Cost Center or Value Center?
In business, a cost center (e.g., IT, HR, Legal) is a team that does not directly generate revenue, regardless of how well it is perceived. Within that category, there can be teams that end up being seen as a low-value cost center. In this writing, I am intentionally conflating the two, and even push for the logic that a cost center team (from a business point of view) can be perceived as a profit center when it increases business efficiency.
My explanation is that this shift into negative happens when these teams' output does not meet the required business outcomes. For example, a software team could be constantly merging code but never ship anything useful or shipping too late: output is high, business outcomes are low. (Read this excellent paper for more details).
Any attempt on the team's part to disprove this negative perception with facts or hard numbers is doomed to fail unless it is about business outcomes. Depending on the organizational maturity, understanding how a team's output influences outcomes can be difficult and sometimes even outside of their control (in the example above, if the team requires another team to test and validate a release before shipping it). The good news is that in most cases the path to overcoming the issue goes through identifying the bottleneck and taking ownership of the constraint by absorbing or eliminating it.
The software team above is a classic example where removing the dependency on the test team improves the flow of the value stream (testing is the bottleneck → remove or absorb the dependency).
In other cases, the approach might be less well studied than in software development. Let's consider for an example an IT team. An IT team could use solved tickets and/or ticket queue length as a measure of their output. What about outcomes? Did the ticket(s) actually connect to a business outcome?
Again, the next step here would be to identify the bottleneck. For example, consider a new employee who starts their first day without a fully set-up laptop and account. Was the ticket that caused this delay held up by a manual process, an external approval, or the need for deeper cross-team cooperation? The next step is again the same as above: own the constraint by absorbing or removing it. For example, the manual process could be automated (in part or full), the approval request could be expedited by following up with reminders instead of "fire and forget," and deeper cooperation can be formed by starting a mini-project with a more suitable form of communication than tickets or emails.
Side note: a more interesting output metric would be the ratio of closed tickets to agents, which is a proxy for efficiency.