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)
No. It comes from choosing somebody at random from a whole group. Get thin sticks (branches from any tree), cut them all around 10 cm and one of them cut it shorter (like 5 cm for example). Now hold the entire bunch of sticks in your hand, carefully to have them same height at visible end (hiding in your hand which one is the short one) and let everybody except yourself draw a stick at random. Whoever gets the short one is the one that would do the task at hand. If everybody draws all long sticks you're the one with the short one at the end. Hence the phrasing.
- 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)