March 24, 2018

How Much Information Do Princeton Grades Convey?

One of the standard arguments against grade inflation is that inflated grades convey less information about students’ performaces to employers, graduate schools, and the students themselves.

In light of the grade inflation debate at Princeton, I decided to apply information theory, a branch of computer science theory, to the question of how much information is conveyed by students’ course grades. I report the results in a four-page memo, in which I conclude that Princeton grades convey 11% less information than they did thirty years ago, and that imposing a 35% quota on A-level grades, as Princeton is proposing doing, would increase the information content of grades by 10% at most.

I’m trying to convince the Dean of the Faculty to distribute my memo to the faculty before the Monday vote on the proposed A quota.

Today’s Daily Princetonian ran a story, by Alyson Zureick, about my study.


  1. Am I missing something here? Apparently the action almost gets you back to where you were 30 years ago. Why is this bad? A 10% improvement in the information content of grading seems like a worthwhile result.

  2. Isn’t the real problem the fact that you can’t compare students from different ERAs? Is a B+ student from 10 years ago better or worse than a B+ student today? Okay, grades have inflated. Does that mean a B+ student yesterday is the same as an A- student today? Or does it mean that students have been getting better and a B+ student yesterday is actually the same as a B+ student today?

  3. Ruidh:

    It’s true that a 10% difference is enough to matter. But most people were under the impression that the difference was much bigger than that. A 10% reduction is not a crisis; and a 10% reduction in the information content of an individual course grade probably does very little to reduce the information content of a student’s GPA.


    It’s already unclear how to use grades to make comparisons between eras, because we don’t know how to relate the performance required to get an A today to that required to get an A in the past. To my knowledge, there’s neither an official doctrine nor a consensus about whether grades are supposed to be assigned on an absolute, time-invariant scale. (If there were such a consensus, it would force us to inflate grades if student performance got better, which it probably has done.

    Having said that, my guess is that people almost never use grades to compare students across eras. Once people are several years out of college, their career prospects depend mostly on what they have done since they graduated, rather than their grades in school.

  4. Sir,

    The “11% less information” number seems to have no context in my mind. Can you explain in more detail what it means?

    Also, do you have the ability to do the study further back in time? I would be curious to see the difference between 2004 and 1954 or 1964.

  5. In my opinion a university does the students a disservice by inflating grades. In effect, they lie to the students, by creating expectations of high rating without high achievement or high effort, and by creating artificially high self worth.

    Real life doesn’t inflate grades. When they get out of school and have to compete,

    To those who suggest that students today are performing better than students of 30 years ago, I would ask if they perceive that the students are working any harder.

  6. Anonymous says:

    “Real life doesn’t inflate grades. When they get out of school and have to compete”

    If you believe this, then you haven’t lived in the same “real world” that I do.

  7. I think the “real life” equivalent of grade inflation is title inflation

    “President of Assistance to the Associate Deputy Vice-President”, or some such.

  8. Todd Jonz says:

    I am somewhat amused to see that college administrators’ fervor for tinkering with the arbitrary metrics of academic achievement have not waned since my undergraduate days.

    When I entered Yale in 1970, we were awarded grades of Honors, High Pass, Pass and Fail. In theory, a Pass indicated that one had satisfactorily complete the course work at the level expected of a Yale student, and it was anticipated that the majority of students would receive a Pass for their work; a small number who did distinguished work would receive a High Pass, and a *very* small number who did “publication quality” work would receive a grade of Honors. An F was an F until a couple of years later, when the Fail grade was eliminated altogether; if a student failed a course, no record was made of the student having ever registered for the course. The thinking behind this decision was that it would encourage students to take more risks by taking more challenging classes rather than loading up on “guts” to bolster their number of high marks.

    It was a noble effort, since in an ideal world an academic grade should do nothing more than communicate to a student how close to excellence his or her work has been. But ours is not an ideal world, and it wasn’t long before a Pass became equated with a C on the traditional grading scale, a High Pass with a B, and an Honors with an A — or at least that was how the admissions officers at graduate schools were interpreting Yale grades for lack of any better conversion factor. Needless to say, the curve rapidly started to skew toward the top. And with the demise of the Fail grade, students at risk of receiving a grade of Pass would simply fail to show up for the final exam, ensuring that they would fail the course and have all traces of their having attended the class disappear altogether from their records.

