*A significant number of USC students do not enter as freshmen in the fall. The university offers alternative enrollment options to inflate incoming freshmen statistics and make their student-body appear higher-quality than it actually* is.

Something about USC doesn’t add up.

Every fall approximately 3,200 wide-eyed freshmen matriculate. They were admitted from a pool of more than 60,000 applicants and are among the best of what high schools in the 21st-century have to offer. In 2019, the middle 50% range of their SAT scores was 1360-1530. The same stat for GPAs was 3.72 – 3.99. Roughly 20% of enrollees have rèsumès good enough to warrant merit scholarships.

This is impressive. For most of its history, USC was academically underpowered. It was better known for its football team and fraternities than serious study until the university launched a status-raising campaign in the 2000s. Now, some of the brightest high-schoolers in the country become Trojans.

But look closer. For the 2019-2020 academic year, USC claims to have around 20,500 undergraduates enrolled. If approximately 3,200 freshmen enroll every year, and that has been the case for the last 4 years, then USC should only have 3,200 * 4 = 12,800 students. In fact, if you sum the actual number of freshmen that USC reports matriculated in fall 2016, 2017, 2018, and 2019, you only get 3,068 + 3,358 + 3,401 + 3,168 = 12,995 students.

Where is everybody? If we grant that the 20,500 figure is correct, then there are roughly 7,000 students at USC who are unaccounted for on this naive model. In other words, it’s not obvious how almost 35% of the student body got into USC, or how they compare academically to their peers.

In the next section, I want to establish that the freshmen/total enrollment discrepancy at USC is real and significant compared to similar institutions. Afterward, we will discuss possible explanations for the gap.

1. The discrepancy

1.1 Methodology

The guiding thought is we should be able to get reasonably close to a university’s reported undergraduate population by counting all the students they say enroll. For instance, if a university says they enroll 250 freshmen each year, we might expect their total number of undergrads to be around 1,000. Students should graduate in 4 years, so the only people on campus should be those who enrolled 1, 2, 3, or 4 years ago.

If only college was that simple. There are good reasons why the simple calculation I just described will be inaccurate. Not everybody finishes their degree in 4 years, so students who enrolled 5 or 6 years ago might still be on campus. Matriculating class sizes might vary dramatically over that period as well. Adding a couple of numbers together also can’t account for people like dropouts and transfers who might affect the size of a student body.

We can account for all of these concerns. Many universities (including USC) publish their matriculating class sizes on their websites, either part of the Common Data Set or other statistics they distribute. The same schools also frequently publish the number of transfers they receive. As a result, we can get an exact sense of student inflow over the past 4 years.

We can also roughly approximate the number of students who take more than 4 years to graduate. Universities publish 6 and 4 year graduation rates as part of the Student Right-to-Know Act. From these figures, we can estimate the number of students in a freshmen cohort who graduate on time. We assume the rest of the students in the cohort graduate in 5 or 6 years, getting an idea of how many people who enrolled more than 4 years ago contribute to the student population.

(I acknowledge this is an overcount since some students who don’t graduate in 4 years drop out. Yet, note that overcounts are in USC’s favor. Our naive calculations show there are 7,000 missing students, so any fudgery that accounts for more undergrads helps them).

Handling dropouts who enrolled in the past 4 years is tricky but doable. Universities don’t publish the exact number of students who drop out and when, so making any kind of exact calculation is difficult. For instance, a freshman enrolling in 2015 might count towards undergrad enrollment in 2015, 2016, and 2017, but then drop out. If we knew what percent of a freshmen cohort dropped out every year, we could just “thin” their class accordingly and be done with it.

Our strategy is to perform two sets of calculations. The first assumes everybody that enrolls eventually finishes their degree. This is a “best-case scenario” and will give us an upper bound on the student body. Imagine the student who enrolls in 2015 but drops out in 2017. If we’re trying to calculate undergraduate population in 2018 under the assumption of no dropouts, she’s going to be counted even though she’s no longer enrolled. As a result, if we pretend every freshman sticks around and eventually graduates, we’re going to overshoot the number of people actually on campus by tallying people that have already left school.

