulas, but they only work for a few levels (3-4 at a time).

Save yourself some trouble, use the table
ShadowDragon8685
02-11-07, 01:00 PM Actually mathematically speaking the curve MUST be representable by a function, but it might be an ugly one.

The one posted by Bob Loblaw actually works quite well, past level 3 it scores within 5% if the table value, often within less than 1%. Considering this table is nothing more than a guideline, it would actually work, but it is not something you will calculate in your head while creating an NPC on the fly.

I can come up with relatively simple formulas, but they only work for a few levels (3-4 at a time).

Save yourself some trouble, use the table

I think the point is that some of us don't have access to the table, or have access all the time.

The 450*n*n-1 thing I came up with works up through 6th level, anyway. That's a nice run.

Let me haul out my TI-83 and see if I can remember how to make a proper curve... Bah.

Forgot I loaned out my TI-83, and I don't know how to access the right features on my 89. someone else have a crack at it.
GSonic7
02-11-07, 02:04 PM For f(x)=92.6664234x^2.84388169, there is a correlation value of .99155876, but gets to be too low after about level 16 or so.

f(x)=19.537735x^4-553,17051x^3+6356.82965x^2-26235.477x+35605.2631 is pretty close as well, but its line of reflection is around 2 or 3 (the screen on my calculator is pretty small).
FrostHammer
02-11-07, 02:32 PM Damn it. It's been WAY too long since I've done any trig and calculus. I've forgotten how to do these things! Noooooo!
danielinthewolvesden
02-12-07, 01:50 AM Gee, why not just turn to page 135 of the DMG?:confused:
StoneStokes
02-12-07, 03:46 AM The data can be fit exactly by a 19th degree (or lower) polynomial, but I don't think that's what the OP intended, as most won't consider it elegant.

The data itself does not really follow a nice progression (in the vein that the XP table does so). In fact, the 2nd-order differences between entries are sometimes ZERO! This prevents completely fitting the data by any exponential-like or fibonacci-like sequence.

However, you can get a good approximation to this table (within 10%) up to level 14 by doing the following:
Wealth at level 2 is 900.
To compute the wealth at level X, take the wealth at level X-1, add 1900, and add 4 times 1/10th the XP required to reach the level X-2.

Examples:
3rd-level. 900 + 1900 + (4/10)(0) = 2800.
4th-level. 2800 + 1900 + (4/10)(1000) = 5100.
5th-level. 5100 + 1900 + (4/10)(3000) = 8200 (this is the largest error before level 14).

A couple of Notes:

This is pretty far from a perfect fit, because,
It is a cubic approximation to a 19th-degree polynomial (Bob Lablaw's 6th-degree approximation will be better because it is higher-order), but
It does follow a fibonacci-like progression, and
The second-order differences are always 400/level^2 (instead of sometimes 2000, sometimes 4000, sometimes 0, sometimes 10,000, sometimes 20,000). This also means that the cubic polynomial underlying my progression does not have any of its "wiggles" (of any order) in the range [2, 20]. The same is not true for the WotC wealth-by-level progression.

I need to get a job...

