Average Emails Worked Per Hour

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We are looking for an OOTB or custom report that will show us the average emails worked per hour for each agent.  We need to see the average per hour by specific day, week or month.  We need these numbers to monitor our agents performance, as our agents are required to work an average of 10 to 12 emails an hour when they are not assigned to be available in Chat.  When the agent is assigned to Chat they are not required to work emails.  Have we overlooked an OOTB report or do we need to create one to do this?