Who's #1?: The Science of Rating and Ranking

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Princeton University Press, Feb 26, 2012 - Computers - 272 pages

A website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exactly do they work? Who's #1? offers an engaging and accessible account of how scientific rating and ranking methods are created and applied to a variety of uses.


Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field's pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can't be expected from the most widely used systems.


The science of rating and ranking touches virtually every facet of our lives, and now you don't need to be an expert to understand how it really works. Who's #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.

 

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Contents

Chapter 1 Introduction to Ranking
1
Chapter 2 Masseys Method
9
Chapter 3 Colleys Method
21
Chapter 4 Keeners Method
29
Chapter 5 Elos System
53
Chapter 6 The Markov Method
67
Chapter 7 The OffenseDefense Rating Method
79
Chapter 8 Ranking by Reordering Methods
97
Chapter 12 Incorporating Weights
147
Chapter 13 What If Scenarios and Sensitivity
155
Chapter 14 Rank AggregationPart 1
159
Chapter 15 Rank AggregationPart 2
183
Chapter 16 Methods of Comparison
201
Chapter 17 Data
217
Chapter 18 Epilogue
223
Glossary
231

Chapter 9 Point Spreads
113
Chapter 10 User Preference Ratings
127
Chapter 11 Handling Ties
135

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About the author (2012)

Amy N. Langville is associate professor of mathematics at the College of Charleston. Carl D. Meyer is professor of mathematics at North Carolina State University. They are the authors of Google's PageRank and Beyond: The Science of Search Engine Rankings (Princeton).

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