Chapter 11 Further Reading: Regularized Adjusted Plus-Minus (RAPM)
Annotated Bibliography
This annotated bibliography provides resources for deeper exploration of RAPM methodology, from foundational papers to advanced extensions and practical applications.
Foundational Papers
Rosenbaum, D. T. (2004). "Measuring How NBA Players Help Their Teams Win." 82games.com.
Summary: The seminal paper introducing adjusted plus-minus to basketball analytics. Rosenbaum presents the conceptual framework of using regression to isolate individual player contributions from lineup data, establishing the foundation for all subsequent APM/RAPM work.
Key Contributions: - First systematic application of regression to basketball lineup data - Demonstration that raw plus-minus fails to measure individual value - Introduction of the design matrix structure for player indicators
Recommended For: Anyone wanting to understand the historical origins and basic motivation for RAPM.
Sill, J. (2010). "Improved NBA Adjusted +/- Using Regularization and Out-of-Sample Testing." MIT Sloan Sports Analytics Conference.
Summary: The paper that introduced ridge regularization to adjusted plus-minus, creating what we now call RAPM. Sill demonstrates that regularization dramatically improves out-of-sample prediction and produces more sensible player rankings.
Key Contributions: - Identification of collinearity as the fundamental APM problem - Introduction of ridge regression as the solution - Empirical validation using out-of-sample testing - Practical guidance on regularization parameter selection
Recommended For: Essential reading for understanding why regularization is necessary and how it works.
Engelmann, J. (2017). "Regularized Adjusted Plus-Minus." In Basketball Analytics (ed. K. Pape), Chapter 12. CRC Press.
Summary: A comprehensive textbook treatment of RAPM methodology, including mathematical derivations, implementation details, and extensions to offensive/defensive splits.
Key Contributions: - Complete mathematical framework for RAPM - Discussion of offensive and defensive RAPM - Multi-year modeling approaches - Practical implementation guidance
Recommended For: Readers wanting a thorough, textbook-level understanding of RAPM.
Statistical Methodology
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning, 2nd ed. Springer.
Summary: The definitive textbook on statistical learning, including comprehensive coverage of ridge regression, cross-validation, and the bias-variance tradeoff.
Key Chapters: - Chapter 3: Linear Methods for Regression (ridge regression) - Chapter 7: Model Assessment and Selection (cross-validation) - Chapter 18: High-Dimensional Problems
Recommended For: Building deep statistical foundations for RAPM and related methods.
Hoerl, A. E., & Kennard, R. W. (1970). "Ridge Regression: Biased Estimation for Nonorthogonal Problems." Technometrics, 12(1), 55-67.
Summary: The original paper introducing ridge regression. Essential for understanding the theoretical foundations of the regularization approach used in RAPM.
Key Contributions: - Demonstration that biased estimators can have lower MSE than OLS - Derivation of the ridge regression solution - Analysis of the bias-variance tradeoff
Recommended For: Those interested in the statistical theory underlying ridge regression.
Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. MIT Press.
Summary: Comprehensive machine learning textbook with excellent coverage of Bayesian linear regression, which provides the probabilistic interpretation of ridge regression.
Key Chapters: - Chapter 7: Linear Regression - Chapter 13: Sparse Linear Models
Recommended For: Understanding the Bayesian interpretation of RAPM and extensions to more sophisticated priors.
Advanced Extensions
Jacobs, D. & Silver, N. (2019). "Introducing RAPTOR, Our New Metric For The Modern NBA." FiveThirtyEight.
Summary: Introduction of RAPTOR, a state-of-the-art player impact metric that combines RAPM with box score priors and tracking data. Represents the current frontier of public plus-minus metrics.
Key Contributions: - Integration of multiple data sources (box scores, tracking, play-by-play) - Sophisticated prior construction using machine learning - Separate offensive and defensive components - Public availability and ongoing updates
Recommended For: Understanding how modern hybrid metrics extend basic RAPM.
Link: https://fivethirtyeight.com/features/introducing-raptor-our-new-metric-for-the-modern-nba/
Ilardi, S. (2007). "Adjusted Plus-Minus: An Idea Whose Time Has Come." 82games.com.
Summary: Early exploration of APM extensions including offensive/defensive splits and multi-year modeling. Provides practical insights from implementing APM systems.
Key Contributions: - Discussion of O-APM and D-APM interpretation - Analysis of sample size requirements - Comparison with other impact metrics
Recommended For: Historical perspective on APM development and practical implementation insights.
Winston, W. L. (2009). Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football. Princeton University Press.
Summary: Accessible introduction to sports analytics including a chapter on plus-minus methods in basketball. Good for building intuition before diving into technical details.
Key Chapters: - Chapter 23: Player Evaluation in Basketball
Recommended For: General audience seeking intuitive understanding of plus-minus concepts.
Practical Implementation
Kubatko, J., Oliver, D., Pelton, K., & Rosenbaum, D. T. (2007). "A Starting Point for Analyzing Basketball Statistics." Journal of Quantitative Analysis in Sports, 3(3).
