The expression keep your eye on the ball is reported by folks who live in Fremantle (Western Australia) to have originated with a local ceremony.
At 1 p.m. every day they fire a cannon as a time signal. Navigators on the ships, in the old days, used that signal to synchronize their clocks. When the cannon is fired a ball drops (just like in Times Square at New Years) above the cannon. If folks on the various ships wait untilthey hear the cannon that happens (because sound travels slower than light) a few seconds after the shot is fired and the ball begins to drop. No biggie you say? Well if a clock is a few seconds off on the return trip to Australia (coming East from Africa) that few seconds difference will make a big deference in the ship’s location. It could mean that the ship can be as much as 200 miles off-course and instead of sailing into Fremantle, they could wind up on the rocks in another area. Hence the advice to navigators to keep their eye on the ball and use the visual of the ball beginning to drop and not the sound of the cannon, as the time signal for synchronizing their clocks. So now you know.