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This companion workbook to the new edition of the insightful and eloquent How to Measure Anything walks readers through sample problems and exercises in which they can master and apply the methods discussed in the book. The book explains practical methods for measuring a variety of intangibles, including approaches to measuring customer. Cloij420fgwwhytjg1767 - Read and download Douglas W. Hubbard's book How to Measure Anything: Finding the Value of Intangibles in Business, Edition 3 in PDF, EPub online. Free How to Measure Anything: Finding the Value of Intangibles in Business, Edition 3 book by Douglas W.

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How to Measure Anything Finding the Value of ‘‘Intangibles’’ in Business
Douglas W. Hubbard
John Wiley & Sons, Inc.
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How to Measure Anything
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How to Measure Anything Finding the Value of ‘‘Intangibles’’ in Business
Douglas W. Hubbard
John Wiley & Sons, Inc.
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1 This book is printed on acid-free paper. 0001 Copyright # 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. Wiley Bicentennial Logo: Richard J. Pacifico No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site at http://www.wiley.com. Library of Congress Cataloging-in-Publication Data: Hubbard, Douglas W., 1962How to measure anything : finding the value of ‘‘intangibles’’ in business / Douglas W. Hubbard. p. cm. Includes index. ISBN 978-0-470-11012-6 (cloth) 1. Intangible property—valuation. I. Title. HF5681.I55H83 2007 6570 .7–dc22 2007004998 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
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I dedicate this book to the people who are my inspirations for so many things: my wife Janet and to our children Even, Madeleine, and Steven who show every potential for being renaissance people. I also would like to dedicate this book to the military men and women of the United States, so many of whom I know personally. I’ve been out of the Army National Guard for many years, but I hope my efforts at improving battlefield logistics for the U.S. Marines by using better measurements have improved their effectiveness and safety.
& Contents Preface Acknowledgments SECTION
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Measurement: The Solution Exists
CHAPTER 1
The Intangibles and the Challenge
CHAPTER 2
An Intuitive Measurement Habit: Eratosthenes, Enrico, & Emily How an Ancient Greek Measured the Size of Earth Estimating: Be Like Fermi Experiments: Not Just for Adults Notes on What to Learn from Eratosthenes, Enrico, and Emily
CHAPTER 3
SECTION
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CHAPTER 4
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The Illusion of Intangibles: Why Immeasurables Aren’t The Concept of Measurement The Object of Measurement The Methods of Measurement Economic Objections to Measurement The Broader Objection to the Usefulness of ‘‘Statistics’’ Ethical Objections to Measurement Toward a Universal Approach to Measurement
3 7 8 9 12 16
19 20 24 27 33 34 36 39
Before You Measure Clarifying the Measurement Problem Getting the Language Right: What ‘‘Uncertainty’’ and ‘‘Risk’’ Really Mean Examples of Clarification: Lessons for Business from, of All Places, Government
43 45 47 vii
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CHAPTER 5
CHAPTER 6
CHAPTER 7
SECTION
Calibrated Estimates: How Much Do You Know Now? Testing Your Ability to Assess Odds Calibration Exercise Further Improvements on Calibration Conceptual Obstacles to Calibration The Effects of Calibration Measuring Risk: Introduction to the Monte Carlo Simulation An Example of the Monte Carlo Method and Risk Tools and Other Resources for Monte Carlo Simulations The Risk Paradox Measuring the Value of Information The Chance of Being Wrong and the Cost of Being Wrong: Expected Opportunity Loss The Value of Information for Ranges The Imperfect World: The Value of Partial Uncertainty Reduction The Epiphany Equation: The Value of a Measurement Changes Everything Summarizing Uncertainty, Risk, and Information Value: The First Measurements
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III Measurement Methods
CHAPTER 8
CHAPTER 9
The Transition: From What to Measure to How to Measure Tools of Observation: Introduction to the Instrument of Measurement Decomposition Secondary Research: Assuming You Weren’t the First to Measure It The Basic Methods of Observation: If One Doesn’t Work, Try the Next Measure Just Enough Consider the Error Choose and Design the Instrument Sampling Reality: How Observing Some Things Tells Us about All Things Building an Intuition for Random Sampling: The Jelly Bean Example
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A Little About Little Samples: A Beer Brewer’s Approach The Easiest Sample Statistics Ever A Biased Sample of Sampling Methods Measure to the Threshold Experiment Seeing Relationships in the Data: An Introduction to Regression Modeling CHAPTER 10
SECTION
Bayes: Adding to What You Know Now Simple Bayesian Statistics Using Your Natural Bayesian Instinct Heterogeneous Benchmarking: A ‘‘Brand Damage’’ Application Getting a Bit More Technical: Bayesian Inversion for Ranges
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133 138 141 147 151 155
161 161 165 170 174
IV Beyond the Basics
CHAPTER 11
CHAPTER 12
Preference and Attitudes: The Softer Side of Measurement Observing Opinions, Values, and the Pursuit of Happiness A Willingness to Pay: Measuring Value via Trade-offs Putting It All on the Line: Quantifying Risk Tolerance Quantifying Subjective Trade-offs: Dealing with Multiple Conflicting Preferences Keeping the Big Picture in Mind: Profit Maximization versus Subjective Trade-offs The Ultimate Measurement Instrument: Human Judges Homo absurdus: The Weird Reasons behind Our Decisions Getting Organized: A Performance Evaluation Example Surprisingly Simple Linear Models How to Standardize Any Evaluation: Rasch Models Removing Human Inconsistency: The Lens Model Panacea or Placebo?: Questionable Methods of Measurement Comparing the Methods
183 183 187 192 195 199
203 204 207 208 210 214 219 226
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CHAPTER 13
CHAPTER 14
APPENDIX INDEX
New Measurement Instruments for Management The Twenty-First-Century Tracker: Keeping Tabs with Technology Measuring the World: The Internet as an Instrument Prediction Markets: Wall Street Efficiency Applied to Measurements A Universal Measurement Method: Applied Information Economics Bringing the Pieces Together Case: The Value of the System That Monitors Your Drinking Water Case: Forecasting Fuel for the Marine Corps Ideas for Getting Started: A Few Final Examples Summarizing the Philosophy Calibration Tests
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& Preface
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wrote this book to correct a costly myth that permeates many organizations today: that certain things can’t be measured. The widely held belief must be a significant drain on the economy, public welfare, the environment, and even national security. ‘‘Intangibles’’ such as the value of quality, employee morale, or the economic impact of cleaner water are frequently part of some critical business or government policy decision. Often, an important decision requires better knowledge of the alleged intangible but when an executive believes something to be immeasurable, attempts to measure it will not even be considered. As a result, decisions are less informed than they could be. The chance of error increases. Resources are misallocated, good ideas are rejected, and bad ideas are accepted. Money is wasted. In some cases life and health are put in jeopardy. The belief that some things—even very important things—might be impossible to measure is sand in the gears of the entire economy. Any important decision maker could benefit from learning that anything they really need to know is measurable. On the other hand, in a democracy and a free enterprise economy, voters and consumers count among these ‘‘important decision makers.’’ Chances are, your decisions in some part of your life or your professional responsibilities would be improved by better measurement. And it’s virtually certain that your life has already been affected—negatively—by the lack of measurement in someone else’s decisions. I’ve made a career out of measuring the sorts of things many thought were immeasurable. I first started to notice the need for better measurement in 1988, shortly after I started working for Coopers & Lybrand as a brand-new MBA in their management consulting practice. I was surprised at how often xi
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a client would dismiss a critical quantity—something that would affect a major new investment or policy decision—as completely beyond measurement. Statistics and quantitative methods courses were still fresh in my mind and I in some cases when someone called something ‘‘immeasurable,’’ I would remember a specific example where it was actually measured. I began to suspect any claim of immeasurability as possibly premature and I would do research to confirm or refute the claim. Time after time, I kept finding that the allegedly immeasurable thing was already measured by an academic or perhaps professionals in another industry. At the same time, I was observing that books about quantitative methods didn’t focus on making the case that everything is measurable. They also did not focus on making the material accessible to the people who really needed it. They start with the assumption that the reader already believes something to be measurable, and it is just a matter of executing the appropriate algorithm. And these books tended to assume that the objective of the reader was a level of rigor that would suffice for publication in a scientific journal—not merely a decrease in uncertainty about some critical decision with a method a non-statistician could understand. In 1995, after years of these observations, I decided that a market existed for better measurements for managers. I pulled together methods from several fields to create a solution. The wide variety of measurement-related projects I had since 1995 allowed me to fine-tune this method. Not only was every alleged immeasurable turning out not to be so, the most intractable ‘‘intangibles’’ were often being measured by surprisingly simple methods. It was time to challenge the persistent belief that important quantities were beyond measurement. In the course of writing this book, I felt as if I was exposing a big secret and that once the secret was out, perhaps a lot of things will be different. I even imagined it would be a small ‘‘scientific revolution’’ of sorts for managers—a distant cousin of the methods of ‘‘scientific management’’ introduced a century ago by Frederick Taylor. This material should be even more relevant than Taylor’s methods turned out to be for twenty-first century managers. Whereas scientific management originally focused on optimizing labor processes we now need to optimize measurements for management decisions. Formal methods for measuring those things management usually ignores has barely reached the level of alchemy. We need to move from alchemy to the equivalent of chemistry and physics.
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The publisher and I considered several titles. All the titles considered started with ‘‘How to Measure Anything’’ but it wasn’t always followed by ‘‘Finding the Value of Intangibles in Business.’’ I give a seminar called ‘‘How to Measure Anything, But Only What You Need To.’’ Since the methods in this book include computing the economic value of measurement (so that we know where to spend out measurement efforts), it seemed particularly appropriate. We also considered ‘‘How to Measure Anything: Valuing Intangibles in Business, Government and Technology’’ since there are so many technology and government examples in this book alongside the general business examples. But the title ‘‘How to Measure Anything: Finding the Value of Intangibles in Business’’ seemed to grab the right audience and convey the point of the book without necessarily excluding much of what the book is about. The book is organized into four sections. The chapters and sections should be read in order because the first three sections rely on instructions from the earlier sections. Section I makes the case that everything is measurable and offers some examples that should inspire readers to attempt measurements even when it seems impossible. It contains the basic philosophy of the entire book and, if you don’t read anything else, read this section. In particular, the specific definition of measurement discussed in this section is critical to correctly understand the rest of the book. Section II begins to get into more specific substance about how to measure things—specifically uncertainty, risk—and the value of information. These are not only measurements in their own right but, in the approach I’m proposing, prerequisites to all measurements. The reader will learn how to measure their own subjective uncertainty with ‘‘calibrated probabilities assessments’’ and how to use that information to compute risk and the value of additional measurements. It is critical to understand these concepts before moving on to the next section. Section III deals with how to reduce uncertainty by various methods of observation including random sampling and controlled experiments. It provides some short-cuts for quick approximations when possible. It also discusses methods to improve measurements by treating each observation as updating and marginally reducing a previous state of uncertainty. It reviews some material that readers may have seen in first-semester statistics courses, but it is written specifically to build on the methods discussed in the previous section. Some of the more elaborate discussions on regression
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modeling and controlled experiments could be skimmed over or studied in detail, depending on the needs of the reader. Section IV is an eclectic collection of interesting measurement solutions and case examples. It discusses methods for measuring such things as preferences, values, flexibility, or quality. It covers some new or obscure measurement instruments including calibrated human judges or even the Internet. It summarizes and pulls together the approaches covered in the rest of the book with detailed discussions of two case studies and other examples. In Chapter 1, I suggested a challenge for readers and I will reinforce that challenge by mentioning it here. Write down one or more measurement challenges you have in home life or work and read this book with the specific objective of finding a way to measure them. If those measurement influence a decision of any significance, then the cost of the book and the time to study it will be paid back many fold.
& Acknowledgments
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o many contributed to the content of this book through their suggestions, reviews and as sources of information about interesting measurement solutions. In no particular order I would like to thank the following: Freemon Dyson Peter Tippett Barry Nussbaum Skip Bailey James Randi Chuck McKay Ray Gilbert Henry Schaffer Leo Champion Tom Bakewell Bill Beaver Juliana Hale James Hammitt Rob Donat
Pat Plunkett Art Koines Terry Kunneman Luis Torres Mark Day Ray Epich Dominic Schilt Jeff Bryan Peter Schay Betty Koleson Arkalgud Ramaprasad Harry Epstein Rick Melberth Sam Savage
Jack Stenner Robyn Dawes Jay Edward Russo Reed Augliere Linda Rosa Mike McShea Robin Hansen Mary Lundz Andrew Oswald George Eberstadt David Grether Todd Wilson Emile Servan-Schreiber
Special thanks to Dominic Schilt at Riverpoint Group LLC who saw the opportunities with this approach in 1995 and gave so much support since then.
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Measurement: The Solution Exists
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& The Intangibles and the Challenge
When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science. —LORD KELVIN nything can be measured. If a thing can be observed in any way at all, it lends itself to some type of measurement method. No matter how ‘‘fuzzy’’ the measurement is, it’s still a measurement if it told you more than you knew before. And those very things most likely to be seen as immeasurable are, virtually always, solved by relatively simple measurement methods. As the title of this book indicates, we will discuss how to find the value of those things often called ‘‘intangibles’’ in business. There are two common understandings of the word intangible. First, it is routinely applied to things that, while they are literally not tangible (i.e., touchable, solid objects), can still be measured. Things like time, budget, patent ownership, and so on are
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good examples of things that you cannot touch but yet are measured. In fact, there is a well-established industry around valuing intangibles such as copyright and trademark ownership. But the word ‘‘intangible’’ has also come to mean utterly immeasurable in any way at all, directly or indirectly. It is in this context that I argue intangibles do not exist. You’ve heard of ‘‘intangibles’’ in your own organization—things that presumably defy measurement of any type. The presumption of immeasurability is, in fact, so strong that no attempt is even made to make any observations that might tell you something—anything—about the alleged immeasurable that you might be surprised to learn. You have may have run into one or more of these real-life examples: 000f
The ‘‘flexibility’’ to create new products
000f
The risk of failure of an information technology (IT) project
000f
The public health impact of a new government environmental policy
000f
The productivity of research
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The value of information
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The chance of one political party winning the White House
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Quality
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Public image
Each of these examples can very well be relevant to some major decision an organization must make. It could even be the single most important impact of an expensive new initiative in either business or government policy. Yet in most organizations, because the specific ‘‘intangible’’ was assumed to be immeasurable, the decision was not nearly as informed as it could have been. One place I’ve seen this many times is in the ‘‘steering committees’’ that review proposed projects and decide which to accept or reject. Often the proposed projects are related to IT in some way. In some cases, the committees were categorically rejecting any investment where the benefits were primarily ‘‘soft’’ ones. Important factors with names like ‘‘improved word-of-mouth advertising,’’ ‘‘reduced strategic risk,’’ or ‘‘premium brand positioning’’ were being ignored in the evaluation process because they were considered immeasurable. It’s not as if the project was being rejected simply because the person proposing it hadn’t measured the benefit (a valid
the intangibles and the challenge
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objection to a proposal); rather it was believed that the benefit couldn’t possibly be measured—ever. Consequently, some of the most important strategic proposals were being overlooked in favor of minor cost-savings ideas simply because everyone knew how to measure those things and didn’t know how to measure others. The fact of the matter is that a few organizations have succeeded in analyzing and measuring all of the listed items, using methods that are probably less complicated than you would think. The purpose of this book is to show organizations two things: 1. Intangibles that appear to be completely intractable can be measured. 2. This measurement can be done in a way that is economically justified. With a title like How to Measure Anything, anything less than a multivolume text would be sure to leave out something. My objective does not include every area of physical science or economics, especially where measurements are well developed. Those disciplines have measurement methods for a variety of interesting problems and are already much less inclined even to apply the label ‘‘intangible’’ to something they are curious about. The focus here is on measurements that are relevant—even critical—to major organizational decisions and yet don’t seem to lend themselves to an obvious and practical measurement solution. This book addresses some common misconceptions about intangibles, describes a ‘‘universal approach’’ to show how to go about measuring an ‘‘intangible,’’ and backs it up with some interesting methods for particular problems. Throughout, I attempted to include some ‘‘inspirational’’ examples on how people have tackled some of the most ‘‘immeasurable’’ things I could find. Without compromising substance, this book will also make some of the more seemingly esoteric statistics around measurement as simple as it can be. Whenever possible, math is converted into simpler charts, tables, and procedures. Some of the methods are so much simpler than what is taught in the typical ‘‘intro to stats’’ course that we should be able to overcome many phobias about the use of quantitative measurement methods. The reader does not need any advanced training in any mathematical methods at all. Readers just need some aptitude for clearly defining problems.
