Pay-By-Play

"Pay-by-Play reveals how salary cap models impact pay-for-performance equity across women’s pro leagues, turning econometric rigor into roster decisions."

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Inspiration

Women’s professional sports represent the most dynamic frontier in sports business, yet they operate under drastically divergent compensation architectures:

  • PWHL: A centralized system with strict team average salary bands ($60,100 ± 10%) and full base salary transparency.
  • WNBA: A traditional hard tiered salary cap with fixed veteran and rookie scales.
  • WPL (Cricket): A high-stakes dynamic open micro-auction.

I asked a fundamental question: "Does pay follow play, and how does the compensation structure change the answer?"

Sports analytics too often produces toxic "overpaid" lists that weaponize compensation data against athletes. As a solo developer and researcher, I wanted to build an ethical econometric framework and decision-support suite that flips the script: identifying Confident Bargains—underpaid athletes whose on-field surplus value warrants immediate raise consideration.

What it does

Pay-by-Play evaluates how compensation mechanisms translate on-field production into financial compensation across the PWHL ((n=194)), WNBA ((n=160)), and WPL ((n=60)):

  • Cross-League Fairness & Misallocation: Quantifies within-league fairness (Spearman rank correlation (\rho)) and the Misallocation Index (the percentage of payroll that would need to shift for pay shares to match production shares).
  • The Two-Lens Framework: Separates contract rationality at signing (Lens A, prior-season performance) from realized active return-on-investment (Lens B, current-season production), tracking breakout surges with (\Delta = \text{Gap}_B - \text{Gap}_A).
  • Empirical Bayes Shrinkage: Shrinks small-sample variance toward positional priors so reserve players with small minute totals don't distort league percentiles: $$\widehat{V}i = \mu{\text{pos}} + B_i \cdot (V_{\text{obs}, i} - \mu_{\text{pos}})$$ $$B_i = \frac{\tau^2}{\tau^2 + \frac{\sigma^2}{\text{exposure}_i}}$$
  • 1,000-Rep Bootstrap Engine: Simulates 80% confidence intervals for every surplus gap ((\text{gap}_i = \text{value_pct}_i - \text{pay_pct}_i)) to verify statistically robust Confident Bargains ((\text{ci_low} > 0)).
  • Interactive De Stijl Modernist Streamlit App: A 7-tab dashboard featuring interactive PyDeck geographic maps, 4-quadrant value-vs-pay Plotly scatter plots, raise-radar dumbbell charts, and Roster Lab—a Mixed-Integer Linear Programming (MILP) solver optimizing compliant PWHL rosters under CBA band constraints.

How I built it

Working solo across the full stack, I built the project from raw data ingestion to econometric modeling and interactive deployment:

  1. Data Engineering & Parsing: Ingested and parsed data from disparate sources—official PWHLPA Salary Guide PDFs using pdfplumber, WNBA cap hits from Her Hoop Stats, WPL auction logs from Cricbuzz and ball-by-ball events from Cricsheet, and official game logs via sportsdataverse. Reconciled all payrolls against deterministic cent-level checksums (e.g., Boston's exact $1,436,173.50 across 25 contracts).
  2. Econometric Pipeline: Implemented Empirical Bayes shrinkage, pre-registered value composites (testing primary, impact, and sensitivity specifications), Spearman rank metrics, and 1,000-iteration block bootstrapping using scipy, statsmodels, numpy, and pandas. Exported analytical tables into compressed Parquet files for sub-second app queries.
  3. Linear Optimization: Formulated PWHL collective bargaining constraints ($60,100 ± 10% average salary band and positional roster requirements) as a Mixed-Integer Linear Program using PuLP and the HiGHS solver.
  4. UI & Brand Identity: Designed a custom visual system inspired by Dutch De Stijl / Bauhaus Modernism (Mondrian/Rietveld inspired primary palette: Blue for contract baseline, Red for athletic play, Canary Yellow for value gap, and Ink structural grid lines). Implemented the 7-tab dashboard using Streamlit, Plotly, and PyDeck.

Challenges I ran into

  • Fragmented & Opaque Data: Women's sports financial data is notoriously fragmented across PDFs, unstructured tables, and emerging APIs. Normalizing cross-sport player names, mapping positions, and verifying salary figures required building strict validation gates (and intentionally excluding leagues like the NWSL where public disclosure is too incomplete to model responsibly).
  • Small-Sample Volatility: Short seasons (24–30 games) create extreme variance for role players with brief spurts of high efficiency. Formulating and tuning the Empirical Bayes shrinkage estimator ((B_i)) was essential to prevent small-sample noise from generating false bargains without dampening genuine breakout talent.
  • Solo Pipeline Scope: Designing the theoretical econometric framework, writing automated data scrapers, building an MILP solver, and crafting a polished front-end design system single-handedly required disciplined modular architecture and end-to-end automated testing.

Accomplishments that I'm proud of

  • Complete Solo Execution: Researched, engineered, modeled, designed, and deployed the entire econometric platform independently.
  • Empirical Hypothesis Validation:
    • H1 (PWHL Draft Primacy): Proved draft pick position correlates with rookie salary at (\rho = -0.92) ((p = 4.95 \times 10^{-18})), whereas actual on-ice performance correlation is only (\rho = 0.44).
    • H2 (WNBA Raise Determinants): Proved prior performance explains only 26.9% of raise variance ((R^2 = 0.269)), with over 73% dictated by cap constraints, service time, and bargaining leverage.
  • Placebo Permutation Testing: Confirmed the statistical validity of the within-league fairness metric ((\rho = 0.598)) by proving it collapses to zero under 20 random pay-permutation shuffles ((|\bar{\rho}_{\text{placebo}}| = 0.053)).
  • Ethical, Athlete-First Analytics: Replaced negative "overpaid" rhetoric with an objective framework that surfaces under-compensated talent.

What I learned

  • Cap Mechanics Dictate Equity: How differing salary cap mechanisms directly shape compensation fairness—the PWHL's transparent average salary band achieves much higher rank alignment ((\rho = 0.60)) than the WNBA's tiered hard cap ((\rho = 0.42)), where max contracts artificially compress elite surplus value.
  • Operations Research in Sports: How to formulate and solve real-world collective bargaining constraints using Mixed-Integer Linear Programming.
  • Communicating Uncertainty: How to present complex econometric concepts (shrinkage, bootstrap confidence intervals, misallocation indices) into intuitive, interactive decision-support tools for coaches, agents, and fans.

What's next for Pay-By-Play

  • Expanding Emerging Leagues: Incorporating upcoming compensation datasets from leagues like Unrivaled basketball and LOVB volleyball.
  • Multi-Year Longitudinal Modeling: Tracking career surplus trajectories across multiple CBA renewal cycles and media rights expansions.
  • Agent & Executive Negotiation Dossiers: Generating one-click PDF dossiers that players and agents can bring directly into contract negotiations to substantiate raise proposals.

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