Valen0604

Athletic Spending and Academic Outcomes at NCAA Public Institutions

Does the share of institutional spending allocated to athletics predict 6-year graduation rates once student composition and total resources are accounted for? Cross-sectional analysis of 445 NCAA public institutions (Divisions I–III, 2022–23), built from five federal datasets.

📄 Full writeup 🐍 Python notebook

TL;DR

Athletic spending share has no detectable association with graduation rate once total per-student resources are in the model.

The estimate is null without controls, then changes sign three times as controls are added. With student composition controlled but per-student spending left out, it looks negative and significant (−0.35, p = 0.002). That is the estimate that looks like a finding, and it is a denominator artifact: the spending share is athletic spending ÷ total spending, so at a fixed enrollment a high share proxies a small budget. Put per-student spending in the model and the coefficient is +0.11 (p = 0.32, 95% CI −0.11 to +0.33) — about half a graduation point per 5 points of share, with the interval spanning ±1 point.

Three checks that make no linearity assumption agree. A tuned gradient-boosting model assigns athletic share no predictive value; drop-column ablation shows the model predicts slightly better without it; and its partial dependence is flat.

Graduation rates are driven by who a school enrolls and what it has per student: Pell share (largest effect), admission selectivity, test scores, enrollment size, and per-student spending explain about 85% of the cohort-weighted variance. Division differences are almost entirely composition. FBS and FCS institutions spend near-identical shares on athletics (7.2% vs 7.7%) and differ by 14 graduation points, tracking a 120-point gap in median test score, a threefold gap in size, and a 50% gap in spending per student.

Findings are descriptive, not causal. There is no evidence of an association in either direction.

Data

Five federal datasets merged on UNITID, with NCAA classification from EADA:

Source	Role	Key variables
EADA 2023	Athletic spending (numerator), NCAA division	`Grand Total Expenses`, `Classification Name`
IPEDS Finance F1A 2022–23	Total, instructional, administrative, hospital, independent-ops expenses	`F1C191`, `F1C011`, `F1C071`, `F1C121`, `F1C131`
IPEDS Graduation Rates 2023	Outcome: 6-year completion, cohort size	`GRTYPE 8, 9`
IPEDS Admissions 2023	Admission rate, SAT/ACT midpoints	`APPLCN`, `ADMSSN`, `SATVR50`, `SATMT50`, `ACTCM50`
IPEDS Student Financial Aid 2022–23	Undergraduate enrollment, Pell share	`SCUGRAD`, `UPGRNTP`

Final sample after inner joins and NCAA filtering: 445 institutions (108 FBS, 75 FCS, 46 D-I no football, 143 D-II, 73 D-III).

Construction notes

Hospital services and independent operations are subtracted from total expenses so institutions with medical centers or federal labs are not inflated.
ACT composite midpoints are concorded to the SAT scale and combined with SAT midpoints, weighted by number of submitters, into a single testScore.
Missing admission rates and test scores are median-imputed with indicator flags; non-reporting is informative (open-enrollment and test-optional institutions).
Per-student spending is total expenses (net of hospital and independent ops) ÷ undergraduate headcount. Limitation. F1A covers public institutions only (GASB). Private nonprofits report on F2 (FASB) and are excluded. The sample includes nearly every major public D-I program but under-represents D-III, which is heavily private.

Methods

R pipeline (Code/Project.Rmd) — data construction, EDA, and unweighted exploratory regressions: pooled OLS, within-division slopes, additive and interaction models with division dummies, F-test, one-way ANOVAs, diagnostics. Establishes the descriptive picture: inside every division, schools with a higher athletic share graduate fewer students.

Python extension (Python_Extension/) — the primary analysis:

Feature engineering (dataProcess.py) — admissions, test score, enrollment, Pell, and per-student spending joined to the R output.
Weighted regression path — the spending coefficient across five nested specifications (pooled → +division → +size → +student composition → +per-student resources), weighted by graduation cohort size with HC3 robust SEs. A rate estimated from 5,000 students is more precise than one from 80. Robustness: top-5% cohort trim.
Model comparison — linear, ridge, random forest, and tuned gradient boosting under 5×5 repeated CV on an 80% stratified training split. Fitting and scoring are cohort-weighted.
Feature selection — RFECV on the GBM with the one-SE rule, plus a full RFE ranking.
Drop-column ablation — each raw feature (and two feature groups) removed in turn; ΔRMSE computed as paired fold-by-fold differences to strip out fold-difficulty noise.
Held-out evaluation — linear and GBM scored once on the 20% test split.
Partial dependence — GBM and linear PDPs overlaid for every feature; hinge tests where they disagree.

Key Results

Spending-share coefficient path (WLS, HC3, n = 445)

Specification	β (spendRate)	p
Pooled	−0.20	0.37
+ division	−1.19	< 0.001
+ log total expenses	+0.73	< 0.001
+ Pell, test score, enrollment, admission rate (no resource control)	−0.35	0.002
+ log per-student spending, instructional & admin shares, test-score flag	+0.11	0.32

Interaction F-test (slopes vary by division): F = 1.88 on 4 df, p = 0.11 — no evidence slopes differ. Trimming the top 5% of cohorts leaves the final estimate near zero and insignificant.

