Americans knew where, when, and in what strength the Japanese would arrive at Midway. Nimitz knew that the Japanese had ruined their advantage in number of ships by dividing their ships into four groups, all too separated to be able to support each other. Nimitz calculated that the aircraft on his three carriers, plus those on Midway Island, gave the U.S. rough parity with Yamamoto's four carriers, mainly because American carrier air groups were larger than Japanese ones. The Japanese, by contrast, remained almost totally unaware of their opponent's true strength and dispositions even after the battle began.