While i have no exact numbers at hand right now, i can say that the overall effectiveness of this measure was quite low. There were some spectacular successes, especially when such boats first showed up in 1943. But a small submarine makes a bad and unstable firing platform, constantly rolling and stompin in any but the calmes sea states. To fight it out with one ore more bombers was in fact a desperate measure by by the german navy, as the uboats were more frequently caught on the surface by radar equipped planes with no time to crashdive to a safe depth. In absence of any "true" submarines, there was the choice of a) fighting back or/and b) install a snorkel. In the long run, the snorkel was FAR better for survival than mounting additional flaks, even if it severly limited the tactical and operational capabilities of that boats.
