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<blockquote data-quote="Cheiromancer" data-source="post: 1517497" data-attributes="member: 141">Just a recap about my XP system: it's based on the idea that doubling the CR of a creature increases its EL by +4, and that increase corresponds to a quadrupling of XP awarded.&nbsp; That idea I lifted directly from the tables for Challenging Challenge Ratings and Encountering Encounter Levels.I wondered what kind of function had the property that doubling the input quadrupled the output.&nbsp; I realized that f(x)=ax^2 fit the bill.&nbsp; It turns out that the particular function we want is a=75, though a=90 or a=100 would also probably work.It's easy to verify that for f(x)=75x^2, f(2x)=4*f(x).&nbsp; Just plug in a few numbers.&nbsp; f(8)=4,800, and f(4)=1,200.&nbsp; In other words, f(8)=4*f(4).&nbsp; More generally,[code]If f(x) = ax^2, then&nbsp;&nbsp; f(2x)= a(2x)^2&nbsp; &nbsp; &nbsp; &nbsp; = a*2x*2x&nbsp; &nbsp; &nbsp; &nbsp; = 4ax*x&nbsp; &nbsp; &nbsp; &nbsp; = 4ax^2&nbsp; &nbsp; &nbsp; &nbsp; = 4f(x)[/code]A little creative rounding makes some nice looking tables.&nbsp; For CR of 2 or higher, round down to the nearest 100.[code]CR&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; XP1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 75 2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 3003&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 675 ===&gt; 6004&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1,2005&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1,875 =&gt; 1,800etc.[/code]A party of four 1st level characters needs 13.333 CR 2 encounters to get to 2nd level (because of the standard array they are CR 2, so a CR 1 encounter would be too easy).&nbsp; That's 13.3333 encounters worth 300 xp (before being divided 4 ways) or 1000 xp each.Four 2nd level PCs need 13.333 CR 3 encounters to get to 3rd level, which is 2,000 more xp each, for a total of 3,000 xp.&nbsp; So the first few levels are:[code]Level&nbsp; &nbsp; &nbsp; XP1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 02&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1,0003&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3,0004&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7,0005&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 13,000[/code]To extend the table, calculate 100*level^3, and round up to the nearest 1000.&nbsp; [code]Level&nbsp; &nbsp; &nbsp; XP2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 800 ====&gt; 1,0003&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2,700 ==&gt; 3,0004&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 6,400 ==&gt; 7,0005&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 12,500 =&gt; 13,0006&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 21,600 =&gt; 22,0007&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 34,300 =&gt; 35,0008&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 51,200 =&gt; 52,000etc.[/code]At higher levels the influence of rounding becomes less important.&nbsp; The difference in xp between levels becomes equal to 100*[(x+1)^3-(x^3)], or 100*(3x^2+3x+1).&nbsp; If x is small compared to x^2, you could treat this as 300*x^2.&nbsp; Four characters require a total of four times as much xp, so 1200*x^2 xp at level x.&nbsp; This is exactly 16 times the xp awarded for an encounter whose CR is equal to x.&nbsp; A little slower than the standard progression, but it is likely that characters will take on CRs high enough that 13 encounters will be enough for them to advance.To see this, note that a fair encounter for a character of level x tends to be higher than x+1.&nbsp; Better stats than the standard array, more equipment, or the fact that 1 character level = +1.15 CR (at least if the silver rule is ignored) all make the characters more capable.&nbsp; So a fair encounter will not be one whose CR is equal to x, but a little higher.&nbsp; Higher CR encounters mean more xp, which mean fewer encounters per level.&nbsp; The exact number is hard to estimate, but could easily fall in the desired 12 to 14 range.Since the standard treasure for a character is given by Upper Krust as being (level x level x level) x 100 gp, it turns out the treasure value of an encounter should be about equal to the xp value of that encounter.&nbsp; I regard that as being a nice coincidence.</blockquote>

[QUOTE="Cheiromancer, post: 1517497, member: 141"] Just a recap about my XP system: it's based on the idea that doubling the CR of a creature increases its EL by +4, and that increase corresponds to a quadrupling of XP awarded. That idea I lifted directly from the tables for Challenging Challenge Ratings and Encountering Encounter Levels. I wondered what kind of function had the property that doubling the input quadrupled the output. I realized that f(x)=ax^2 fit the bill. It turns out that the particular function we want is a=75, though a=90 or a=100 would also probably work. It's easy to verify that for f(x)=75x^2, f(2x)=4*f(x). Just plug in a few numbers. f(8)=4,800, and f(4)=1,200. In other words, f(8)=4*f(4). More generally, [code] If f(x) = ax^2, then f(2x)= a(2x)^2 = a*2x*2x = 4ax*x = 4ax^2 = 4f(x)[/code] A little creative rounding makes some nice looking tables. For CR of 2 or higher, round down to the nearest 100. [code] CR XP 1 75 2 300 3 675 ===> 600 4 1,200 5 1,875 => 1,800 etc.[/code] A party of four 1st level characters needs 13.333 CR 2 encounters to get to 2nd level (because of the standard array they are CR 2, so a CR 1 encounter would be too easy). That's 13.3333 encounters worth 300 xp (before being divided 4 ways) or 1000 xp each. Four 2nd level PCs need 13.333 CR 3 encounters to get to 3rd level, which is 2,000 more xp each, for a total of 3,000 xp. So the first few levels are: [code] Level XP 1 0 2 1,000 3 3,000 4 7,000 5 13,000[/code] To extend the table, calculate 100*level^3, and round up to the nearest 1000. [code] Level XP 2 800 ====> 1,000 3 2,700 ==> 3,000 4 6,400 ==> 7,000 5 12,500 => 13,000 6 21,600 => 22,000 7 34,300 => 35,000 8 51,200 => 52,000 etc.[/code] At higher levels the influence of rounding becomes less important. The difference in xp between levels becomes equal to 100*[(x+1)^3-(x^3)], or 100*(3x^2+3x+1). If x is small compared to x^2, you could treat this as 300*x^2. Four characters require a total of four times as much xp, so 1200*x^2 xp at level x. This is exactly 16 times the xp awarded for an encounter whose CR is equal to x. A little slower than the standard progression, but it is likely that characters will take on CRs high enough that 13 encounters will be enough for them to advance. To see this, note that a fair encounter for a character of level x tends to be higher than x+1. Better stats than the standard array, more equipment, or the fact that 1 character level = +1.15 CR (at least if the silver rule is ignored) all make the characters more capable. So a fair encounter will not be one whose CR is equal to x, but a little higher. Higher CR encounters mean more xp, which mean fewer encounters per level. The exact number is hard to estimate, but could easily fall in the desired 12 to 14 range. Since the standard treasure for a character is given by Upper Krust as being (level x level x level) x 100 gp, it turns out the treasure value of an encounter should be about equal to the xp value of that encounter. I regard that as being a nice coincidence. [/QUOTE]

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