The Book One of the most extraordinary books ever written about chess and chessplayers, this authoritative study goes well beyond a lucid explanation of how today's chessmasters and tournament players are rated. Twenty years' research and practice produce a wealth of thought-provoking and hitherto unpublished material on the nature and development of high-level talent: Just what constitutes an 'exceptional performance' at the chessboard? Can you really profit from chess lessons? What is the lifetime pattern of Grandmaster development? Where are the masters born? Does your child have master potential? The step-by-step rating system exposition should enable any reader to become an expert on it. For some it may suggest fresh approaches to performance measurement and handicapping in bowling, bridge, golf and elsewhere. 43 charts, diagrams and maps supplement the text. How and why are chessmasters statistically remarkable? How much will your rating rise if you work with the devotion of a Steinitz? At what age should study begin? What toll does age take, and when does it begin? Development of the performance data, covering hundreds of years and thousands of players, has revealed a fresh and exciting version of chess history. Two of the many tables identify more than 500 all-time chess greats, with personal data and top lifetime performance ratings. Just what does government assistance do for chess? What is the Soviet secret? What can we learn from the Icelanders? Why did the small city of Plovdiv produce three Grandmasters in only ten years? Who are the untitled dead? Did Euwe take the championship from Alekhine on a fluke? How would Fischer fare against Morphy in a ten-wins match? 'It was inevitable that this fascinating story be written,' asserts FIDE President Max Euwe, who introduces the book and recognises the major part played by ratings in today's burgeoning international activity. Although this is the definitive ratings work, with statistics alone sufficient to place it in every reference library, it was written by a gentle scientist for pleasurable reading - for the enjoyment of the truths, the questions, and the opportunities it reveals. The second edition of this brilliant and invaluable reference work contains the current FIDE Titles Regulations and the Administrative Rules of the FIDE Rating System. The list of FIDE titleholders has likewise been brought up to the date of the 1985 FIDE Congress. More significantly, the book has been expanded to include a new section on application of the Rating System to handicap tournaments, a section on historical perspective and more examples to reinforce the empirical evidence for the efficacy of the system. HE RATING OF CHESSPLAYERS, PAST AND PRESENT Second Edition blished under the CACDEC Program of FIDE o GENS UNA SUMUS THE RATING OF CHESSPLAYERS, PAST AND PRESENT Second Edition By ARPAD E. ELO Secretary, Qualification Committee World Chess Federation (FIDE) Chairman, Rating Committee United States Chess Federation 1959-1976 Member of PhYSics Faculties MarQuette University University of Wisconsin 1926-1972 ARCO PUBLISHING. INC. New York ISBN �668-04711·6 Published under grant from the American Chess Foundation. New York Copyright © 1978 by Arpad E. Elo. First published 1978. Second Edition 1986. Artwork and filmset by Zastrow Studios, Thiensville, Wisconsin, U.S.A. Second Edition printed in the Philippines by Vera-Reyes, Inc. iv Contents Editor's Foreword ix Introductory Note to the Second Edition x Introductory Note to the First Edition xi Preface to the Second Edition xiii Preface to the First Edition xiv Acknowledgements xvi 1. The Elo Raring System 1.1 Measurement of Chess Performance 3 1.2 The Rating Scale 4 1.3 The Normal Distribution Function 7 1.4 The Normal Probability Function 9 1.5 The Performance Rating Formula- Periodic Measurement 12 1.6 The CurrentRat ing Formula- Continuous Measurement 13 1.7 Rating a Round Robin 15 1.8 Linear Approximation Formulae 16 1.9 Diverse Newer Applications 17 2. Tools and Tests of the Elo System 2.1 The Percentage Expectancy Table 19 2.2 Symbols and Nomenclature 21 2.3 The Working Formulae of the Elo System 22 2.4 Examples of Calculations 23 2.5 Reliability of the Ratings 28 2.6 Tests of the Rating System 31 2.7 The U .S. Open Tournaments Test 33 2.8 The Test of Time 36 v 3. Radng System Administradon 3.1 Ratings and Chess Activity 37 3.2 Rating System Regulations 38 3.3 Rating a Group of Unrated Players 41 3.4 The Method of Successive Approximations 44 3.5 The Integrity of the Ratings 46 3.6 The Management of Deflation 48 3.7 Deflation Control Processes 50 3.8 Monitoring the Rating Pool 51 3.9 TheRating System in Handicap Competition 52 4. Internadonal Titles and Internadonal Radngs 4.1 The Concept of Titles 58 4.2 International Recognition of Chessplayers 58 4.3 International Titles and the Current Regulations 64 4.4 The FIDE Rating System 71 4.5 Calculation Procedures 74 4.6 Special Character of the FIDE Pool 75 4.7 The Titles in Practice- the First 32 Years 76 5. Past and Present - Historical Radngs 5.1 Past vs Present 79 5.2 Chess and Physics 80 5.3 Footracing and Chess 82 5.4 The Crosstables of 120 Years 84 5.5 The 500 Best Five-Year Averages 86 5.6 Some Incidental Discoveries 91 5.7 A Century of Improvement 92 6. Development of Chessmaster Proficiency 6. 