If the time on the critical path is worth a lot of money and a support group is on the path, you should measure the group on response time, not efficiency.
Higher efficiency doesn't always lead to a fast response time because higher efficiency means not having waste, so the team doesn't have slack and operates at maximum capacity utilization.
If response times drive economics, you should align measurements and incentives for support groups to respond time. A straightforward way to move in this direction is to create a quality service agreement that spells out the response in time that users can expect from the department.
For example, in a development team, the developers are always on the critical path of projects. So you should measure how fast they respond to changes, not how many tasks they deliver in a week. This is the core of business agility.