The phrase "being in the running" implies competition, involvement, and a chance of winning. The antonyms for this phrase would be "not in the running," "out of the competition," "eliminated," or "disqualified." Other antonyms could include "uninvolved," "uninterested," or "not a contender." These phrases suggest a lack of engagement or interest in the competition. Furthermore, antonyms could be "inactive," "passive," or "not competing," which describes people or things that are not actively participating but rather standing on the sidelines. Using these terms in place of "being in the running" signifies a lack of engagement or investment in a competition.