What's your optimal GPA? 

 This may not be new to anybody but me, but recent  news  at UNC brought the so-called "Achievement Index" to my attention.  The Achievement Index is a way of calculating GPA that takes into account not only how well one performs in a class, but also how hard the class is relative to others in the institution.  It was first suggested by Valen Johnson, a professor of statistics at Duke University, in a paper in  Statistical Science  titled "An Alternative to Traditional GPA for Evaluating Student Performance." (The paper is available on  his website ; you can also find a more accessible  pdf  description here). 

 This seems like a great idea to me. The model, which is Bayesian, calculates "achievement index" scores for each student as latent variables that best explain the grade cutoffs for each class in the university.  As a result, it captures several phenomena: (a) if a class is hard and full of very good students, then a high grade is more indicative of ability (and a low grade less indicative of lack of ability); (b) if a class is easy and full of poor students, then a high grade doesn't mean much; (c) if a certain instructor always gives As then the grade isn't that meaningful -- though it's more meaningful if the only people who take the class in the first place are the extremely bright, hard-working students.   Your "achievement index" score thus reflects your actual grades as well as the difficulty level of the classes you have chosen. 

 Why isn't this a standard measure of student performance?  10 years ago it was proposed at Duke but failed to pass, and at UNC they are currently debating it -- but what about other universities?  The Achievement Index addresses multiple problems.  There would be less pressure toward grade inflation, for one thing.  For another, it would address the unfortunate tendency of students to avoid "hard" classes for fear of hurting their GPA. Students in hard majors or taking hard classes also wouldn't be penalized in university-wide, GPA-based awards.   


 One might argue that students shouldn't avoid hard classes simply because of their potential grade, and I tend to agree that they  shouldn't  -- it was a glorious moment in my own college career when I finally decided "to heck with it" and decided to take the classes that interested me, even if they seemed really hard.  But it's not necessarily irrational for a student to care about GPA, especially if important things -- many of which I didn't have to worry about -- hinge on it: things like scholarships or admission to medical school.  Similarly, instructors  shouldn't  inflate grades and create easy classes, but it is often strictly "rational" to do so: giving higher grades can often mean better evaluations and less stress due to students whinging for a higher grade, and easier classes are also easier to teach. Why not try to create a system where the rational thing to do within that system is also the one that's beneficial for the university and the student in the long run?  It seems like the only ones who benefit from the current system are the teachers who inflate their grades and teach "gimme" courses and the students who take those easy courses. The ones who pay are the teachers who really seek to challenge and  teach  their students, and the students who want to learn, who are intellectually curious and daring enough to take courses that challenge them.  Shouldn't the incentive structure be the opposite? 

 I found a  petition  against the Achievement Index online, and I'm not very persuaded by their arguments.   One problem they have is that it's not transparent how it works, which I could possibly see being a concern... but there are two kinds of transparency, and I think only one really matters.  If it's not transparent because it's biased or subjective, then that's bad; but if it's not transparent simply because it's complicated (as this is), but is in fact totally objective and is published how it works - then, well, it's much less problematic.  Sometimes complicated is better: and other things that matter a great deal for our academic success -- such as SATs and GREs -- aren't all that transparent either, and they are still very valuable.  The petition also argues that using the AI system will make students more competitive with each other, but I confess I don't understand this argument at all: how will it increase competition above and beyond the standard GPA?  

 Anyway, it might seem like I'm being fairly dogmatic about the greatness of the Achievement Index, but I don't intend to be.  I have no particular bone to pick, and I got interested in this issue originally mainly just because I wanted to understand the model.  It's simply that I don't really see any true disadvantages and I wonder what I'm missing.  Why don't more universities try to implement it?  Can anyone enlighten me?