The second set of calculations gives us a “worst-case scenario.” We assume everyone who will drop out does so the moment they set foot on campus. The proportion of a freshmen cohort that drops out can be approximated via published graduation rates. In our minds, those who will drop out are counted as enrolled freshmen and then disappear. If we’re doing these calculations for 2018, they will not count our hypothetical student who drops out in 2017. In fact, they wouldn’t count her in 2015, 2016, or 2017, even though she was enrolled then. Under this assumption, we get a lower bound on the student body by ignoring attendees who will eventually drop out, even if they are still enrolled.

With rough upper and lower bounds, we can be reasonably confident the number of students we can trace back to freshmen enrolled in the fall or transfers lies somewhere between the two figures. Roughly, the bounds will be computed as follows:

*Upper bound = (number of freshmen enrolled over last 4 years) + (transfers from last 2 years) + (students who take 5-6 years to graduate from freshmen cohorts 5 and 6 years ago)*

*Lower bound = (number of freshmen expected to graduate who enrolled over the last 4 years) + (transfers from last 2 years) + (students who take 5-6 years to graduate from freshmen cohorts 5 and 6 years ago)*

What’s left is to compile the data, run the numbers, and see if the bounds on the number of students we can trace back differ significantly from the number of undergrads a university says it has.

1.2 Numbers

By looking through a combination of Common Data Sets, enrollment reports, and university fact pages, I was able to gather the necessary data and compute lower and upper bounds for 8 schools, including USC. In an effort to compare apples to apples, I tried to include schools that are private and similarly sized. Data for those institutions aren’t always available, so the sample also includes public schools of similar size, and smaller, private ones (with UCLA thrown in for good measure).

Below is a table with the 8 schools and their respective reported undergraduate enrollments.

Using the ideas outlined in the previous section, we calculate the number of students traceable to either freshmen or transfer enrollment. The next table displays the upper and lower bounds as a percentage of the undergraduate population.

Let’s look at the University of Virginia (UVA) to start. If we add up all the students the University says have enrolled as freshmen in the past 4 years, adjust for students that enrolled 5 and 6 years ago who are taking extended time, and assume nobody drops out, we can account for 102.38% of the students on campus. If we assume all the freshmen that are going to drop out do so immediately, we can account for 97.91% of the students on campus. In this case, our upper and lower bounds contain the number of reported students. This is a sign as our method does a decent job of predicting how many undergrads a university should have given the numbers they publish.

However, this does not always happen. A percentage greater than 100 indicates an overshoot. For instance, if we assumed all the students we expected were going to drop out of Baylor did so immediately, we should expect their undergraduate population to be 114% of their current one.

As Table 1 suggests, our method does not yield pinpoint accuracy. We don’t hit actual undergraduate population numbers exactly, but two things are notable. First, our new model tends to overshoot. Half of the schools in the sample have lower bounds that are greater than stated enrollment, and the lower bounds of two more come within 8% of the actual figure. The upper bounds of 6 schools are well over 100%, or very close. This suggests there may be outflows of students I haven’t considered, leading to systemic overcounts.

The second feature is BU and USC are outliers. BU comes reasonably close in the upper bound, but its lower bound is nearly 15% below stated enrollment. USC is even worse. Its upper bound is 83.99%, which is even lower than BU’s lower bound. Remember, 83.99% as an upper bound means we can only account for that percentage of students if we make the rosy assumption nobody drops out. USC’s lower bound also dips into the 70s, which is far worse than any other school considered.

USC, and to a lesser extent, BU, have notable discrepancies between their published freshmen/transfer numbers and total enrollments. Their published student inflows do not come close to accounting for the students they have. The fact USC and BU’s freshmen/transfer enrollment numbers under predict student population — when the model overshoots considerably for other schools — suggests something is afoot.

