Correct way to count incidents First Responded by a given Group?

Summary

Seeking best way to count incidents Initially responded to by an Agent Group

Content

Hi all - we pay our frontline Call Centre based on # Incidents where they sent an Initial Response, even though they may subsequently escalate the incidents to another agent group. To validate their invoicing , we want to run a monthly report checking their numbers.

I'm finding I get fairly different results depending on how I try to run this, and I'm hoping someone can help me find an obvious '"right" way to do this.   Here are the 3 ways I can see, each of which yields results that vary from one another: