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.

I have done both percentages and points in my career, the latter being the most recent and preferred.

Percentages: The only advantage I can see is that, especially in high school, this seems to be the dominant way of grading, so students and teachers are accustomed to it. Disadvantages are that students can have a difficult time tracking their progress, or knowing, for example, how well they must do on a test to keep their grade above a certain percentage. In my experience, it also takes more time as a teacher - determining how many questions to put on a test or quiz so that percentages can be more easily calculated, for example.

As relates to programming specifically, I always struggled with the fact that I wanted programming exercises to count heavily but had a hard time making that happen with percentages. Students, parents, and administrators expect tests to be worth more than anything else, so if I gave tests the normal 40% weight, then that left programming exercises, quizzes, and classwork (study guides or worksheets) to split the remaining 60%, and I could just never get it "right", meaning feeling comfortable with the distribution.

Points: The major advantage of points the OP has already noted - students, parents, and teachers alike can instantly look at assignments and ascertain which assignments are worth more (I'm assuming all are using electronic gradebook of some kind), and students who want to remain at a minimum certain level find that easier to do.

Going to points solved the problem for me of knowing how much to weight each type of assignment - all assignments are weighted the same, and if I feel the assignment is worth more, I give it more points. So I can look at how many programming exercises I assign in one semester (depending on the course, 80 to 100), determine points for those (say 10 points each), and base the points for everything else on that total. If I determine a certain test is going to be worth 112 points because it has 56 questions, then the students see it as a large chunk, so they don't blow it off, but it is also not going to sink them if they fail it.

Rework: By extension, rework is made easier with a grading by points system. I've also found that "extra credit" makes much more sense for students in the points system, and they are more motivated to attempt it, because they can more readily see how the extra points are going to impact their grade.