2. Explanations

There are two general ways to account for USC and BU’s enrollment discrepancies. The first is to claim they’ve made a mistake. For one reason or another, the reasoning goes, both universities don’t have a grip on either their total enrollment or the number of freshmen/transfers that enroll every year. This could be caused by problems with their internal systems, apathy, or communication issues.

I don’t think this is plausible. For one thing, knowing how many freshmen enroll is crucial to universities. Tuition is a large source of revenue, so institutions invest a lot in ensuring incoming cohorts have the correct size and socioeconomic makeup. Unexpected freshmen yields can also lead universities to rescind acceptances, which is bad for students and administrators alike. Along the same lines, it seems unlikely a university also doesn’t know how many total undergraduates they have. Every student is a paying customer, so I’d imagine schools would know the size of a major income source.

Deceit is also a possibility, but if schools are lying about their enrollments, we have a much larger problem than can be discussed in this blog post. For that reason, I will not consider it.

The second general explanation is USC and BU have additional student inflows that aren’t matriculating freshmen or transfers. This sounds strange: doesn’t everyone enroll as either a fall freshman or a transfer? How else are you admitted to a school?

It turns out there’s a third way. USC and BU both admit applicants for the spring semester. This means a high school senior submits their application like everyone else, but instead of being invited to campus in August, the earliest they can enroll is the following January. In USC’s case, we know spring admits aren’t tallied in the freshmen numbers I used to compute the upper and lower bounds. In their matriculating freshmen reports, they are strangely specific in talking about fall admits and fall enrolls.

We can test if spring admits account for the missing students at USC. According to their admissions blog, USC enrolls between 500 and 600 spring freshmen every year. Let’s be conservative and assume the number is 500 while supposing the practice has been active for the last 4 years. We can account for this in our model by adding 500 to every fall matriculating class going back to 2016.

Table 2 demonstrates the new upper and lower bounds with this assumption. Consult Appendix A for details on how the bounds were computed.

There’s improvement. 93.74% as an upper bound approaches respectability, but 87.89% as a lower one is still concerning.

At this point in my investigation, I thought there has to be a table where spring admits show up in USC’s Common Data Set. It records everything from Pell Grant recipients to the number of philosophy degrees conferred, so spring admits need to be recorded somewhere, if not under the name.

That’s when the “Other first-year, degree-seeking” row in Section B of USC’s Common Data Set caught my eye. According to the definitions table in the back of the document, “Other first-year, degree-seeking” undergraduates are students that have completed fewer than 30 semester hours (units) and are seeking to graduate at the university in question. These are contrasted with “Degree-seeking, first-time, freshmen” who are undergraduates in their first year that have not attended a prior postsecondary institution. In other words, “Degree-seeking, first-time, freshmen” are traditional freshmen. “Other first-year, degree-seeking” students are freshmen that have attended a prior institution.

Two pieces of evidence that suggest this row in the Common Data Set counts spring admits. First, USC recommends spring admits to go to community college or study abroad during the fall semester. On their website, they say “most first-year spring admits choose to enroll in community college during the fall.” For the cosmopolitans (or those that can afford it), they even have fall-semester programs in places like Rome and Prague at partner universities exclusively for USC spring admits.

The second piece is the actual values in the “Other first-year, degree-seeking” row. As mentioned, USC says between 500 and 600 spring admits enroll every year. It turns out, for the last 3 years, the number of “Other’s” has been around 600, with a spike 4 years ago. If we update our upper and lower bounds by adding the number of “Other’s” to the freshmen enrollment numbers for the last 4 years, we get the following:

We’re much closer. Our upper bound is nearly 100%, and the lower one is a respectable 93.63%. For USC, I’m more confident than not the “Others” row approximates their spring admits. As a result, I believe USC’s policy of offering spring admission more or less explains the apparent discrepancy between matriculating freshmen numbers and total undergraduate enrollment.