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the intangibles and the challenge
Readers are encouraged to use this book’s Web site at www.howto measureanything.com. There, you will find a library of downloadable spreadsheets for many of the more detailed calculations shown in this book. There will also be additional learning aids, examples, and a discussion board for questions about the book or measurement challenges in general. It also provides a way for me to discuss new technologies or techniques that were not available when this book was printed. I have one recommendation for a useful exercise to try. As you read through the chapters, write down those things you believe are immeasurable or, at least, you are not sure how to measure. After reading this book, my goal is that you are able to identify methods for measuring each and every one of them.
chapter
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& An Intuitive Measurement Habit: Eratosthenes, Enrico, & Emily
etting out to develop the skills for any kind of measurement seems pretty ambitious, and a journey like that needs a light at the end of the tunnel. What we need are some best-in-class examples to follow for measurement—individuals who saw measurement solutions intuitively and often solved measurement problems with surprisingly simple methods. Fortunately, we have many people—at the same time inspired and inspirational—to show us what such a skill would look like. It’s revealing, however, to find out that so many of the best examples seem to be from outside of business. In fact, this book will borrow heavily from outside of business to reveal measurement methods that can be applied to business. Here are just a few people who, while they weren’t working on measurement within business, can teach businesspeople quite a lot about what an intuitive feel for quantitative investigation should look like.
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In ancient Greece, a man estimated the circumference of Earth by looking at the different lengths of shadows in different cities at noon and by applying some simple geometry.
0001
A Nobel Prize–winning physicist taught his students how to estimate by estimating the number of piano tuners in Chicago.
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A nine-year-old girl set up an experiment that debunked the growing medical practice of ‘‘therapeutic touch’’ and, two years later, became the youngest person ever to be published in the Journal of the American Medical Association. 7
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You may have heard of these individuals, or at least one or two of them. Even if you vaguely remember something about them, it is worth reviewing each in the context of the others. None of these people ever met each other personally (none lived at the same time), but each showed an ability to size up a measurement problem and identify quick and simple observations that have revealing results. They were able to estimate unknowns quickly by using simple observations. It is important to contrast their approach with what you might typically see in a business setting. The characters in these examples are or were real people named Eratosthenes, Enrico, & Emily.
How an Ancient Greek Measured the Size of Earth Our first mentor of measurement did something that was probably thought by many in his day to be impossible. An ancient Greek named Eratosthenes (ca. 276–194 BC) made the first recorded measurement of the circumference of Earth. If he sounds familiar, it might be because he is mentioned in many high school trigonometry and geometry textbooks. Eratosthenes didn’t use accurate survey equipment, and he certainly didn’t have lasers and satellites. He didn’t even embark on a risky and probably lifelong attempt at circumnavigating Earth. Instead, while in the Library of Alexandria, he read that a certain deep well in Syene, a city in southern Egypt, would have its bottom entirely lit by the noon sun one day a year. This meant the sun must be directly overhead at that point in time. But he also observed that at the same time, vertical objects in Alexandria, almost straight north of Syene, cast a shadow. This meant Alexandria received sunlight at a slightly different angle at the same time. Eratosthenes recognized that he could use this information to assess the curvature of Earth. He observed that the shadows in Alexandria at noon at that time of year made an angle that was equal to an arc of one-fiftieth of a circle. Therefore, if the distance between Syene and Alexandria was one-fiftieth of an arc, the circumference of Earth must be 50 times that distance. Modern attempts to replicate Eratosthenes’s calculations vary by exactly how much the angles were, conversions from ancient units of measure, and the exact distances between the ancient cities, but typical results put his answer within 3% of the actual value.1 Eratosthenes’s calculation was a huge improvement over previous knowledge, and his error was less than the error modern scientists
estimating: be like fermi
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had just a few decades ago for the size and age of the universe. Even 1,700 years later, Columbus was apparently unaware of or ignored Eratosthenes’s result; his estimate was fully 25% short (this is one of the reasons Columbus thought he might be in India, not another large, intervening landmass). In fact, a more accurate measurement than Eratosthenes’s would not be available for another 300 years after Columbus. By then, two Frenchmen, armed with the finest survey equipment available in late-eighteenth-century France, numerous staff, and a significant grant, were finally able to do better than Eratosthenes.2 Here is the lesson for business: Eratosthenes made what might seem an impossible measurement by making a clever calculation on some simple observations. When I ask participants in my measurement and risk analysis seminars how they would make this estimate, without modern tools, they usually identify one of the ‘‘hard ways’’to do it (e.g., circumnavigation). But Eratosthenes, in fact, may not have even left the vicinity of the library to make this calculation. One set of observations that would have answered this question would have been very difficult to make, but his measurement was based on other, simpler, observations. He wrung more information out of the few facts he could confirm instead of assuming the hard way was the only way.
Estimating: Be Like Fermi Another example from outside business that might inspire measurements within business is Enrico Fermi (1901–1954), a physicist who won the Nobel Prize in physics in 1938. He had a well-developed knack for intuitive, even casual-sounding measurements. One renowned example of his measurement skills was demonstrated at the first detonation of the atom bomb, the Trinity Test site, on July 16, 1945, where he was one of the atomic scientists observing the blast from base camp. While final adjustments were being made to instruments used to measure the yield of the blast, Fermi was making confetti out of a page of notebook paper. As the wind from the initial blast wave began to blow through the camp, he slowly dribbled the confetti into the air, observing how far back it was scattered by the blast (taking the farthest scattered pieces as being the peak of the pressure wave). Fermi concluded that the yield must be greater than 10 kilotons. This would have been news, since other initial observers of the blast did not know that lower
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limit. After much analysis of the instrument readings, the final yield estimate was determined to be 18.6 kilotons. Like Eratosthenes, Fermi was aware of a rule relating one simple observation—the scattering of confetti in the wind —to a quantity he wanted to measure. The value of quick estimates was something Fermi was familiar with throughout his career. He was famous for teaching his students skills at approximation of fanciful-sounding quantities that, at first glance, they might presume they knew nothing about. The best-known example of such a ‘‘Fermi question’’ was Fermi asking his students to estimate the number of piano tuners in Chicago. His students—science and engineering majors— would begin by saying that they could not possibly know anything about such a quantity. Of course, some solutions would be to simply do a count of every piano tuner perhaps by looking up advertisements, checking with a licensing agency of some sort, and so on. But Fermi was trying to teach his students how to solve problems where the ability to confirm the results would not be so easy. He wanted them to figure out that they knew something about the quantity in question. He would start by asking them to estimate other things about pianos and piano tuners that, while still uncertain, might seem easier to estimate. These included the current population of Chicago (a little over 3 million in the 1930s to 1950s), the average number of people per household (2 or 3), the share of households with regularly tuned pianos (not more than 1 in 10 but not less than 1 in 30), the required frequency of tuning (perhaps 1 a year, on average), how many pianos a tuner could tune in a day (4 or 5, including travel time), and how many days a year the turner works (say, 250 or so). The result would be computed: Tuners in Chicago ¼ Population=people per household 0002 percentage of households with tuned pianos 0002 tunings per year=ðtunings per tuner per day 0002 workdays per yearÞ Depending on which specific values you chose, you would probably get answers in the range of 20 to 200, with something around 50 being fairly common. When this number was compared to the actual number (which Fermi might get from the phone directory or a guild list), it was always closer to the true value than the students would have guessed. This may seem like a
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very wide range, but consider the improvement this was from the ‘‘How could we possibly even guess?’’ attitude his students often started with. This approach also gave the estimator a basis for seeing where uncertainty came from. Was the big uncertainty about the share of households that had tuned pianos, how often a piano needed to be tuned, how many pianos can a tuner tune in a day, or something else? The biggest source of uncertainty would point toward a measurement that would reduce the uncertainty the most. A Fermi question is not yet quite a measurement. It is not based on new observations. It is really more of an assessment of what you already know about a problem in such a way that it can get you in the ballpark. The lesson for business is to avoid the quagmire that uncertainty is impenetrable and beyond analysis. Instead of being overwhelmed by the apparent uncertainty in such a problem, start to ask what things about it you do know. As we will see later, assessing what you currently know about a quantity is a very important step for measurement of those things that do not seem as if you can measure them at all. fermi questions for a new business
Chuck McKay, with Wizard of Ads, encourages companies to use Fermi questions to estimate the market size for a product in a given area. Last year an insurance agent asked Chuck to evaluate an opportunity to open a new office in Wichita Falls, Texas, for an insurance carrier that currently had no local presence there. Is there room for another carrier in this market? To test the feasibility of this business proposition, McKay answered a few Fermi questions with some Internet searches. Like Fermi, McKay started with the big population questions and proceeded from there. According to City-Data.com, there were 62,172 cars in Wichita Falls. According to the Insurance Information Institute, the average automobile insurance annual premium in the state of Texas was $837.40. McKay assumed that almost all cars have insurance, since it is mandatory, so the gross insurance revenue in town was $52,062,833 each year. The agent knew the average commission rate was 12%, so the total commission pool was $6,247,540 per year. According to Switchboard.com, there were 38 insurance agencies in town, a number that is very close to what was reported in Yellowbook.com. When the
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commission pool is divided by those 38 agencies, the average agency commissions are $164,409 per year. This market was probably getting tight since City-Data.com also showed the population of Wichita Falls fell from 104,197 in 2000 to 99,846 in 2005. Furthermore, a few of the bigger firms probably wrote the majority of the business, so the revenue would be even less than that—and all this before taking out office overhead. McKay’s conclusion: A new insurance agency with a new brand in town didn’t have a good chance of being very profitable, and the agent should pass on the opportunity.
Experiments: Not Just for Adults Another person who seemed to have a knack for measuring her world was Emily Rosa. Although Emily published one of her measurements in the Journal of the American Medical Association ( JAMA), she did not have a PhD or even a high school diploma. At the time she conducted the measurement, Emily was a 9-year-old working on an idea for her fourth-grade science fair project. She was just 11 years old when her research was published, making her the youngest person ever to have research published in the prestigious medical journal and perhaps the youngest in any major, peer-reviewed scientific journal. In 1996 Emily saw her mother, Linda, watching a videotape on a growing industry called ‘‘therapeutic touch,’’ a controversial method of treating ailments by manipulating the patients’ ‘‘energy fields.’’ While the patient lay still, a therapist would move his or her hands just inches away from the patient’s body to detect and remove ‘‘undesirable energies,’’ which presumably caused various illnesses. Emily suggested to her mother that she might be able to conduct an experiment on such a claim. Linda, who was a nurse and a long-standing member of the National Council Against Health Fraud (NCAHF), gave Emily some advice on the method. Emily initially recruited 15 therapists for her science fair experiment. The test involved Emily and the therapist sitting on opposite sides of a table. A cardboard screen separated them, blocking each from the view of the other. The screen had holes cut out at the bottom through which the therapist
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would place her hands, palms up, and out of sight. Emily would flip a coin and, based on the result, place her hand four to five inches over the therapist’s left or right hand. The therapists, unable to see Emily, would have to determine whether the girl was holding her hand over their left or right hand by feeling for the girl’s energy field. Emily reported her results at the science fair and got a blue ribbon—as everyone else did. Linda mentioned Emily’s experiment to Dr. Stephen Barrett, whom she knew from the NCAHF. Barrett, intrigued by both the simplicity of the method and the initial findings, then mentioned it to the producers of the TV show Scientific American Frontiers shown on the Public Broadcasting System. In 1997 the producers shot an episode on Emily’s method, and Emily recruited 13 more therapists for the show, for a total of 21. The 21 therapists made a total of 280 individual attempts to feel Emily’s energy field. They correctly identified the position of Emily’s hand just 44% of the time. Left to chance alone, they should get about 50% right with a 95% confidence interval of +/000316%. (If you flipped 280 coins, there is a 95% chance that between 44% and 66% would be heads.) So the therapists may have been a bit unlucky (since they ended up on the bottom end of the range), but their results are not out of bounds of what could be explained by chance alone. In other words, people ‘‘uncertified’’ in therapeutic touch— you or I—could have just guessed and done as well as or better than the therapists. With these results, Linda and Emily thought the work might be worthy of publication. In April 1998 Emily, then 11 years old, had her experiment published in the JAMA. That earned her a place in the Guinness Book of World Records as the youngest person ever to have research published in a major scientific journal and a $1,000 award from the James Randi Educational Foundation. James Randi, retired magician and renowned skeptic, set up a foundation for investigating paranormal claims scientifically. Randi created the $1 million ‘‘Randi Prize’’ for anyone who can scientifically prove extrasensory perception (ESP), clairvoyance, dowsing, and the like. Randi dislikes labeling his efforts as ‘‘debunking’’ paranormal claims since he just assesses the claim with scientific objectivity. But since hundreds of applicants have been unable to claim the prize by passing simple scientific tests of their paranormal claims, debunking has been the net effect. Even before Emily’s experiment was published, Randi was also interested in therapeutic
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touch and was trying to test it. But, unlike Emily, he managed to recruit only one therapist who would agree to an objective test—and that person failed. After these results were published, therapeutic touch proponents stated a variety of objections to the experimental method, claiming it proved nothing. Some stated that the distance of the energy field was really one to three inches, not the four or five inches Emily used in her experiment.3 Others stated that the energy field was fluid, not static, and Emily’s unmoving hand was an unfair test. (This despite the fact that patients usually lie still during their ‘‘treatment.’’)4 None of this surprises Randi. ‘‘People always have excuses afterward,’’ he says. ‘‘But prior to the experiment every one of the therapists were asked if they agreed with the conditions of the experiment. Not only did they agree, but they felt confident they would do well.’’ Of course, the best refutation of Emily’s results would simply be to set up a controlled, valid experiment that conclusively proves therapeutic touch does work. No such refutation has yet been offered. Randi has run into retroactive excuses to explain failures to demonstrate paranormal skills so often that he has added another small demonstration to his tests. Prior to the taking the test, Randi has subjects sign an affidavit stating that they agreed to the conditions of the test, that they would later offer no objections to the test, and that, in fact, they expected to do well under the stated conditions. At that point Randi hands them a sealed envelope. After the test, when they attempt to reject the outcome as poor experimental design, he asks them to open the envelope. The letter in the envelope simply states ‘‘You have agreed that the conditions were optimum and that you would offer no excuses after the test. You have now offered those excuses.’’ Randi observes, ‘‘They find this extremely annoying.’’ The lesson here for business is manyfold. First, even touchy-feelysounding things like ‘‘employee empowerment,’’ ‘‘creativity,’’ or ‘‘strategic alignment’’ must have observable consequences if they matter at all. I’m not saying that such things are ‘‘paranormal,’’ but the same rules apply. Second, Emily’s experiment demonstrated the effectiveness of simple methods routinely used in scientific inquiry, such as a controlled experiment, sampling (even a small sample), randomization, and using a type of ‘‘blind’’ to avoid bias from the test subject or researcher. These simple elements can be combined to allow us to observe and measure a variety of phenomena. Also, Emily showed that useful levels of experimentation can be understood by even a child on a small budget. (Linda Rosa said she spent
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$10 on the experiment.) It’s also interesting to note that Emily could have constructed a much more elaborate clinical trial of the effects of this method using test groups and control groups to test how much therapeutic touch improves health. But she didn’t have to do that because she simply asked a more basic question. If the therapists can do what they claimed, then they must, Emily reasoned, at least be able to feel the energy field. If they can’t do that (and it is the basic assumption of the claimed benefits), then everything about therapeutic touch is in doubt. She could have found a way to spend much more if she had, say, the budget of one of the smaller clinical studies in medical research. But she determined all she needed with more than adequate accuracy. By comparison, how many of your performance metrics methods could get published in a scientific journal? Emily’s example shows us how simple methods can produce a useful result. I have at times heard that ‘‘more advanced’’ measurements like controlled experiments should be avoided because upper management won’t understand them. This seems to assume that all upper management really does succumb to the Dilbert Principle5 (the rule that states that only the least competent get promoted). In my experience, upper management will understand it just fine, if you explain it well. Emily, explain it to them, please. example: mitre information infrastructure
An interesting business example of how a business might measure an ‘‘intangible’’ by first testing if it exists at all is the case of the Mitre Information Infrastructure (MII). This system was developed in the late 1990s by Mitre Corporation, a not-for-profit that provides federal agencies with consulting on system engineering and information technology. MII was a corporate knowledge base that spanned insular departments to improve collaboration. In 2000 CIO Magazine wrote a case study about MII. The magazine’s format for this sort of thing is to have a staff writer do all the heavy lifting for the case study itself and then to ask an outside expert to write an accompanying opinion column the called ‘‘Critical Analysis.’’ The magazine often asked me to write the opinion column when the case was anything about value, measurement, risk, and so on, so I was asked to do so for the MII case.
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The Critical Analysis column is meant to offer some balance in the case study since companies talking about some new initiative are likely to paint a pretty rosy picture. The article quotes Al Grasso, the chief information officer (CIO) at the time: ‘‘Our most important gain can’t be as easily measured—the quality and innovation in our solutions that become realizable when you have all this information at your fingertips.’’ However, in the opinion column, I suggested one fairly easy measure of ‘‘quality and innovation’’: ‘‘If MII really improves the quality of deliverables, then it should affect customer perceptions and ultimately revenue.6Simply ask a random sample of customers to rank the quality of some pre-MII and post-MII deliverables (make sure they don’t know which is which) and if improved quality has recently caused them to purchase more services from Mitre.’’7
Like Emily, I proposed that Mitre not ask quite the same question the CIO might have started with, but a simpler, related question. If quality and innovation really did get better, shouldn’t someone at least be able to tell that there is any difference? If the relevant judges (i.e., the customers) can’t tell, in a blind test, that post-MII research is ‘‘higher quality’’ or ‘‘more innovative’’ than pre-MII research, then MII shouldn’t have any bearing on customer satisfaction or, for that matter, revenue. If, however, they can tell the difference, then you can worry about next question: whether the revenue improved enough to be worth the investment of over $7 million by 2000. Like everything else, if Mitre’s quality and innovation benefits could not be detected, then they don’t matter. I’m told by current and former Mitre employees that my column created a lot of debate. However, they were not aware of any such attempt actually to measure quality and innovation. Remember, the CIO said this would be the most important gain of MII, and it went unmeasured.
Notes on What to Learn from Eratosthenes, Enrico, & Emily Taken together, Eratosthenes, Enrico, & Emily show us something very different from what we are typically exposed to in business. Executives often say ‘‘We can’t even begin to guess at something like that.’’ They dwell ad
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infinitum on the overwhelming uncertainties. Instead of making any attempt at measurement, they prefer to be stunned into inactivity by the apparent difficulty in dealing with these uncertainties. Fermi might say, ‘‘Yes, there are a lot of things you don’t know, but what do you know?’’ Other managers might object: ‘‘There is no way to measure that thing without spending millions of dollars.’’ As a result, they opt not to engage in a smaller study—even though the costs might be very reasonable—because such a study would have more error than a larger one. Yet perhaps even this uncertainty reduction might be worth millions, depending on the size and frequency of the decision it is meant to support. Eratosthenes and Emily might point out that useful observations can tell you something you didn’t know before—even on a budget—if you approach the topic with just a little more creativity and less defeatism. Eratosthenes, Enrico, & Emily inspire us in different ways. Eratosthenes had no way of computing the error on his estimate, since statistical methods for computing error would not be around for two more millennia. However, if he would have had a way to compute error, the errors in measuring distances between cities and exact angles of shadows might have easily accounted for his relatively small error. The concept of measurement as ‘‘error reduction’’ is a central theme of this book. Likewise, our inspiration can be attributed only in part to Enrico Fermi. Since he won a Nobel Prize, it’s safe to assume that Fermi was an especially proficient experimental and theoretical physicist. But the example of his ‘‘Fermi questions’’ showed, even for non-Nobel Prize winners, how we can estimate things that, at first, seem too difficult even to attempt to estimate. Although his insight on advanced experimental methods of all sorts would be enlightening, I find that the reason intangibles seem intangible is almost never for lack of the most sophisticated measurement methods. Usually things that seem immeasurable in business reveal themselves to much simpler methods of observation, once we learn to see through the illusion of immeasurability. In this context, Fermi’s value to us is in how we determine our current state of knowledge about a thing as a precursor to further measurement. Unlike Fermi’s example, Emily’s example is not so much about initial estimation since her experiment made no prior assumptions about how probable the therapeutic touch claims were. Nor is it about using a clever calculation instead of infeasible observations, like Eratosthenes. Her
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calculation was merely based on standard sampling methods and did not itself require a leap of insight like Eratosthenes’s simple geometry calculation. But Emily does demonstrate that useful observations are not necessarily complex, expensive, or even, as is sometimes claimed, beyond the comprehension of upper management even for ephemeral concepts like touch therapy or strategic alignment. And as useful as these lessons are, we will build even further on the lessons Eratosthenes, Enrico, & Emily. We will learn ways to assess your current uncertainty about a quantity that improve on Fermi’s methods, some sampling methods that are in some ways even simpler than what Emily used, and simple methods that would have allowed even Eratosthenes to improve on his estimate.
& endnotes 1. M. Lial and C. Miller, Trigonometry, 3rd ed. (Chicago: Scott, Foresman 1988). 2. Two Frenchmen, Pierre-Franois-Andre´ Me´chain and Jean-Baptiste-Joseph, calculated Earth’s circumference over a seven-year period during the French Revolution on a commission to define a standard for the meter. (The meter was originally defined to be one 10-millionth of the distance from the equator to the pole.) 3. Letter to the Editor, New York Times, April 7, 1998. 4. ‘‘Therapeutic Touch: Fact or Fiction?’’ Nurse Week, June 7, 1998. 5. Scott Adams, The Dilbert Principle. (New York: Harper Business, 1996). 6. Although a not-for-profit, Mitre still has to keep operations running by generating revenue through consulting billed to federal agencies. 7. Doug Hubbard, Critical Analysis column accompanying ‘‘An Audit Trail,’’ CIO Magazine, May 1, 2000.
chapter
3
& The Illusion of Intangibles: Why Immeasurables Aren’t
here are three reasons why people think that something can’t be measured. Each of these three reasons is actually based on misconceptions about different aspects of measurement: concept, object, and method.
T
Concept of measurement. The definition of measurement itself is widely misunderstood. If one understands what it actually means, a lot more things become measurable. Object of measurement. The thing being measured is not well defined. Sloppy and ambiguous language gets in the way of measurement. Methods of measurement. Many procedures of empirical observation are not well known. If people were familiar with some of these basic methods, it would become apparent that many things thought to be immeasurable are not only measurable but may already have been measured. A good way to remember these three common misconceptions is by using a mnemonic like ‘‘howtomeasureanything.com,’’ where the c, o, and m in ‘‘.com’’ stand for concept, object, and method. Once we learn that these three objections are misunderstandings of one sort or another, it becomes apparent that everything really is measurable. In addition to these reasons why something can’t be measured, there are also three common reasons why something ‘‘shouldn’t’’ be measured. The reasons often given for why something ‘‘shouldn’t’’ be measured are: 19
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1. The economic objection to measurement (i.e., any measurement would be too expensive) 2. The general objection to the usefulness and meaningfulness of statistics (i.e., ‘‘You can prove anything with statistics’’) 3. The ethical objection (i.e., we shouldn’t measure it because it would be immoral to measure it) These three objections don’t really argue that a measurement is impossible, just that it is not cost effective, is useless, or is morally objectionable. I will show that only the economic objection has any potential merit, but even that one is overused.
The Concept of Measurement As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. —ALBERT EINSTEIN Although this may seem a paradox, all exact science is based on the idea of approximation. If a man tells you he knows a thing exactly, then you can be safe in inferring that you are speaking to an inexact man. —BERTRAND RUSSELL, BRITISH
MATHEMATICIAN AND PHILOSOPHER
For those who believe something to be immeasurable, the concept of measurement, or rather the misconception of it, is probably the most important obstacle to overcome. If we incorrectly think that measurement means meeting some nearly unachievable criteria, then few things will seem measurable. I routinely ask those who attend my seminars or conference lectures what they think ‘‘measurement’’ means. (It’s interesting to see how much thought this provokes among people who are actually in charge of some measurement initiative in their organization.) I usually get answers like ‘‘to quantify something,’’ ‘‘to compute an exact value,’’ ‘‘to reduce to a single number,’’ or ‘‘to choose a representative amount,’’ and so on. Implicit or explicit in all of these answers is that measurement is certainty—an exact
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quantity with no room for error. If that was really what the term means, then, indeed, very few things would be measurable. But when scientists, actuaries, or statisticians perform a measurement, they seem to be using a different de facto definition. In their special fields, each of these professions has learned the need for a precise use of certain words sometimes very different from how the general public uses a word. Consequently, members of these professions usually are much less confused about the meaning of the word ‘‘measurement.’’ The key to this precision is that their specialized terminology goes beyond a one-sentence definition and are part of a larger theoretical framework. In physics, gravity is not just some dictionary definition, but a component of specific equations that relate gravity to such concepts as mass, distance, and its effect on space and time. Likewise, if we want to understand measurement with that same level of precision, we have to know something about the theoretical framework behind it . . . or we really don’t understand it at all. a definition of measurement
Measurement: A set of observations that reduce uncertainty where the result is expressed as a quantity
For all practical purposes, the scientific crowd treats measurement as a set of observations that reduce uncertainty where the result is expressed as a quantity. A mere reduction, not necessarily elimination, of uncertainty will suffice for a measurement. Even if they don’t articulate this definition exactly, the methods they use make it clear that this is what they really mean. The fact that some amount of error is unavoidable but can still be an improvement on prior knowledge is central to how experiments, surveys, and other scientific measurements are performed. The practical differences between this definition and the most popular definitions of measurement are enormous. Not only does a true measurement not need to be infinitely precise to be considered a measurement, but the lack of reported error—implying the number is exact—can be an indication that empirical methods, such as sampling and experiments, were
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not used (i.e., it’s not really a measurement at all). Real scientific methods report numbers in ranges, such as ‘‘the average yield of corn farms using this new seed increased between 10% and 18% [95% confidence interval]).’’ Exact numbers reported without error might be calculated ‘‘according to accepted procedure,’’ but, unless they represent a 100% complete count (e.g., the change in my pocket), they are not necessarily based on empirical observation (e.g., Enron’s asset valuations). This conception of measurement might be new to many readers, but there are strong mathematical foundations—as well as practical reasons— for looking at measurement this way. Measurement is, at least, a type of information and, as a matter of fact, there is a rigorous theoretical construct for information. A field called information theory was developed in the 1940s by Claude Shannon. Shannon was an American electrical engineer, mathematician, and all-around savant who dabbled in robotics and computer chess programs. In 1948 he published a paper titled ‘‘A Mathematical Theory of Communication,’’ which laid the foundation for information theory and measurement in general. Current generations don’t entirely appreciate this, but his contribution can’t be overstated. Information theory has since become the basis of all modern signal processing theory. It is the foundation for the engineering of every electronic communications system, including every microprocessor ever built. Shannon proposed a mathematical definition of information as the amount of uncertainty reduction in a signal, which he discussed in terms of the ‘‘entropy’’ removed by a signal. To Shannon, the receiver of information could be described as having some prior state of uncertainty. That is, the receiver already knew something, and the new information merely removed some, not necessarily all, of the receiver’s uncertainty. The receiver’s prior state of knowledge or uncertainty can be used to compute such things as the limits to how much information can be transmitted in a signal, the minimal amount of signal to correct for noise, and the maximum data compression possible. This ‘‘uncertainty reduction’’ point of view is what is critical to business. Major decisions made under a state of uncertainty—such as whether to approve large information technology (IT) projects or new product development—can be made better, even if just slightly, by reducing uncertainty. Such uncertainty reduction can be worth millions.
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So a measurement doesn’t have to eliminate uncertainty after all. A mere reduction in uncertainty counts as a measurement and possibly can be worth much more than the cost of the measurement. But there is another key concept of measurement that would surprise most people: A measurement doesn’t have to be about a quantity in the way that we normally think of it. Note where the definition I offer for measurement says ‘‘where the result is expressed as a quantity.’’ The uncertainty, at least, has to be quantified, but the subject of observation might not be a quantity itself—it could be entirely qualitative, such as a membership in a set. For example, we could ‘‘measure’’ whether a patent will be awarded or whether a merger will happen while still satisfying our precise definition of measurement. But our uncertainty about those observations must be expressed quantitatively (e.g., there is an 85% chance we will win the patent dispute; we are 93% certain our public image will improve after the merger, etc.). The view that measurement applies to questions with a yes/no answer or other qualitative distinctions is consistent with another accepted school of thought on measurement. In 1946 the psychologist Stanley Smith Stevens wrote an article called ‘‘On the Theory of Scales and Measurement.’’ In it he describes different scales of measurement, including ‘‘nominal’’ and ‘‘ordinal.’’ Nominal measurements are simply ‘‘set membership’’ statements, such as whether a fetus is male or female, or whether you have a particular medical condition. In nominal scales, there is no implicit order or sense of relative size. A thing is simply in one of the possible sets. Ordinal scales, however, allow us to say one value is ‘‘more’’ than another, but not by how much. Examples of this are the four-star rating system for movies or Mohs hardness scale for minerals. A ‘‘4’’ on either of these scales is ‘‘more’’ than a ‘‘2’’ but not necessarily twice as much. But for homogeneous units such as dollars, kilometers, liters, volts, and the like, we can add these units in a way that makes sense. Whereas seeing four one-star movies is not necessarily as good as seeing one four-star movie, a four-ton rock weighs exactly as much as four one-ton rocks. A unit also allows us to compute ratios that make sense (e.g., four kilometers is really twice as far as two km). Nominal and ordinal scales might challenge our preconceptions about what ‘‘scale’’ really means, but they are still useful observations about things. To a geologist, it is useful to know that one rock is harder than another, without necessarily having to know exactly how much harder—which is all that the Mohs hardness scale really does.
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Stevens and Shannon each challenge different aspects of the popular definition of measurement. Stevens was more concerned about a taxonomy of different types of measurement but was silent on the all-important concept of uncertainty reduction. Shannon, working in a different field altogether, was probably unaware of and unconcerned with how Stevens, a psychologist, mapped out the field of measurements just two years earlier. However, I don’t think a practical definition of measurement that accounts for all the sorts of things a business might need to measure is possible without both concepts of measurement. The field of measurement theory attempts to deal with both of these issues, and more. In measurement theory, a measurement is a type of ‘‘mapping’’ between the thing being measured and numbers. The theory gets very esoteric, but if we focus on the contributions of Shannon and Stevens, there are many lessons for managers. The commonplace notion that presumes measurements are exact quantities ignores the usefulness of simply reducing uncertainty, if eliminating uncertainty is not possible or economical. In business, decision makers make decisions under uncertainty. When that uncertainty is about big, risky decisions, then uncertainty reduction has a lot of value—and that is why we will use that definition of measurement.
The Object of Measurement A problem well stated is a problem half solved. —CHARLES KETTERING (1876–1958), AMERICAN INVENTOR, 300 PATENTS, INCLUDING ELECTRICAL IGNITION FOR
HOLDER OF
AUTOMOBILES
There is no greater impediment to the advancement of knowledge than the ambiguity of words. —THOMAS REID (1710–1769), SCOTTISH
PHILOSOPHER
Even when this more useful concept of measurement is adopted, some things seem immeasurable because we simply don’t know what we mean when we first pose the question. We don’t really know what it is we want to
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measure: the object of measurement. If someone asks how to measure ‘‘strategic alignment’’ or ‘‘flexibility’’ or ‘‘customer satisfaction,’’ I simply ask: ‘‘What do you mean, exactly?’’ It is interesting how often people further refine their use of the term in a way that almost answers the measurement question by itself. At my seminars, I often ask the audience to challenge me with difficult or seemingly impossible measurements. In one case, a participant offered ‘‘mentorship’’ as something difficult to measure. I said, ‘‘That sounds like something one would like to measure. I might say that more mentorship is better than less mentorship. I can see people investing in ways to improve it, so I can understand the why someone might want to measure it. So, what do you mean by ‘mentorship’?’’ The person almost immediately responded, ‘‘I don’t think I know,’’ to which I said, ‘‘Well, then maybe that’s why it seems hard to measure to you. You have to figure out what it is first.’’ If I simply ask people what they mean and how it matters to them, they often answer the measurement question themselves. This is usually my first level of analysis when I conduct what I’ve called clarification workshops. It’s simply a matter of clients stating a particular, but ambiguous, item they want to measure. I follow up by asking ‘‘What do you mean by ?’’ In 2000, when the Department of Veterans Affairs asked me to help them define performance metrics for IT security, I asked: ‘‘What do you mean ‘IT security’?’’ and over the course of two or three more workshops, they defined it for me. They eventually revealed that what they meant by ‘‘IT security’’ were things like a reduction in unauthorized intrusions and virus attacks. They proceeded to describe that these things impact the organization through fraud losses, lost productivity, or even potential legal liabilities (which they may have narrowly averted when they recovered a stolen notebook computer in 2006 that contained the Social Security numbers of 26.5 million veterans). All of the identified impacts were, in almost every case, obviously measurable. ‘‘Security’’ was a vague concept until they decomposed it into what they actually expected to observe. Still, clients often need further direction when defining these original concepts in a way that lends them to measurement. For the tougher jobs, I resort to using a ‘‘clarification chain’’ or, if that doesn’t work, perhaps a type of thought experiment.
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The clarification chain is just a short series of connections that should bring us from thinking of something as an intangible to thinking of it as a tangible. First, we recognize that if X is something that we care about, then X, by definition, must be detectable in some way. How could we care about things like ‘‘quality,’’ ‘‘risk,’’ ‘‘security,’’ or ‘‘public image’’ if these things were totally undetectable, in any way, directly or indirectly? If we have reason to care about some unknown quantity, it is because we think it corresponds to desirable or undesirable results in some way. Second, if this thing is detectable, then it must be detectable in some amount. If you can observe a thing at all, you can observe more of it or less of it. Once we accept that much, the final step is perhaps the easiest. If we can observe it in some amount, then it must be measurable. For example, once we figure out that we care about ‘‘public image’’ because it impacts specific things like advertising by customer referral which affects sales, then we have begun to identify how to measure it. Customer referrals are not only detectable, but detectable in some amount; this means they are measurable. I may not specifically take people through every part of the clarification chain, but if we can keep these three components in mind, the method is fairly successful.
clarification chain
1. If it matters at all, it is detectable/observable. 2. If it is detectable, it can be detected as an amount (or range of possible amounts). 3. If it can be detected as a range of possible amounts, it can be measured.
