The phrase "turn the scale" suggests a change in circumstances, most often in favor of one party or outcome. Some synonyms for this phrase include "tip the balance," "sway the outcome," "shift the advantage," and "tilt the scales." These expressions convey a sense of movement or change toward a particular result. Other phrases with similar connotations include "changing the tide," "altering the balance of power," and "shifting the odds." Overall, these expressions suggest an ability to influence a situation and achieve a desired outcome through strategic action or effort.