What Does A Grade Mean? Informativeness and Strategic Manipulation of Grading Systems

When do university grades permit informative comparisons across courses, and how does transcript adjustment affect student and instructor incentives? A raw grade mixes student performance with course-specific conditions, so grade-only comparisons fail whenever course effects are large enough to reverse ability rankings at grade cutoffs. We show that full transcripts can recover comparable student signals through what we call eigengrades: course-adjusted reports that use common or externally anchored grading standards and enrollment overlap to identify centered student effects. In the scalar additive benchmark, row-mean, affinity-spectral, and graph-Laplacian methods recover the same object. Eigengrades are, therefore, not a separate source of identification; they are a representation of fixed-effect adjustment. The framework also clarifies limits: ordinary letter grades with unanchored course-specific cutoffs do not separate course difficulty from grading standards, and multidimensional transcripts identify a skill-match subspace rather than a unique universal ranking unless the institution specifies a benchmark. Finally, exact difficulty adjustment removes the direct report-mediated incentive to choose easier courses and eliminates a competitive enrollment channel behind grade inflation, while leaving other strategic and governance margins intact.