A lot of results of operations research are counter-intuitive, with the benefits of unescorted convoys vs ships sailing alone being one of them. Fastmongrel has one part of the equation; here's the other bit.
Say a single ship can be spotted because of smoke at 20 nautical miles, and a convoy of 100 ships can be spotted at twice the distance. Say the sea routes between North America and Britain have a total area of 2,000,000 square miles. The convoy can be spotted in an area of about 500 square miles; the single ships each in an area of 125 square miles. However, the 100 ships have a total area where they can be spotted of 12,500 square miles: 25 times greater. Or let's say that each ship has a 0.001 chance of being spotted (1 chance out of a thousand) and the convoy has a 0.01 chance of being spotted. Assuming each ship/submarine encounter is independent, that means that the probability of no ship getting spotted is roughly (1-0.001)^100 or about 90%, i.e., there's a 10% chance of at least one ship being spotted, vs 1% chance for any of the ships of the convoy to be spotted.
Similar non-intuitive results are that landplanes are better for MPA than seaplanes and that the number of casualties is increased by heavy defensive armament in bombers.