Post/Author/DateTime	Post
DrakoShade 07-17-06, 01:55 AM	I'm rather curious as to how WotC determined what the average character wealth should be at any given level. Specifically, I want to know if there's some simple mathematical formula that can be applied. I've managed to build formulai in Excel that can determine minimum experience needed to reach a given level, the maximum experience before you leave that level, all three sets of BAB, and even your total feats and ability point increases at any given level. All of those formulai have a single variable, so it's possible to stick them all on one sheet, put in a single number, and get all that information up front with one round of calculations... ...but the formula for character wealth eludes me. Table 5-1 of the DMG claims to be derived from tables 2-6 and 3-3, but table 3-3 claims to be derived from table 5-1. Obviously, both can't be right... but I still can't figure out a formula that produces the same numbers (or even a recognisably similar curve.) Do any of the math-wizards around here know?
Squirrelloid 07-17-06, 02:14 AM	I'm rather curious as to how WotC determined what the average character wealth should be at any given level. Specifically, I want to know if there's some simple mathematical formula that can be applied. I've managed to build formulai in Excel that can determine minimum experience needed to reach a given level, the maximum experience before you leave that level, all three sets of BAB, and even your total feats and ability point increases at any given level. All of those formulai have a single variable, so it's possible to stick them all on one sheet, put in a single number, and get all that information up front with one round of calculations... ...but the formula for character wealth eludes me. Table 5-1 of the DMG claims to be derived from tables 2-6 and 3-3, but table 3-3 claims to be derived from table 5-1. Obviously, both can't be right... but I still can't figure out a formula that produces the same numbers (or even a recognisably similar curve.) Do any of the math-wizards around here know? Their wealth per level assumes 13 encounters of EL = party level per level (expected number of encounters required to level) with average treasure given for each encounter. This is actually a somewhat complicated calculation, but perfectly doable using just the DMG.
DrakoShade 07-17-06, 02:33 AM	That still leaves the formula at two variables, since the average treasure per encounter doesn't seem to grow in any direct proportion to the level of the encounter. If there is some way-- any way-- to directly relate the treasure value of the encounter to the EL in a mathematical formula, I haven't found it yet. Everything else so far can be derived with that single variable between 1 and 20. Heck, it will take me all of ten minutes to update what changes when you hit epic, so that any number greater than zero will instantly "lookup" all the appropriate tables to show you where the character should be... That's the crux. If I can do that to either table 3-3 or 5-1, then I can also have several other values calculate alongside everything else. Namely, exactly what wealth level the character should have on hitting the level in question, how much they can expect to earn per encounter at that level, and how much that will total over the level. I'm aiming for completeness in my homebrew tool. :rolleyes: I know, it's essentially pointless, but it's an exercise for me simply in whether it can even be done. I don't see why treasure should be any harder than the others to figure a formula for (especially the experience, which required using combinations. Took me three hours to realize that one.)
Squirrelloid 07-17-06, 03:37 AM	That still leaves the formula at two variables, since the average treasure per encounter doesn't seem to grow in any direct proportion to the level of the encounter. If there is some way-- any way-- to directly relate the treasure value of the encounter to the EL in a mathematical formula, I haven't found it yet. Everything else so far can be derived with that single variable between 1 and 20. Heck, it will take me all of ten minutes to update what changes when you hit epic, so that any number greater than zero will instantly "lookup" all the appropriate tables to show you where the character should be... That's the crux. If I can do that to either table 3-3 or 5-1, then I can also have several other values calculate alongside everything else. Namely, exactly what wealth level the character should have on hitting the level in question, how much they can expect to earn per encounter at that level, and how much that will total over the level. I'm aiming for completeness in my homebrew tool. :rolleyes: I know, it's essentially pointless, but it's an exercise for me simply in whether it can even be done. I don't see why treasure should be any harder than the others to figure a formula for (especially the experience, which required using combinations. Took me three hours to realize that one.) Treasure does grow in proportion to CR. In the DMG there's a table for randomly generating treasure by EL. As EL increases, probability of better item types increases. Each item level has an average value. Thus, the Expected value of a treasure for EL N is = sum across types of treasure (P(generating type x given EL N)*Expected Value of that treasure type given EL). And the Expected value of that treasure type is = Sum across quality categories of (P(quality category X) * average value of treasures of quality category X). So if you have a 20% chance of generating magical items, thats .2*average value of magical items at that EL. You then have to look at how many magical items are generated if you generate them - expected number is the average (so 1d4+1 = 3.5). Then you want to know the average value of a given treasure, which will require you knowing the frequency of lesser, moderate, and greater power items (given in the tables) for that EL, and figuring out what the average value of those treasure categories are. You may need to weight by treasure type if you're more likely to generate some types than others (eg, if scrolls are more common than rings, say). Anyway, the DMG has a bunch of tables which will allow you to calculate all this, its just a pain in the behind.
DrakoShade 07-17-06, 04:37 AM	Well, that just figures. (Forgive me for the pun, please.) It couldn't be something simple to do in Excel like the silly "ROUND((0.75*Level)-0.5, 0)" to get the Average BAB. Curse them. This is going to take far longer to set up... Either that, or I could go with a formula that nearly approximates it for the first 20 levels. Epic treasure tables seem to advance at an easier pace to formulate.
Azezel 07-17-06, 05:51 AM	I have also been trying to extrapolate the formula for treater by EL and wealth by levels - it is very hard to do. I begin to wander if there is a formula, or if they just threw it around the WotC offices one night until they arived at some thing that looked 'about right'.
Weaponbreaker 07-17-06, 06:49 AM	I begin to wander if there is a formula, or if they just threw it around the WotC offices one night until they arived at some thing that looked 'about right'. Probly somewhere in the middle. For those that played NWN at first you cold not even equip items whose 'estimated' level was higher than your own......
Azezel 07-17-06, 08:53 AM	I'm pretty sure that that was so you could not cheat your way to omnipotece in multiplayer.