So Ed sent an email which explained the math around calculating variance. That's useful, but probably overkill for our purposes but it's worth going over why.
In fact, what we are trying to do is well understood via "Standard Deviation." Everyone is familiar with Standard Deviation. In charts it looks like this:

If we take this bell curve and put the earliest date a task could possibly be completed as the point 3 standard deviations to the left and the longest a task could possibly take as the point 3 standard deviations to the right, we would have a risk assessment showing a range of likely completion dates for our task assuming it's risk follows a natural bell curve (as we'll see in a moment that the hump for most software tasks is to the right of center).
All things being equal, if you estimated a completion date for a task as right in the middle, you would have 50% chance of being right and a 34.1% to 84.1% chance of finishing within 1 standard deviation of the middle (median) date. How many days or hours is that? Well, that depends on the width of the graph which is found by estimating the earliest possible start date and putting it on the left of the graph and the longest possible completion date on the right. Then draw your bell curve between the two. Simple.
In fact, what we are trying to do is well understood via "Standard Deviation." Everyone is familiar with Standard Deviation. In charts it looks like this:
If we take this bell curve and put the earliest date a task could possibly be completed as the point 3 standard deviations to the left and the longest a task could possibly take as the point 3 standard deviations to the right, we would have a risk assessment showing a range of likely completion dates for our task assuming it's risk follows a natural bell curve (as we'll see in a moment that the hump for most software tasks is to the right of center).
All things being equal, if you estimated a completion date for a task as right in the middle, you would have 50% chance of being right and a 34.1% to 84.1% chance of finishing within 1 standard deviation of the middle (median) date. How many days or hours is that? Well, that depends on the width of the graph which is found by estimating the earliest possible start date and putting it on the left of the graph and the longest possible completion date on the right. Then draw your bell curve between the two. Simple.