Disclaimer: this is for the mathematically inclined with a knack for symmetry, and it is not all that seriously meant (ok, a little bit ). But…
I have been lightly annoyed by the somewhat random increases in XP needed for levelling up. E.g. at level 22, you need 10 000 XP to get to level 23, but only 6 000 XP for level 24. And for level 30 you have to earn 20 000 to get to 31, while it is 10 000 for the levels on either side.
So I thought - what could be a “mathematically correct” formula for the XP increases? It turns out that 200 times level squared (200*XP^2 - and rounded to nearest 1000) pretty much resembles the current XP level curve without the random jumps. You would still hit level 50 at 500 000 XP and level 100 would then be at 2 million and 40 000 XP per level. You could keep going with the formula, but at some point it would be near impossible to level up, so it would probably make sense to go linear at some level (maybe introduce Dan’s for sub-levels above 100 - you should qualify for black belt by then .
The attached image shows the curves together - look at the smoothness of the blue curve