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

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