If the clarification chain doesn’t work, I might try a thought experiment. Imagine you are an alien scientist who can clone pairs not just of sheep or even people, but entire organizations. Let’s say you were studying a particular fast food chain and you were studying the effect of a particular intangible, say ‘‘employee empowerment.’’ You create a pair of the same organization
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calling one the ‘‘test’’ group and one the ‘‘control’’ group. You give the test group a little bit more ‘‘employee empowerment’’ while holding the amount in the control group constant. What do you actually observe—in any way, directly or indirectly—that would change for the first organization? Would you expect decisions to be made at a lower level in the organization? Would this mean those decisions are better or faster? Does it mean that employees require less supervision? Does that mean you can have a ‘‘flatter’’ organization with less management overhead? If you can identify even a single observation that would be different between the two cloned organizations, then you are well on the way to identifying how you would measure it. Identifying the object of measurement really is the beginning of almost any scientific inquiry, including the truly revolutionary ones. Business managers need to realize that some things seem intangible only because the managers just haven’t defined what they are talking about. Figure out what you mean and you are halfway to measuring it.
The Methods of Measurement Some things may seem immeasurable only because the person considering the measurement might not be aware of basic measurement methods — such as various sampling procedures or types of controlled experiments—that can be used to solve the problem. A common objection to measurement is that the problem is unique and has never been measured before, and there simply is no method that would ever reveal its value. It is encouraging to know that several proven measurement methods can be used for a variety of issues to help measure something you may have at first considered immeasurable. Here are a few examples. 000f
Measuring with very small random samples (e.g., can you learn something from a small sample of potential customers, employees, and so on, especially when there is currently a great deal of uncertainty?)
000f
Measuring the population of things that you will never see all of (e.g., the number of a certain type of fish in the ocean, the number of plant species in the rain forests, the number of production errors in a new product or of unauthorized access attempts in your system that go undetected, etc.)
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000f
Measuring when many other, even unknown, variables are involved (e.g., is the new ‘‘quality program’’ the reason for the increase in sales, or was it the economy, competitor mistakes, a new pricing policy, etc.?)
000f
Measuring the risk of rare events (e.g., the chance of a launch failure of a rocket that has never flown before, or another September 11 attack, or another levee failure in New Orleans)
000f
Measuring the value of art, free time, or reducing risk to your life by assessing how much people actually pay for these things
Most of these approaches to measurements are just variations on basic methods involving different types of sampling and experimental controls and, sometimes, choosing to focus on different types of questions. Basic methods of observation like these are mostly absent from certain decisionmaking processes in business, perhaps because such scientific procedures are considered to be some elaborate, overly formalized process. Such methods are not usually considered to be something you might do, if necessary, on a moment’s notice with little cost or preparation. And yet they can be. Here is a very simple example of a quick measurement anyone can do with an easily computed statistical uncertainty. Suppose you want to consider more telecommuting for your business. One relevant factor when considering this type of initiative is how much time the average employee spends commuting every day. You could engage in a formal office-wide census of this question, but it would be time consuming and expensive and will probably give you more precision than you need. Suppose, instead, you just randomly pick five people. There are some other issues we’ll get into later about what constitutes ‘‘random,’’ but, for now, let’s just say you cover your eyes and pick names from the employee directory. Call these people and, if they answer, ask them how long their commute typically is. When you get answers from five people, stop. Let’s suppose the values you get are 30, 60, 45, 80, and 60 minutes. Take the highest and lowest values in the sample of five: 35 and 80. There is a 93% chance that the median of the entire population of employees is between those two numbers. I call this ‘‘the Rule of Five.’’ The Rule of Five is simple, it works, and it can be proven to be statistically valid for a wide range of problems. With a sample this small, the range might be very wide, but if it was significantly narrower than your previous range, then it counts as a measurement.
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rule of five
There is a 93% chance that the median of a population is between the smallest and largest values in any random sample of five from that population.
It might seem impossible to be 93% certain about anything based on a random sample of just five, but it’s true. To understand why it is true, it is important to note that the Rule of Five estimates the median of a population. The median is the point where half the population is above it and half is below it. If we randomly picked five values that were all above the median or all below it, then the median would be outside our range. But what is the chance of that, really? The chance of randomly picking a value above the median is, by definition, 50%— the same as a coin flip resulting in ‘‘heads.’’ The chance of randomly selecting five values that happen to be all above the median is like flipping a coin and getting heads five times in a row. The chance of getting heads five times in a row in a random coin flip is 1 in 32, or 3.125%; the same is true with getting five tails in a row. The chance of not getting all heads or all tails is then 100%: 3.125% 0002 2, or 93.75%. Therefore, the chance of at least one out of a sample of five being above the median and at least one being below is 93.75% (round it down to 93% or even 90% if you want to be conservative). Some readers might remember a statistics class that discussed sampling methods for very small samples. Those methods were a little more complicated than the Rule of Five, but, for reasons I’ll discuss in more detail later, the answer is really not much better. We can improve on a rule of thumb like this by using simple methods to account for certain types of bias. Perhaps recent, but temporary, construction increased everyone’s ‘‘average commute time’’ estimate. Or perhaps people with the longest commutes are more likely to call in sick or otherwise not be available for your sample. Still, even with acknowledged shortcomings, the Rule of Five is something that the person who wants to develop an intuition for measurement keeps handy. Later I’ll consider various methods that are proven to reduce uncertainty further. Some involve (slightly) more elaborate sampling or experimental methods. Some involve methods that are statistically proven simply to
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remove more error from experts’ subjective judgments. There are all sorts of issues to consider if we wish to make even more precise estimates, but, remember, as long as an observation told us something we didn’t know before, it was a measurement. In the meantime, it’s useful to consider why the objection ‘‘A method doesn’t exist to measure this thing’’ is really not valid. In business, if the data for a particular question cannot already be found in existing accounting reports or databases, the object of the question is too quickly labeled as intangible. Even if measurements are thought to be possible, often the methods to do so are considered the domain of specialists or not practical for businesspeople to engage in themselves. Fortunately, this does not have to be the case. Just about anyone can develop an intuitive approach to measurement. An important lesson comes from the origin of the word ‘‘experiment.’’ ‘‘Experiment’’ comes from the Latin ex-, meaning ‘‘of/from,’’ and periri, meaning ‘‘try/attempt.’’ It means, in other words, to get something by trying. The statistician David Moore, the 1998 president of the American Statistical Association, goes so far as to say: ‘‘If you don’t know what to measure, measure anyway. You’ll learn what to measure.’’1 We might call Moore’s approach the Nike method: the ‘‘Just do it’’school of thought. This sounds like a ‘‘Measure first, ask questions later’’ philosophy of measurement, and I can think of a few shortcomings to this approach if taken to extremes. But it has some significant advantages over much of the current measurement-stalemate thinking of some managers. Many decision makers avoideven trying tomake anobservation by thinking of a variety of obstacles to measurements. If you want to measure how much time peoplespend in a particular activity by usinga survey, they mightsay: ‘‘Yes, but people won’t remember exactly how much time they spend.’’ Or if you were getting customer preferences by a survey, they might say: ‘‘There is so much variance among our customers that you would need a huge sample.’’ If you were attempting to show whether a particular initiative increased sales, they respond: ‘‘But lots of factors affect sales. You’ll never know how much that initiative affectedit.’’ Objections like thisare alreadypresuming whatthe results of observations will be. The fact is, these people have no idea whether such issues will make measurement futile. They simply assume it. Such critics are working with a set of assumptions about the difficulty of measurement. They might even claim to have a background in measurement that provides some authority (i.e., they took two semesters of statistics
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20 years ago). I won’t say those assumptions actually turn out to be true or untrue in every particular case. I will say they are unproductive if they are simply assumptions. Let’s propose another set of assumptions that—by being assumptions—may not always be true in every single case but, in practice, turn out to be much more effective. four useful measurement assumptions
1. Your problem is not as unique as you think. 2. You have more data than you think. 3. You need less data than you think. 4. There is a useful measurement that is much simpler than you think.
Assumption 1 It’s been done before. No matter how difficult or ‘‘unique’’ your measurement problem seems to you, assume it has been done before by someone else, perhaps in another field. If this assumption turns out not to be true, then take comfort in knowing that you might have a shot at a Nobel Prize for the discovery. Seriously, I’ve noticed that there is a tendency among professionals in every field to perceive their field as unique in terms of the burden of uncertainty. The conversation generally goes something like this: ‘‘Unlike other industries, in our industry every problem is unique and unpredictable,’’ or ‘‘My industry just has too many factors to allow for quantification,’’ and so on. I’ve done work in lots of different fields, and most of them make these same claims. So far, each one of them has turned out to have fairly standard measurement problems not unlike those in other fields. Assumption 2 You have far more data than you think. Assume the information you need to answer the question is somewhere within your reach and if you just took the time to think about it, you might find it. Few executives are even remotely aware of all the data that are routinely tracked and recorded in their
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organization. The things you care about measuring are also things that tend to leave tracks, if you are resourceful enough to find them. Assumption 3 You need far less data than you think. There are a lot of problems where the Rule of Five really does reduce uncertainty. I’ve met statisticians who didn’t believe in the rule until they worked out the math for themselves. But, as Eratosthenes shows us, there are clever ways to squeeze interesting findings from minute amounts of data. Assumption 4 There is a useful measurement that is much simpler than you think. Assume the first approach you think of is the ‘‘hard way’’ to measure. Assume that, with a little more ingenuity, you can identify an easier way. The Cleveland Orchestra, for example, wanted to measure whether its performances were improving. Many business analysts might propose some sort of randomized patron survey repeated over time. Perhaps they might think of questions that rate a particular performance (if the patron remembers) from ‘‘poor’’ to ‘‘excellent,’’ and maybe they would evaluate them on several parameters and combine all these parameters into a ‘‘satisfaction index.’’ The Cleveland Orchestra was just a bit more resourceful with the data available: It started counting the number of standing ovations. While there is no obvious difference among performances that differ by a couple of standing ovations, if we see a significant increase over several performances with a new conductor, then we can draw some useful conclusions about that new conductor. It was a measurement in every sense, a lot less effort than a survey, and—some would say—more meaningful. (I can’t disagree.) So, don’t assume that the only way to reduce your uncertainty is using an impractically sophisticated method. Are you trying to get published in a peer-reviewed journal, or are you just trying to reduce your uncertainty about a real-life business decision? Think of measurement as iterative. Start measuring it. You can always adjust the method based on initial findings. Above all else, the intuitive experimenter, as the origin of the word ‘‘experiment’’denotes, makes an attempt. It’s a habit. Unless you can precisely predict the outcome of an attempted observation—of any kind —then that
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observation tells you something you didn’t know. Make a few more observations, and you know even more. There might be the rare case where only for lack of the most sophisticated measurement methods, something seems immeasurable. But for those things labeled ‘‘intangible,’’ more advanced, sophisticated methods are almost never what is lacking. Things that are thought to be intangible tend to be so uncertain that even the most basic measurement methods are likely to reduce some uncertainty.
Economic Objections to Measurement The concept, object, and method objections, we learned, are all simply illusions. But there are also objections to measurement based not on the belief that a thing can’t be measured but that it shouldn’t be measured. Perhaps the only valid basis to say that a measurement shouldn’t be made is that the cost of the measurement exceeds its benefits. This certainly happens in the real world. In 1995 I developed a method I called Applied Information Economics, a method for assessing uncertainty, risks, and intangibles in any type of big, risky decision you can imagine. A key step in the process (in fact, the reason for the name) is the calculation of the economic value of information. I’ll say more about this later, but a proven formula from the field of decision theory allows us to compute a monetary value for a given amount of uncertainty reduction. I put this formula in an Excel macro and, for years, I’ve been computing the economic value of measurements on every variable in dozens of various large business decisions. I found some fascinating patterns through this calculation but, for now, I’ll mention just one: Most of the variables in a business case had an information value of zero. In each business case, something like one to four variables were both uncertain enough and had enough bearing on the outcome of the decision to merit deliberate measurement efforts. only a few things matter In business cases, only a few key variables merit deliberate measurement efforts. The rest of the variables have an ‘‘information value’’ at or near zero.
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However, while there are certainly variables that do not justify measurement, a persistent misconception is that unless a measurement meets an arbitrary standard (e.g., adequate for publication in an academic journal or meets generally accepted accounting standards), it has no value. This is a slight oversimplification, but what really makes a measurement of high value is a lot of uncertainty combined with a high cost of being wrong. Whether it meets some other standard is irrelevant. If you are betting a lot of money on the outcome of a variable that has a lot of uncertainty, then even a marginal reduction in your uncertainty has a computable monetary value. For example, suppose you think developing an expensive new product feature will increase sales in one particular demographic by up to 12%, but it could be a lot less. Furthermore, you believe the initiative is not costjustified unless sales are improved by at least 9%. If you make the investment and the increase in sales turns out to be less than 9%, then your effort will not reap a positive return. If the increase in sales is very low, or even possibly negative, then the new feature will be a disaster. Measuring this would have a very high value. When someone says a variable is ‘‘too expensive’’ or ‘‘too difficult’’ to measure, we have to ask ‘‘Compared to what?’’ If the information value of the measurement is literally or virtually zero, of course, no measurement is justified. But if the measurement has any significant value, we must ask: ‘‘Is there any measurement method at all that can reduce uncertainty enough to justify the cost of the measurement?’’ Once we recognize the value of even partial uncertainty reduction, the answer is usually ‘‘Yes.’’
The Broader Objection to the Usefulness of ‘‘Statistics’’ After all, facts are facts, and although we may quote one to another with a chuckle the words of the Wise Statesman, ‘‘Lies—damned lies—and statistics,’’ still there are some easy figures the simplest must understand, and the astutest cannot wriggle out of. —LEONARD COURTNEY, FIRST BARON COURTNEY, ROYAL STATISTICAL SOCIETY PRESIDENT (1897–1899) Another objection is based on the idea that, even though a measurement is possible, it would be meaningless because statistics and probability itself is
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meaningless. (‘‘Lies, Damned Lies, and Statistics,’’ as it were.2) Even among educated professionals, there are often profound misconceptions about simple statistics. Some are so stunning that it’s hard to know where to begin to address them. Here are a few examples I’ve run into: ‘‘Everything is equally likely, because we don’t know what will happen.’’ —Mentioned by someone who attended one of my seminars ‘‘I don’t have any tolerance for risk at all because I never take risks.’’ —The words of a midlevel manager at an insurance company client of mine ‘‘How can I know the range if I don’t even know the mean?’’ —Said by a client of Sam Savage, PhD, colleague and promoter of statistical analysis methods ‘‘How can we know the probability of a coin landing on heads is 50% if we don’t know what is going to happen?’’ —A graduate student (no kidding) who attended a lecture I gave at the London School of Economics ‘‘You can prove anything with statistics.’’ —A very widely-used phrase about statistics Let’s address this last one first. I will offer a $10,000 prize, right now, to anyone who can use statistics to prove the statement ‘‘You can prove anything with statistics.’’ By ‘‘prove’’ I mean in the sense that it can be published in any major math or science journal. The test for this will be that it is published in any major math or science journal (such a monumental discovery certainly will be). By ‘‘anything’’ I mean, literally, anything, including every statement in math or science that has already been conclusively disproved. I will use the term ‘‘statistics,’’ however, as broadly as possible. The recipient of this award can resort to any accepted field of mathematics and science that even partially addresses probability theory, sampling methods, decision theory, and so on. The point is that when people say ‘‘You can prove anything with statistics,’’ they probably don’t really mean ‘‘statistics,’’ they just mean broadly the use of numbers (especially, for some reason, percentages). And they really don’t mean ‘‘anything’’ or ‘‘prove.’’ What they really mean is that ‘‘numbers can be used to confuse people, especially the gullible ones lacking basic skills with numbers.’’ With this, I completely agree.
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The other statements I list tend to be misunderstandings about more fundamental concepts behind probabilities, risk, and measurements in general. Clearly, the reason we use probabilities is specifically because we can’t be certain of outcomes. Obviously, we all take some risks just driving to work, and we all, therefore, have some level of tolerance for risk. I sometimes find that the people making these irrational claims don’t even quite mean what they say, and their own choices will betray their stated beliefs. If you ask someone to enter a betting pool to guess the outcome of the number of heads in 12 coin tosses, even the person who claims odds can’t be assigned will prefer the numbers around or near 6 heads. The person who claims to accept no risk at all will still fly to Moscow using Aeroflot (an airline with a safety record much worse than any U.S. carrier) to pick up a $1 million prize. The basic misunderstandings around statistics and probabilities come in a bewildering array that can’t be completely anticipated. Some publications, such as the Journal of Statistics Education, are almost entirely dedicated to identifying basic misconceptions, even among business executives, and ways to overcome them. Suffice it to say, the reader who finishes this book will probably have fewer misconceptions about statistics.
