I would think a conservative estimate for n is roughly (number of surface-to-air missiles ready to fire in the battle group) + (number of hits needed to sink a

I would think a conservative estimate for n is roughly (number of surface-to-air missiles ready to fire in the battle group) + (number of hits needed to sink a carrier) / (probability of hitting). I suspect the first term will dominate. If the battle group has one Gerald R. Ford class carrier, two Ticonderoga class cruisers, and three Arleigh Burke class destroyers, then it has up to 2 * 8 + 122 * 4 + 96 * 4 = 888 RIM-162 ESSM missiles and 2 * 21 = 42 RIM-116 RAM missiles, for 930 missiles total. The carrier also has Phalanx. Three guns, 1550 rounds each, maybe ~100 rounds per kill, effective range just under 1.5 km - a distance which a missile doing Mach 0.7 will cross in under seven seconds. My vague impression is that these can't be relied on to make much difference to the numbers. Maybe there are lasers and whatnot around now. Not enough to make a significant difference. Note that these numbers assume that the escorts' VLSs are loaded entirely with ESSM, and that all the carrier's weapons can be brought to bear on the incoming missiles, neither of which are realistic assumptions. But it's also assuming the carrier's air wing doesn't get to do any air defence, which is probably also not realistic. Anyway, given all those assumptions, 1000 missiles and you have a very strong chance of a kill. 2000 and the carrier is toast. If cruise missiles cost 1.5 million dollars each (roughly what Harpoon and Tomahawk cost, although what things cost in defence budgeting is a bit of a metaphysical question), the toast option is 3 billion in ammunition, plus there will be costs for launchers and various other sundries. The carrier alone is 10+ billion, so that looks like decent value.