1 A Tool for Gerontology 95 6.2 The Composite Player Development Curve 95 6.3 The Ideal Curves for ChessmasterDevelopment 96 6.4 Effect of Age at Introduction to the Game 97 6.5 Effect of Individual Circumstances 99 6.6 Effects of Age and Experience 101 6.7 The Serrated Nature of Development 103 VI 7. Some Demographic Aspects 7.1 Statistical Densities of Players and Talent 105 7.2 The Soviet School of Chess 110 7.3 The Distribution of Chess Proficiencies 112 7.4 The Influenceof Genetics 116 7.5 Where the Masters Were Born 119 7.6 An Historical Perspective 130 7.7 A Chessmaster Profile 132 8. Rating System Theory 8.1 Rating System Methodology 135 8.2 Development of the Elo System 136 8.3 Verhulst Distribution and the Logistic Function 144 8.4 Logistic Probability as a Ratings Basis 147 8.5 Rectangular Distribution as a Ratings Basis 149 8.6 Valued Game Points in Rating System Design 152 8.7 Comparative Summations 154 8.8 Binomial Distribution and Small Samples 159 8.9 Sundry Theoretical Topics 162 9. Appendix 9.1 The Maxwell-Boltzmann Distribution and Chess Ratings 171 9.2 Some Physical Analogies to Chessmaster Development 175 9.3 Editorial Notes 176 9.4 All-Time List of FIDE Titleholders 184 9.5 All-Time List of Great Untitled Players 213 9.6 Bibliography 218 9.7 Index 221 About the Author 229 vii GENS UNA SUMUS VIII Editor's Foreword The first edition of this book, published in 1978, has admirably achieved its objective - to provide an intelligent appreciation of the theory, application and significance of the Elo Rating System. The technical competence of Professor Arpad E. Elo and his exceptional expository ability were undoubtedly responsible for its success. Eight years have elapsed since the publication of the first edition during which time chess activity was swiftly expanding and the FIDE Titles Regulations and Rating System Administrative Rules were changing. The demands of contemporary chess praxis have made an updated edition both desirable and inevitable. In bringing his book up to date, the author has also enriched it with fresh material- the product of his untiring search for new applica­ tions of the rating system. The world chess community acknowledges with profound grati­ tude the great amount of work and talent contributed by Professor Elo towards the rapid growth and development of chess knowledge. The excellent quality of contemporary chess games and the very high level of technical skillwith which the game of chess is currently being played are certainly attributable in no small measure to the strong competitive spirit engendered by the knowledgeable employ­ ment of the Elo Rating System. ELMER D. SANGALANG Associate Editor Manila, Philippines February, 1986 ix Introductory Note to the Second Edition Today, the rating system is an inseparable partner to high-level chess. The holding of competitions without the benefit of the system is unthinkable. The system provides the individual chess­ player with a reliable means for monitoringhis progress in chess. It measures for the organizer the strength ofhis tournament. It gives the spectator a sound basis for predicting the score of his favorite player. And FIDE has an objective criterion for awarding titles. Professor Arpad E. Elo refined the rating system to its nearly ideal formand the chess world owes himno less than the enjoyment chessplayers derive fromchasi ng and earningthe Elo numbers. The rapid and continuing growth of chess activity is a natural benefit from the system. As President of FIDE I am privileged to express, in behalf of the organization, the chess world's appreciation to Professor Elo for his immeasurable contribution to chess. With his rating system, Professor Elo has provided impetus for chess growth. With this book, he documents the system for posterity and, in the process, enriches chess literature. As ifthese were not enough,he assignsto FIDE his royalties and the publication and distribution rights to the second edition of his book. In keeping with this noble and generous gesture, FIDE in turn is distributing the book , under the CACDEC Program, to the developing federations where its impact should be in largest measure.