The layered fleet defense against massed air attack

What fleet formation best protected ships from massed aircraft attack in World War II?

A dense layered formation: fighters outside, heavy and medium anti-aircraft fire inside them, close-range guns at the core, plus maneuver and smoke.

Fighters first break up an incoming attack beyond the fleet. Heavy anti-aircraft fire disrupts it further, medium guns engage aircraft that continue inward, and light weapons cover the final approach. Ship manoeuvres and smoke add to these defences. Making the layers effective requires enough cruisers, destroyers, and capital ships to supply a dense volume of fire. Treaty limits had restricted the number of ships Britain and the United States could build, leaving shortages when war began. Their peacetime exercises supplied a workable doctrinal starting point, but combat exposed refinements and force levels that exercises could not fully establish.