Grading Scales and Regression Lines

I make hard tests and quizzes. Because of this, I usually incorporate a scale of some form. The simplest one to use is a square root scale: take the square root of the number of points that the student earned and divide by the square root of the total points. While definitely helping scores, this gives a much more generous scale to students who do very poorly while giving almost no scale to those who do well. My tests are hard, but I don't like the amount of increase it gives to students who fair poorly on my tests.

Because of that, I started establishing cutoffs for the different letter grades. I would enter these into the lists in my calculator and create a cubic or quadratic regression line through the points. Although this helped normalize what was happening for those who were passing the exam, it again gave very large scales for those who were only getting a couple of questions right.

Last test, I used a logarthmic scale with my cutoffs and I am much happier with the results. This places the high scoring students closer together in final grades while lower scoring students are not getting as much of a cushion. I'll have to test this out on a few more assessments to see if I like this scale more, but right now I think it'll give my students who have been coasting the incentive to work a little harder.