Did slang "hang" meaning "turn" as in "hang a left" relate at all to boxing slang?

Solution 1:

So far, the turning hang has plausible explanations without resorting to boxing jargon, though so far this is a partial answer.

Here is the directional use for hang, v., as reported in the Oxford English Dictionary, and first attested in 1967:

colloquial (originally and chiefly U.S.). to hang a left, to hang a right, etc. (also jocular with proper names having the appropriate initial letter, as Louie, Ralph, etc.): to go or turn in the specified direction, esp. while travelling in a motor vehicle or on skis. Cf. sense 11d below.

1967 Evening Standard 26 July 13/3 If you're in your pig [sc. car, in Detroit] and you ‘hang a Louie’, you've just turned left. If you ‘hang a Ralph’, it's a right turn, ‘hang a Sam’ is go straight and ‘hang a Ulysses’ means make a U-turn.

1975 L. Dills CB Slanguage Dict. 39 Hang a right (left), turn right or left.

Sense 11d refers to a horse veering to one side:

d. Of a horse: to veer towards one side.

1951 E. Rickman Come Racing with Me ii. 16 Sarda II ‘hanging’ towards Native Heath..who won by a short head.

And this, in turn, is grouped with hang as leaning or hanging to one side (forward, backward, or to the side):

a. To have the top bending or projecting beyond the lower part; to bend forward or downward; to lean over; (also) to incline steeply (see hanging adj. 2).

OE Beowulf 1363 Se mere..ofer þæm hongiað hrinde bearwas.

[over it hangs frost-covered groves, source for translation]

So, one explanation would be that hang a left or hang a right would relate to the leaning action a horserider, skier, or other mover might do as they turn. This seems plausible. For a vehicle with an axle, it's as dead a metaphor as turning on a smartphone.

Meanwhile, the meaning of a punch may come from this meaning (under "to hang on"):

6. to hang one on: to deal (someone) a blow.

1908 K. McGaffey Sorrows of Show Girl 200 Hauling off wifey hangs one on Alla's map.

1960 B. Crump Good Keen Man 44 I'd thought for a moment he was going to hang one on me. The idea..had got his goat all right.

Note, however, that the OED is limited on this point, and does not reflect the usages like hang a left jab you found. So my next steps will be to try to find a connection between hang as a blow and hang as a turn that isn't reflected in the OED.