# Are Project Overruns a Statistical Artifact?

Anyone who built software for a while knows that estimating how long something is going to take is hard. It’s hard to come up with an unbiased estimate of how long something will take, when fundamentally the work in itself is about solving something. One pet theory I’ve had for a really long time, is that some of this is really just a statistical artifact.

Let’s say you estimate a project to take 1 week. Let’s say there are three equally likely outcomes: either it takes 1/2 week, or 1 week, or 2 weeks. The median outcome is actually the same as the estimate: 1 week, but the mean (aka average, aka expected value) is 7/6 = 1.17 weeks. The estimate is actually calibrated (unbiased) for the median (which is 1), but not for the the mean.

The full article is worth a read, both for its content and the elegant presentation. There are some useful insights, particularly that tasks with the greatest uncertainty rather than the greatest size are likely to dominate a project’s outcome. Interestingly, most lists of reasons for project failure neglect uncertainty just as they neglect dynamics.

However, I think the statistical explanation is only part of the story. There’s an important connection to project structure and dynamics.

First, if you accept that the distribution of task overruns is lognormal, you have to wonder where that heavy-tailed distribution is coming from in the first place. I think the answer is, positive feedbacks. Projects are chock full of reinforcing feedback, from rework cycles, Brooks’ Law, schedule pressure driving overtime leading to errors and burnout, site congestion and other effects. These amplify the right tail response to any disturbance.

Second, I think there’s some reason to think that the positive feedbacks operate primarily at a high level in projects. Schedule pressure, for example, doesn’t kick in when one little subtask goes wrong; it only becomes important when the whole project is off track. But if that’s the case, Bernhardsson’s heavy-tailed estimation errors will provide a continuous source of disturbances that stress the project, triggering the multitude of vicious cycles that lie in wait. In that case, a series of potentially modest misperceptions of uncertainty can be amplified by project structure into a catastrophic failure.

An interesting question is why people and organizations don’t simply adapt, adding a systematic fudge factor to estimates to account for overruns. Are large overruns to rare to perceive easily? Or do organizational pressures to set stretch goals and outcompete other projects favor naive optimism?

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