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<blockquote data-quote="Kaffis" data-source="post: 4226017" data-attributes="member: 10305">To follow up on my musings over exponential growth vs. pseudo-exponential growth, I went and calculated an appropriate progression for a true exponential system, then rounded to the nearest 25 for less cumbersome values (in the first tier, this rounding never amounted to more than 6gp, though the 6gp rounding I did on the 2, 7, 12, ... progression was amplified in the later tiers as I chose to keep the factor of 5 every 5 levels. The end result is that level 27 is something like 18,000gp cheaper than a strict exponential curve would dictate... 10,000 out of around a million... others were less than 1,000 &quot;off&quot;), to arrive at the table as follows:[code]Level&nbsp; BuyVal&nbsp; SellVal&nbsp; ExtWizVal&nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; 275&nbsp; &nbsp; &nbsp;&nbsp; 55&nbsp; &nbsp; &nbsp; &nbsp; 360&nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; 375&nbsp; &nbsp; &nbsp;&nbsp; 75&nbsp; &nbsp; &nbsp; &nbsp; 520&nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; 525&nbsp; &nbsp; &nbsp; 105&nbsp; &nbsp; &nbsp; &nbsp; 680&nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; 725&nbsp; &nbsp; &nbsp; 145&nbsp; &nbsp; &nbsp; &nbsp; 840&nbsp;5&nbsp; &nbsp; &nbsp; 1,000&nbsp; &nbsp; &nbsp; 200&nbsp; &nbsp; &nbsp; 1,000&nbsp;6&nbsp; &nbsp; &nbsp; 1,375&nbsp; &nbsp; &nbsp; 275&nbsp; &nbsp; &nbsp; 1,800&nbsp;7&nbsp; &nbsp; &nbsp; 1,875&nbsp; &nbsp; &nbsp; 375&nbsp; &nbsp; &nbsp; 2,600&nbsp;8&nbsp; &nbsp; &nbsp; 2,625&nbsp; &nbsp; &nbsp; 525&nbsp; &nbsp; &nbsp; 3,400&nbsp;9&nbsp; &nbsp; &nbsp; 3,625&nbsp; &nbsp; &nbsp; 725&nbsp; &nbsp; &nbsp; 4,20010&nbsp; &nbsp; &nbsp; 5,000&nbsp; &nbsp; 1,000&nbsp; &nbsp; &nbsp; 5,00011&nbsp; &nbsp; &nbsp; 6,875&nbsp; &nbsp; 1,375&nbsp; &nbsp; &nbsp; 9,00012&nbsp; &nbsp; &nbsp; 9,375&nbsp; &nbsp; 1,875&nbsp; &nbsp;&nbsp; 13,00013&nbsp; &nbsp;&nbsp; 13,125&nbsp; &nbsp; 2,625&nbsp; &nbsp;&nbsp; 17,00014&nbsp; &nbsp;&nbsp; 18,125&nbsp; &nbsp; 3,625&nbsp; &nbsp;&nbsp; 21,00015&nbsp; &nbsp;&nbsp; 25,000&nbsp; &nbsp; 5,000&nbsp; &nbsp;&nbsp; 25,00016&nbsp; &nbsp;&nbsp; 34,375&nbsp; &nbsp; 6,875&nbsp; &nbsp;&nbsp; 45,00017&nbsp; &nbsp;&nbsp; 46,875&nbsp; &nbsp; 9,375&nbsp; &nbsp;&nbsp; 65,00018&nbsp; &nbsp;&nbsp; 65,625&nbsp;&nbsp; 13,125&nbsp; &nbsp;&nbsp; 85,00019&nbsp; &nbsp;&nbsp; 90,625&nbsp;&nbsp; 18,125&nbsp; &nbsp; 105,00020&nbsp; &nbsp; 125,000&nbsp;&nbsp; 25,000&nbsp; &nbsp; 125,00021&nbsp; &nbsp; 171,875&nbsp;&nbsp; 34,375&nbsp; &nbsp; 225,00022&nbsp; &nbsp; 234,375&nbsp;&nbsp; 46,875&nbsp; &nbsp; 325,00023&nbsp; &nbsp; 328,125&nbsp;&nbsp; 65,625&nbsp; &nbsp; 425,00024&nbsp; &nbsp; 453,125&nbsp;&nbsp; 90,625&nbsp; &nbsp; 525,00025&nbsp; &nbsp; 625,000&nbsp; 125,000&nbsp; &nbsp; 625,00026&nbsp; &nbsp; 869,375&nbsp; 171,875&nbsp; 1,125,00027&nbsp; 1,171,875&nbsp; 234,375&nbsp; 1,625,00028&nbsp; 1,640,625&nbsp; 328,125&nbsp; 2,125,00029&nbsp; 2,265,625&nbsp; 453,125&nbsp; 2,625,00030&nbsp; 3,125,000&nbsp; 625,000&nbsp; 3,125,000[/code]Now, comparing that with the extrapolated Wizards' values, we see what's to be expected. A true exponential value curve values the levels after a 5-level cluster less than the Wizards' &quot;incremental bumps&quot; system. A level 26 item is worth 869,375 instead of 1,125,000, a level 11 item is worth 6,875 instead of 9,000, etc. Not a problem in itself, because both the costs and the sell prices scale to the same &quot;melt down X items to produce Y same-level item&quot; ratio, 5:1.But what occurred to me while making this list, is that Wizards, in spreading the marginal increases evenly between each grouping of 5 levels, is valuing each progression within a bonus tier equally, while clustering the values more strongly by bonus. That is, a pure exponential growth scenario means that whatever items fall in the 1,6,11,etc. progression (the low end of the bonus tier) can be had much more cheaply than the high end, and now I'm not so sure that's appropriate.Without double checking myself, I seem to remember that Frost weapons are level 3's. Is having a +1 bonus with a frost effect half as valuable as a +1 with a fire effect, or 2/3s as valuable? That's what the question really