Agile and scrum in managing (criminal) investigations

What outcomes are you hoping to achieve from agile practice? How would they differ from the outcomes being obtained now?

I can only give an opinion as I am not familiar with investigative work.

In general, I believe Scrum can be beneficial, if as a starting point one can construct a prioritized backlog with work (cases) or product items, and a self-managing team can pull items from this backlog. The two critical starting points, in my opinion, are a prioritized product backlog and a self-managing team. Once the above is in place, the Scrum framework—with its events and artifacts—can be implemented, allowing the process to evolve over time.

For Scrum to give value the items in the product backlog need to be prioritized, and the self-managing team takes responsibility for the backlog items they pull to work on as a team. 

Thank you so much for your replies Ian and Pierre. 

Ian- Outcomes: Increased overall throughput by spending less time on cases we end up closing (while still conducting a due diligence investigation). I see this as our biggest constraint. 

Pierre- I like what you said and how you said it. Yes! A prioritized backlog the self managing teams pull from. We have case reviews (sprint planning) every 4 weeks (sprint) with each agent concerning their caseloads (~18 cases). An investigator obviously can't work them all in a 4 week sprint. We prioritize the cases they need to work on on what needs to be done for each case. I am thinking I need or can design a simple tool to make those sprint backlog items more transparent. 

From what you describe there are no significant risks or uncertainties to mitigate on a Sprint by Sprint basis. Can you give examples of the kind of Sprint Goals that need to be addressed so innovation is then harnessed?