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Who's #1? : the science of rating and ranking

Author: Amy N Langville; Carl Dean Meyer
Publisher: Princeton : Princeton University Press, 2012.
Edition/Format:   Print book : EnglishView all editions and formats

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Document Type: Book
All Authors / Contributors: Amy N Langville; Carl Dean Meyer
ISBN: 9780691162317 069116231X
OCLC Number: 978427259
Description: XVI, 247 p. : il. ; 25 cm
Contents: Preface xiiiPurpose xiiiAudience xiiiPrerequisites xiiiTeaching from This Book xivAcknowledgments xivChapter 1. Introduction to Ranking 1Social Choice and Arrow's Impossibility Theorem 3Arrow's Impossibility Theorem 4Small Running Example 4Chapter 2. Massey's Method 9Initial Massey Rating Method 9Massey's Main Idea 9The Running Example Using the Massey Rating Method 11Advanced Features of the Massey Rating Method 11The Running Example: Advanced Massey Rating Method 12Summary of the Massey Rating Method 13Chapter 3. Colley's Method 21The Running Example 23Summary of the Colley Rating Method 24Connection between Massey and Colley Methods 24Chapter 4. Keener's Method 29Strength and Rating Stipulations 29Selecting Strength Attributes 29Laplace's Rule of Succession 30To Skew or Not to Skew? 31Normalization 32Chicken or Egg? 33Ratings 33Strength 33The Keystone Equation 34Constraints 35Perron-Frobenius 36Important Properties 37Computing the Ratings Vector 37Forcing Irreducibility and Primitivity 39Summary 40The 2009-2010 NFL Season 42Jim Keener vs. Bill James 45Back to the Future 48Can Keener Make You Rich? 49Conclusion 50Chapter 5. Elo's System 53Elegant Wisdom 55The K-Factor 55The Logistic Parameter ? 56Constant Sums 56Elo in the NFL 57Hindsight Accuracy 58Foresight Accuracy 59Incorporating Game Scores 59Hindsight and Foresight with ? = 1000, K = 32, H = 15 60Using Variable K-Factors with NFL Scores 60Hindsight and Foresight Using Scores and Variable K-Factors 62Game-by-Game Analysis 62Conclusion 64Chapter 6. The Markov Method 67The Markov Method 67Voting with Losses 68Losers Vote with Point Differentials 69Winners and Losers Vote with Points 70Beyond Game Scores 71Handling Undefeated Teams 73Summary of the Markov Rating Method 75Connection between the Markov and Massey Methods 76Chapter 7. The Offense-Defense Rating Method 79OD Objective 79OD Premise 79But Which Comes First? 80Alternating Refinement Process 81The Divorce 81Combining the OD Ratings 82Our Recurring Example 82Scoring vs. Yardage 83The 2009-2010 NFL OD Ratings 84Mathematical Analysis of the OD Method 87Diagonals 88Sinkhorn-Knopp 89OD Matrices 89The OD Ratings and Sinkhorn-Knopp 90Cheating a Bit 91Chapter 8. Ranking by Reordering Methods 97Rank Differentials 98The Running Example 99Solving the Optimization Problem 101The Relaxed Problem 103An Evolutionary Approach 103Advanced Rank-Differential Models 105Summary of the Rank-Differential Method 106Properties of the Rank-Differential Method 106Rating Differentials 107The Running Example 109Solving the Reordering Problem 110Summary of the Rating-Differential Method 111Chapter 9. Point Spreads 113What It Is (and Isn't) 113The Vig (or Juice) 114Why Not Just Offer Odds? 114How Spread Betting Works 114Beating the Spread 115Over/Under Betting 115Why Is It Difficult for Ratings to Predict Spreads? 116Using Spreads to Build Ratings (to Predict Spreads?) 117NFL 2009-2010 Spread Ratings 120Some Shootouts 121Other Pair-wise Comparisons 124Conclusion 125Chapter 10. User Preference Ratings 127Direct Comparisons 129Direct Comparisons, Preference Graphs, and Markov Chains 130Centroids vs. Markov Chains 132Conclusion 133Chapter 11. Handling Ties 135Input Ties vs. Output Ties 136Incorporating Ties 136The Colley Method 136The Massey Method 137The Markov Method 137The OD, Keener, and Elo Methods 138Theoretical Results from Perturbation Analysis 139Results from Real Datasets 140Ranking Movies 140Ranking NHL Hockey Teams 141Induced Ties 142Summary 144Chapter 12. Incorporating Weights 147Four Basic Weighting Schemes 147Weighted Massey 149Weighted Colley 150Weighted Keener 150Weighted Elo 150Weighted Markov 150Weighted OD 151Weighted Differential Methods 151Chapter 13. "What If . . ." Scenarios and Sensitivity 155The Impact of a Rank-One Update 155Sensitivity 156Chapter 14. Rank Aggregation-Part 1 159Arrow's Criteria Revisited 160Rank-Aggregation Methods 163Borda Count 165Average Rank 166Simulated Game Data 167Graph Theory Method of Rank Aggregation 172A Refinement Step after Rank Aggregation 175Rating Aggregation 176Producing Rating Vectors from Rating Aggregation-Matrices 178Summary of Aggregation Methods 181Chapter 15. Rank Aggregation-Part 2 183The Running Example 185Solving the BILP 186Multiple Optimal Solutions for the BILP 187The LP Relaxation of the BILP 188Constraint Relaxation 190Sensitivity Analysis 191Bounding 191Summary of the Rank-Aggregation (by Optimization) Method 193Revisiting the Rating-Differential Method 194Rating Differential vs. Rank Aggregation 194The Running Example 196Chapter 16. Methods of Comparison 201Qualitative Deviation between Two Ranked Lists 201Kendall's Tau 203Kendall's Tau on Full Lists 204Kendall's Tau on Partial Lists 205Spearman's Weighted Footrule on Full Lists 206Spearman's Weighted Footrule on Partial Lists 207Partial Lists of Varying Length 210Yardsticks: Comparing to a Known Standard 211Yardsticks: Comparing to an Aggregated List 211Retroactive Scoring 212Future Predictions 212Learning Curve 214Distance to Hillside Form 214Chapter 17. Data 217Massey's Sports Data Server 217Pomeroy's College Basketball Data 218Scraping Your Own Data 218Creating Pair-wise Comparison Matrices 220Chapter 18. Epilogue 223Analytic Hierarchy Process (AHP) 223The Redmond Method 223The Park-Newman Method 224Logistic Regression/Markov Chain Method (LRMC) 224Hochbaum Methods 224Monte Carlo Simulations 224Hard Core Statistical Analysis 225And So Many Others 225Glossary 231Bibliography 235Index 241
Other Titles: Science of rating and ranking
Who is number one?
Responsibility: Amy N. Langville and Carl D. Meyer.


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"[A] thorough exploration of the methods and applications of ranking for an audience ranging from computer scientists and engineers to high-school teachers to 'people interested in wagering on just Read more...

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