Ever wonder why, in World War II, ships in convoys were safer than ships traveling on their own? Most people assume it was due to the protection afforded by military escort vessels, of which there was a limited supply (insufficient to protect ships traveling on their own).

Actually, most of the benefit came from the much lower overall detection rate. Understanding this requires examination of the probabilities involved. Consider a 40-ship convoy. It is somewhat easier to detect than a single ship, but, if its 40 ships were to sail alone, it is much more likely that at least one of them would be detected. True, in the event of an attack, the convoy sustains somewhat more damage, on average, than a single ship. But this factor is also far outweighed by the greatly reduced exposure resulting from taking just one trip (albeit at moderately enhanced risk), compared to 40.

For a discussion of the variables involved, including number of ships, convoy speed, submarine approach method and angle, radar, sonar and visual detection limits, ship smoking, submarine attack strategies, and number of escort ships), see http://www.ibiblio.org/hyperwar/USN/rep/ASW-51/ASW-10.html . It’s a fascinating and detailed window into the contribution of statistics and operations research to military strategy.