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Message: <blockquote data-quote="mneme" data-source="post: 5222775" data-attributes="member: 59248">I killed the <a href="http://www.enworld.org/forum/4e-discussion/278847-how-much-treasure-going-lvl-11-lvl-12-a.html" target="_blank">"how much treasure do you get going between level 11 and 12"</a> thread with this concept, so I figured I'd give it its own thread instead.I hadn't looked at the numbers, but an examination of Wizards' magic item prices (and by extention, their treasure guidelines for how much gold players get) reveals some really odd discontinuities.We all know the theoretical rule -- an item that is 5 levels higher always costs 5x as much.  But a cursory examination of the treasure tables reveals a very interesting fact: The intervening values don't actually follow this progression--instead, it looks like Wizards picked some numbers that at the +2 number resemble the actual just tempered curve (more on this later), and then just multiplied them all up the level chart.This means that in every sub-tier (1-5, 6-10, etc), the numbers/costs are relatively flat (level 2, 6, etc items are overpriced, but there's a sharp dropoff as you approach the end of the subtier) -- and there's a sharp jump as you cross subtiers, when the cost/treasure jumps from less than 3x the base cost of the tier up to 5x that number--nearly doubling.  The problem is, we have a really good method of tempering these numbers so that the curve is even -- in fact, we've had such a method since the 1700s, when it was developed as a method of tuning an insturment (typically, a piano) with even spacings between the notes so it would be equally in tune [or out of tune <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" />] in every key.  It's called "equal tempering", it works by making the relationship between the steps multiples of (period) to the power of ({iteration, starting at 0} / (period)) -- so for the D&D example, the a first level item will cost 360 * (5 ** (0 / 5)) = 360, a 6th level item will cost 360 * (5 ** (5/5)) = 1800 -- just like in PH1 -- but using this calculation method, every single cost will have exactly the same relationship to the previous cost (barring corrections for rounding) as the one before it did -- a smooth curve.Admittedly, there is one big advantage to the PH1 system: it under-prices 5th, 10th, etc level items.  As those items typically -are- substantially less powerful than the items just one level higher, there's some argument for doing so.  OTOH, given that the characters are getting the same item set over each level as the one before, there's not a great argument for doing the same with player treasure.As such, if I were to run a game, I'd be tempted to stick with the PH1 numbers for item costs, but give treasure along the true curve.  This does give out a bit more treasure than the PH1 version suggests (a party gets an extra 700 by 5th level, an extra 5k by 10th level, an extra 25k by 15th level, etc), but it's just not a huge deal. FWIW, here's the 6 line perl one liner I used to produce my comparison data (I'm working with the "amount of treasure earned by the party between levels" number, which is 2x the item cost for that level, but the ratio between numbers is identical.perl -e 'use strict; my $sum; use POSIX("ceil"); my @adds; @adds[1..29] = ((320) x 4,(1600) x 5,(8000) x 5,(40_000) x 5, (200_000) x 5,(1_000_000) x 5  ); for(0..29) { my $tres = ceil(720 * (5)**($_/5)); $sum+=$tres; print "$tres/$sum "; (($_+1) % 5) ==0 and print "\n"; }; print "\nsmooth total: $sum\n"; $sum=0; for my $lvl (0..29) { my $tres = 720; for(my $i=0; $i<=$lvl; $i++) { if($adds[$i]) { $tres+=$adds[$i] } } $sum+=$tres; print "$tres/$sum "; ($lvl+1) % 5 == 0  and print "\n"; } print "\nwotc total: $sum\n" 'And here are my results (first my expected/smooth numbers, then, for comparison, I recalculated Wizards' numbers by the formula MrMyth gave in the <a href="http://www.enworld.org/forum/4e-discussion/278847-how-much-treasure-going-lvl-11-lvl-12-a.html" target="_blank">how much treasure  </a>thread -- the first number in each pair is the treasure (2x the item cost) for that level, the second is the total earned by the party over the entire course of the game:720/720 994/1714 1371/3085 1892/4977 2610/75873600/11187 4968/16155 6854/23009 9456/32465 13047/4551218000/63512 24836/88348 34266/122614 47278/169892 65231/23512390000/325123 124176/449299 171329/620628 236388/857016 326151/1183167450000/1633167 620879/2254046 856645/3110691 1181938/4292629 1630755/59233842250000/8173384 3104392/11277776 4283222/15560998 5909688/21470686 8153772/29624458smooth total: 29624458720/720 1040/1760 1360/3120 1680/4800 2000/68003600/10400 5200/15600 6800/22400 8400/30800 10000/4080018000/58800 26000/84800 34000/118800 42000/160800 50000/21080090000/300800 130000/430800 170000/600800 210000/810800 250000/1060800450000/1510800 650000/2160800 850000/3010800 1050000/4060800 1250000/53108002250000/7560800 3250000/10810800 4250000/15060800 5250000/20310800 6250000/26560800wotc total: 26560800 Any thoughts?</blockquote>

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