What the Massey Ratings Are
The Massey Ratings are a sports rating system developed by mathematician Ken Massey as an undergraduate honors project in the 1990s. Like the Colley Matrix, they gained prominence as one of the computer polls used by the Bowl Championship Series (BCS) in American college football.
The system is built on least-squares regression: it finds the set of team ratings that best explains all game outcomes simultaneously.
What the Massey Ratings Rank
The method ranks teams within a connected competition — leagues or divisions where schedules interlink.
A distinctive property of Massey ratings is their interval scale: the difference between two teams’ ratings has predictive meaning, estimating the expected point difference in a game between them.
Core Inputs Used by the Massey Ratings
The core model uses:
- Game outcomes — results across the full schedule
- Margin of victory — in the standard formulation, point differences carry information
- Home-field adjustments — can be incorporated as a parameter
A win-loss-only variant (used during the BCS era, which prohibited margin of victory in its computer polls) restricts inputs to results alone.
How Massey Ratings Are Calculated (High-Level)
The method frames ranking as a curve-fitting problem:
- Assume every game outcome equals the difference between the two teams’ true ratings, plus noise.
- Write one equation per game, producing an overdetermined system — more equations than unknowns.
- Solve by least squares: find the ratings that minimize the total squared error between predicted and actual results.
- The resulting ratings form a consistent scale — rating gaps translate directly into expected scoring margins.
Conceptual model: Draw the best-fit line through an entire season of results at once — every game pulls every rating toward consistency.
Key Parameters or Factors
- Margin of victory weighting — full, capped, or excluded depending on the variant
- Home-field parameter — estimated from the data rather than assumed
- Schedule connectivity — the regression requires teams to be linked through shared opponents
Update Frequency
Massey ratings are recalculated whenever new results enter the dataset — typically weekly during a season.
Known Limitations and Criticisms
- Margin sensitivity — lopsided wins against weak opponents can inflate ratings (the reason the BCS barred margin-based computers)
- Whole-season smoothing — early and late games count equally, so ratings may lag current form
- Requires connected schedules — like all simultaneous methods, it struggles to compare isolated groups
- Noise amplification — with few games played, small upsets can swing the fit
Where the Massey Ratings Are Used
The method is used in:
- College football and basketball analysis (including the long-running Massey Ratings site comparing dozens of ranking systems)
- Sports betting research, where rating differences map to point spreads
- Academic work on ranking methodology
Summary
The Massey Ratings treat an entire season as one giant regression problem: choose the ratings that best explain every result at once. The payoff is a rating scale with real predictive meaning — and the price is sensitivity to how much you trust margins of victory.
References and Sources
- Massey, K. Statistical Models Applied to the Rating of Sports Teams (honors thesis).
- Wikipedia. Massey Ratings.
- Langville, A. N., & Meyer, C. D. Who’s #1? The Science of Rating and Ranking.