    The NFL draft is this weekend, and “my” team, the 49ers, is in desparate need of a good wide receiver, having lost both of last season’s starters to free agency. Fortunately this year’s “entering class” is rich in receiving talent. Would it be useful if they left college with grades for their football skills? Would an A+ receiver from a NCAA Division I school compare with an A+ receiver from the Ivy League? When I left college and entered the job market, I was never asked about my college GPA. On the other hand, the mere fact that I had attended Yale served me very well.

    It seems to me that undergraduate grades might be considered useful to the graduates of top tier schools competing for admission to top tier graduate schools, but even in this they are of limited value. While low marks will surely get you eliminated at the first cut, the final cut will be made on a number of far more important criteria than one’s GPA. As has already been mentioned, one’s grades are really of little value after college. In the “real” world beyond academia, a Princeton degree will be equally valuable regardless of whether 35% or 50% or 70% of the grades awarded to Princeton students are As. Surely the Princeton administration and faculty have better things to occupy their very capable minds than making minor adjustments to the grading system.

    Now, on to more important matters: will the Tigers be graduating any good wide receivers this year?

  9. Ed, I think this is my favorite post of all time from you. It’s just so wonderful in so many ways. Regarding grades, my perspective is colored by my experience at a small liberal arts school in NY where they don’t issue grades.

    Impractical, yes, but classes were only around 10 in size, and students take three classes for a whole year. So two written evaluations per year were possible in a 10 unit class. We were encouraged not to think about ranking and grades, but rather to learn as much as possible. In fact, it’s the place that really taught me to learn how to learn for myself. That, and that fact that there aren’t tests but rather papers for everything (even my calculus class required a weekly 5 pager on theory and my views) meant students had to think, not to mention discuss in class.

    Anyway, I may or may not be better for that experience, but I do know that the freedom from grading/ranking caused me to spend my time on the reading and writing and issue analysis.

    Not sure how you would calculate the information value of my evaluations. One of them once said that I missed class too much (28 in a semester, but at the bottom of the form, there was a place to put in the number attended – which was 27 out of 28). Anyway, it was subjective in the end, though demphasizing of grades none-the-less. By emphasizing grades, grade inflation, grade information, Princeton might be missing the point of school.

    The point at my school was to understand more about the world, evaluate it, analyze and think, and return something original and contributory. I don’t think I really succeeded all that well at 18, but I tried. And for many years grades were totally unimportant, until starting at Berkeley, they suddenly took over again. Though I hope they don’t matter for graduate school so much. I have straight A’s now, but for one grade. But what does that mean? Nothing really. I still have to go out and make something constructive in the world. Literally no potential partner or employer has been interested. But I suppose if I applied for further academic study it would matter. But then, if it only matters for that, can’t Princeton take that into account on the backchannel?

  10. Blog Outsourcing

    Today, instead of blogging myself, I’ve decided to leave comments on other blogs. Some on grade information and inflation at Freedom to Tinker and some with Jeff Jarvis on representation of the public by the press. It’s just easier than…

  11. In reply to Tom J: Indeed, 11% is a lot of information. Below I post a simple explanation that we sent to the Daily Princetonian.

    I’m actually on the Princeton faculty. Today we voted to pass the proposal. Just to put my two cents into this forum, a big issue that has not received much attention is that internally we had a big problem: we lacked standardization between departments. In Humanities and Engineering about half the grades are A’s, while in Molecular Biology (where I am) it is 36%. I am hoping that this proposal will fix that.

    Loss of grades’ information content is not trivial

    Regarding ‘Felten analysis refutes grade inflation claims’ (April 23):

    Professor Felten’s analysis uses a quantity, information content, that is somewhat technical in nature. We want to point out that a 11 percent loss of information is, in fact, a lot.

    Imagine that we can assign eight grades — from A+ to F — and we use them all equally (not exactly true, but good enough for an example). If we do away with the F, we are down to seven steps (a 6 percent loss), and if we do away with C and F then we are down to six steps (a 14 percent loss). An 11 percent loss, as Prof. Felten has calculated, is intermediate between these cases.

    In other words, an 11 percent loss is, in a sense, like doing away with C’s and F’s. Brief contemplation leads to two conclusions:

    – This is indeed a significant loss of information.

    – It’s not so far from what has happened in real life.

    It’s always good to interpret quantitative analysis in terms of everyday experience. In this case, grade inflation amounts to asking instructors to remove from their grading vocabulary two words out of eight.

    Sam Wang and Michael Berry
    Assistant professors of molecular biology

  12. Princeton Faculty Passes Grade Quota

    Yesterday the Princeton faculty passed the proposed grade inflation resolution (discussed here), establishing a quota on A-level grades. From now on, no more than 35% of the course grades awarded by any department may be A-level grades, and no more tha…