# Taking the Fun Out of Puzzles & Games

## Thursday, October 19, 2017

### A summary of an idea from Goldratt's Critical Chain

When talking about task duration estimates, I'll define a "true" estimate as an estimate in which we have 50% confidence, that is, an estimate that has a 50% probability of being greater than or equal to the actual duration. Similarly, a "safe" estimate is an estimate in which we have 90% confidence.

People want to be seen as reliable, so they tend to give safe estimates. But their stakeholders tend to try to whittle down the estimate, so the person often has to fight for their estimate. Now they might look dumb if they finish much sooner than the estimate for which they just fought so hard. Even if the stakeholder is initially pleased when this happens, the person knows that, in the future, their estimates may be seen as inflated.

If you were to draw a graph of the likelihood of a task finishing at various points in time, it would commonly look something like this:

Here, the X axis represents time (say, in weeks), and the area under the curve from x1 to x2 is the probability that the task will take between x1 and x2 weeks to complete. Since there a chance that the task will take a long time, the curve has a long tail on the right-hand side (not shown completely in this graph) that drifts down to 0 very slowly. The area under the entire curve is 1, reflecting an unrealistic assumption that the task will definitely be completed at some point in time.

The area under the curve from 0 to 1 is about 0.5 (as you can see noting that the green area of the graph is slightly less than a 1 x 0.6 rectangle), so the probability that this task will take less than 1 week is about 50%. In other words, the 50th percentile time for this task is 1 week. The probability that it will take between 1 and 2 weeks is about 25%. The probability that it will take between 2 and 4 weeks is about 15%. And the probability that it will take longer than 4 weeks is about 10%. Adding these numbers up, we see that this task has a 50% chance of finishing in less than a week, a 75% chance of taking less than 2 weeks, and a 90% chance of taking less than 4 weeks.

So, an estimate with 90% confidencea safe estimatewill have to be many times longer than a true estimate.

For more on this topic, see Cutting Edge's excellent white paper on Managing Duration Uncertainty.