Reply to thread

Message: <blockquote data-quote="eamon" data-source="post: 5001746" data-attributes="member: 51942">Wealth By Level mathematically analyzed.Item Value By Level:Items values scale almost geometrically, though there is a bit of  a zig-zag (levels 5n+1 and 5n+2 are worth a little more and levels 5n+4  and 5n+5 are worth a little less than expected).  For simplicity, I'll  just take the average here.  Both geometric and arithmetic averages are  actually close here; the worth of a n-th level item is about  244 * 5[sup]n/5[/sup].  This is useful because now we can express  everything in terms of #'s of items of the PC's level.  I'll call the  unit for wealth for a level+0 equivalent item 1ei.Wealth By Level:I've looked at expected wealth by level before on the wizard's forums:<a href="http://community.wizards.com/go/thread/view/75882/19635490/WealthByLevel_guidelines_for_highlevels_characters_are_totally_wack?num=10&pg=2" target="_blank">Wealth-By-Level guidelines for high-levels...</a>In short, your wealth should increase by a factor five over the span of five levels, or, on average, by a factor 1.38 each level.If you look at the DMG guidelines, a character is expected to have a net  worth of 2x a level-1 item + a level+0 item + level+1 item. Wealth by level is thus 3.83ei at the start of the level.  To maintain parity, thus, you must increase your wealth by 1.45ei (being 38% of 3.83ei) over the span of the level.  Any more than this, and you'll be slightly ahead of new characters, any less and new characters will actually have more wealth.  I don't think it's good if new characters start off at an advantage, so any guideline should have at least this much.  Due to the exponential nature of the curve, if you earn more than this, you'll only be a limited fraction of a level ahead of the curve.  Earning a full factor 5 to much each level would represent a 5 level head start, but small errors tend not to matter much (a good thing!).Treasure Per Level:The DMG guidelines suggest that a 5-person party finds about the equivalent worth of 11.5 ei.  2ei hereof is in raw wealth (i.e. plain gold or equivalent).  So, you find about 2.3ei per person (0.4ei hereof in gold) but gain only 1.45ei: the rest is presumably loss or a head start vs. new characters.  In short, you expected to lose no more than 0.85ei; otherwise you'd actually come out ahead by recreating a character (not a good thing for the game).  This is about equivalent to selling 1ei, since that's about 0.8ei loss - plus some some extra loss.  This will be our key balancing point.Treasure System Guarantees:The system should ensure that characters gain at least 1.45ei in wealth but certainly no more than 2.3ei (which would represent the absolutely lossless optimal character that retains full value from all items he ever finds for all levels).  The lossless character is not even 1.5 levels ahead of a new character, which demonstrates the stability of the base system.  Ideally, earnings would be about 2.3ei, and losses also about equivalent, but that less important, crucial is net wealth.</blockquote>

Verification