comes down to. Presumably, level 1 weapon effects (and thus level 6's, level 11's, etc) will have a weaker daily power. So Wizards' system values the +2 with the less powerful effect much more strongly than the +1 with the good effect. On the other hand, the suggestion has been that the effects are the real power of magical weapons, moreso than the bonuses, so it may be that they deliberately chose this progression scheme not only because it's easier to bandy about 2,125,000 gp than it is 1,640,125 or what have you, but also to encourage players to find &quot;sweet spots&quot; in cost-to-benefit in taking the good effect over a bland effect with a slightly better number bonus.In short, I'm still up in the air on it, but I figured I'd share the crunching I did to come up with the exponential table.</blockquote>

[QUOTE="Kaffis, post: 4226017, member: 10305"] To follow up on my musings over exponential growth vs. pseudo-exponential growth, I went and calculated an appropriate progression for a true exponential system, then rounded to the nearest 25 for less cumbersome values (in the first tier, this rounding never amounted to more than 6gp, though the 6gp rounding I did on the 2, 7, 12, ... progression was amplified in the later tiers as I chose to keep the factor of 5 every 5 levels. The end result is that level 27 is something like 18,000gp cheaper than a strict exponential curve would dictate... 10,000 out of around a million... others were less than 1,000 "off"), to arrive at the table as follows: [code]Level BuyVal SellVal ExtWizVal 1 275 55 360 2 375 75 520 3 525 105 680 4 725 145 840 5 1,000 200 1,000 6 1,375 275 1,800 7 1,875 375 2,600 8 2,625 525 3,400 9 3,625 725 4,200 10 5,000 1,000 5,000 11 6,875 1,375 9,000 12 9,375 1,875 13,000 13 13,125 2,625 17,000 14 18,125 3,625 21,000 15 25,000 5,000 25,000 16 34,375 6,875 45,000 17 46,875 9,375 65,000 18 65,625 13,125 85,000 19 90,625 18,125 105,000 20 125,000 25,000 125,000 21 171,875 34,375 225,000 22 234,375 46,875 325,000 23 328,125 65,625 425,000 24 453,125 90,625 525,000 25 625,000 125,000 625,000 26 869,375 171,875 1,125,000 27 1,171,875 234,375 1,625,000 28 1,640,625 328,125 2,125,000 29 2,265,625 453,125 2,625,000 30 3,125,000 625,000 3,125,000[/code] Now, comparing that with the extrapolated Wizards' values, we see what's to be expected. A true exponential value curve values the levels after a 5-level cluster less than the Wizards' "incremental bumps" system. A level 26 item is worth 869,375 instead of 1,125,000, a level 11 item is worth 6,875 instead of 9,000, etc. Not a problem in itself, because both the costs and the sell prices scale to the same "melt down X items to produce Y same-level item" ratio, 5:1. But what occurred to me while making this list, is that Wizards, in spreading the marginal increases evenly between each grouping of 5 levels, is valuing each progression within a bonus tier equally, while clustering the values more strongly by bonus. That is, a pure exponential growth scenario means that whatever items fall in the 1,6,11,etc. progression (the low end of the bonus tier) can be had much more cheaply than the high end, and now I'm not so sure that's appropriate. Without double checking myself, I seem to remember that Frost weapons are level 3's. Is having a +1 bonus with a frost effect half as valuable as a +1 with a fire effect, or 2/3s as valuable? That's what the question really comes down to. Presumably, level 1 weapon effects (and thus level 6's, level 11's, etc) will have a weaker daily power. So Wizards' system values the +2 with the less powerful effect much more strongly than the +1 with the good effect. On the other hand, the suggestion has been that the effects are the real power of magical weapons, moreso than the bonuses, so it may be that they deliberately chose this progression scheme not only because it's easier to bandy about 2,125,000 gp than it is 1,640,125 or what have you, but also to encourage players to find "sweet spots" in cost-to-benefit in taking the good effect over a bland effect with a slightly better number bonus. In short, I'm still up in the air on it, but I figured I'd share the crunching I did to come up with the exponential table. [/QUOTE]

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