The question is whether you get wetter by walking or running a given distance through rain that is falling at a constant rate. An early appearance of this problem was in Bagley's Paradox Pie (1944). A simple answer is that moving faster is better. If the rain falls vertically and the density of water in the air is assumed constant, then, no matter what your speed, you'll sweep out the same volume and will always get the same amount of water hitting your front. However, running rather than walking will reduce the amount of water landing on your head.