The Zealous Equation

There is a bit more information that can be extracted from the completion graphs for the Blessed Exchange. The onset, the part of the graph before it reaches the linear regime, can be modelled too. It seems there at the onset, there is a certain number Nz of very zealous pilots, who want to accomplish the goal as soon as they can. Their number will decrease in time, since when they complete their contribution, they are done. 

Plotting their contribution over time on a long-linear scale reveals a line - which suggest and exponential time dependence. The number of contributions can then modeled as N(t) = Nz  [1−exp(−t/τ)], with τ being a typical completion time for a zealous pilot. Adding in the linear part, with a velocity of completion v, gives 

N(t) = Nz  [1−exp(−t/τ)] + v t

as a proposed fitting equation for the completion data. And indeed, it fits well! If we go back to our earlier example, the hacking in lowsec, then it gives this:

The blue dots are the data points observed, and the red graph is the result of the equation proposed above. From the fit we can read off a velocity of completion of 15 pilot contributions per day, and an amount of "lowsec-hacking zealous pilots" of around 190, with a time-to-zealous-completion of about 4 and a half days.

This can be used actually to estimate completion dates of unfinished goals perhaps slightly more accurately. 

The proof of the pudding is in the eating, so let us see how well the extrapolation works. Let us look at the newest Raspite mining challenge. It is clear that the curve's overall shape is quite similar to that of the lowsec hacking one, but the scales are different:

Here, we see that there velocity of completion is rather high, about 100 pilot contributions per day. There are more casual miners, but the number of zealous highsec miners is somewhat less than the hackers: around 130. Perhaps more people feel that it is not needing such a hurry. But those that did decide to go at it immediately, have a small time to zealous completion, merely half a day. 

The extrapolation predicts it will be 100% completed on September 16th, around noon (12:00). 

If this predictio works out, it will give a bit of confidence in this type of fit. Then, using it, there is a good deal of information to be gleaned about the most zealous pilots of other empires as well, their numbers per type of occupation (miner/explorer/soldier) and their efficiency.