Ann, if I can offer a couple of ways to determine how the number of officers are determined. The first review you need to do is department operations. By that, I mean unlike police departments, fire departments nearly always operate in group environments. Group dynamics suggest that because of the amount and kind of decision-making required on emergency scenes, someone within the group needs to be given the responsibility and authority to make decisions, i.e. the officer. So perspective #1 is, within department operations, how many staffed units could potentially be operating independently, either on separate incidents or separate functions within the same incident, and therefore requiring a supervisor?
In addition, as Jerrold said, the extent of the interaction between supervisor and subordinate generally dictates the officer:subordinate ratio. The more interaction required, the lower the ratio. Current emergency scene ICS protocols teach a maximum span of control of 5-7 however that does not mean that less than that does not require a supervisor, only that the span of control is the suggested maximum.
Second perspective is related to your platoon leaders who are most often initial emergency scene incident commanders on multi-unit incidents. Again, 5-7 is what is taught as maximum span of control. If an incident will have multiple units engaged in various aspects of an emergency scene, an overall incident commander is required. Taking this incident commander from first-line units tends to short-staff the operation and safety significantly.
Lastly, you can look also look at reducing the number of ranked officers and replacing them with "acting up" officers that rotate, volunteer, etc. however, the quality and efficiency of the operation and its leadership will never be as equal as with an individual who is formally assigned responsibility, authority, and accountability. And then of course, there are other non-emergency scene requirements for organizational leaders such as personnel development and functional responsibilities.
Hope this helps,
Chris Truty, MS
Deputy Fire Chief
Mount Prospect, IL