LonePaladin
Explorer
The experience chart (PH, p. 29) seems a little... odd. It took me some playing around with the numbers to figure out what was bothering my inner mathematician.
After 2nd level, the amount of experience you need to gain a level goes up by 250 points (i.e., you need +1,000 to reach level 2, +1,250 to reach level 3, etc.). After four levels of this, the 'additional' amount increases to 500. About the point you'd expect this to continue, it gets extremely erratic on levels 11 (+1,500) and 12 (+500), then reverts back to +1,000 at 13th and 14th. Levels 15-18 add +2,000 each, and 19-20 start at +4,000 -- this implies the amount added doubles every four levels.
Except that level 21 adds +8,000, and 22 adds +3,000. After that little bit of weirdness, it does +10,000 for four levels, and +25,000 for the last four.
Clearly, there was a pattern here, but it looks like they mangled it a bit halfway to make the numbers look pretty and end up with an even million at 30th level. Those changes result in some really weird differences, and though overall there is a gradual increase in XP costs (including a rather sharp rise at level 23), if you made a chart of the XP table it would have a noticeable dip at level 22.
Just to see how it would play out, I took the implied progression and smoothed it out. I also took the idea that the increase would actually double every 4 levels, instead of having the last eight levels jump up by an arbitrary amount. (Both of these have the end-result of lowering the XP needed to reach level 30; the former by about 30K, the latter by about 175K.)
Granted, this last step was largely unnecessary, since there won't be any advancement past 30th level, but I included it as a thought experiment. I'd considered reworking it to use the last three parts (4K-10K-25K), and have the increase go up by 2.5× each time, but the results were unreadable.
The first 10 levels are identical (they don't start doing weird things with it until 11th). From 11th to 20th level, the variant methods only vary from the RAW by 500 XP. At 21st level, though, the difference jumps up to 4,500 XP, and increases by another 3,000 each level. (With the doubling method, the difference goes up even more at 23rd level and beyond.)
Here's a rough chart of the results; the first column is from the RAW, the second removes the 'jagged' parts, and the third assumes a simple doubling every time. The numbers on the latter two look funny, but the progression itself is easier to predict.
After 2nd level, the amount of experience you need to gain a level goes up by 250 points (i.e., you need +1,000 to reach level 2, +1,250 to reach level 3, etc.). After four levels of this, the 'additional' amount increases to 500. About the point you'd expect this to continue, it gets extremely erratic on levels 11 (+1,500) and 12 (+500), then reverts back to +1,000 at 13th and 14th. Levels 15-18 add +2,000 each, and 19-20 start at +4,000 -- this implies the amount added doubles every four levels.
Except that level 21 adds +8,000, and 22 adds +3,000. After that little bit of weirdness, it does +10,000 for four levels, and +25,000 for the last four.
Clearly, there was a pattern here, but it looks like they mangled it a bit halfway to make the numbers look pretty and end up with an even million at 30th level. Those changes result in some really weird differences, and though overall there is a gradual increase in XP costs (including a rather sharp rise at level 23), if you made a chart of the XP table it would have a noticeable dip at level 22.
Just to see how it would play out, I took the implied progression and smoothed it out. I also took the idea that the increase would actually double every 4 levels, instead of having the last eight levels jump up by an arbitrary amount. (Both of these have the end-result of lowering the XP needed to reach level 30; the former by about 30K, the latter by about 175K.)
Granted, this last step was largely unnecessary, since there won't be any advancement past 30th level, but I included it as a thought experiment. I'd considered reworking it to use the last three parts (4K-10K-25K), and have the increase go up by 2.5× each time, but the results were unreadable.
The first 10 levels are identical (they don't start doing weird things with it until 11th). From 11th to 20th level, the variant methods only vary from the RAW by 500 XP. At 21st level, though, the difference jumps up to 4,500 XP, and increases by another 3,000 each level. (With the doubling method, the difference goes up even more at 23rd level and beyond.)
Here's a rough chart of the results; the first column is from the RAW, the second removes the 'jagged' parts, and the third assumes a simple doubling every time. The numbers on the latter two look funny, but the progression itself is easier to predict.
Code:
[B] RAW Smooth Doubler[/B]
1 0 0 0
2 1,000 1,000 1,000
3 2,250 2,250 2,250
4 3,750 3,750 3,750
5 5,500 5,500 5,500
6 7,500 7,500 7,500
7 10,000 10,000 10,000
8 13,000 13,000 13,000
9 16,500 16,500 16,500
10 20,500 20,500 20,500
11 26,000 25,500 25,500 <- 500 XP difference
12 32,000 31,500 31,500
13 39,000 38,500 38,500
14 47,000 46,500 46,500
15 57,000 56,500 56,500
16 69,000 68,500 68,500
17 83,000 82,500 82,500
18 99,000 98,500 98,500
19 119,000 118,500 118,500
20 143,000 142,500 142,500
21 175,000 170,500 170,500 <- 4,500 XP difference
22 210,000 202,500 202,500 <- 7,500 XP difference
23 255,000 244,500 242,500 <- 10,500/12,500
24 310,000 296,500 290,500 <- 13,500/19,500
25 375,000 358,500 346,500 <- 16,500/28,500
26 450,000 430,500 410,500 <- 19,500/39,500
27 550,000 527,500 490,500 <- 22,500/59,500
28 675,000 649,500 586,500 <- 25,500/88,500
29 825,000 796,500 698,500 <- 28,500/126,500
30 1,000,000 968,500 826,500 <- 31,500/176,500
