The story
First attested in the 1960s in the context of aviation, in reference to ball-shaped grips on an aircraft's engine controls (typically throttle, prop pitch and fuel mixture). Pushing these "balls to the wall" would put the aircraft at maximum thrust. Analogous to pedal to the metal. Not related to the term balls-out, which refers to a ball governor on a steam engine. Neither balls-out nor balls to the wall is connected with the vulgar sense of balls (“testicles”) except via folk etymology.
First known use, by meaning
- since the 1960s Full throttle; (at) maximum speed.
Etymology from Wiktionary, CC BY-SA 4.0.