Summary: Foundational paper on basketball statistics including possession estimation, efficiency metrics, and the relationship between individual and team statistics.
Key Contributions: - Possession estimation formula - Definitions of offensive and defensive rating - Framework for relating individual and team statistics
Recommended For: Understanding the data transformations required for RAPM implementation.
Myers, D. (2011). "About Box Plus/Minus (BPM)." Basketball-Reference.com.
Summary: Documentation of Box Plus-Minus, a metric designed to approximate RAPM using only box score statistics. Understanding BPM helps clarify what RAPM captures beyond box scores.
Key Contributions: - Regression coefficients linking box scores to RAPM - Discussion of which box score stats predict RAPM - Limitations of box-score-only approaches
Recommended For: Understanding the relationship between box scores and RAPM.
Link: https://www.basketball-reference.com/about/bpm2.html
Data Sources
NBA Stats API Documentation
Summary: Official documentation for the NBA's statistics API, which provides access to play-by-play data, tracking statistics, and aggregated metrics necessary for RAPM implementation.
Key Resources: - Play-by-play endpoints - Player tracking data - Box score data
Link: https://github.com/swar/nba_api (unofficial Python wrapper)
Basketball-Reference.com
Summary: Comprehensive basketball statistics database including historical play-by-play data, box scores, and advanced metrics.
Key Features: - Historical data back to 1946 - Play-by-play from 1996-97 onward - Pre-computed advanced metrics for comparison
Link: https://www.basketball-reference.com
Related Metrics and Comparisons
Goldsberry, K. (2019). SprawlBall: A Visual Tour of the New Era of the NBA. Houghton Mifflin Harcourt.
Summary: Accessible exploration of modern basketball analytics with emphasis on spatial analysis and player evaluation. Provides context for how RAPM fits into the broader analytics ecosystem.
Recommended For: Understanding the role of various metrics in player evaluation.
Pelton, K. (2012). "Rating the Rating Systems." ESPN Insider.
Summary: Comparative analysis of various player impact metrics including RAPM, PER, Win Shares, and others. Helpful for understanding RAPM's strengths and weaknesses relative to alternatives.
Key Contributions: - Side-by-side comparison of major metrics - Discussion of what each metric captures - Recommendations for metric selection
Recommended For: Deciding which metrics to use for different purposes.
Academic Papers
Macdonald, B. (2011). "An Expected Goals Model for Evaluating NHL Teams and Players." MIT Sloan Sports Analytics Conference.
Summary: Application of adjusted plus-minus methodology to hockey, demonstrating the generalizability of RAPM concepts across sports.
Recommended For: Understanding how RAPM principles apply beyond basketball.
Schuckers, M. & Curro, J. (2013). "Total Hockey Rating (THoR): A Comprehensive Statistical Rating of National Hockey League Forwards and Defensemen Based Upon All On-Ice Events." MIT Sloan Sports Analytics Conference.
Summary: Another hockey application of plus-minus methodology with interesting extensions including game state adjustments.
Recommended For: Ideas for RAPM extensions (e.g., adjusting for score differential).
Online Resources
Thinking Basketball (YouTube/Podcast)
Summary: Ben Taylor's video series and podcast providing deep analysis of player value using advanced metrics including RAPM-style approaches.
Link: https://www.youtube.com/c/ThinkingBasketball
Cleaning the Glass
Summary: Subscription analytics platform providing advanced statistics and analysis, including play-type data and on/off statistics that complement RAPM analysis.
Link: https://cleaningtheglass.com
Nylon Calculus (SB Nation)
Summary: Basketball analytics blog featuring articles on methodology and player evaluation using advanced metrics.
Link: https://www.sbnation.com/nylon-calculus
Recommended Reading Order
For Beginners
- Winston (2009) - Mathletics chapter on basketball
- Rosenbaum (2004) - Original APM paper
- Sill (2010) - Introduction of regularization
- Myers (2011) - BPM documentation for context
For Intermediate Readers
- Engelmann (2017) - Comprehensive RAPM treatment
- Hastie et al. (2009) - Statistical foundations
- Jacobs & Silver (2019) - Modern extensions
- Kubatko et al. (2007) - Data preparation context
For Advanced Readers
- Hoerl & Kennard (1970) - Ridge regression theory
- Murphy (2012) - Bayesian interpretation
- Academic papers on extensions (hockey applications, etc.)
- Original implementation and replication using real data
Citation Format
When citing RAPM methodology in academic or professional work, consider the following key citations:
Sill, J. (2010). Improved NBA Adjusted +/- Using Regularization and
Out-of-Sample Testing. MIT Sloan Sports Analytics Conference.
Rosenbaum, D. T. (2004). Measuring How NBA Players Help Their Teams Win.
82games.com. Retrieved from http://www.82games.com/comm30.htm
For the statistical methodology:
Hoerl, A. E., & Kennard, R. W. (1970). Ridge Regression: Biased Estimation
for Nonorthogonal Problems. Technometrics, 12(1), 55-67.