woodelf said:
I think you're using the wrong math. It looks to me like it's basically an exponential function, with some rounding to get "nice" numbers.
His "doubling the increase every four levels" example is basically a form of exponential function - at least closer to it than the actual chart. it seems like they have based the chart on an exponentuial function, rounded some numbers and tweaked it here and there so that they would reach certain numbers in certain places. I also think Hong is right in pointing out that there are bumps where you move from one tier to another.
Mathematically the bumpy chart means a few small things to players' progressions:
1. A normal monster is worth a tenth of what is needed for the next level (like a 11 level monster is worth 600 XP) but at level 20 a normal monster is worth 2800, not 3200 - making that level slightly longer (a 10th level monster is worth 500, not 550 following the same pattern).
2. As players do not only run into monsters of exactly their own levels, this can lead to weird costs for monsters outside their own levels if you yourself are close to a bump level, level 21-23 monsters give quite a bit more xp than level 18-20 for example.
3. On the other hand the players gain more at level 11 and 21 than at other levels, so hopefully the monsters are also balanced for that. (Meaning that the monsters also get a performance bump there compared to other level differences.) This will not happen when we tweak monsters with templates or the basic method, but that should not make a huge difference.
In other words, they certainly made the chart based on maths, but tweaked it so that certain level gains will be more important. This has the advantage of making it easier for a DM to set campaign climaxes at levels 10 and 20, which I am very pleased with myself. (It means one extra encounter needed on before reaching level 11, and one or two more before reaching level 21.) At certain points it might mean that certain monsters pay a little bit more or less in XP than they should, but that could possibly only matter if a DM did everything in their power to break the system.
As the formula seems to be changed in the epic level, I will make a second post exploring what that means to encounter maths.