The green bar is as I understand it actually compartment efficiency by default. Too little green your engines won't run, your gunners can barely hit the ocean, and so on. This can be a result of too few crewmen trying to run things, or anything that makes a crewman unable to do his job such as exhaustion or injury, which has the same effect as the crewman not being there thus lowering efficiency.
Boatswains and officers are better at their jobs as such add more to the bar than an equal number of sailors all else being equal, qualifications boost that effect even further.
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