Why software projects take longer than you think – a statistical model

This has the property that the median of the distribution is exactly one week, but the mean is much larger:

If we take the logarithm of the blowup factor, we end up with a plain old normal distribution centered around 0. Let’s do a quick scatter plot of estimated vs actual time to completion:

The median “blowup factor” (actual time divided by estimated time) turns out to be exactly 1x for this dataset, whereas the mean blowup factor is 1.81x. Again, this confirms the hunch that developers estimate the median well, but the mean ends up being much higher. The parameters of the t-distribution also define the inverse Gamma distribution of the σ values:

Note that values like are incredibly unlikely, but when they happen, they cause a mean blowup of several thousand times.

Source: erikbern.com