well-known expression

[detective]

Which well-known expression originated in the late 1920's during radio commentaries of football matches?

[halfadaily]

"back to square one". radio times listeners would have a plan printed in it with the areas of the pitch numbered so that they could follow the game. I'm assuming square one was the goalie.

[osprey]

Almost correct halfadaily. There are various suggestions as to the origin of this phrase, others bieing snakes and ladders where one would return down the snake to square one from near the end. As for the football expression you suggested, there was a rectangular grid printed in the Radio Times divided into 8 squares numbered 1 - 4 along the top and 2 - 8 along the bottom from left to right with 1 being in the top left corner.

[lankeela]

He's scored?

[Quizmonster]

The Oxford English Dictionary (TOED) states that the football-pitch story (quote) "cannot be upheld with any certainty" and seems to favour the board-game possibility.
However, this was one of the phrases featured in the recent Victoria Coren TV series 'Balderdash & Piffle' which tried to establish earlier uses of phrases than the one recorded in TOED. The dictionary's earliest reference comes from 1960, but I cannot for the life of me remember whether this was one of the examples for which an earlier provenance was discovered.
Whatever...it's far from certain that 'Back to square one' is an accurate answer to your question, Detective.