This is a (modern, mistaken) conjoining of two similar phrases - drawing the short stick (where you hold five sticks / matches, in your hand one of which is cu

This is a (modern, mistaken) conjoining of two similar phrases - drawing the short stick (where you hold five sticks / matches, in your hand one of which is cut short but no one can tell cos they are held in someone's hand) - Grabbing the shitty end of the stick. Which seems fairly obvious if a stick was used for any clearing out style work. (there seems to be no obvious "short end" of a stick)