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I spend probably a pretty unusual amount of time estimating things for fun, and have come to use more or less this exact process on my own over time from doing it.

One thing I've observed, but haven't truly tested, is my geometric means seem to be much more effective when I'm willing to put a more tight guess on them. I started off bounding them with what I thought the answer conceivably could be, which seemed objective and often felt easier to estimate. The problem was that often either the lower or upper bound was too arbitrary relative to it's weight on my final estimate. Say, average times an average 15 year old sends an mms photo in a week. My upper bound may be 100ish but my lower bound could be 2 almost as easily as it could be 5 which ranges my final estimate quite a bit, between 14 and 22.