Previous comments have been made about the nature of XP growth, and another noder observed that "your XP grows exponentially". Nobody has troubled to make an effort to quantify the nature of XP growth here on Everything2, a simple application of differential calculus.
For the purposes of this model, I make a number of reasonable assumptions. First, I assume a relatively constant rate of noding, as well as a generally similar level of node quality. These two functions both seem impractical to model with insufficient data, and treating quality and noding rate as constants rather than time-functions is convenient.
How does a node pick up XP? It seems that immediately upon a node's introduction, there is a fast potential to gain a large amount of XP, and the rate then slows to an extended slow trickle. We shall treat these two elements separately, to begin with.
Let us take the following as variables:
X(t) = total XP accumulated as a function of time
n(t) = total nodes accumulated as a function of time
N = average nodes authored per day
c = a measure of the "coolness" of the noder in question
k = an undetermined constant "fudging factor" relating to initial XP gain
t = time elapsed since a noder's first authoring attempts
We then have, obviously:
n(t) = Nt
The average node's initial fast gain of XP should be proportional to the noder's "coolness" and to some arbitrary constant k. Slow-gained XP should be a direct function of total node-time and coolness. Note that total node-time should be calculated from the average number of nodes a user has had, or n(t)/2. Hence,
X = nck + nct/2
Substituting to eliminate the time-dependent variable, we have:
X = Ntck + Nct2/2
The first derivative, or XP gain per day, will be:
dx/dt = Nck + Nct
The second derivative, although probably of less interest, will represent the speed with which daily XP gain increases, and will be given by:
d2x/dt2 = Nc
The observant reader will no doubt notice the similarity to the physical system of motion in one direction with constant acceleration, usually addressed early in physics classes.
Clearly, this analysis falls a good deal short of a quantitative analysis of actual XP gain numbers. I should like to see several users contribute a daily log of their node creation rate and total accumulated XP. Given this data, we could attempt to solve for the coolness of each user (a more accurate measure of noding prowess than the voting-influenced node-fu), and perhaps for the initial fudging factor. Stay tuned for updates.