[redcalx]

So basically, if there's a distribution of possible outcomes (with estimated duration plotted on the x-axis, and probability on the y-axis), then we put bounds on either side of the distribution and take a 'central' point on the x-axis between them. But instead of a simple average, we can use a log scale on the x-axis, so that we represent estimates of different magnitudes well. Now the simple half way point on the x-axis is on a log scale, and (I think) equivalent to the approach you described.

[infogulch]

The geometric mean being equivalent to the arithmetic mean of values transformed under a log scale is an interesting perspective that I haven't considered, but appears to be well known. https://en.wikipedia.org/wiki/Geometric_mean