There are numerous synonyms for the phrase "by great deal." These include "by far," "by a long shot," "by a landslide," "by an enormous margin," "by a considerable amount," "by a substantial degree," and "by a significant measure." All of these phrases express the idea of a significant difference or distance between two things. "By great deal" can be used to describe anything from a substantial lead in a race to a significant price difference between two products. The key is to use the synonym that best conveys the degree of difference or distance that you want to express.