Ethical Objections to Measurement Let’s discuss one final reason why someone might argue that a measurement shouldn’t be made. This objection comes in the form of some sort of ethical objection to measurement. The potential accountability and perceived finality of numbers combine with a previously learned distrust of ‘‘statistics’’ to create resistance to measurement. Measurements can even sometimes be perceived as ‘‘dehumanizing’’ an issue. There is often a sense of righteous indignation when someone attempts to measure touchy topics, such as the value of an endangered species or even a human life. Yet it is done and done routinely for good reason. The Environmental Protection Agency (EPA) and other government agencies have to allocate limited resources to protect our environment, our health, and even our lives. One of the many IT investments I helped the EPA
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assess was a Geographic Information System (GIS) for better tracking of methyl mercury—a substance suspected of actually lowering the IQ of children who are exposed to high concentrations. To assess whether this system is justified, we must ask an important, albeit uncomfortable, question: Is the potentially avoided IQ loss worth the investment of more than $3 million over a five-year period? Someone might choose to be morally indignant at the very idea of even asking such a question, much less answering it. You might think that any IQ point for any number of children is worth the investment. But wait. The EPA also had to consider investments in other systems that track effects of new pollutants that sometimes result in premature death. The EPA has limited resources, and there are a large number of initiatives it could invest in that might improve public health, save endangered species, and improve the overall environment. It has to compare initiatives by asking ‘‘How many children and how many IQ points?’’ as well as ‘‘How many premature deaths?’’ Sometimes we even have to ask ‘‘How premature is the death?’’ Should the death of a very old person be considered equal to that of a younger person, when limited resources force us to make choices? At one point, the EPA considered using what it called a ‘‘senior death discount.’’ A death of a person over 70 was valued about 38% less than a person under 70. Some people were indignant at this and, in 2003, the controversy caused then EPA administrator Christine Todd Whitman to announce that this discount was used for ‘‘guidance,’’ not policy making and that it was discontinued.3 Of course, even saying they are the same is itself a measurement of how we express our values quantitatively. But if they are the same, I wonder how far we can take that equivalency. Should a 99-year-old with several health problems be worth the same effort to save as a 5-year-old? Whatever your answer is, it is a measurement of the relative value you hold for each. If we insist on being ignorant to the relative values of various public welfare programs (which is the necessary result of a refusal to measure their value), then we will almost certainly allocate limited resources in a way that solves less valuable problems for more money. This is because there is a large combination of possible investments to track such things and the best answer, in such cases, is never obvious without some understanding of magnitudes.
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In other cases, it seems the very existence of any error at all (which, we know, is almost always the case in empirical measurements) makes an attempted measure morally outrageous. Stephen J. Gould, author of The Mismeasure of Man, has vehemently argued against the usefulness, or even morality, of measurements of the intellect like IQ or ‘‘g’’ (the general factor or intelligence that is supposed to underlie IQ scores). He said: ‘‘‘g’ is nothing more than an artifact of the mathematical procedure used to calculate it.’’4 Although IQ scores and g surely have various errors and biases, they are, of course, not just mathematical procedures, but are based on observations (scores on tests). And since we now understand that measurement does not mean ‘‘total lack of error,’’ the objection that intelligence can’t be measured because tests have error is toothless. Furthermore, other researchers point out that the view that measures of intelligence are not measures of any real phenomenon is inconsistent with the fact that these different ‘‘mathematical procedures’’ are highly correlated with each other5 and even correlated with social phenomena like criminal behavior or income.6 How can IQ be a purely arbitrary figure if it correlates with observed reality? I won’t attempt to resolve that dispute here, but I am curious about how Gould would address certain issues like the environmental effects of a toxic substance that affects mental development. Since one of the most ghastly effects of methyl mercury on children, for example, are potential IQ points lost, is Gould saying no such effect can be real, or is he saying that even if it were real, we dare not measure it because of errors among the subjects? Either way, we would have to end up ignoring the potential health costs of this toxic substance and we might be forced— lacking information to the contrary—to reserve funds for another program. Too bad for the kids. The fact is that the preference for ignorance over even marginal reductions in ignorance is never the moral high ground. If decisions are made under a self-imposed state of higher uncertainty, policy makers (or even businesses like, say, airplane manufacturers) are betting on our lives with a higher chance of erroneous allocation of limited resources. In measurement, as in many other human endeavors, ignorance is not only wasteful but can be dangerous. Ignorance is never better than knowledge. —ENRICO FERMI, WINNER OF THE 1938 NOBEL PRIZE FOR PHYSICS
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Toward a Universal Approach to Measurement We’ve heard of some people with interesting and intuitive approaches to measurement. We’ve also learned how to address the basic objections to measurement, including some ‘‘measurement maxims’’ and a few interesting measurement examples. We find that the reasons why something is considered immeasurable are each actually mere misconceptions. In different ways, all of these lessons combine to paint some of the edges of a general framework for measurement. We’ll need to add a few more concepts to make it complete. This framework also happens to be the basis of the Applied Information Economics method I developed. Even with all the different types of measurements there are to make, we can still construct a set of steps that apply to virtually any type of measurement. We can construct a universal approach. Every component of this approach is well known to some particular field of research or industry, but no one routinely puts them together into a coherent method. In this universal approach, six questions need to be asked: 1. What are you trying to measure? What is the real meaning of the alleged ‘‘intangible’’? 2. Why do you care—what’s the decision and where is the ‘‘threshold’’? 3. How much do you know now—what ranges or probabilities represent your uncertainty about this? 4. What is the value of the information? What are the consequences of being wrong and the chance of being wrong, and what, if any, measurement effort would be justified? 5. Within a cost justified by the information value, which observations would confirm or eliminate different possibilities? For each possible scenario, what is the simplest thing we should see if that scenario were true? 6. How do you conduct the measurement that accounts for various types of avoidable errors (again, where the cost is less than the value of the information)? I will add more detail to each step in this approach in later chapters, but I’ve discussed each of them in part already.
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The benefits of seeing the world through ‘‘calibrated’’ eyes that see everything in a quantitative light have been a historical force propelling both science and economic productivity. Humans possess a basic instinct to measure, yet this instinct is suppressed in an environment that emphasizes committees and consensus over making simple observations. It simply won’t occur to many managers that an ‘‘intangible’’ can be measured with simple, cleverly designed observations. We have all been taught several misconceptions about measurement and what it means from our earliest exposure to the concept. We may have been exposed to basic concepts of measurement in, say, a chemistry lab in high school, but it’s unlikely we learned much besides the idea that measurements are exact and apply only to the obviously and directly observable quantities. College statistics, however, probably helps to confuse as many people as it informs. When we go on to the workplace, professionals at all levels in all fields are inundated with problems that don’t have the neatly measurable factors we saw in high school and college problems. We learn, instead, that some things are simply beyond measurement. However, as we saw, ‘‘intangibles’’ are a myth. The measurement dilemma can be solved. The ‘‘how much?’’ question frames any issue in a valuable way, and even the most controversial issues of measurement can be addressed when the consequences of not measuring are understood. & endnotes 1. Cobb, George W. (1993). Reconsidering Statistics Education: A National Science Foundation Conference. Journal of Statistics Education, 1, 63–83. 2. This statement is often incorrectly attributed to Mark Twain, although he surely helped to popularize it. Twain got it from either one of two nineteenth-century British politicians, Benjamin Disraeli or Henry Labouchere. 3. Katharine Q. Seelye and John Tierney, ‘‘ ‘Senior Death Discount’ Assailed: Critics Decry Making Regulations Based on Devaluing Elderly Lives,’’ New York Times, May 8, 2003. 4. Stephen Jay Gould, The Mismeasure of Man, (New York: W. W. Norton & Company, 1981). 5. Reflections on Stephen Jay Gould’s The Mismeasure of Man (1981): John B. Carroll, ‘‘A Retrospective Review,’’ Intelligence 21 (1995): 121–134. 6. K. Tambs, J. M. Sundet, P. Magnus, and K. Berg, ‘‘Genetic and Environmental Contributions to the Covariance between Occupational Status, Educational Attainment, and IQ: A Study of Twins,’’ Behavior Genetics 19, no. 2 (March 1989): 209–222.
section two
Before You Measure
chapter
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& Clarifying the Measurement Problem
onfronted with apparently difficult measurements, it helps to put the proposed measurement in context. Before we measure we should ask five questions:
C
1. What is the decision this is supposed to support? 2. What really is the thing being measured? 3. Why does this thing matter to the decision being asked? 4. What do you know about it now? 5. What is the value to measuring it further? In the Applied Information Economics method I developed and have used since 1995, I’ve been asking these questions systematically with everything we need to measure. The AIE approach has been applied in a total of over 50 major decision and measurement problems in a variety of organizations.1 Stopping to ask these questions often completely changes not just how organizations should measure something but what they should measure. The first three questions define what this thing is within the framework of what decisions depend on this measurement. If a measurement matters at all, it is because it must have some conceivable effect on decisions and behavior. If we can’t identify what decisions could be affected by a proposed measurement and how that measurement could change them, then the measurement simply has no value. 43
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For example, if you wanted to measure ‘‘product quality,’’ it becomes relevant to and what could be affected by it and to ask the more general question of what ‘‘product quality’’ means. Are you using the information to decide on whether to change an ongoing manufacturing process? If so, how bad does quality have to be before you make changes to the process? Are you measuring product quality to compute management bonuses in a quality program? If so, what’s the formula? All this, of course, depends on you knowing exactly what you mean by ‘‘quality’’ in the first place. When I was with Coopers & Lybrand in the late 80’s, we were on a consulting engagement with a small regional bank that was wondering how to streamline its reporting processes. The bank had been using a microfilmbased system to store the 60+ reports it got from branches every week, most of which were elective, not required for regulatory purposes. These reports were generated because someone in management thought they needed to know the information. These days, a good Oracle programmer might argue that it would be fairly easy to create and manage these queries; at the time, however, keeping up with these requests for reports was beginning to be a major burden. When I asked bank managers what decisions these reports supported, they could identify only a few cases where the elective reports had, or ever could, change a decision. Perhaps not surprisingly, the same reports that could not be tied to real management decisions were rarely even read. Even though someone initially had requested each of these reports, the original need was apparently forgotten. Once the managers realized that many reports simply had no bearing on decisions, they understood that those reports must, therefore, have no value. Years later, a similar question was posed by staff of the Office of the Secretary of Defense (OSD). They wondered what the value was of a large number of weekly and monthly reports. When I asked if they could identify a single decision that each report could conceivably affect, they found quite a few that had no effect on any decision. Likewise, the information value of those reports was zero. You also must ask the two other questions before you design a particular measurement method: How much do you know about this now and what is it worth to measure? Obviously, you have to know what it is worth to measure because you would probably come up with a very different measurement for quality if measuring it is worth $10 million per year than if it is worth $10,000 per year. And we can’t compute the value until we know
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how much we know now and how the measurement affects specific decisions. In the chapters that follow, we will discuss some examples regarding how to answer these questions. While exploring these ‘‘premeasurement’’ issues, we will show how the answers to some of these questions about uncertainty, risk, and the value of information are useful measurements in their own right.
Getting the Language Right: What ‘‘Uncertainty’’ and ‘‘Risk’’ Really Mean As discussed, in order to measure something, it helps to figure out exactly what we are talking about and why we care about it. Information technology (IT) security is a good example of a problem that any modern business can relate to and needs a lot of clarification before it can be measured. To measure IT security, we would to ask such questions as ‘‘What do we mean by ‘security’?’’ and ‘‘What decisions depend on my measurement of security?’’ To most people, an increase in security should ultimately mean more than just, for example, who has attended security training or how many desktop computers have new security software installed. If security is better, then some risks should decrease. If that is the case, then we also need to know what we mean by ‘‘risk.’’ Actually, that’s the reason I’m starting with an IT security example. Clarifying this problem requires that we jointly clarify ‘‘uncertainty’’ and ‘‘risk.’’ Not only are they measurable, they are key to understanding measurement in general. Even though ‘‘risk’’ and ‘‘uncertainty’’ frequently are dismissed as immeasurable, a thriving industry depends on measuring both and does so routinely. One of the industries I’ve consulted with the most is insurance. I remember once conducting a business-case analysis for a director of IT in a Chicago-based insurance company. He said, ‘‘Doug, the problem with IT is that it is risky, and there’s no way to measure risk.’’ I replied, ‘‘But you work for an insurance company. You have an entire floor in this building for actuaries. What do you think they do all day?’’ His expression was one of epiphany. He had suddenly realized the incongruity of declaring risk to be immeasurable while working for an a company that measures risks of insured events on a daily basis.
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The meaning of ‘‘uncertainty’’ and ‘‘risk’’ and the distinction between them seems ambiguous even for some experts in the field. Consider this quotation from Frank Knight, a University of Chicago economist in the early 1920s: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. . .. The essential fact is that ‘‘risk’’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.2
This is precisely why it is important to understand what decisions we need to support when defining our terms. Knight is speaking of the inconsistent and ambiguous use of ‘‘risk’’ and ‘‘uncertainty’’ by some unidentified groups of people. However, that doesn’t mean we need to be ambiguous or inconsistent. In fact, these terms are described fairly regularly in the decision sciences in a way that is unambiguous and consistent. Regardless of how some might use the terms, we can choose to define them in a way that is relevant to the decisions we have to make. definitions for uncertainty, risk, and their measurements
Uncertainty: The lack of complete certainty, that is, the existence of more than one possibility. The ‘‘true’’ outcome/state/result/value is not known. Measurement of Uncertainty: A set of probabilities assigned to a set of possibilities. For example: ‘‘There is a 60% chance this market will more than double in five years, a 30% change it will grow at a slower rate, and a 10% chance the market will shrink in the same period.’’ Risk: A state of uncertainty where some of the possibilities involve a loss, catastrophe, or other undesirable outcome. Measurement of Risk: A set of possibilities each with quantified probabilities and quantified losses. For example: ‘‘We believe there is a 40% chance the proposed oil well will be dry with a loss of $12 million in exploratory drilling costs.’’
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We will get to how we assign these probabilities a little later, but at least we have defined what we mean—which is always a prerequisite to measurement. We chose these definitions because they are the most relevant to how we measure the example we are using here: security and the value of security. But, as we will see, these definitions also are the most useful when discussing any other type of measurement problem we have. Whether others will continue to use ambiguous terms and have endless philosophical debates is of less concern to a decision maker faced with an immediate dilemma. The word ‘‘force,’’ for example, was used in the English language for centuries before Sir Isaac Newton defined it mathematically. Today it is sometimes used interchangeably with terms like ‘‘energy’’ or ‘‘power’’—but not by physicists and engineers. When aircraft designers use the term, they know precisely what they mean in a quantitative sense (and those of us who fly frequently appreciate their effort at clarity). Now that we have defined ‘‘uncertainty’’ and ‘‘risk,’’ we have a better tool box for defining terms like ‘‘security’’ (or ‘‘safety,’’ ‘‘reliability,’’ and ‘‘quality,’’ but more on that later). When we say that security has improved, we generally mean that particular risks have decreased. If I apply the definition of risk given earlier, a reduction in risk must mean that the probability and/or severity (loss) of a certain list of events decrease. That is the approach I briefly mentioned earlier to help measure one very large IT security investment— the $100 million overhaul of IT security for the Department of Veterans Affairs.
Examples of Clarification: Lessons for Business from, of All Places, Government Many government employees imagine the commercial world as an almost mythical place of incentive-driven efficiency and motivation where fear of going out of business keeps everyone on their toes. I often hear government workers lament that they are not more like business. To those in the business world, however, the government (federal, state, or other) is a synonym for bureaucratic inefficiency and unmotivated workers counting the days to retirement. I’ve done a lot of consulting in both worlds, and I would say that neither generalization is entirely right or entirely wrong. Many people on either side would be surprised to learn that I think there are many things the
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commercial world can learn from (at least some) government agencies. The fact is that large businesses with vast internal structures still have workers so far removed from the economic realities of business that their jobs are as bureaucratic as any job in government. And I’m here to bear witness to the fact that the U.S. federal government, while certainly the largest bureaucracy in history, has many motivated and passionately dedicated workers. In that light, I will use a few examples from my government clients as great examples for business to follow. Here is a little more background on the IT security measurement project for Veterans Affairs, which I briefly mentioned in the last chapter. In 2000, an organization called Federal CIO Council wanted to conduct some sort of test to compare different performance measurement methods. As the name implies, the Federal CIO Council is an organization consisting of the chief information officers of federal agencies and many of their direct reports. The council has its own budget and it sometimes sponsors research that can benefit all federal CIOs. After reviewing several approaches, the CIO Council decided it should test Applied Information Economics. The CIO Council decided it would test AIE on the massive, newly proposed IT security portfolio at the Department of Veterans Affairs (VA). My task was to identify performance metrics for each of the security-related systems being proposed and to evaluate the portfolio, under the close supervision of the council. Whenever I had a workshop or presentation of findings, several council observers from a variety of agencies were often in attendance. At the end of each of the projects, they compiled their notes and wrote a detailed comparison of AIE to another popular method currently used in other agencies. The first question I asked the VA is similar to the first question I ask on most measurement problems: ‘‘What do you mean ‘IT security’?’’ In other words, what does improved IT security look like? What would we see or detect that was different if security was better or worse? Furthermore, what do we mean by the ‘‘value’’ of security? IT security might not seem like the most ephemeral or vague concept we need to measure, but project participants soon found that they didn’t quite know what they meant by that term. It was clear, for example, that reduced frequency and impact of ‘‘pandemic’’ virus attacks is an improvement in security, but what is
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‘‘pandemic’’ or, for that matter, ‘‘impact’’? Also, it might be clear that an unauthorized access to a system by a hacker is an example of a breach of IT security, but is a theft of a laptop? How about a data center being hit by a fire, flood, or tornado? At the first meeting, participants found that while they all thought IT security could be better, they didn’t have a common understanding of exactly what IT security was. It wasn’t that different parties had already developed detailed mental pictures of IT security and that they had a different picture in mind from someone else. Up to that point, nobody had thought about those details in the definition of IT security. Once group members were confronted with specific, concrete examples of IT security, they came to agreement on a very unambiguous and comprehensive model of what it is. They resolved that improved IT security means a reduction in the frequency and severity of a specific list of undesirable events. In the case of the VA, they decided these events should specifically include virus attacks, unauthorized access (logical and physical), and certain types of other disasters (e.g., losing a data center to a fire or hurricane). Each of these types of events entails certain types of cost. Exhibit 4.1 presents the proposed systems, the events they meant to avert, and the costs of those events.
