I've seen lots of metrics to decide if an open source project is alive: age of bugs, number of pull requests open, number of commits in a time period.
When choosing libraries, I've realised I only look at the last commit time. That's sufficient activity IME.
miniblog.
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PYPL: PopularitY of Programming Language https://pypl.github.io/PYPL.html is a nice PL metrics tracker that's an alternative to TIOBE.
It has a clear methodology and it carefully chooses keywords to avoid e.g. Python metrics being affected by interest in snakes.
On the limits and perils of being data driven: https://twitchard.github.io/posts/2022-08-26-metrics-schmetrics.html
(Worthwhile improvements are often not amenable to A/B testing, and metrics can harm intrinsic motivation.)
I really value builds, lints and coverage metrics on pull requests. This still feels like an underexplored area though.
There's no Travis equivalent AFAIK for performance. I'd love to have automatic benchmarking on contributions.