That's kind of a weird question to ask because it's like asking what the average amout of officers per shift is. The answer really varies from agency to agency. It depends on the type of case, caseload, how many detectives on the department, how big the agency is. Some departments don't even have full time detectives.
When in doubt, just bullsh*t. What is the average number of detectives assigned to ask you to do their research for them? ;)
"We enjoy freedom and the rule of law on which it depends, not because we deserve it, but because others before us put their lives on the line to defend it."
- Thomas Sowell