> I want to quantify my reasons for automation
The best reason for automation is cost reduction. This is your ultimate metric.
Calculate how much time your automation + execution takes, and how much time execution without automation takes. The difference is your reason. If you can show how automation provides cumulative settings over time, you'll get a management buy in without problems.
I would expect automation and execution effort to be higher than normal work in the beginning, and decreasing over time first to the zero balance, and then to the savings.
And yes,
> So i decided to come up with a set of metrics.
If you cannot make sense of metrics, ditch them.