# Back of the (virtual) envelope calculations (#1170)

Topics/tags: Overcommitment

My recent work on my triennial salary review got me thinking about numbers. What kinds of numbers? Mostly, two kinds of numbers that have relevance in the review, or at least in the context of the review: The number of majors per faculty member (or regular faculty member) in each department and the number of advisees per faculty member.

You’d think that these would be numbers that the College would make easily available. But when I’ve asked for them, or for related numbers, I’m often told that I can’t receive that information. And that’s even given that we released all of the advisee counts just a few years ago. I do expect to get the average number of advisees sometime soon. In contrast, the hardest number to get seems to be the number of regular faculty lines per department [1,2].

Why do I care? Because the faculty salary rubric indicates that advising an especially large number of students is one of the kinds of teaching the College values and because I’d like to better quantify the enrollment pressures on our department.

Since I don’t have the numbers, I’m going to have to approximate, to write what many folks call a back of the envelope calculation. But my envelope is electronic, rather than physical.

Let’s start with the number of majors in one class year per faculty member. While this appears to be the number of students in a class year divided by the number of faculty, many factors complicate this computation? For example, many faculty give up their advisees while they are on leave and some students declare multiple majors. In addition, I’m not sure that we have easy access to the number of faculty.

Our US News report says that we have an 8:1 student-to-faculty ratio. That suggests that there are about 2 students in each class year per faculty member. I think that’s per FTE faculty member, but not per regular FTE faculty member. I should pay attention to the number of regular faculty for advising, but perhaps not for majors per faculty member.

What factors do I need to consider for that computation. If I recall correctly, about 1/3 of Grinnell students declare two majors. That number has been rising significantly in recent years, so it may be higher. Let’s say 40% of students declare two majors [3]. That gives us 2.8 majors per faculty member. There are, of course, some complexities. For example, you might expect departments with a large number of service courses (e.g., Mathematics and Statistics) to have fewer majors per faculty member and departments with fewer service courses (I’m not sure what those are) to have more majors per faculty member. But it’s close enough. Our envelope only has so much space.

Now we’re ready to consider our first question. How is Grinnell CS doing in terms of majors per faculty member? About a decade ago, we had four tenure-line faculty members and 3/5 of another regular faculty member [4]. We only hired visitors when someone was on leave. We graduated 12–15 students per year. 2.8 * 4.6 is about 13. So we were at about the average staffing level per major.

This year, we have six tenure-line faculty members and two visitors (not leave replacements). Don’t worry; we’re on track to hire more tenure-line faculty. But we’re staffed at 8. 2.8 * 8 is somewhere between 22 and 23. We graduate sixty CS majors per year. We appear to have nearly triple the number of CS majors per faculty member as the College average. You’ve probably heard my concerns about that ratio already: It affects advising, research opportunities, class sizes, and more.

Speaking of advising, we should probably see what that looks like. We’re going to focus on major advising.

Grinnell has a relatively high percentage of regular faculty, so let’s say that 20% of the faculty in any one year are visitors. That suggests we have about 3.5 majors per class year per regular faculty member.

But faculty take leave, and many faculty give up their advisees when they are on leave [5]. Since sabbaticals are every seven years, about 1/7 of the faculty should be on leave. And yes, this is a rough calculation. It also doesn’t handle folks who are, say, in the Dean’s office. But I don’t think those folks are counted in the number of faculty. So this should be an okay calculation. We are now up to 4 major advisees per class year per faculty member. If we ignore the fraction of the year that a faculty member has three years of major advisees, most faculty members should have about 8 major advisees. Of course, it doesn’t cover the undeclared advisees that faculty have, most frequently from Tutorial.

Damn. It’s time to go back to the original numbers, without the major scale. 2 students per year per faculty member. 20% of faculty are visitors. That brings us to 2.5 students per year per regular faculty member. 1/7 of regular faculty are on leave.
Wow, that’s about 3 students per year per regular faculty member not on leave.

According to those computations, the average faculty member should have about 14 advisees. I recall being told that the average is closer to twelve. It appears my estimates are a bit off. Or maybe the number has changed. But it’s close enough.

There’s also some variation. Some faculty teach Tutorial often enough that it affects their numbers. Some faculty are in departments with higher major-to-faculty ratios. How much variation? I have no idea; it would be nice to have the standard kinds of data, not just the average, but also the standard deviation. Oh well. Perhaps I’ll get the data later.

In any case, it’s time for some more questions.

Was I advising an especially large average number of students during this four-year period? Let me check the data [6].

• Fall 2017: 57
• Spring 2018: 60
• Fall 2018: 46
• Spring 2019: 50
• Fall 2019: 15
• Spring 2020: 27
• Fall 2020: 31
• Spring 2021: 29

I tend to ignore spring data, since it potentially includes three years of majors and because students declare majors at different times [7].

But it’s an exceptional number of students, no matter how you count it, particularly since I had both a fellowship and a sabbatical during this time [8]. Maybe I’ll get extra credit [9].

What does this suggest for advising loads in the CS department? If we were a normal department, we’d just have the regular faculty serving as advisors. 120 majors across two class years, six regular faculty. That’s twenty majors per regular faculty member, significantly more than the average of eight. Next year, we’ll have two regular faculty members on leave. We’ll have one new regular faculty member, but people shouldn’t advise in their first semester. So 120 majors with four regular faculty. Thirty per returning regular faculty member. Nope, that’s not tenable.

Fortunately, one of the faculty on leave is keeping advisees [10]. And we have three extra people who are taking advisees. 120 majors with seven people is a bit better. 17 majors per person, only about twice the College average. Of course, it doesn’t quite work that way, since we’ll also have the dozen or so students from Tutorial to add to the mix. And I’m not sure how long the fallback options will be available. I hope the Dean’s office is making plans.

[1] A regular faculty member is either a tenure-line faculty member or a faculty member with expected contract renewals, such as members of the library and PE faculty or faculty designated as senior lecturers.

[2] I think they won’t give out that info because they don’t want us to know just how imbalanced things are

[3] A few students have three majors. The number of triple majors seems to be small enough that it’s noise in this incredibly rough calculation.

[4] Perhaps 2.5/5, since this person taught Introductory Linguistics every-other year. However, I’m going to leave it as 3/5 in my calculations.

[5] I’m not sure that I’ve ever given up advisees while on leave. I plan to take fewer advisees during my next leave, but I’ll still have some.

[6] I’ve been told that there are some issues with the data. I’m not sure what they are. The numbers seem about right to me.

[7] CS now requires almost all of its students to declare at the same time.

[8] Can you tell when?

[9] Insert smiley.

[10] Yeah, that’s me [11].

[11] Don’t worry Michelle! It will only be a dozen or so.

Version 1.0 of 2021-10-28.