EXHIBIT 4.1
IT SECURITY FOR THE DEPARTMENT OF VETERANS AFFAIRS
Security Systems Public Key Infrastructure (key encryption/ decryption, etc.) Biometric/single sign-on (fingerprint readers, security card readers, etc.) Intrusion-detection systems A security-compliance certification program for new systems New antivirus software A security incident reporting system Additional security training
Events Averted or Reduced
Costs Averted
Pandemic virus attacks
Productivity losses
Unauthorized system access: external (hackers) or internal (employees)
Fraud losses
Unauthorized physical access to facilities or property Other disasters; fire, flood, tornado, etc.
Legal liability/ improper disclosure Interference with mission (for theVA this mission is the care of veterans)
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Each of the proposed systems reduced the frequency or impact of specific events. Each of those events would have resulted in a specific combination of costs. A virus attack, for example, tends to have an impact on productivity, while unauthorized access might result in productivity loss, fraud, and perhaps even legal liability resulting from improper disclosure of private medical data and the like. With these definitions, we have a much more specific understanding of ‘‘improved IT security’’really means and, therefore, how to measure it. When I ask the question ‘‘What are you observing when you observe improved IT security?’’ VA management can now answer specifically. The VA participants realized that when they observe ‘‘better security,’’ they are observing a reduction in the frequency and impact of these detailed events. They achieved the first milestone to measurement. You might take issue with some aspects of the definition. You may (justifiably) argue that a fire is not, strictly speaking, an IT security risk. Yet the VA participants determined that, within their organization, they did mean to include the risk of fire. Still aside from some minor differences about what to include on the periphery, I think what we developed is really the basic model for any IT security measurements. The VA’s previous approach to measuring security was very different. It was actually using measures like the number of people who completed certain security training courses and the number of desktops that had certain systems installed. In other words, the VA wasn’t measuring results at all. All previous measurement effort focused on things that were ‘‘easier’’ to measure. Prior to my work with the CIO Council, some people considered the ultimate impact of security immeasurable, so no attempt was made to achieve even marginally less uncertainty. With the parameters we developed, we were set to measure some very specific things. We built a spreadsheet model that included all of these effects. This was really just another example of asking a few ‘‘Fermi’’ questions. For virus attacks, we asked the following: 0001
How often does the average pandemic (agency-wide) virus attack occur?
0001
When such an attack occurs, how many people are affected?
0001
For the affected population, how much did their productivity decrease relative to normal levels?
examples of clarification
0001
What is the duration of the downtime?
0001
What is the cost of labor lost during the productivity loss?
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If we knew the answer to each of these questions, we could compute the cost of agency-wide virus attacks as: Average Annual Cost of Virus Attacks ¼ number of attacks 0002 average number of people affected 0002 average productivity loss 0002 average duration of downtime 0002 annual cost of labor 0003 2080 hours per year3 Of course, this calculation is only considering the cost of the equivalent labor that would have been available if the virus attack had not occurred. It does not tell us how the virus attack affected the care of veterans or other losses. Nevertheless, even if this calculation excludes some losses, at least it gives us a conservative lower bound of losses. Exhibit 4.2 shows the answers for each of these questions. These ranges reflect the uncertainty of security experts who have had previous experience with virus attacks at the VA. With these ranges, the experts are saying that there is a 90% chance that the true values will fall between the upper and lower bounds given. I trained these experts so that they were very good at assessing uncertainty quantitatively. In effect, they were ‘‘calibrated’’ like any scientific instrument to be able to do this.
EXHIBIT 4.2
DEPARTMENT OF VETERANS AFFAIRS ESTIMATES FOR THE EFFECTS OF VIRUS ATTACKS The value is 90% likely to fall between or be equal to these points:
Uncertain Variable Agency-wide virus attacks per year (for the next 5 years)
2
4
Average number of people affected
25,000
65,000
Percentage productivity loss
15%
60%
Average duration of productivity loss
4 hours
12 hours
Loaded annual cost per person (most affected staff would be in the lower pay scales)
$ 50,000
$ 100,000
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These ranges may seem merely subjective, but the subjective estimates of some persons are demonstrably better than those of others. We were able to treat these ranges as valid because we knew the experts had demonstrated, in a series of tests, that when they said they were 90% certain, they would be right 90% of the time. So far, you have seen how to take an ambiguous term like ‘‘security’’ and break it down into some relevant, observable components. By defining what security means, the VA made a big step toward measuring it. By this point, the VA had not yet made any observations to reduce their uncertainty. All they did was quantify their uncertainty by using probabilities and ranges. It turns out that the ability of a person to assess odds can be calibrated—just like any scientific instrument is calibrated to ensure it gives proper readings. Calibrated probability assessments are the key to measuring your current state of uncertainty about anything. Learning how to quantify your current uncertainty about any unknown quantity is an important step in determining how to measure something in a way that is relevant to your needs. Developing this skill is the focus of the next chapter.
& endnotes 1. Between August 1995 and August 2006, there were 30 contracts with a total of 15 distinct companies or government agencies where some contracts covered the analysis of several major decisions. 2. Frank Knight, Risk, Uncertainty and Profit (New York: Houghton Mifflin Company, 1921), p 19–20. 3. 2080 hours per year is an Office of Management and Budget and Government Accountability Office standard for converting loaded annual salaries to equivalent hourly rates.
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& Calibrated Estimates: How Much Do You Know Now?
Testing Your Ability to Assess Odds ow many hours per week do employees spend addressing customer complaints? How much would sales increase with a new advertising campaign? Even if you don’t know the exact values to questions like these, you still know something. You know that some values would be impossible or at least highly unlikely. Knowing what you know now about something actually has an important and often surprising impact on how you should measure it or even whether you should measure it. What we need is a way to express how much we know now, however little that may be. On top of that, we need a way to know if we are any good at expressing uncertainty. One method to express our uncertainty about a number is to think of it as a range of probable values. In statistics, a range that has a particular chance of containing the correct answer is called a confidence interval (CI). A 90% CI is a range that has a 90% chance of containing the correct answer. For example, you can’t know for certain exactly how many of your current prospects will turn into customers in the next quarter, but you think that probably no less than 3 prospects and probably no more than 7 prospects will sign contracts. If you are 90% sure the actual number will fall between 3 and 7, then we can say you have a 90% CI of 3 to 7. You may have computed these values with all sorts of sophisticated statistical inference methods, but you might just have picked them out based on your experience. Either way, the values should be a reflection of your uncertainty about this quantity.
H
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You can also use probabilities to describe your uncertainty about specific future events, such as whether a given prospect will sign a contract in the next month. You can say that there is a 70% chance that this will occur, but is that ‘‘right’’? One way we can determine if a person is good at quantifying uncertainty is to look at all the prospects the person assessed and ask, ‘‘Of all the prospects she was 70% certain about closing, did about 70% actually close? Where she said she was 80% confident in closing a deal, did about 80% of them close?’’ And so on. This is how we know how good we are at subjective probabilities. We compare our expected outcomes to actual outcomes. two extremes of subjective confidence
Overconfidence: When an individual routinely overstates knowledge and is correct less often than he or she expects. For example, when asked to make estimates with a 90% confidence interval, many fewer than 90% of the true answers fall within the estimated ranges. Underconfidence: When an individual routinely understates knowledge and is correct much more often than he or she expects. For example, when asked to make estimates with a 90% confidence interval, many more than 90% of the true answers fall within the estimated ranges.
Unfortunately, very few people are naturally calibrated estimators. Most of us tend to be biased either toward over- or underconfidence about our estimates. Putting odds on uncertain events or ranges on uncertain quantities is not a skill that arises automatically from experience and intuition. Fortunately, several academic studies have proved that better estimates are attainable when estimators have been trained to remove their personal estimating biases.1 Calibrated probability assessments were an area of research in decision psychology in the 1970s and 1980s and to a somewhat lesser degree today. Decision psychology concerns itself with how people actually make decisions, however irrational, in contrast to many of the ‘‘management science’’ or ‘‘quantitative analysis’’ methods taught in business schools, which focus on how to work out ‘‘optimal’’ decisions in specific, well-defined problems.
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Researchers discovered that oddsmakers and bookies were generally better at assessing the odds of events than, say, executives. They also made some disturbing discoveries about how bad physicians are at putting odds on unknowns like ‘‘The chance there is a malignant tumor’’ or ‘‘The chance this chest pain is a heart attack.’’ They reasoned that this variance among different professions shows that putting odds on uncertain things must be a learned skill. Researchers learned how experts can measure whether they are systematically ‘‘underconfident,’’ ‘‘overconfident,’’ or have other biases about their estimates. Once this self-assessment has been conducted, they can learn several techniques for improving estimates and measuring the improvement. In short, researchers discovered that assessing uncertainty is a general skill that can be taught with a measurable improvement. That is, when calibrated sales managers say they are 75% confident that a new competitor will not get your major customer, there really is a 75% chance you will retain the customer. Let’s benchmark how good you are at quantifying your own uncertainty by taking a short quiz. Exhibit 5.1 contains 10 90% CI questions and 10 binary (i.e. True/False) questions. These are general knowledge questions that, unless you are a Jeopardy grand champion, you probably will not know with certainty. But they are all questions you probably have some idea about. These are similar to the exercises I give attendees in my workshops and seminars. The only difference is that the tests I give have more questions of each type, and I present several tests with feedback after each test. This calibration training generally takes about half a day. But even with this small sample we will be able to detect some important aspects of your skills. More important, the exercise should get you to think about the fact that your current state of uncertainty is itself something you can quantify.
Calibration Exercise Instructions: Exhibit 5.1 contains 10 of each of these two types of questions. 90% Confidence Interval (CI). For each of the 90% CI questions, provide both an upper bound and a lower bound. Remember that the range should be wide enough that you believe there is a 90% chance that the answer will be between your bounds.
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SAMPLE CALIBRATION TEST
Question
90% Confidence Interval Lower Bound Upper Bound
1 In 1938 a British steam locomotive set a new speed record by going how fast (mph)? 2 In what year did Sir Isaac Newton publish the Universal Laws of Gravitation? 3 How many inches long is a typical business card? 4 The Internet (then called ‘Arpanet’) was established as a military communications system in what year? 5 In what year was William Shakespeare born? 6 What is the air distance between New York and Los Angeles (miles)? 7 What percentage of a square could be covered by a circle of the same width? 8 How old was Charlie Chaplin when he died? 9 How many days does it actually take the Moon to orbit Earth? 10 The TV show Gilligan’s Island first aired on what date?
Statement
Answer (True/False)
Confidence that you are correct (Circle one)
1 The ancient Romans were conquered by the ancient Greeks.
50% 60% 70% 80% 90% 100%
2 There is no species of three-humped camels.
50% 60% 70% 80% 90% 100%
3 A gallon of oil weighs less than a gallon of water.
50% 60% 70% 80% 90% 100%
4 Mars is always farther away from Earth than Venus.
50% 60% 70% 80% 90% 100%
5 The Boston Red Sox won the first World Series.
50% 60% 70% 80%90% 100%
6 Napoleon was born on the island of Corsica.
50% 60% 70% 80% 90% 100%
7 'M' is one of the three most commonly used letters.
50% 60% 70% 80% 90% 100%
8
In 2002 the price of the average new desktop computer purchased was under $1,500.
50% 60% 70% 80% 90% 100%
9 Lyndon B. Johnson was a governor before becoming vice president.
50% 60% 70% 80% 90% 100%
10 A kilogram is more than a pound.
50% 60% 70% 80% 90% 100%
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Binary Questions. Answer whether each of the statements ‘‘true’’ or ‘‘false,’’ then circle the probability that reflects how confident you are in your answer. For example, if you are absolutely certain in your answer, you should say you have a 100% chance of getting the answer right. If you have no idea whatsoever, then your chance should be the same as a coin flip (50%). Otherwise (probably usually), it is one of the values between 50% and 100%. Of course, you could just look up the answers to any of these questions, but we are using this as an exercise to see how well you estimate things you can’t just look up (e.g., next month’s sales or the actual productivity improvement from a new IT system). Important Hint: The questions vary in difficulty. Some will seem easy while others may seem too difficult to answer. But no matter how difficult the question seems, you still know something about it. Focus on what you do know. For the range questions, you know of some bounds beyond which the answer would seem absurd (e.g., you probably know Newton wasn’t alive in ancient Greece or in the twentieth century). Similarly, for the binary questions, even though you aren’t certain, you have some opinion, at least, about which answer is more likely. After you’ve finished, but before you look up the answers, try a small experiment to test if the ranges you gave really reflect your 90% CI. Consider one of the 90% CI questions, let’s say the one about when Newton published the Universal Laws of Gravitation. Suppose I offered you a chance to win $1,000 in one of the two following ways: 1. You will win $1,000 if the true year of publication of Newton’s book turns out to be between the numbers you gave for the upper and lower bound. If not, you win nothing. 2. You spin a dial divided into two unequal ‘‘pie slices,’’ one comprising 90% of the dial and the other just 10%. If the dial lands on the large slice, you win $1,000. If it lands on the small slice, you win nothing. (i.e., there is a 90% chance you win $1,000). Which do you prefer? The dial has a stated chance of 90% that you win $1,000, a 10% chance you win nothing. If you are like most people (about 80%), you prefer to spin the dial. But why would that be? The only
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10% Win $0
EXHIBIT 5.2
90%
Spin to Win!
explanation is that you think the dial has a higher chance of a payoff. The conclusion we have to draw is that the 90% CI you first estimated is really not your 90% CI. It might be your 50%, 65%, or 80% CI, but it can’t be your 90% CI. This is called being overconfident, statistically speaking. You express your uncertainty in a way that indicates you have less uncertainty than you really have. An equally undesirable outcome is to prefer option A, where you win $1,000 if the correct answer is within your range. This means that you think there is more than a 90% chance your range contains the answer, even though you are representing yourself as being merely 90% confident in the range. The only desirable answer you can give is if you set your range just right so that you would be indifferent between options A and B. This means that at least you believe you have a 90% chance—not more and not less—that the answer is within your range. For an overconfident person (i.e., most of us), this means increasing the width of the range until options A and B are considered equivalent. You can apply the same test, of course, to the binary questions. Let’s say you were 80% confident about your answer to the question about Napoleon’s birthplace. Again, you give yourself a choice between betting on your answer being correct or spinning the dial. In this case, however, the dial pays off 80% of the time. If you prefer to spin the dial, you are probably less than 80% confident in your answer. Now let’s suppose we change the payoff odds on the dial to 70%. If you then consider spinning the dial just as good a bet (no better or worse) as betting on your answer, then you should say that you are really about 70% confident that your answer to the question is correct. In my calibration training classes, I’ve been calling this the ‘‘equivalent bet test.’’ As the name implies, it tests to see whether you are really 90%
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confident in a range by comparing it to a bet that you should consider equivalent. Research indicates that even just pretending to bet money significantly improves a person’s ability to assess odds.2 In fact, actually betting money turns out to be only slightly better than pretending to bet (more on this in the Chapter 13 discussion about prediction markets). Methods like the equivalent bet test help estimators give more realistic assessments of their uncertainty. People who are very good at assessing their uncertainty (i.e., they are right 80% of the time they say they are 80% confident, etc.) are called calibrated. There are a few other simple methods for improving your calibration, but first, let’s see how you did on the test. The answers are in Appendix A. To see how calibrated you are, we need to compare your expected results to your actual results. Since the range questions you answered were asking for a 90% CI, you are, in effect, saying that you expect 9 out of 10 of the true answers to be within your ranges. However, if you are like most people, you got less than that within your stated bounds. Granted, these are very small samples, so they can’t measure your calibration precisely, but they’re good approximate measures. Even with this small sample, if you got less than 7 answers within your bounds, then you are probably overconfident. If you got less than 5 within your bounds (as most people do), then you are very overconfident. For the 90% CI questions in the test, you ‘‘expected’’ to get 9 within your ranges while the actual result was probably something less than that. Now you need to compute the ‘‘expected’’ value for your binary questions. For each of the answers, you said you were 50%, 60%, 70%, 80%, 90%, or 100% confident. Convert each of the percentages you circled to a decimal (i.e., 0.5, 0.6. . .1.0) and add them up. Let’s say your confidence in your answers was 1, .5, .9, .6, .7, .8, .8, 1, .9, and .7, making your total 7.9. Your ‘‘expected’’ number correct was 7.9. Again, 10 is a small sample, but if your actual number correct was 2.5 or more lower than the expected correct number, you are probably overconfident.
