I am trying to be more open minded about your work but I can't understand how developer productivity could be measured with any of these metrics. I'm not aware of any prior work or research that shows that either. Writing software is a complex task and quantising it in this way seems reductive and problematic.
I would welcome being wrong about this. What am I missing?
We've found that evaluating individuals, stack ranking teams, and measuring an individual's 'productivity' to be an ultimately futile effort.
It's more important to focus on team delivery as described in many research studies. My favorite being the book Accelerate by nicole forsgren. If you haven't, I do encourage you to check it out!
As the founder of Haystack I can be seen as biased so its probably more helpful to checkout their research across thousands of teams on what makes an 'elite engineering team' and how elite engineering teams ultimately help drive successful organizations across profitability, market share, and customer satisfaction :)