So, there is no objective way to measure performance of a manager ? It sounds similar to measuring the productivity of developer.

Measuring scope to evaluate performance is like saying developer who works on most number of tickets/bugs is the highest performer.

We know that's not true and we also know how it can and will be fudged(w.r.t managers its increasing un-necessary headcount).

If we are able to come up with a solution for developers it shouldn't be too difficult for managers too.