If what I’m saying is correct, we can follow an identical process with BU and create better upper and lower bounds. Yet, there are slight differences that prevent this. BU’s “Other” rows are often in the low teens. This means very few freshmen have attended a prior institution before landing at BU. However, I attribute this to the nature of their spring admission policy. It appears almost all delayed admits arrive at BU as part of the College of General Studies (CGS). This is a 2-year program where students arrive in the winter, take classes, and then study abroad for the summer after their freshman year. On the CGS FAQ, they recommend students spend their gap semester volunteering, working, traveling, or taking a class. The next entry in the FAQ explicitly prohibits CGS students from enrolling in another institution for the fall semester. If students want to take non-degree courses during the fall, BU advises them to consult their CGS academic advisor.

In other words, BU does not present taking classes during fall as an attractive option. For this reason, I am not surprised the “Other” row in their Common Data Set is so low. Yet, we can still update our bounds by taking into account the number of first-year CGS students. From their website, they claim to enroll approximately 600 students annually. If we add 600 to every freshmen class going back 4 years, our new bounds are:

These look similar to bounds created for other institutions. Taking delayed admissions into account, we can resolve BU’s apparent discrepancy between freshmen enrollment and total undergraduate population. As mentioned, I believe the same is true of USC. Every year, both schools enroll around 600 freshmen during the second semester.

3. Motives

I believe USC and BU do this to inflate the statistics of their freshmen classes. The thought is if they can exclude academically weaker students from matriculating in the fall, their student-body will appear better and more selective than it actually is. After all, spring admits aren’t included in the fancy documents USC spins up for their “Class of 202X” promotions, and I doubt CGS statistics are included in BU materials. Based on my calculations, USC could have inflated their admit rate by ~1.3% in 2018. Consult Appendix B for the exact methodology.

Colleges have another incentive to delay admission for weaker students. US News and World Report uses the test scores and high school GPAs of first-time, first-year students who enter in the fall to calculate their rankings. If students are admitted in the spring, their statistics are irrelevant from US News’ perspective. This means spring admission is a way for schools to shield weaker students from prying eyes. Every year, the high-school performance of around 600 USC and BU freshmen is not considered when calculating college rankings. Put differently, 15% of their entering class is invisible to those who want to discern the academic quality of the average Trojan or Terrier. I would be surprised if including that 15% helped USC or BU’s cause.

Deirdre Fernandes, reporting in the Boston Globe, describes the phenomena.

Many of the students targeted for delayed admissions would have traditionally been wait listed or rejected because their test scores or grades may not have been as strong as other applicants. But since these students aren’t counted as part of the entering fall class, their academic histories don’t weigh down the school’s overall average for that particular year.

There is also a wealth dimension.

The freshmen who come in likely wouldn’t have been accepted for the traditional freshman class because their grades weren’t as strong, but they are usually wealthier and can afford to pay for a spot without relying on financial aid from the school.

Put bluntly,

“The college banks on the fact that the student wants to go there,” said Todd Weaver, a vice president with Strategies for College Inc., a Norwood-based private counseling firm. “This student might not be a best fit, but their bank account is.”

In addition to being academically weaker than traditional admits, it appears colleges also target the students that can afford to pay full freight. Observational evidence stands in favor of this point for USC. To be clear, I do not have data on USC spring admit income. Yet, of the three students who gave testimonials about their spring admit experience on USC’s delayed admission page, two went to $40,000 a year college prep high schools. This is far from damning evidence, but it is suggestive.

I acknowledge there are non-deceitful reasons why a university might offer spring admission. For instance, staggering the arrival of students allows institutions to enroll more people. Spring freshmen can replace upperclassmen that are studying abroad for the semester, which leads to efficient use of dormitory space. Personally, I believe more students should take time off between high school and college, and we can see delayed admissions as an embrace of the idea.

