Metrics for measuring impact of investment in an open source project?

For any organizations that fund open source software (either out of their core budget, or as part of grant funding that you apply for), do you have metrics that use to demonstrate the impact of the investment? There are some sorta standard analytics: users, website hits, time spent on a page, form submissions, total projects created. But many of these don't really get at describing change or measuring impact? Do you have any clever ideas for how to measure and show that an investment in functionality improvements to open source software is making your work better, faster, stronger?

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Financial savings = (staff time saved through replacing paper with an ODK workflow) * (staff salary) * number of workflows (e.g. an ODK form for turtle strandings).
E.g. 500 turtle strandings reported through ODK saves us AUD 100k in staff salary and provides near real-time data. Non-tangible benefits are richer data (photos) and more reliable (metadata timestamp, one button Geolocation instead of hand-written place names).

I've used page hits on certain chapters in the documentation as a proxy for a colleague getting self help instead of asking me per email. That's me typing the answer once (for the docs) instead of over and over again in emails (related salary cost). So at a stretch, (docs page hits) * (salary cost for me to write a polite 20 min email) is a metric for savings through documentation.

Non measurable impacts are if management decisions can be made in real time (based on data from ODK forms) instead of at the end of a season (when the paper datasheets get digitised and sent in), e.g. reacting to predation from feral foxes on a certain turtle nesting beach while there are still unpredated turtle nests left (all my examples are turtle-flavoured unfortunately).

Other impacts that have savings outside of my insight are if I post a tutorial or maintain ruODK, which hopefully saves others some time. If anyone were to add new features to ODK Build, I suspect the Build users could also save themselves a few manual editing steps.