Chapter 33: Further Reading

Foundational References

  1. Stern, H. S. (1991). "On the Probability of Winning a Football Game." The American Statistician, 45(3), 179-183. One of the earliest rigorous treatments of in-game win probability estimation using statistical methods. Stern's framework for modeling the remaining game as a random process laid groundwork that modern live betting models still build upon. Essential reading for understanding how score differential and time remaining combine to determine win probability.

  2. Lock, D. & Nettleton, D. (2014). "Using Random Forests to Estimate Win Probability Before Each Play of an NFL Game." Journal of Quantitative Analysis in Sports, 10(2), 197-205. Demonstrates the application of random forests to NFL play-by-play data for real-time win probability estimation. The paper shows how to handle the rich game state (down, distance, field position, score, time) and evaluates calibration against historical outcomes. A practical bridge between statistical theory and live betting model implementation.

  3. Lopez, M. J. (2020). "Bigger Data, Better Questions, and a Return to Fourth Down Decision-Making." Statistical Science, 35(1), 4-22. While focused on fourth-down decisions, this paper demonstrates state-of-the-art methods for estimating game-state-dependent outcome probabilities from large play-by-play datasets. The methodology for building expected points and win probability models from NFL data is directly applicable to live betting model construction.

Bayesian Methods and Real-Time Updating

  1. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC. The definitive reference on Bayesian statistics. Chapters on conjugate priors, hierarchical models, and computation are directly relevant to building the real-time updating models discussed in this chapter. The treatment of normal conjugate models provides the mathematical foundation for the win probability engine.

  2. Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. MIT Press. Chapters on state-space models, Kalman filtering, and particle filtering provide the theoretical foundation for the advanced latent-state models discussed in Section 33.2. The treatment of online learning and sequential updating is particularly relevant to real-time sports modeling.

  3. Kschischang, F. R., Frey, B. J., & Loeliger, H.-A. (2001). "Factor Graphs and the Sum-Product Algorithm." IEEE Transactions on Information Theory, 47(2), 498-519. For readers interested in the more advanced probabilistic graphical model approach to game-state modeling. Factor graphs provide a natural framework for representing the dependencies in complex game states (e.g., NFL games with multiple interacting state variables).

Market Microstructure and Execution

  1. Hasbrouck, J. (2007). Empirical Market Microstructure. Oxford University Press. While written for financial markets, the concepts of market microstructure -- bid-ask spreads, adverse selection, price discovery, and information asymmetry -- map directly to live sports betting markets. Understanding how financial markets handle similar challenges provides valuable perspective for sports betting system design.

  2. Vlastakis, N., Dotsis, G., & Markellos, R. N. (2009). "How Efficient is the European Football Betting Market? Evidence from Arbitrage and Trading Strategies." Journal of Forecasting, 28(5), 426-444. Examines market efficiency in European football betting, including in-play markets. The paper documents the existence of exploitable inefficiencies and the role of market microstructure in creating and limiting arbitrage opportunities. Relevant context for understanding the structure of live betting markets.

  3. Croxson, K. & Reade, J. J. (2014). "Information and Efficiency: Goal Arrival in Soccer Betting." The Economic Journal, 124(575), 62-91. Studies how live soccer betting markets process the information contained in goals. The paper quantifies the speed of price adjustment and the efficiency of information incorporation, providing empirical evidence on mispricing window durations in live markets.

Sports-Specific Probability Models

  1. Kovalchik, S. A. (2016). "Searching for the GOAT of Tennis Win Prediction." Journal of Quantitative Analysis in Sports, 12(3), 127-138. Comprehensive comparison of tennis win probability models, from simple Markov chains to complex hierarchical models. Tennis is the sport where live probability modeling is most mature, and the methods developed here -- particularly the point-by-point Markov chain approach -- are instructive for other sports.

  2. Cervone, D., D'Amour, A., Bornn, L., & Goldsberry, K. (2016). "A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes." Journal of the American Statistical Association, 111(514), 585-599. Develops a sophisticated model for basketball possession outcomes using spatial tracking data. While primarily a research model, the multiresolution approach -- modeling at different time scales simultaneously -- is directly relevant to building real-time basketball win probability models.

  3. Pelechrinis, K., Winston, W., Sagarin, J., & Cabot, V. (2019). "Evaluating NFL Plays: Expected Points Adjusted for Schedule." Proceedings of the 13th MIT Sloan Sports Analytics Conference. Describes the construction of expected points models for NFL play-by-play data, which are the building blocks of NFL win probability models. The schedule adjustment methodology is particularly relevant for building pre-game priors that feed into the live model.

System Architecture and Engineering

  1. Kleppmann, M. (2017). Designing Data-Intensive Applications. O'Reilly Media. The definitive reference for building reliable, scalable data systems. The chapters on stream processing, message queues, and event-driven architectures are directly applicable to the live betting system architecture described in Section 33.5. Essential reading for anyone building a production live betting platform.

  2. Nygard, M. T. (2018). Release It! Design and Deploy Production-Ready Software (2nd ed.). Pragmatic Bookshelf. Practical guidance on building resilient production systems, including circuit breakers, timeout patterns, and failure recovery strategies. The stability patterns described in this book are critical for live betting systems that must operate reliably during high-stakes, time-sensitive situations.

Live Betting Strategy and Analysis

  1. Buraimo, B., Forrest, D., & Simmons, R. (2008). "Insights for Clubs from Modelling Match Attendance in Football." Journal of the Operational Research Society, 59(10), 1371-1381. Provides context on the growth and economics of live betting markets, particularly in European football. Understanding the market dynamics and participant behavior is valuable for identifying where inefficiencies are most likely to persist.

  2. Easton, T. & Uylangco, K. (2010). "Forecasting Outcomes in Tennis Matches Using Within-Match Betting Markets." International Journal of Forecasting, 26(3), 564-575. Examines how within-match (live) betting prices evolve in tennis and whether they contain exploitable information. The paper provides empirical evidence on the efficiency of live tennis markets and the speed of price adjustment, which is directly relevant to live betting strategy design.

  3. Brown, A. & Yang, F. (2019). "The Wisdom of Large and Small Crowds: Evidence from Repeated Natural Experiments in Sports Betting." International Economic Review, 60(4), 1789-1827. Studies how betting market prices aggregate information from participants of different sophistication levels. The findings on how quickly markets incorporate new information -- and when they fail to do so -- are directly applicable to understanding when live betting edges are most likely to exist.