Cheers,
StoneStokes

Post/Author/DateTime	Post
NiteCyper 02-11-07, 12:18 AM	So is there a formula for character wealth by level? Formula, not table. It's not in the SRD so it'd help to have a formula. The formula for XP required for a certain level is the level times half the level minus 0.5 times one-thousand. X(X/2-0.5)1000. According to Lordspecineff from the chat, DragonChild declares it simply came out of WotC's arse. I think I may have to agree.
Light_Colonel 02-11-07, 12:26 AM	I think it is not in the SRD for legal reasons and I think those reasons prohibit you from posting the table here. I am not quite sure though, just giving you a warning that you may wanna ask a WizO.
pukunui 02-11-07, 12:56 AM	I think it is not in the SRD for legal reasons and I think those reasons prohibit you from posting the table here. I am not quite sure though, just giving you a warning that you may wanna ask a WizO. It is indeed against the Code of Conduct to post the character wealth by level info from the DMG. NiteCyper, you're going to want to remove that info from your post.
Bob Loblaw 02-11-07, 01:09 AM	Your formula is incorrect for all levels, save one. Looks like the table is a violation.
ShadowDragon8685 02-11-07, 01:10 AM	Up until level 7, this holds true: 450xy, where X is the level you're attaining, and y is the previous level. After that this formula falls behind, but I'm certain it's some formula, probably a simple one. Maybe a Logarythmic? I dunno, I can't quite figure it - it's been a semester since I took college algebra, and we barely covered this stuff. As for levels, it's not too hard. It's 1000X+Y, where Y is the amount of XP required to get to the previous level. This may not seem useful, but if you have to (and you have a TI-83 or 89), you can just plug in (10001)+(10002)+(10003), etcetera, until you reach the level before the level you're to attain.
NiteCyper 02-11-07, 01:28 AM	Your formula is incorrect for all levels, save one. Looks like the table is a violation.Are you mixing up my XP formula for my character wealth by level formula that I have no statement for? 20(20/2-0.5=)9.51000 = 190,000 XP. That is the XP requirement for level 20. I don't see how it is wrong.Up until level 7, this holds true: 450xy, where X is the level you're attaining, and y is the previous level. After that this formula falls behind, but I'm certain it's some formula, probably a simple one. Maybe a Logarythmic? I dunno, I can't quite figure it - it's been a semester since I took college algebra, and we barely covered this stuff. As for levels, it's not too hard. It's 1000X+Y, where Y is the amount of XP required to get to the previous level. This may not seem useful, but if you have to (and you have a TI-83 or 89), you can just plug in (10001)+(10002)+(10003), etcetera, until you reach the level before the level you're to attain. I don't know if you're talking about XP or Wealth, but I assume wealth. I don't know because the poster previous seems to be talking about XP. I think. :S Yeah, it does get screw once you hit level 7.
BlueFlames 02-11-07, 01:40 AM	I've tried crunching the numbers on the wealth-by-level table a few times before, and I'm reasonably sure it's just an ugly piece-wise function. You might get something that works for three or four levels, but you'll have to work out another formula for the next three or four levels. If I had to guess, I'd say this was done for the purely mercenary reason of preventing anyone without a DMG from being able to extrapolate the whole table from knowledge of just a few data points.
pukunui 02-11-07, 01:53 AM	You know, someone around here has got a link to formulas for everything (including wealth by level) in their sig, but I can't for the life of me remember who that is ... Have you tried googling something like "character wealth by level formula"?
Tyler Do'Urden 02-11-07, 02:13 AM	The formula for XP required for a certain level is the level times half the level minus 0.5 times one-thousand. X(X/2-0.5)1000. It's actually simpler than that. The XP required to reach level n is n x n-1 x 500. 10th level would be 10 x 9 x 500, which is 45,000 and matches the table. There's no elegant formula for character wealth by level that I've been able to discern. It's not something you need very often. As a player, you really only need it once: at character creation. As a DM, you only really need it when you're checking how far ahead or behind the curve your PCs are, and since you probably need the DMG open for item prices, you may as well just keep a finger on page 135.
Bob Loblaw 02-11-07, 09:09 AM	Are you mixing up my XP formula for my character wealth by level formula that I have no statement for? 20(20/2-0.5=)9.51000 = 190,000 XP. That is the XP requirement for level 20. I don't see how it is wrong. I was, sorry. You skipped topics mid paragraph and I didn't notice. I put the numbers into Excel, made a graph, and came up with this formula (I hope everyone likes it): Y= Gold Pieces X= Level y = 0.08x^6 - 4.2123x^5 + 96.452x^4 - 1075.1x^3 + 6515.4x^2 - 16716x + 15808 It's also not prefect. It requires some unreasonable rounding and still can't hit every level correctly even though the R^2 value is 1. I doubt there is an actual formula for the table.
ridiculous 02-11-07, 10:50 AM	Actually mathematically speaking the curve MUST be representable by a function, but it might be an ugly one. The one posted by Bob Loblaw actually works quite well, past level 3 it scores within 5% if the table value, often within less than 1%. Considering this table is nothing more than a guideline, it would actually work, but it is not something you will calculate in your head while creating an NPC on the fly. I can come up with relatively simple formulas, but they only work for a few levels (3-4 at a time). Save yourself some trouble, use the table
ShadowDragon8685 02-11-07, 01:00 PM	Actually mathematically speaking the curve MUST be representable by a function, but it might be an ugly one. The one posted by Bob Loblaw actually works quite well, past level 3 it scores within 5% if the table value, often within less than 1%. Considering this table is nothing more than a guideline, it would actually work, but it is not something you will calculate in your head while creating an NPC on the fly. I can come up with relatively simple formulas, but they only work for a few levels (3-4 at a time). Save yourself some trouble, use the table I think the point is that some of us don't have access to the table, or have access all the time. The 450nn-1 thing I came up with works up through 6th level, anyway. That's a nice run. Let me haul out my TI-83 and see if I can remember how to make a proper curve... Bah. Forgot I loaned out my TI-83, and I don't know how to access the right features on my 89. someone else have a crack at it.
GSonic7 02-11-07, 02:04 PM	For f(x)=92.6664234x^2.84388169, there is a correlation value of .99155876, but gets to be too low after about level 16 or so. f(x)=19.537735x^4-553,17051x^3+6356.82965x^2-26235.477x+35605.2631 is pretty close as well, but its line of reflection is around 2 or 3 (the screen on my calculator is pretty small).
FrostHammer 02-11-07, 02:32 PM	Damn it. It's been WAY too long since I've done any trig and calculus. I've forgotten how to do these things! Noooooo!
danielinthewolvesden 02-12-07, 01:50 AM	Gee, why not just turn to page 135 of the DMG?:confused:
StoneStokes 02-12-07, 03:46 AM	The data can be fit exactly by a 19th degree (or lower) polynomial, but I don't think that's what the OP intended, as most won't consider it elegant. The data itself does not really follow a nice progression (in the vein that the XP table does so). In fact, the 2nd-order differences between entries are sometimes ZERO! This prevents completely fitting the data by any exponential-like or fibonacci-like sequence. However, you can get a good approximation to this table (within 10%) up to level 14 by doing the following: Wealth at level 2 is 900. To compute the wealth at level X, take the wealth at level X-1, add 1900, and add 4 times 1/10th the XP required to reach the level X-2. Examples: 3rd-level. 900 + 1900 + (4/10)(0) = 2800. 4th-level. 2800 + 1900 + (4/10)(1000) = 5100. 5th-level. 5100 + 1900 + (4/10)(3000) = 8200 (this is the largest error before level 14). A couple of Notes: This is pretty far from a perfect fit, because, It is a cubic approximation to a 19th-degree polynomial (Bob Lablaw's 6th-degree approximation will be better because it is higher-order), but It does follow a fibonacci-like progression, and The second-order differences are always 400/level^2 (instead of sometimes 2000, sometimes 4000, sometimes 0, sometimes 10,000, sometimes 20,000). This also means that the cubic polynomial underlying my progression does not have any of its "wiggles" (of any order) in the range [2, 20]. The same is not true for the WotC wealth-by-level progression. I need to get a job... Cheers, StoneStokes