From Max Cryer’s CURIOUS English words and phrases – the truth behind the expressions we use:
(Out for a) duck
Cricket usually has a visual scoreboard and if a player leaves the field having made no runs, a great big zero stands next to his or her name on the scoreboard. A practice arose many years ago of referring to this zero – because of its shape- as a duck’s egg, and this was shortened to just a duck. So if he or she was out for a duck, it means there was no score.