I want to track each agent's productivity and see if they are accepting chats assigned to them. Is it possible to track chats that agents did not accept?
Yes, the acceptance metric is a good way to measure the agent's acceptance rate. Accepted chats are the number of chats that the agent accepted from the system assigned chats. If the agent doesn’t accept chat that is assigned through the assigned routing option, then the acceptance rate decreases.
The acceptance rate of your agents can be viewed through your Analytics in the Chat dashboard. Go to Analytics > Agent reports > Activity breakdown. For more information about the Chat Analytics, see the article: Monitoring chat activity with Analytics.
With the Chat dataset in Zendesk Explore, you can also create a custom query with the % Assignment acceptance metric.