Full model, other coefficients (cohort-weighted, HC3)

Effect	Estimate
Pell share 20% → 50%	≈ −11 graduation points
Doubling per-student spending	≈ +3.5 points
Doubling enrollment	≈ +4 points
Admission rate (per 10 points)	≈ −1.8 points
Test score (per 100 points)	≈ +4 points
Test score not reported	≈ +4 points (test-optional selective schools)
D-III vs FBS	≈ +7 points; other divisions +2–3 and marginal
Instructional share, administrative share	not significant

Model comparison (5×5 repeated CV, cohort-weighted)

Model	RMSE	R²
Linear	0.063	0.82
Ridge	0.063	0.82
Tuned GBM	0.065	0.81
Random forest	0.067	0.79

Held-out test (n = 89): linear RMSE 0.060 / R² 0.85; GBM 0.065 / 0.83. The linear model wins; the GBM is the cross-check.

Drop-column ablation (tuned GBM, ΔRMSE as % of baseline, paired-fold SE)

Feature dropped	% of baseline RMSE	Mean/SE
Pell share	12.0	5.5
Admission rate + missing flag	7.0	2.2
log enrollment	4.3	1.8
All four spending measures (group)	4.2	1.5
Test score	3.3	1.3
Per-student spending	3.1	1.3
Division	0.3	0.7
Athletic spending share alone	−0.9	−1.2

Pell share is the one feature the model cannot do without. Test score, enrollment, and per-student spending are individually weak because they substitute for each other. Division is nothing. The spending group’s contribution comes from per-student spending; athletic share alone makes the model slightly worse.

Partial dependence. GBM and linear PDPs agree over the central 80% of the data for every feature except enrollment, where the GBM is flat below ~3,000 undergraduates and rising above. Hinge terms at 3,000 and 8,000 do not significantly improve the WLS fit (HC3 p = 0.06 and 0.09), so the linear form is retained. Athletic share is flat under both models.

Composition by division (medians)

Division	n	Test score	Pell	Enrollment	Adm. rate	Spend / student	Athletic share	Grad rate
D-I FBS	108	1199	0.26	22,674	0.77	$49,213	0.072	0.672
D-I FCS	75	1080	0.33	8,215	0.86	$32,650	0.077	0.531
D-I no football	46	1114	0.33	11,962	0.81	$35,168	0.043	0.555
D-II	143	1075	0.37	5,265	0.87	$25,448	0.057	0.473
D-III	73	1173	0.34	4,859	0.81	$33,766	0.022	0.584

Repository Structure

.
├── Code/
│   └── Project.Rmd                  # Data construction, EDA, exploratory regressions
├── Python_Extension/
│   ├── dataProcess.py               # Adds admissions, test score, enrollment, Pell, per-student spending
│   └── main.ipynb                   # Weighted regressions, ML benchmark, ablation, PDPs
├── Data/
│   ├── Raw/                         # EADA, IPEDS F1A, GR, ADM, SFA as downloaded
│   └── Clean/
│       ├── univData.csv             # R output: merged finance + graduation + division
│       └── features.csv             # Python output: full feature set
├── Output/
│   ├── Plots/                       # 01–06 from R, 07–12 from Python
│   └── Tables/                      # 01–06 from R, 07–12 from Python
├── Athletic_Spending_Outcomes.md    # Full writeup
└── README.md                        # This file

Reproducing the Analysis

Prerequisites

R 4.0+:

install.packages(c("dplyr", "tidyr", "ggplot2", "broom", "scales", "readr"))

Python 3.10+:

pip install pandas numpy "scikit-learn>=1.4" statsmodels matplotlib joblib

Steps — run in order; each stage reads the previous one’s output:

Knit Code/Project.Rmd. Reads Data/Raw/, writes Data/Clean/univData.csv and Output/ items 01–06.
Run python Python_Extension/dataProcess.py. Reads univData.csv plus the admissions and financial-aid files, writes Data/Clean/features.csv.
Open Python_Extension/main.ipynb and run all cells. The RFECV fit takes a few minutes. Writes Output/ items 07–12. Raw data files are included. To refresh from source:

EADA 2023: https://ope.ed.gov/athletics/
IPEDS Finance F1A 2022–23: https://nces.ed.gov/ipeds/datacenter/data/F2223_F1A.zip
IPEDS Graduation Rates 2023: https://nces.ed.gov/ipeds/datacenter/data/GR2023.zip
IPEDS Admissions 2023: https://nces.ed.gov/ipeds/datacenter/data/ADM2023.zip
IPEDS Student Financial Aid 2022–23: https://nces.ed.gov/ipeds/datacenter/data/SFA2223.zip

What I’d Do Differently

Multi-year panel. Ten-plus years of EADA and IPEDS would allow institution fixed effects, identifying the relationship from within-school changes rather than between-school differences.
Event studies on exogenous shocks. FCS-to-FBS reclassifications and conference realignments produce discrete shifts in athletic spending suitable for difference-in-differences designs.
Private institutions. Harmonizing F2 (FASB) finance data with F1A would roughly double the sample and bring in the D-III institutions that are currently under-represented.
Align spending with the cohort. The 2023 graduation rate describes students who entered around 2017; spending is measured in 2022–23. A spending measure averaged over the cohort’s enrollment years would remove that timing mismatch.

References

Anderson, M. L. (2017). The benefits of college athletic success: An application of the propensity score design. Review of Economics and Statistics, 99(1), 119–134.

Pope, D. G., & Pope, J. C. (2009). The impact of college sports success on the quantity and quality of student applications. Southern Economic Journal, 75(3), 750–780.

Hoffer, A., Humphreys, B. R., Lacombe, D. J., & Ruseski, J. E. (2015). Trends in NCAA athletic spending: Arms race or rising tide? Journal of Sports Economics, 16(6), 576–596.

Full reference list with data source citations in Athletic_Spending_Outcomes.md.

Author

Valentino Salerni · MS Business Analytics candidate, Carlson School of Management (University of Minnesota) · B.B.A., University of Houston