[pph]

The estimate-confidence relation is not linear. In my experience it follows some kind of S-curve, with 0% confidence approaching impossibly short times and 100% approaching infinity (like a logistic function).

[trashtester]

I think software projects are best estimated as gamma distributions. To express that as confidence levels, you use the cumulative distribution function of the gamma, which are kind of S shaped, but stretched to the right.

https://en.wikipedia.org/wiki/Gamma_distribution

[trashtester]

For instance, if you have a task that you cannot imagine taking less than 50 days, the actual time can follow the following distribution:

https://www.wolframalpha.com/input?i=gamma+distribution+with...

And the confidence distribution would be:

https://www.wolframalpha.com/input?i=cumulative+gamma+distri...

[staunton]

The logistic function is bounded, so I'm not sure what you mean...

[trashtester]

Time spent is on the x-axis and confidence on the y axis. To reach 100% confidence, you have to supply an infinite estiamate.