Before today, the only sense of “round robin” that I was familiar with was “a competition in which each member plays each other” and some related senses. (This would be the OED’s 10a)
Wondering why “robin” got messed up in this, I looked it up in the OED. Turns out this expression has a number of different meanings.
Summarising from the OED:
I) A circular object
I1) A disparaging name for: the consecrated Host at the Eucharist.
I2) A type of small ruff
I3a) A rim or plate designed to prevent dirt from affecting the movement of a carriage axle
I3b) A loop of leather or rubber through which passes a pole, spring, or other part of a carriage and by which it is suspended
I4) A small pancake
II) A person, fish, or plant.
II5) Chiefly depreciative. Applied to a man (in various allusive uses)
II6a) A freshwater sunfish of eastern North America, either the pumpkinseed, Lepomis gibbosus, or the redbreast sunfish, L. auritus
II6b) Any of various marine fishes of the genus Decapterus (family Carangidae), characterized by a fusiform body almost circular in cross-section; esp. the round scad, D. punctatus, of Atlantic coastal waters, widely fished for food and as bait. Also called cigar-fish.
II6c)The anglerfish Lophius piscatorius
II7) Any of several hedgerow plants with pink flowers, esp. the red campion, Silene dioica.
III) Other uses.
III8) A document (esp. one embodying a complaint, remonstrance, or request) having the names of the signatories arranged in a circle so as to disguise the order in which they have signed.
III9a) A letter copied and sent to several recipients.
III9b) A letter, piece of writing, etc., sent around the members of a group, and added to by each recipient in turn.
III10a) A tournament in which every player or team competes once with each of the others
III10b) A group activity consisting of successive participation from each member of the group.
III11) A wager consisting of three selections in different events, which are combined in various ways to produce ten individual bets (three doubles and a treble, and three pairs of ‘up-and-down’ bets).
It’s not clear to me why round robin got such generous treatment.