Heh, in support it would be kind of like metrics on numbers of tickets.

The first thing you game would be splitting any big work tickets in to smaller and smaller tickets. In some senses you should ensure any 'different' work on the same call is already split up, but typically you do this within reason.

After that you get into the bullshit number generating phase. Tickets for work not done (fraud imposed by unrealistic number requirements), tickets that have zero relevance or meaning (ticket stuffing). Tickets covering conversations or other things that shouldn't be a ticket.

You're not measuring what you actually want, you're measuring what you can measure, so people start producing what you can measure and not what you really want. Aka, Goodhart's Law.