Those are two different concepts hiding in similar words. You can't [numerically or precisely] measure productivity, but some engineers are vastly more productive [such that you can easily tell the difference without a formal measurement].
Gut feeling uses all your internal predispositions and biases.
you don't need to rely on gut feeling and risk bias. You can stop looking for the "productivity metric" and instead bet on <some> measure, then track the change over time. It's the only thing that's ever worked for me.
Sure, but which measure you pick is itself a gut feeling and biased. It's the easy way to miss people doing whatever sort of work that you aren't measuring that may be what's letting everyone else excel at what you are measuring.