The short end of the stick
To get the short end of the stick is to come off worst in a bargain or contest.
The expression 'the ... end of the stick' comes in many forms. The majority of these refer to getting the worse or, occasionally, the better part of a bargain. They inserted adjectives which indicate the bad outcome are 'short', 'crappy' or 'blunt' (or their synonyms or antonyms). There is also the phrase 'getting the wrong end of the stick', which has a different meaning, i.e. 'having the facts wrong' or simply 'being mistaken'.
Taking the occurrence of these in search engines as a guide, the four forms rank in popularity of current usage like this:
Both meanings of the phrase, i.e. bad bargain or wrong facts, originated with a negative connotation. The 'long end of the stick' and 'right end of the stick' were coined later as simple opposites of their respective original form.
The 'worst end of a bargain' form of the expression is quite an old phrase and, in keeping with its mediaeval origins, originally referred to a staff, rather than a stick; for example, the phrase occurs in Nicolas Udall's Apophthegmes, that is to saie, prompte saiynges, 1542:
As often as thei see theim selfes to haue the wurse ende of the staffe in their cause.
The jump from staff to stick was made explicit soon afterwards, when John Heywood published his notable reference work, The proverbs, epigrams, and miscellanies of John Heywood, 1562:
"The worst end of the staff", we now say "wrong end of the stick".
Heywood makes it eminently clear that, in the 16th century, 'the wrong end of the stick' meant the same as 'the worst end of the stick'. The meaning of that phrase didn't change, i.e. people didn't start getting the wrong end of the stick in the sense of 'being mistaken', until the mid 19th century. The earliest use that I can find of the phrase in that context is in the British political magazine The New Monthly Magazine, 1850:
"I am so stupid - I am so apt to take things up in a wrong light. In fact, I am always getting hold of the wrong end of the stick."
'The short end of the stick' is by far the most commonly used form of the phrase. That is rather odd, in that the ends of sticks can be dirty or pointy, they can even be iridescent or hirsute, but it is difficult to see how they can be short. This has spawned the suggestion that 'short' is simply a euphemism for 'shit' - after all sticks can be shitty and that form of the phrase is also commonplace.
The date of 'the shit end of the stick' makes this theory at least plausible, in that the phrase was known in that form by the mid 19th century, as in this example from The Swell's Night Guide, 1846:
Which of us had hold of the crappy (sh-ten) end of the stick?
I can find no examples of 'the short end of the stick' with the current figurative meaning that predate that example.
To take the case for the opposition to the 'short' equals 'shit' premise, it isn't difficult to find examples in print of people grasping 'the short end of the stick' that are clearly intended to be literal, i.e. a real stick was involved. What a short end of a stick is still unclear to me, but it seems that others, in the 19th century at least, knew what it meant. The jury is still out