Perhaps university administrators have these thoughts, but the consequences for ranking and status are just too convenient. Universities live off their reputations and, notwithstanding the coronavirus, are finding it more difficult to fund themselves; we should be skeptical of professed altruistic motives. Anyone should have a hard time believing colleges engage in policies that hide low-quality admits and allow them to enroll more wealthy students for reasons other than their own advancement.

4. Normative claims

I’m going to pick on USC because it was the original subject of my investigation, though I believe everything below also applies to BU.

There’s an equality argument against USC’s spring admission policy. As described, they advantage rich, under-qualified applicants who otherwise would have little chance of being accepted. We believe wealth should have no role in allocating educational opportunity, so our ideals about merit and social mobility are violated. Hence, spring admissions policies are inconsistent with our values and should be abolished or altered. I believe this is an effective and important argument but will not pursue it at length. We all know its steps and understand how much of an issue social mobility is.

A more interesting argument concerns honesty.

Suppose you don’t mind whether private institutions lower academic standards for wealthy students. You might not believe these universities deserve tax breaks, but in principle, there’s nothing wrong with private actors imposing an income qualification on applicants. In the same way only the wealthy can buy birken bags, only the rich can get a degree from USC.

In light of this, you can still think spring admission is problematic because it functions to misrepresent the institution. Perhaps it’s within USC’s right to compromise rigor in admitting some students, but their statistics should reflect that. It’s disingenuous to tout 96th percentile SAT scores and falling acceptance rates when 15% of freshmen are not included in those figures. It’s deceptive to submit unrepresentative data to college rankings for status and prestige while slipping in hundreds of students that might be under-qualified.

I think it’s admirable USC is on such a deliberate campaign to improve itself. It’s clearly a much better institution than it was in the past, but only substantive growth should be rewarded. Its spring admissions policies are evidence it wants all the benefits of a high-powered student body while still reserving the right to lower standards for the wealthy. It cannot pick both and remain honest. If USC wants to remain a playground for the rich, so be it, though it should not pretend otherwise.

5. Conclusion

I could be wrong. It’s possible all spring admits are highly qualified, even more so than regular admits. In fact, some of them probably are [1]. It’s also possible most spring admits are low-income first-generation students, on their way up the socioeconomic ladder. Given the evidence, though, I think this is unlikely. The consequences for universities are just too convenient. I invite USC, BU, and all other universities to release statistics on spring admits. Until then, I stand by my critique.

My criticisms are also directed entirely towards institutions, not individuals. Being accepted to any college, during any semester, is a reason to celebrate. When confronted with opportunity, individuals are obliged to take it. Yet, this does not prevent debate at the institutional level about how some opportunities are allocated, or if organizations are being dishonest about who receives them.

[1] Let F(1): (1) is a spring admit and G(1): (1) is academically underqualified.

My position is not:

∀x(Fx⇒Gx)

But rather:

∀x[P(Gx|Fx) > P(Gx)]

(with a little abuse of notation)

Appendix A: Calculations

Let’s begin with an example. Here is the excel sheet I used to calculate UVA’s figures.

The calculations start with the same intuition we had in the introduction: adding up freshmen enrollment numbers over the last 4 years, should reasonably approximate total undergraduate population. This happens in the “Fall matriculating class size” column. The total of 4 years of freshmen enrollment is tallied at the bottom.

The figures in the “students expected to graduate” column are calculated by multiplying the corresponding fall matriculating class size with the university’s 6-year graduation rate. UVA’s 6-year graduation rate is 95%. This means the “students expected to graduate” figure for 2017 is 3788*(.95) = 3598.6.

Transfers per year are often obtained from the latest edition of a university’s Common Data Set. Occasionally, transfer numbers aren’t available for the year 2019-2020, so in that case I assume they took in the same number of transfers as in 2018-2019. Recall that I’m assuming all transfers stay on campus for only 2 years. This means the only transfers on campus are those who arrived this year or the one prior.

