Submarine strategy and diminishing returns

Would increasing the number of deployed submarines have produced a proportional increase in merchant shipping losses?

Probably not; boats had to be available in the right places, while convoys, traffic analysis, intelligence, target speed, and theater-specific tactics all create diminishing returns.

Submarine effectiveness depended on operational position, intelligence, and target selection. Early kill rates benefited from ships still sailing independently, while very fast liners could outrun a submarine unless caught in a favorable ambush position. British Enigma work and traffic analysis, together with the time needed to organize convoy compliance, make simple boat-count projections unreliable. American, British, Dutch, Italian, and Japanese submarine campaigns offer comparisons, but their different weapons, tactics, and convoy systems prevent a clean one-for-one model.