The worst example I have seen is incentivized story points. Bad news: you just ruined your estimation process.
Managers end up trying to put in counter measures and the whole thing becomes a convoluted mess.
Personally, I think PR are a decent metric, but you need an engineering manager to review (and understand) the work that the team is doing (and the team dynamics—who’s doing what).
Basically, the only way to really understand productivity is to be close to the team. This takes time, and it requires hiring the right manager, so a lot of companies opt for off the shelf solutions (Pluralsight, Jellyfish, etc).
Not saying this is good or bad, it’s just what I have observed.