- Cover
- Half title
- Title
- Copyright
- Contents
- Preface
- Chapter 1. Introduction to Ranking
- Chapter 2. Massey’s Method
- Chapter 3. Colley’s Method
- Chapter 4. Keener’s Method
- Strength and Rating Stipulations
- Selecting Strength Attributes
- Laplace’s Rule of Succession
- To Skew or Not to Skew?
- Normalization
- Chicken or Egg?
- Ratings
- Strength
- The Keystone Equation
- Constraints
- Perron–Frobenius
- Important Properties
- Computing the Ratings Vector
- Forcing Irreducibility and Primitivity
- Summary
- The 2009–2010 NFL Season
- Jim Keener vs. Bill James
- Back to the Future
- Can Keener Make You Rich?
- Conclusion
- Chapter 5. Elo’s System
- Elegant Wisdom
- The K-Factor
- The Logistic Parameter ξ
- Constant Sums
- Elo in the NFL
- Hindsight Accuracy
- Foresight Accuracy
- Incorporating Game Scores
- Hindsight and Foresight with ξ = 1000, K = 32, H = 15
- Using Variable K-Factors with NFL Scores
- Hindsight and Foresight Using Scores and Variable K-Factors
- Game-by-Game Analysis
- Conclusion
- Chapter 6. The Markov Method
- Chapter 7. The Offense–Defense Rating Method
- OD Objective
- OD Premise
- But Which Comes First?
- Alternating Refinement Process
- The Divorce
- Combining the OD Ratings
- Our Recurring Example
- Scoring vs. Yardage
- The 2009–2010 NFL OD Ratings
- Mathematical Analysis of the OD Method
- Diagonals
- Sinkhorn–Knopp
- OD Matrices
- The OD Ratings and Sinkhorn–Knopp
- Cheating a Bit
- Chapter 8. Ranking by Reordering Methods
- Rank Differentials
- The Running Example
- Solving the Optimization Problem
- The Relaxed Problem
- An Evolutionary Approach
- Advanced Rank-Differential Models
- Summary of the Rank-Differential Method
- Properties of the Rank-Differential Method
- Rating Differentials
- The Running Example
- Solving the Reordering Problem
- Summary of the Rating-Differential Method
- Chapter 9. Point Spreads
- What It Is (and Isn’t)
- The Vig (or Juice)
- Why Not Just Offer Odds?
- How Spread Betting Works
- Beating the Spread
- Over/Under Betting
- Why Is It Difficult for Ratings to Predict Spreads?
- Using Spreads to Build Ratings (to Predict Spreads?)
- NFL 2009–2010 Spread Ratings
- Some Shootouts
- Other Pair-wise Comparisons
- Conclusion
- Chapter 10. User Preference Ratings
- Chapter 11. Handling Ties
- Chapter 12. Incorporating Weights
- Chapter 13. “What If . . .” Scenarios and Sensitivity
- Chapter 14. Rank Aggregation–Part 1
- Chapter 15. Rank Aggregation–Part 2
- The Running Example
- Solving the BILP
- Multiple Optimal Solutions for the BILP
- The LP Relaxation of the BILP
- Constraint Relaxation
- Sensitivity Analysis
- Bounding
- Summary of the Rank-Aggregation (by Optimization) Method
- Revisiting the Rating-Differential Method
- Rating Differential vs. Rank Aggregation
- The Running Example
- Chapter 16. Methods of Comparison
- Qualitative Deviation between Two Ranked Lists
- Kendall’s Tau
- Kendall’s Tau on Full Lists
- Kendall’s Tau on Partial Lists
- Spearman’s Weighted Footrule on Full Lists
- Spearman’s Weighted Footrule on Partial Lists
- Partial Lists of Varying Length
- Yardsticks: Comparing to a Known Standard
- Yardsticks: Comparing to an Aggregated List
- Retroactive Scoring
- Future Predictions
- Learning Curve
- Distance to Hillside Form
- Chapter 17. Data
- Chapter 18. Epilogue
- Glossary
- Bibliography
- Index
-
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