Further Improvements on Calibration The academic research so far indicates that training has a significant effect on calibration. We already mentioned the equivalent bet test, which allows
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us to pretend we are tying personal consequences to the outcomes. Research (and my experience) also proves that another key method in calibrating a person’s ability to assess uncertainty is repetition and feedback. To test this, we ask participants a series of trivia questions similar to the quiz you just took. They give me their answers, then I show them the true values, and they test again. However, it doesn’t appear that any single method completely corrects for the natural overconfidence most people have. To remedy this, I combined several methods and found that most people could be nearly perfectly calibrated. Also, I routinely asked people to identify pros and cons for the validity of each of their estimates. A pro is a reason why the estimate is reasonable; a con is a reason why it might be overconfident. For example, your estimate of sales for a new product may be in line with sales for other start-up products with similar advertising expenditures. But when you think about your uncertainty regarding catastrophic failures or runaway successes in other companies as well as your uncertainty about the overall growth in the market, you may reassess the initial range. Academic researchers found that this method by itself significantly improves calibration.3 Finally, I also asked experts who were providing range estimates to look at each bound on the range as a separate ‘‘binary’’ question. A 90% CI interval means there is a 5% chance the true value could be greater than the upper bound and a 5% chance it could be less than the lower bound. This means that estimators must be 95% sure that the true value is less than the upper bound. If they are not that certain, they should increase the upper bound until they are certain. A similar test is applied to the lower bound. Performing this test seems to avoid the problem of ‘‘anchoring’’ by estimators. Anchoring is the effect of narrowing a range toward a certain number once you have that number in your mind. Some estimators say that when they provide ranges, they think of a single number and then add or subtract an ‘‘error’’to generate their range. This might seem reasonable, but it actually tends to cause estimators to produce overconfident ranges (i.e., ranges that are too narrow). Looking at each bound alone as a separate binary question of ‘‘Are you 95% sure it is over/under this amount?’’ cures our tendency to anchor. After a few calibration tests and practice with methods like listing pros and cons, using the equivalent bet, and anti-anchoring, estimators learn to
conceptual obstacles to calibration EXHIBIT 5.3
61
METHODS TO IMPROVE YOUR PROBABILITY CALIBRATION
1. Repetition and feedback.Take several tests in succession, assessing how well you did after each one and attempting to improve your performance in the next one. 2. Equivalent bets. For each estimate, set up the equivalent bet to test if that range or probability really reflects your uncertainty. 3. Consider two pros and two cons.Think of at least two reasons why you should be confident in your assessment and two reasons you could be wrong. 4. Avoid anchoring.Think of range questions as two separate binary questions of the form ‘‘Are you 95% certain that the true value is over/under (pick one) the lower/upper (pick one) bound?’’
fine-tune their ‘‘probability senses.’’ Most people get nearly perfectly calibrated after just a half day of training. Most importantly, even though subjects may have been training on general trivia, the calibration skill transfers to any area of estimation. I’ve provided two additional calibration tests of each type—ranges and binary—in the Appendix. Try applying the methods summarized in Exhibit 5.3 to improve your calibration.
Conceptual Obstacles to Calibration The methods just mentioned don’t help if someone has irrational ideas about calibration or probabilities in general. While I find that most people in decisionmaking positions seem to have or are able to learn useful ideas about probabilities, some have surprising misconceptions about these issues. Here are some comments I’ve received while taking groups of people through calibration training or eliciting calibrated estimates after training: 000f
My 90% confidence can’t have a 90% chance of being right because a subjective 90% confidence will never have the same chance as an objective 90%.
000f
This is my 90% confidence interval but I have absolutely no idea if that is right.
000f
We couldn’t possibly estimate this. We have no idea.
000f
If we don’t know the exact answer, we can never know the odds.
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The first statement was made by a chemical engineer and it is indicative of the problem he was initially having with calibration. As long as he sees his subjective probability as inferior to objective probability, then he won’t get calibrated. However, after a few calibration exercises, he did find that he could subjectively apply odds that were correct as often as the odds implied; in other words, his 90% confidence intervals contained the correct answers 90% of the time. The rest of the objections are fairly similar. They are all based in part on the idea that not knowing exact quantities is the same as knowing nothing of any value. The woman who said she had ‘‘absolutely no idea’’ if her 90% confidence interval was right was talking about her answer to one specific question on the calibration exam. The trivia question was ‘‘What is the wingspan of a 747, in feet?’’ Her answer was 100 to 120 feet. Here is an approximate re-creation of the discussion: Me: Are you 90% sure that the value is between 100 and 120 feet? Calibration Student: I have no idea. It was a pure guess. Me: But when you give me a range of 100 to 120 feet, that indicates you at least believe you have a pretty good idea. That’s a very narrow range for someone who says they have no idea. Calibration Student: Okay. But I’m not very confident in my range. Me: That just means your real 90% confidence interval is probably much wider. Do you think the wingspan could be, say, 20 feet? Calibration Student: No, it couldn’t be that short. Me: Great. Could it be less than 50 feet? Calibration Student: Not very likely. That would be my lower bound. Me: We’re making progress. Could the wingspan be greater than 500 feet? Calibration Student: [pause]. . .No, it couldn’t be that long. Me: Okay, could it be more than a football field, 300 feet? Calibration Student: [seeing where I was going]. . .Okay, I think my upper bound would be 250 feet.’’ Me: So then you are 90% certain that the wingspan of a 747 is between 50 feet and 250 feet? Calibration Student: Yes. Me: So your real 90% confidence interval is 50 to 250 feet, not 100 to 120 feet.
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During our discussion, the woman progressed from what I would call an unrealistically narrow range to a range she really felt 90% confident contained the correct answer. She no longer said she had ‘‘no idea’’ that the range contained the answer because the new range represented what she actually knew. This example is one reason I don’t like to use the word ‘‘assumption’’ in my analysis. An assumption is a statement we treat as true for the sake of argument, regardless of whether it is true. Assumptions are necessary if you have to use deterministic accounting methods with exact points as values. You could never know an exact point with certainty so any such value must be an assumption. But if you are allowed to model your uncertainty with ranges and probabilities, you never have to state something you don’t know for a fact. If you are uncertain, your ranges and assigned probabilities should reflect that. If you have ‘‘no idea’’ that a narrow range is correct, you simply widen it until it reflects what you do know. It is easy to get lost in how much you don’t know about a problem and forget that there are still some things you do know. There is literally nothing we will likely ever need to measure where our only bounds are negative infinity to positive infinity. The next example is a little different from the last dialog, where the woman gave an unrealistically narrow range. The next conversation comes from the security example we were working on with the VA. The expert initially gave no range at all and simply insisted that it could never be estimated. He went from a saying he knew ‘‘nothing’’ about a variable, only to later concede that he actually is very certain about some bounds. Me: If your systems are being brought down by a computer virus, how long does the downtime last, on average? As always, all I need is a 90% confidence interval. Security Expert: We would have no way of knowing that. Sometimes we were down for a short period, sometimes a long one. We don’t really track it in detail because the priority is always getting the system back up, not documenting the event. Me: Of course you can’t know it exactly. That’s why we only put a range on it, not an exact number. But what would be the longest downtime you ever had? Security Expert: I don’t know, it varied so much. . .
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Me: Were you ever down for more than two entire work days? Security Expert: No, never two whole days. Me: Ever more than a day? Security Expert: I’m not sure. . .probably. Me: We are looking for your 90% confidence interval of the average downtime. If you consider all the downtimes you’ve had due to a virus, could the average of all of them have been more than a day? Security Expert: I see what you mean. I would say the average is probably less than a day. Me: So your upper bound for the average would be. . .? Security Expert: Okay, I think its highly unlikely that the average downtime could be greater than 10 hours. Me: Great. Now let’s consider the lower bound. How small could it be? Security Expert: Some events are corrected in a couple of hours. Some take longer. Me: Okay, but do you really think the average of all downtimes could be 2 hours? Security Expert: No, I don’t think the average could be that low. I think the average is at least 6 hours. Me: Good. So is your 90% confidence interval for the average duration of downtime due to a virus attack 6 hours to 10 hours? Security Expert: I took your calibration tests. Let me think. I think there would be a 90% chance if the range was, say, 4 to 12 hours.
This is a typical conversation for a number of highly uncertain quantities. Initially the experts resist giving any range at all, perhaps because they have been taught that in business, the lack of an exact number is the same as knowing nothing or perhaps because they will be ‘‘held accountable for a number.’’ But the lack of having an exact number is not the same as knowing nothing. The security expert knew that an average virus attack duration of 24 working hours (three workdays), for example, would have been absurd. Likewise, it was equally absurd that it could be only an hour. But in both cases this is knowing something, and it quantifies the expert’s uncertainty. A range of 6 to 10 hours is much less uncertainty than a range of 2 to 20 hours. Either way, the amount of uncertainty itself is of interest to us. I call the method I used in the previous two dialogs the ‘‘absurdity test,’’ and I apply it whenever I get the ‘‘there is no way I could know that’’
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response or the ‘‘Here’s my range, but it’s a guess’’ response. No matter how little experts think they know about a quantity, it always turns out that there are still values they know are absurd. The point at which a value ceases to be absurd and starts to become unlikely but somewhat plausible is the edge of their uncertainty about the quantity. As a final test, I give them an equivalent bet to see if the resulting range is really a 90% confidence interval.
The Effects of Calibration Since I started practicing this type of consulting in 1995, I’ve been tracking how well people do on the trivia tests and even how well calibrated people do in estimating real-life uncertainties, after those events have come to pass. My calibration methods and tests have evolved a lot since 1995 but have been fairly consistent since 2001. Since then, I have taken a total of 142 people through the calibration training. For all those people, I’ve tracked their expected and actual results on several calibration tests, given one after the other during a half-day workshop. Since I was familiar with the research in this area, I expected significant, but imperfect, improvements toward calibration. What I was less certain of was the variance I might see in the performance from one individual to the next. The academic research usually shows aggregated results for all the participants in the research, so we can only see an average for a group. When I aggregate the performance of those in my workshops, I get a result very similar to the prior research. But because I could break down my data by specific subjects, I saw another interesting phenomenon. Exhibit 5.4 shows the aggregated results of the range questions for all 142 participants for each of the tests given in the workshop. Those who showed significant evidence of good calibration early were excused from subsequent tests. (This turned out to be a strong motivator for performance.) The bar at the bottom of the chart shows what percentage of workshop participants ended their testing on that test number (i.e., were excused from further tests). For each test, the vertical line shows performance of the middle 90% of students and the black diamond shows the group mean. The target, of course, is to be at the thick horizontal line that indicates that 90% of the answers fell within respondents’ stated 90% confidence intervals.
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% within expected 90% CI
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calibrated estimates
Target
100% 90% 80% 60% 40% 20% 0%
Test 1 0
Test 2 0
Test 3 7
Test 4
Test 5
38
55
% finished on this test
142 total participants – 90% performance range and Mean for Each Test EXHIBIT 5.4
Aggregated Results of 90% CI Tests in Calibration Training
The results seem to indicate significant improvement in the first three tests, but then a leveling-off short of ideal calibration. Even taking into account the fact that only the poor performers took the fourth and fifth tests, it looks like even three to four hours of intense training falls just short of the mark. But when I broke down my data by student, I saw that most students perform superbly by the end of the training and it is a few poor performers who bring down the average. Statistically, we have to allow for some deviation from the target even for a perfectly calibrated person. Allowing only for this statistical error in the testing, fully 70% of participants are ideally calibrated after training. They are neither underconfident nor overconfident. Their 90% CI have about a 90% chance of containing the correct answer. Another 20% show significant improvement but don’t quite reach ideal calibration. And 10% show no significant improvement at all from the first test they take. So why is it that about 1 in 10 people are apparently unable to improve at all in calibration training? Whatever the reason, it turns out not to be that relevant. Every single person we ever relied on for actual estimates was in the first two groups and almost all were in the first ideally calibrated group. Those who seemed to resist any attempt at calibration were, even before the testing, never considered to be the relevant expert or decision maker for a particular problem. It may be that they were less motivated, knowing their opinion would not have much bearing. Or it could be that those who lacked aptitude for such problems just don’t tend to advance to the level of the people we need for the estimates. Either way, it’s academic.
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We see that training works very well for most people. But does proven performance in training reflect an ability to assess the odds of real-life uncertainties? The answer here is an unequivocal yes. I’ve had many opportunities to track how well calibrated people do in real-life situations, but one particular controlled experiment stands out. In 1997, I was asked to train the analysts of the IT advisory firm Giga Information Group (since acquired by Forrester Research, Inc.) in assigning odds to uncertain future events. Giga was an ITresearch firm that sold its research to other companies on a subscription basis. Giga had adopted the method of assigning odds to events they were predicting for clients, and it wanted to be sure it was performing well. I trained 16 Giga analysts using the methods I described earlier. At the end of the training, I gave them 20 specific IT industry predictions they would answer as true or false and to which they would assign a confidence. The test was given in January 1997, and all the questions were stated as events occurring or not occurring by June 1, 1997 (e.g., ‘‘True or False: Intel will release its 300 MHz Pentium by June 1,’’ etc.). As a control, I also gave the same list of predictions to 16 of their CIO-level clients at various organizations. After June 1 we could determine what actually occurred. I presented the results at Giga World 1997, their major symposium for the year. Exhibit 5.5 shows the results. The horizontal axis is the chance the participants gave to their prediction on a particular issue being correct. The vertical axis shows how many of those predictions turned out to be correct. An ideally calibrated person should be plotted right along the thick dotted line. This means the person was right 70% of the time he or she was 70% confident in the predictions, 80% right when he or she was 80% confident, and so on. You see that the analysts’ results (where the points are indicated by small squares) were very close to the ideal confidence, easily within allowable error. The results appear to deviate the most from ‘‘perfect calibration’’ at the low end of the scale, but this part is still within acceptable limits of error. (The acceptable error range is wider on the left of the chart and narrows to zero at the right.) Of all the times participants said they were 50% confident, they turned out to be right about 65% of the time. This means they might have known more than they let on and—only on this end of the scale—were a little underconfident. It’s close; these results might be due to chance. There is 1% chance that 44 or more out of 68 would be right just by flipping a coin.
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100% 17
% Actually Correct
90%
“Ideal” Confidence 45
80% 70%
21
Giga-Clients
65 68
152 21
60% 75
71
65
50%
Giga-Analysts
58
40%
99
# of Responses
25
30% 50%
60%
70%
80%
90% 100%
Assessed Chance of Being Correct EXHIBIT 5.5
Calibration Experiment Results for 20 IT Industry Predictions in 1997
The deviation is a bit more significant—at least statistically if not visually—at the other end of the scale. Chance alone only would have allowed for slightly less deviation from expected, so they are a little overconfident on that end of the scale. But, overall, they are very well calibrated. In comparison, the clients’s results (indicated by the small triangles) who did not receive any calibration training were very overconfident. The numbers next to their calibration results show that 58 times a particular client said he or she was 90% confident in a particular prediction. Of those times, the clients got less than 60% of those predictions correct. The clients who even said they were 100% confident in a prediction in 21 specific responses got only 67% of those correct. Equally interesting is the fact that the Giga analysts didn’t actually get more answers correct. (The questions were general IT industry, not focusing on analyst specialties.) They were simply more conservative—but not overly conservative—about when they would put high confidence on a prediction. Prior to the training, however, the calibration of the analysts on general trivia questions was just as bad as the clients were on predictions of actual events. The results are clear: The difference in accuracy is due entirely to calibration training, and the calibration training works for real-world predictions. Even though a few individuals have had some initial difficulties with calibration, most are entirely willing to accept calibration and see it as a key skill in estimation. Pat Plunkett is the program manager for Information
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Technology Performance Measurement at the Department of Housing and Urban Development (HUD) and a thought leader in the U.S. government for the use of performance metrics. He has has seen people from various agencies get calibrated since 2000. In 2000, Plunkett was still with the GSA and was the driver behind the CIO Council experiment that brought these methods into the VA. Plunkett sees calibration as a profound shift in thinking about uncertainty. He says: ‘‘Calibration was an eye-opening experience. Many people, including myself, discovered how optimistic we tend to be when it comes to estimating. Once calibrated, you are a changed person. You have a keen sense of your level of uncertainty.’’ Perhaps the only U.S. government employee who has seen more people get calibrated than Plunkett is Art Koines, a senior policy advisor at the Environmental Protection Agency, where dozens of people have been calibrated. Like Plunkett, he was also surprised at the level of acceptance. ‘‘People sat through the process and saw the value of it. The big surprise for me was that they were so willing to provide calibrated estimates when I expected them to resist giving any answer at all for such uncertain things.’’ The calibration skill was a big help to the VA team in the IT security case. The VA team needed to show how much it knew now and how much it didn’t know now in order to quantify their uncertainty about security. The initial set of estimates (all ranges and probabilities) represent the current level of uncertainty about the quantities involved. This level provided the basis for the next steps: using odds in a decision model and computing information values. You now understand how to quantify your current uncertainty by learning how to provide calibrated probabilities. Knowing how to provide calibrated probabilities is critical to the next steps in measurement. Chapters 6 and 7 will teach you how to use calibrated probabilities to compute risk and the value of information.
