The phenomenon of school grading is examined by the authors from the perspective of its attribution within internal education quality assessment systems (EQAS). The results of a survey of school principals and practicing experts on the significant characteristics of EQAS as generators and regulators of school grades are presented. The thesis of collective-distributed responsibility of teachers for the uniformity of approaches to grading, ensuring the objectivity and informativeness of grades, is put forward. Objectivity and informativeness, reinforced by the formative impact of grades on students’ academic success, are considered as the main units of effectiveness of school grades. The authors’ position on the influence of various components of EQAS on achieving this effectiveness is outlined. Special attention is paid to the assessment competencies of teachers regulated by their job responsibilities. Relevant positions in the list of job duties that potentially stimulate methodological efforts of teachers to change grading practices are proposed. The necessity and possibility of administrative interventions to develop corresponding competencies among teachers are noted.