You use the singular if the score is based on one outcome. You use the plural if the score is based on more than one outcome.
For example, if you take an exam, a friend might ask about your result. But if that exam has more than one part, and each part has a different score (such as the IELTS exam, which has a reading, writing, and listening score), a friend might ask about your results, because they might want to know the result of each section.