& endnotes 1. B. Fischhoff, L. D. Phillips, and S. Lichtenstein, ‘‘Calibration of Probabilities: The State of the Art to 1980,’’ Judgement under Uncertainty: Heuristics and Biases, ed. D. Kahneman and A. Tversky, (New York: Cambridge University Press, 1982). 2. ibid 3. ibid
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& Measuring Risk: Introduction to the Monte Carlo Simulation
It is better to be approximately right than to be precisely wrong. —WARREN BUFFETT
e’ve defined the difference between uncertainty and risk. Initially, measuring uncertainty is just a matter of putting our calibrated ranges or probabilities on unknown variables. Subsequent measurements, whatever they may be about, also measure uncertainty, with each measurement reducing uncertainty further. Risk is simply a state of uncertainty where a possible outcome involves a loss of some kind. Generally, the implication is that the loss is something dramatic, not minor. With calibration methods, we see how to quantify our initial state of uncertainty with ranges and probabilities. The same is true when applying calibration methods to measuring risk. What many organizations do to ‘‘measure’’ risk is not very enlightening. The methods for assessing risk which I’m about to describe would be familiar to an actuary, statistician, or financial analyst. But some of the most popular methods for measuring risk look nothing like what an actuary might
W
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see. Many organizations simply say a risk is ‘‘high,’’ ‘‘medium,’’ or ‘‘low.’’ Or perhaps they rate it on a scale of 1 to 5. When I find situations like this, I sometimes ask how much ‘‘medium’’ risk really is. Is a 5% chance of losing more than $5 million a low, medium, or high risk? Nobody knows. Is a medium-risk investment with a 15% return on investment better or worse than a high-risk investment with a 50% return? Again, nobody knows. To illustrate why these sorts of classifications are not as useful as they could be, I ask attendees in seminars to consider the next time they have to write a check (or pay over the Web) for their next auto or homeowner’s insurance premium. Where you would usually see the ‘‘amount’’ field on the check, instead of writing a dollar amount, write the word ‘‘medium’’ and see what happens. You are telling your insurer you want a ‘‘medium’’ amount of risk mitigation. Would that make sense to the insurer in any meaningful way? It probably doesn’t to you, either. Using ranges to represent your uncertainty instead of unrealistically precise point values clearly has advantages. When you allow yourself to use ranges and probabilities, you don’t really have to assume anything you don’t know for a fact. But precise values have the advantage of being simple to add, subtract, multiply, and divide in a spreadsheet. So how do we add, subtract, multiply, and divide in a spreadsheet when we have no exact values, only ranges? Fortunately, a fairly simple trick can be done on any PC-Monte Carlo simulations, which were developed to do exactly that. One of our measurement mentors, Enrico Fermi, was an early user of what was later called a Monte Carlo simulation. A Monte Carlo simulation uses a computer to generate a large number of scenarios based on probabilities for inputs. For each scenario, a specific value would be randomly generated for each of the unknown variables. Then these specific values would go into a formula to compute an output for that single scenario. This process usually goes on for thousands of scenarios. Fermi, used Monte Carlo simulations to work out the behavior of large numbers of neutrons. In 1930, he knew that he was working on a problem that could not be solved with conventional integral calculus. But he could work out the odds of specific results in specific conditions. He realized that he could, in effect, randomly sample several of these situations and work out how large numbers of neutrons would behave in a system. In the 1940s and 1950s several mathematicians continued to work on similar problems in nuclear physics and started using computers to generate the random
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scenarios—most famously Stanislaw Ulam, John von Neumann, and Nicholas Metropolis. This time they were working on the atomic bomb in the Manhattan Project and, later, the hydrogen bomb at Los Alamos. At the suggestion of Metropolis, Ulam named this computer-based method of generating random scenarios after Monte Carlo, a famous gambling hotspot, in honor of Ulam’s uncle, a gambler.1 What Fermi begat, and what was later reared by Ulam, von Neumann, and Metropolis, is today widely used in business, government, and research. A simple application of this method is working out the return on an investment when you don’t know exactly what the costs and benefits will be. I once met with the chief information officer (CIO) of an investment firm in Chicago to talk about how the company can measure the value of information technology (IT). She said that they had a ‘‘pretty good handle on how to measure risk’’ but ‘‘I can’t begin to imagine how to measure benefits.’’ On closer look, this is a very curious combination of positions. She explained that most of the benefits the company attempts to achieve in IT investments are improvements in basis points (1 basis point = 0.01% yield on an investment)—the return the company gets on the investments it manages for clients. The firm hopes that the right IT investments can facilitate a competitive advantage in collecting and analyzing information that affects investment decisions. But when I asked her how the company does it now, she said staffers ‘‘just pick a number.’’ In other words, as long as enough people are willing to agree on (or at least not too many object to) a particular number for increased basis points, that’s what the business case is based on. While it’s possible this number is based on some experience, it was also clear that she was more uncertain about this benefit than any other. But if this is true, how is the company measuring risk? Clearly, it’s a strong possibility that the firm’s largest risk, if it was measured, would be the firm’s uncertainty about this benefit. She was not using ranges to express her uncertainty about the basis point improvement, so she had no way to incorporate this uncertainty into her risk calculation. Even though she felt confident the firm was doing a good job on risk analysis, it’s unlikely that it was doing much risk analysis at all. In fact, all risk in an investment ultimately can be expressed by one method: the ranges of uncertainty on the costs and benefits. If you know precisely the amount and timing of every cost and benefit (as is implied by traditional business cases based on fixed point values), then you literally have
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no risk. There is no chance that any benefit would be lower or cost would be higher than you expect. But all we really know about these things is the range, not exact points. And because we only have broad ranges, there is a chance we will have a negative return. That is the basis for computing risk, and that is what the Monte Carlo simulation is for.
An Example of the Monte Carlo Method and Risk This is an extremely basic example of a Monte Carlo simulation for people who have never worked with them before but have some familiarity with the Excel spreadsheet. If you have worked with a Monte Carlo tool before, you probably can skip these next few pages. Let’s say you are considering leasing a new machine for one step in a manufacturing process. The annual lease is $400,000 and you have to sign a multiyear contract. So if you aren’t breaking even, you are stuck with it for a while. You are considering signing the contract because you think the more advanced device will save some labor and raw materials and because you think the maintenance cost will be lower than the existing process. Your calibrated estimators gave these ranges for savings in maintenance, labor, and raw materials. They also estimated the annual production levels for this process. 0002
Maintenance savings (MS):
$10 to $20 per unit
0002
Labor savings (LS):
-$2 to $8 per unit
0002
Raw materials savings (RMS):
$3 to $9 per unit
0002
Production level (PL):
15,000 to 35,000 units per year
0002
Annual lease (breakeven):
$400,000
Now you compute your annual savings very simply as: Annual Savings ¼ ðMS þ LS þ RMSÞ 0001 PL Admittedly, this is an unrealistically simple example. The production levels could be different every year, perhaps some costs would improve
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further as experience with the new machine improved, and so on. But we’ve deliberately opted for simplicity over realism in this example. If we just took the midpoint of each of these ranges, we get Annual Savings ¼ ð$15 þ $3 þ $6Þ 0001 25;000 ¼ $600;000 It looks like we do better than the required breakeven, but there are uncertainties. So how do we measure the risk of this investment? First, let’s define risk for this context. Remember, to have a risk, we have to have uncertain future results with some of them being a quantified loss. One way of looking at risk would be the chance that we don’t break even—that is, we don’t save enough to make up for the $400,000 lease. The farther we undershoot the lease, the more we lost. The $600,000 is the middle of a range. How do we compute what that range really is and, thereby, compute the chance that we don’t break even? Since these aren’t exact numbers, usually we can’t just do a single calculation to determine whether we met the required savings or not. Some methods allow us to compute the range of the result given the ranges of inputs under some limited conditions, but in most real-life problems, those conditions don’t exist. As soon as we begin adding and multiplying different types of distributions, the problem usually becomes what a mathematician would call ‘‘unsolvable’’ or ‘‘having no solution’’ with calculus. This is exactly the problem the physicists working on fission ran into. So, instead, we use a brute-force approach made possible with computers. We randomly pick a bunch of exact values—thousands—according to the ranges we prescribed and compute a large number of exact values. The Monte Carlo simulation is an excellent method for solving this problem. We would have to randomly generate values within the stated ranges, put them into the annual savings formula, and compute a result. Some of the results will be higher than the $600,000 midpoint we computed and some will be lower. Some will even be lower than the $400,000 required to break even. You can run a Monte Carlo simulation easily with Excel on a PC, but we need a bit more information than just the 90% confidence interval (CI) itself. We also need the shape of the distribution. Some shapes are more appropriate for certain values than other shapes. The one generally used with the 90% CI is the well-known ‘‘normal’’ distribution. The normal distribution is the familiar-looking bell curve where the probable outcomes are bunched near
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What a “Normal Distribution” looks like: 90% Confidence Interval
Characteristics: Values near the middle are more likely than values farther away. The distribution is symmetrical, not lopsided—the mean is exactly halfway between the upper and lower bounds of a 90% CI. The ends trail off indefinitely to ever more unlikely values, but there is no “hard stop”; a value far outside of a 90% CI is possible but not likely. How to make a random distribution with this shape in Excel: =norminv(rand(),A, B) A=mean = (90% CI upper bound + 90% CI lower bound)/2 and B=“standard deviation” =(90% CI upper bound – 90% CI lower bound)/3.29 EXHIBIT 6.1
The Normal Distribution
the middle but trail off to ever less likely values in both directions. (See Exhibit 6.1.) With the normal distribution, I will briefly mention a related concept called the standard deviation. People don’t seem to have an intuitive understanding of standard deviation, and because it can be replaced by a calculation based on the 90% CI (which people do understand intuitively), I won’t focus on it here. Exhibit 6.1 shows that there are 3.29 standard deviations in one 90% CI, so we just need to make the conversion. For our problem, we can just make a random number generator in a spreadsheet for each of our ranges. Following the instructions in Exhibit 6.1, we can generate random numbers for Maintenance savings with the Excel formula: ¼ norminv(rand(),15,(20 0003 10)=3.29) Likewise, we follow the instructions in Exhibit 6.1 for the rest of the ranges. Some people might prefer using the Random Number Generator in the Excel Analysis Toolpack, and you should feel free to experiment with it. I’m showing this formula in Exhibit 6.2 for a bit more of a hands-on approach.
an example of the monte carlo method and risk
Scenario #
Maintenance Savings
Labor Savings
Materials Savings
Units Produced
Total Savings
Breakeven Met?
1
$ 9.27
$ 4.30
$
7.79
23,955
$511,716
Yes
2
$ 15.92
$ 2.64
$
9.02
26,263
$724,127
Yes
3
$ 17.70
$ 4.63
$
8.10
20,142
$612,739
Yes
4
$ 15.08
$ 6.75
$
5.19
20,644
$557,860
Yes
5
$ 19.42
$ 9.28
$
9.68
25,795
$990,167
Yes
6
$ 11.86
$ 3.17
$
5.89
17,121
$358,166
No
7
$ 15.21
$ 0.46
$
4.14
29,283
$580,167
Yes
9,999
$ 14.68
$ (0.22)
$
5.32
33,175
$655,879
Yes
10,000
$ 7.49
$ (0.01)
$
8.97
24,237
$398,658
No
EXHIBIT 6.2
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Simple Monte Carlo Layout in Excel
We arrange the variables in columns as shown in Exhibit 6.2. The last two columns are just the calculations based on all the previous columns. The Total Savings column is the formula for annual savings (shown earlier) based on the numbers in each particular row. For example, scenario 1 in Exhibit 6.2 shows its Total Savings as ($9.27 + $4.30 + $7.79) 0001 23,955 = $511,716. You don’t really need the ‘‘Breakeven Met?’’ column; I’m just showing it for reference. Now let’s copy it down and make 10,000 rows. We can use a couple of other simple tools in Excel to get a sense of how this turns out. The ‘‘=countif()’’ function allows you to count the number values that meet a certain condition—in this case, those that are less than $400,000. Or, for a more complete picture, you can use the histogram tool in the Analysis Toolpack. That will count the number of scenarios in each of several ‘‘buckets,’’ or incremental groups. Then you can make a chart to display the output, as shown in Exhibit 6.3. This chart shows how many of the 10,000 scenarios came up in each $100,000 increment. For example, just over 1,000 scenarios had values between $300,000 and $400,000. You will find that about 14% of the results were less than the $400,000 breakeven. This means there is a 14% chance of losing money. That is a
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2000 1500 1000 50
1,400
1,300
1,200
1,100
1,000
900
800
700
600
500
400
300
200
0 100
Scenarios in Increment
2500
Savings per Year ($000s in 100,000 increments) EXHIBIT 6.3
Histogram
meaningful measure of risk. But risk doesn’t have to mean just the chance of a negative return on investment. In the same way we can measure the ‘‘size’’ of a thing by its height, weight, girth, and so on, there are a lot of useful measures of risk. Further examination shows that there is a 3.5% chance that the factory will lose more than $100,000 per year, instead of saving money. However, generating no revenue at all is virtually impossible. This is what we mean by ‘‘risk analysis.’’ We have to be able to compute the odds of various levels of losses. If you are truly measuring risk, this is what you can do. For a spreadsheet example of this Monte Carlo problem, see the supplementary Web site at www.howtomeasureanything.com. A shortcut can apply in some situations. If we had all normal distributions and we simply wanted to add or subtract ranges—such as a simple list of costs and benefits—we might not have to run a Monte Carlo simulation. If we just wanted to add up the three types of savings in our example, we can actually use a simple calculation. Use these six steps to produce a range: 1. Subtract the midpoint from the upper bound for each of the three cost savings ranges: or $20 0003 $15 ¼ $5 for maintenance savings; we also get $5 for labor savings and $3 for materials savings. 2. Square each of the values from the last step: $5 squared is $25, and so on. 3. Add up the results: $25 þ $25 þ $9 ¼ $59 4. Take the square root of the total: $59^.5 ¼ $7.68
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5. Total up the means: $15 + $3 + $6 = $24 6. Add and subtract the result from step 4 from the sum of the means to get the upper and lower bounds of the total, or $24 þ $7.68 ¼ $31.68 for the upper bound, $24 0003 $7.68 ¼ $16.32 for the lower bound. So the 90% CI for the sum of all three 90% CI for maintenance, labor, and materials is $16.32 to $31.68. In summary, the range interval of the total is equal to the square root of the sum of the squares of the range intervals. You might see someone attempting to do something similar by adding up all the ‘‘optimistic’’ values for an upper bound and ‘‘pessimistic’’ values for the lower bound. This would result in a range of $11 to $37 for these three CI. This slightly exaggerates the 90% CI. When this calculation is done with a business case of dozens of variables, the exaggeration of the range becomes too significant to ignore. It is like thinking that rolling a bucket of dice will produces all 1’s or all 6’s. Most of the time, we get a combination of all the values, some high, some low. This is a common error and no doubt has resulted in a large number of misinformed decisions. Yet the simple method I just showed works perfectly well when you have a set of 90% CIs you would like to add up. But we don’t just want to add these up, we want to multiply them by the production level, which is also a range. The simple range addition method doesn’t work with anything other than subtraction or addition. A Monte Carlo simulation is also required if these were not all normal distributions. Although a wide variety of shapes of distributions for all sorts of problems are beyond the scope of this book, it is worth mentioning two others besides the normal distribution: a uniform distribution and the binary distribution. (See Exhibits 6.4 and 6.5.) Each of these will come up later when we discuss the value of information.
Tools and Other Resources for Monte Carlo Simulations Fortunately, you really don’t have to build Monte Carlo simulations from scratch these days. Many tools can be very helpful and improve the productivity of an analyst trained in the basics. They range from simple sets of Excel macros—what I use—combined with a practical consulting approach to very sophisticated packages.
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What a “Uniform Distribution looks like: 100% Confidence Interval
Characteristics: All values between the bounds are equally likely. The distribution is symmetrical, not lopsided—the mean is exactly halfway between the upper and lower bounds. The bounds are “hard stops” and are, in effect, a “100% CI”—nothing above the upper bound nor below the lower bound is possible. How to make a random distribution with this shape in Excel: =rand()*(UB-LB)+LB UB=Upper bound LB=Lower bound
The Uniform Distribution
EXHIBIT 6.4
What a “Binary Distribution” looks like: 60% 40%
0
1
Characteristics: Produces only two possible values. There is a single probability that one value will occur (60% in the chart), and the other value occurs the rest of the time. How to make a random distribution with this shape in Excel: =if(rand()