I am also a manager of managers. I agree 100% that managers/leadership makes a big difference in performance.

But I don't see the difference being systems and metrics. I see it much more as interpersonal relationships, respect, and caring about the people that work for you. The manager's competence in the domain itself is also important.

Selecting the right person for the job is also vital, but you are specifically addressing different performance by the same team with a different manager.