It depends upon what the score represents.
A typical goal of standardized testing is to rank the test-takers on a percentile scale. This permits comparisons of different groups of people; for example, students at two different schools.
If we were to administer an algebra test to 100,000 eighth-graders, and the goal was to determine how well the concepts had been learned, we would not want to make the test so easy that a significant percentage make a perfect score. It might be reasonable to design the test so that only twenty-percent would correctly answer more than half the questions.
If a sample population showed eighty-percent scoring only 40% correct answers, then the test should be made easier. If eighty-percent scored 60%, then the test should be made more difficult. By making such adjustments, the test scores would form a distribution without too large a percentage of students either getting all questions right or all questions wrong.
Assuming that the sample population was sufficiently representative of the target population, then the test could be administered to the 100,000 students with the expectation that eighty-percent of the total will score below 50%.
A school whose students had an average score of 50% on this test could be given a "score" of "80", representing the fact that the average student scored at the 80th percentile; that is, higher than eighty percent of all students taking that test.
The problem with such a test is that it cannot be used to determine whether the average student, or even the most advanced student, has "learned algebra". Only a test designed to demonstrate some minimum level of proficiency can do that. My point is that "proficiency" testing is one thing and "qualification" testing is quite another thing.
The article tells us that the New York school system is quite confused about its testing. It doesn't tell us anything about whether the students are learning what they need to be taught. But my guess is that they are not now nor have they ever been taught what they need to know.
You're absolutely right, and I know it quite well; I spent 13 years in NYC public education - 5 in high school to boot.
I can only speak for Georgia - where the test represent nothing more than the standards in the curriculum.
One year, a 51 scales to 82 while the next year a 36 scales to an 82 while the next year a 77 scales to an 82.
FWIW the state will not release its formula for scaling.