If you divide by the average score at the school, it assumes professors grade on an absolute scale that matches across universities, that a 4.0 is the same anyw

If you divide by the average score at the school, it assumes professors grade on an absolute scale that matches across universities, that a 4.0 is the same anywhere. Since this is not the case, then there already is built-in bias to the 4.0 at a certain school. At least if it is normalized to a C average, you'd know how a student stands compared to his classmates. You can then scale by the approximate academic rigor of the institution. If you don't remove the DC offset to the grade, then you would need to know both the individual's GPA along with the average GPA anyway to understand the number. This normalizing to a C average saves a step.