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The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

Sam L. Savage, Jeff Danziger (Illustrator), Harry M. Markowitz (Foreword by)

ISBN: 978-0-471-38197-6

Jun 2009

416 pages

In Stock



A must-read for anyone who makes business decisions that have a major financial impact.

As the recent collapse on Wall Street shows, we are often ill-equipped to deal with uncertainty and risk. Yet every day we base our personal and business plans on uncertainties, whether they be next month’s sales, next year’s costs, or tomorrow’s stock price. In The Flaw of Averages, Sam Savage­known for his creative exposition of difficult subjects­ describes common avoidable mistakes in assessing risk in the face of uncertainty. Along the way, he shows why plans based on average assumptions are wrong, on average, in areas as diverse as healthcare, accounting, the War on Terror, and climate change. In his chapter on Sex and the Central Limit Theorem, he bravely grasps the literary third rail of gender differences.

Instead of statistical jargon, Savage presents complex concepts in plain English. In addition, a tightly integrated web site contains numerous animations and simulations to further connect the seat of the reader’s intellect to the seat of their pants.

The Flaw of Averages typically results when someone plugs a single number into a spreadsheet to represent an uncertain future quantity. Savage finishes the book with a discussion of the emerging field of Probability Management, which cures this problem though a new technology that can pack thousands of numbers into a single spreadsheet cell.

Praise for The Flaw of Averages

“Statistical uncertainties are pervasive in decisions we make every day in business, government, and our personal lives. Sam Savage’s lively and engaging book gives any interested reader the insight and the tools to deal effectively with those uncertainties. I highly recommend The Flaw of Averages.”
William J. Perry, Former U.S. Secretary of Defense

“Enterprise analysis under uncertainty has long been an academic ideal. . . . In this profound and entertaining book, Professor Savage shows how to make all this practical, practicable, and comprehensible.”
­Harry Markowitz, Nobel Laureate in Economics

Preface xv

Acknowledgments xix

Introduction Connecting the Seat of the Intellect to the Seat of the Pants 1


Part 1 The Big Picture 9

Chapter 1 The Flaw of Averages 11

Chapter 2 The Fall of the Algebraic Curtain and Rise of the Flaw of Averages 22

Chapter 3 Mitigating the Flaw of Averages 26

Chapter 4 The Wright Brothers Versus the Wrong Brothers 34

Chapter 5 The Most Important Instrument in the Cockpit 40

Part 2 Five Basic MINDles for Uncertainty 45

Chapter 6 MINDles Are to MINDs What HANDles Are to HANDs 49

Chapter 7 Mindle 1: Uncertainty Versus Risk 52

Chapter 8 Mindle 2: An Uncertain Number Is a Shape 55

Chapter 9 Mindle 3: Combinations of Uncertain Numbers 67

Chapter 10 I Come to Bury SIGMA, Not to Praise it 78

Chapter 11 Mindle 4: Terri Dial and the Drunk in the Road 83

Chapter 12 Who Was Jensen and Why Wasn’t He Equal? 91

Chapter 13 Mindle 5: Interrelated Uncertainties 98

Part 3 Decisions and Information 109

Chapter 14 Decision Trees 111

Chapter 15 The Value of Information 118

Part 4 The Seven Deadly Sins of Averaging 127

Chapter 16 The Seven Deadly Sins of Averaging 129

Chapter 17 The Flaw of Extremes 133

Chapter 18 Simpson’s Paradox 139

Chapter 19 The Scholtes Revenue Fallacy 142

Chapter 20 Taking Credit for Chance Occurrences 147


Part 5 The Flaw of Averages in Finance 155

Chapter 21 Your Retirement Portfolio 157

Chapter 22 The Birth of Portfolio Theory: The Age of Covariance 163

Chapter 23 When Harry Met Bill(y) 169

Chapter 24 Mindles for the Financial Planning Client 175

Chapter 25 Options: Profiting from Uncertainty 181

Chapter 26 When Fischer and Myron Met Bob: Option Theory 192

Chapter 27 Prices, Probabilities, and Predictions 200

Part 6 Real Finance 213

Chapter 28 Holistic Versus Hole-istic 215

Chapter 29 Real Portfolios at Shell 222

Chapter 30 Real Options 228

Chapter 31 Some Gratuitous Inflammatory Remarks on the Accounting Industry 236

Part 7 The Flaw of Averages in Supply Chains 245

Chapter 32 The DNA of Supply Chains 247

Chapter 33 A Supply Chain of DNA 254

Chapter 34 Cawlfield’s Principle 257

Part 8 The Flaw of Averages and Some Hot Button Issues 263

Chapter 35 The Statistical Research Group of World War II 265

Chapter 36 Probability and the War on Terror 272

Chapter 37 The Flaw of Averages and Climate Change 289

Chapter 38 The Flaw of Averages in Health Care 299

Chapter 39 Sex and the Central Limit Theorem 307


Part 9 Toward a Cure for the Flaw of Averages 317

Chapter 40 The End of Statistics as You Were Taught It 319

Chapter 41 Visualization 324

Chapter 42 Interactive Simulation: A New Lightbulb 328

Chapter 43 Scenario Libraries: The Power Grid 332

Chapter 44 The Fundamental Identity of SLURP Algebra 341

Chapter 45 Putting It into Practice 343

Chapter 46 The CPO: Managing Probability Management 354

Chapter 47 A Posthumous Visit by My Father 364

Red Word Glossary 367

Notes 371

About the Author 382

Index 383