A must. It's an indicator of the company growth. Once it grows accordingly, please refer to the coverage and peak hours/days/months.
Avg. Reply Time, Avg. First Reply Time, Avg. Handle Time
A healthy Avg. First Reply Time: live chat - 1-2 min, email - up to 12-24h
(Avg. Handle Time, responses/ticket)
How many steps does it normally take to solve issues? "Pen-friends" is not the name of the game, even with the non-typical issues. To make this number smart, you'll need to make sure the conversations are getting closed properly. In the case you decide pay per reply, you'll be also able to check if a freelancer/a company is farming replies you pay for.
Some ticketing systems provide this metrics, some do not. Even in the case you are dealing with the live chat replies, you can find out the average replies/conversation index by dividing the number of replies by the number of conversations.
If your customers are really happy, they will generate more customers. You need to find out if they are happy. And why. The options:
1) You can ask them. Using emails, surveys, popups, calls and channels you can find floating around the Internet. Your team can do it, or an agency can do it for you.y
2) Satisfaction score - if your customer can tag each conversation with "+" or "-" depending on his final impression and mood, you'll get the metrics and the general idea quite soon. The team can also do it before closing the chat.
3) Wow stories - a detailed reply from your customer expressing his gratitude and astonishment by your customer care. As they say, "it was so good they couldn't stop talking about it".