What are the advantages and disadvantages of cumulative vs percentage grading?

There are many ways to grade students. One is to provide a fixed body of student work and then give a percentage grade for assignments, with the overall grade representing the percentage achieved of some ideal. 90% = A, etc. The student is expected to work on each assignment. This is Grading by Percentages.

Another way (Grading by Points, Cumulative Grading) is to provide a body of assignments with a point total assigned to each part, preferably with small granularity but totaling, say 1000 points. The grading is done cumulatively with, say, 900 or more points required for an A grade. The instructor evaluates each assignment and gives points based on quality, etc. perhaps giving 40 points on an assignment that is "worth" 50. Here the student can work until they have enough points to achieve a grade that is acceptable to them. After that, they no longer need to do anything and can focus on other courses or commitments. It is, of course, good to warn students who are intending to go on that learning is still required to meet their greater goals and not to be too complacent.

In either case, the instructor may permit re-work on assignments. If Grading by Points the rework earns additional points, but perhaps not up to the full marks for the work, but some positive increment.

The writer used Grading by Points in the latter part of his career. What advantages and disadvantages are there of each scheme. What improvements can you make to either or both of these?

For clarity, the real difference is that in Cumulative Grading, the rubric tells the student how many points are needed for each grade and they can choose to get them any way that they like, spread over the assignments, whose totals are also known. In percentage grading, especially with different things worth different "weights" it is (a bit) harder for the student to know where they are likely to wind up. They know their "average" perhaps, but every assignment affects the average. Therefore with Cumulative Grading, the student always increases their points, where with percentage grading, each assignment can get you closer or farther away from your goal.