I also attempt to approximate the number of students who enrolled as freshmen more than 4 years ago but are still on campus. These are the “students taking non-standard time.” To approximate the number of students from the freshmen class of 2014 that are still at UVA, I multiplied the total freshmen class by (1-[4-year graduation rate]). The rough thought is if you don’t graduate in 4 years, you will in 5 or 6. UVA’s 2014 freshmen enrollment is 3672 and their 4-year graduation rate is 89%. Hence, the number of freshmen from 2014 who are still around is 3672*(1-.89) = 403.92.

The upper bound of accounted-for students is calculated by summing the totals of “fall matriculating class size,” “transfers per year,” and “students taking non-standard time.” This assumes that every freshmen in the 4 prior classes is still around. The lower bound is calculated similarly, but the total of “fall matriculating class size” is replaced by that of “students expecting to graduate.” This calculation assumes all the students that are expected to drop out will immediately, and don’t contribute to the current undergraduate population.

The following table results:

“Students accounted for (no dropouts)” is the upper bound, and “Students accounted for (all dropout immediately)” is the lower bound.

The full excel sheet I used can be found here. It includes additional notes on where I found enrollment data and graduation rates, and the assumptions I made when those weren’t available.

Appendix B: admit rate

Approximating how much USC inflates their admission rate is straightforward. Let’s use their published data from 2018 as an example, as this is the latest year where good data are available.

In 2018, USC admitted 8,339 students for the fall from a pool of 64,352 applicants. This translates into a 8,339/64,362 = 12.9% acceptance rate. However, in order to get a better sense of their total acceptance rate, we must factor in those they rejected for fall but admitted for spring. To my knowledge, you can’t directly apply for spring admission to USC, so the spring admits must have come from fall applications.

If what I mentioned about the “Other first-year, degree-seeking” row in the Common Data set is correct, USC had 642 spring admits enroll in 2018. Note that fewer students enroll than are admitted. Hence, the total number of spring admits is likely higher than the 642 recorded in the “Other” row. If we knew the “yield rate,” or percentage of students offered spring enrollment who took it, we could divide 642 by the rate and get the number of students accepted for the spring. To my knowledge, USC doesn’t publish that figure.

Yet, we can estimate a yield rate. Suppose it’s true the students offered spring admission to USC are academically under-whelming relative to fall admits. This means they probably would not have been accepted to USC, or schools of similar quality, under regular circumstances. As a result, even though USC offered them a spring position, it’s likely the best option they have. In other words, the choice could be between attending a #22 ranked college in the spring, or a #32 ranked college in the fall. I imagine most students opt for the former, leading to a higher yield rate.

Other factors can also influence the rate. Even though USC might be the best option for many students, it could still be unattractive to start in the spring. Students might want the entire “freshmen experience” that comes with arriving in the fall with other freshmen. Starting in the spring jeopardizes that.

It’s clear USC realizes the concern and took pains to alleviate it. As mentioned, it offers numerous foreign programs with other USC students to make spring admits feel they are not missing out. This increases the appeal of a spring enrollment.

How do we balance these competing concerns? USC’s fall 2018 yield rate was 41%. Harvard’s 2018 yield rate was 82%. I propose we think of a spring admission from USC as more attractive than a fall offer (given the spring admits’ poorer alternatives) but less attractive than Harvard (given the need to delay enrollment on campus). I think a fair figure is 75%. After all, spring admission programs are popular. In 2019, Babson College offered spring admission to 100 students and 86 took the offer. Babson is a small, specialized school, though, so I’m unwilling to read too much into their 86% yield. Still, it indicates rates should be higher rather than lower.

Using admit and application data, we can estimate USC’s actual 2018 admit rate given a 75% spring enrollment yield.

Our assumptions entail USC is inflating their admit rate by around 1.3%. This might look paltry, but every percentage point counts in the prestige arms race.