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



“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

A Groundbreaking must-read for anyone who makes business decisions in the face of uncertainty

As the recent collapse on Wall Street shows, we are often ill-equipped to deal effectively with uncertainty and risk. Yet every day we base our personal and business plans on these kinds of uncertainties, whether they be next month’s sales, next year’s costs, or tomorrow’s stock price.

In The Flaw of Averages, Sam Savage—known for his creative exposition of difficult subjects—describes common avoidable mistakes in assessing risk in the face of uncertainty. He explains why plans based on average assumptions are wrong, on average, in areas as diverse as finance, healthcare, accounting, the war on terror, and climate change. Instead of the usual anachronistic statistical jargon, Savage presents complex concepts in plain English, connecting the seat of the reader’s intellect to the seat of their pants.

Savage also presents the emerging field of Probability Management aimed at curing the Flaw of Averages through more transparent communication of uncertainty and risk. Savage argues that this is a problem that must be solved if we are to improve the stability of our economy, and that we cannot repeat the recent mistakes of applying “steam era” statistics to “information age” risks.

Sam L. Savage is a Consulting Professor of Management Science and Engineering at Stanford University, and a Fellow of the Judge Business School at the University of Cambridge.


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


Part 1 The Big Picture.

Chapter 1 The Flaw of Averages.

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

Chapter 3 Mitigating the Flaw of Averages.

Chapter 4 The Wright Brothers Versus the Wrong Brothers.

Chapter 5 The Most Important Instrument in the Cockpit.

Part 2 Five Basic MINDles for Uncertainty.

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

Chapter 7 Mindle 1: Uncertainty Versus Risk.

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

Chapter 9 Mindle 3: Combinations of Uncertain Numbers.

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

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

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

Chapter 13 Mindle 5: Interrelated Uncertainties.

Part 3 Decisions and Information.

Chapter 14 Decision Trees.

Chapter 15 The Value of Information.

Part 4 The Seven Deadly Sins of Averaging.

Chapter 16 The Seven Deadly Sins of Averaging.

Chapter 17 The Flaw of Extremes.

Chapter 18 Simpson’s Paradox.

Chapter 19 The Scholtes Revenue Fallacy.

Chapter 20 Taking Credit for Chance Occurrences.


Part 5 The Flaw of Averages in Finance.

Chapter 21 Your Retirement Portfolio.

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

Chapter 23 When Harry Met Bill(y).

Chapter 24 Mindles for the Financial Planning Client.

Chapter 25 Options: Profiting from Uncertainty.

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

Chapter 27 Prices, Probabilities, and Predictions.

Part 6 Real Finance.

Chapter 28 Holistic Versus Hole-istic.

Chapter 29 Real Portfolios at Shell.

Chapter 30 Real Options.

Chapter 31 Some Gratuitous Inflammatory Remarks on the Accounting Industry.

Part 7 The Flaw of Averages in Supply Chains.

Chapter 32 The DNA of Supply Chains.

Chapter 33 A Supply Chain of DNA.

Chapter 34 Cawlfield’s Principle.

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

Chapter 35 The Statistical Research Group of World War II.

Chapter 36 Probability and the War on Terror.

Chapter 37 The Flaw of Averages and Climate Change.

Chapter 38 The Flaw of Averages in Health Care.

Chapter 39 Sex and the Central Limit Theorem.


Part 9 Toward a Cure for the Flaw of Averages.

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

Chapter 41 Visualization.

Chapter 42 Interactive Simulation: A New Lightbulb.

Chapter 43 Scenario Libraries: The Power Grid.

Chapter 44 The Fundamental Identity of SLURP Algebra.

Chapter 45 Putting It into Practice.

Chapter 46 The CPO: Managing Probability Management.

Chapter 47 A Posthumous Visit by My Father.

Red Word Glossary.


About the Author.