The last time I wrote about the curvature of project estimations, I was just speculating. Since then, I've discovered that FogBugz does track estimation over time, with a daily estimation record, and offers a graph of the 0, 50, and 100 percent estimates over time. I've been watching this develop for a small time, working more with tracked estimates, and I think some expansion on my thoughts is ready.
You can see my own estimation graph here and it demonstrates exactly what I predicted. I suspect a more complex plotting of points would emerge with the length of the project, but I have a few curiosities about how this would expand over time. The basic prediction of a generally unchanging estimation from the start, an increase in the estimation's growth in the middle, and ending with a calming and final flattening on the systems best guesses, as you slow down how many cases you file for every case that you close.
Steep hills in the estimation happen because for every case you close, you file some bugs, related features, and other cases that were brought to light or just gotten around to filing at that time. You can break down the states of case closure versus creation into three.
When you complete work in line with estimates, then things are On Track. This is misleading, but a good state at any rate. If you have ten hours worth of cases, spend 4 hours, and close about 4 hours worth of estimated cases, the target times on the project remain steady. If you keep this up until all the cases are closed and the project is finished, you can consider your estimations successful. Of course, it is more complicated.
As the design and plans are fleshed out, you'll find developers file more bugs than they close. The estimation is pushed further and further back. This isn't because the project gets more complicated or behind, although it could be so, but that the bulk of the estimation cases needed to represent the entire work of the project hasn't been filed yet. If we could design the entire thing up front, enter the cases, and never change them, we could keep a static estimation, if we remained On Track. We know that we can not and should not design everything up front, so we need to understand and work with changing estimations.
I'm going to make a second prediction about the estimation curve. I predict the curve presents itself in many steps. There are likely to be spurts of case filing and periods of working steadily on those that exist. The developers may have these steps in overlap. Taking some steps back, the steps will smooth into a larger, similar curve for the entire project. Each of these filing spurts will be the start, work, and wrapping up of some component inside the greater breadth of the project.