NOTES - The Drunkard's Walk: How Randomness Rules Our Lives - Leonard Mlodinow

The Drunkard's Walk: How Randomness Rules Our Lives - Leonard Mlodinow (2008)



1. Stanley Meisler, “First in 1763: Spain Lottery—Not Even War Stops It,” Los Angeles Times, December 30, 1977.

2. On basketball, see Michael Patrick Allen, Sharon K. Panian, and Roy E. Lotz, “Managerial Succession and Organizational Performance: A Recalcitrant Problem Revisited,” Administrative Science Quarterly 24, no. 2 (June 1979): 167-80; on football, M. Craig Brown, “Administrative Succession and Organizational Performance: The Succession Effect,” Administrative Science Quarterly 27, no. 1 (March 1982): 1-16; on baseball, Oscar Grusky, “Managerial Succession and Organizational Effectiveness,” American Journal of Sociology 69, no. 1 (July 1963): 21-31, and William A. Gamson and Norman A. Scotch, “Scapegoating in Baseball,” American Journal of Sociology70, no. 1 (July 1964): 69-72; on soccer, Ruud H. Koning, “An Econometric Evaluation of the Effect of Firing a Coach on Team Performance,” Applied Economics 35, no. 5 (March 2003): 555-64.

3. James Surowiecki, The Wisdom of Crowds (New York: Doubleday, 2004), pp. 218-19.

4. Armen Alchian, “Uncertainty, Evolution, and Economic Theory,” Journal of Political Economy 58, no. 3 (June 1950): 213.

Chapter 1: Peering through the Eyepiece of Randomness

1. Kerstin Preuschoff, Peter Bossaerts, and Steven R. Quartz, “Neural Differentiation of Expected Reward and Risk in Human Subcortical Structures,” Neuron 51 (August 3, 2006): 381-90.

2. Benedetto De Martino et al., “Frames, Biases, and Rational Decision-Making in the Human Brain,” Science 313 (August 4, 2006): 684-87.

3. George Wolford, Michael B. Miller, and Michael Gazzaniga, “The Left Hemisphere’s Role in Hypothesis Formation,” Journal of Neuroscience 20: RC64 (2000): 1-4.

4. Bertrand Russell, An Inquiry into Meaning and Truth (1950; repr., Oxford: Routledge, 1996), p. 15.

5. Matt Johnson and Tom Hundt, “Hog Industry Targets State for Good Reason,” Vernon County ( Wisconsin ) Broadcaster, July 17, 2007.

6. Kevin McKean, “Decisions, Decisions,” Discover, June 1985, pp. 22-31.

7. David Oshinsky, “No Thanks, Mr. Nabokov,” New York Times Book Review, September 9, 2007.

8. Press accounts of the number of rejections these manuscripts received vary slightly.

9. William Goldman, Adventures in the Screen Trade (New York: Warner Books, 1983), p. 41.

10. See Arthur De Vany, Hollywood Economics (Abington, U.K.: Routledge, 2004).

11. William Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (New York: John Wiley and Sons, 1957), p. 68. Note that for simplicity’s sake, when the opponents are tied, Feller defines the lead as belonging to the player who led at the preceding trial.

12. Leonard Mlodinow, “Meet Hollywood’s Latest Genius,” Los Angeles Times Magazine, July 2, 2006.

13. Dave McNary, “Par Goes for Grey Matter,” Variety, January 2, 2005.

14. Ronald Grover, “Paramount’s Cold Snap: The Heat Is On,” BusinessWeek, November 21, 2003.

15. Dave McNary, “Parting Gifts: Old Regime’s Pics Fuel Paramount Rebound,” Variety, August 16, 2005.

16. Anita M. Busch, “Canton Inks Prod’n Pact at Warner’s,” Variety, August 7, 1997.

17. “The Making of a Hero,” Time, September 29, 1961, p. 72. The old-timer was Rogers Hornsby.

18. “Mickey Mantle and Roger Maris: The Photographic Essay,” Life, August 18, 1961, p. 62.

19. For those who don’t know baseball, the plate is a rubber slab embedded in the ground, which a player stands before as he attempts to hit the ball. For those who do know baseball, please note that I included walks in my definition of opportunities. If the calculation is redone employing just official at bats, the result is about the same.

20. See Stephen Jay Gould, “The Streak of Streaks,” New York Review of Books, August 18, 1988, pp. 8-12 (we’ll come back to their work in more detail later). A compelling and mathematically detailed analysis of coin-toss models in sports appears in chapter 2 of a book in progress by Charles M. Grinstead, William P. Peterson, and J. Laurie Snell, tentatively titled Fat Chance;

Chapter 2: The Laws of Truths and Half-Truths

1. Daniel Kahneman, Paul Slovic, and Amos Tversky, eds., Judgment under Uncertainty: Heuristics and Biases (Cambridge: Cambridge University Press, 1982), pp. 90-98.

2. Amos Tversky and Daniel Kahneman, “Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment,” Psychological Review 90, no. 4 (October 1983): 293-315.

3. Craig R. Fox and Richard Birke, “Forecasting Trial Outcomes: Lawyers Assign Higher Probabilities to Possibilities That Are Described in Greater Detail,” Law and Human Behavior 26, no. 2 (April 2002): 159-73.

4. Plato, The Dialogues of Plato, trans. Benjamin Jowett (Boston: Colonial Press, 1899), p. 116.

5. Plato, Theaetetus (Whitefish, Mont.: Kessinger, 2004), p. 25.

6. Amos Tversky and Daniel Kahneman, “Availability: A Heuristic for Judging Frequency and Probability,” Cognitive Psychology 5 (1973): 207-32.

7. Reid Hastie and Robyn M. Dawes, Rational Choice in an Uncertain World: The Psychology and Judgement of Decision Making (Thousand Oaks, Calif.: Sage, 2001), p. 87.

8. Robert M. Reyes, William C. Thompson, and Gordon H. Bower, “Judgmental Biases Resulting from Differing Availabilities of Arguments,” Journal of Personality and Social Psychology 39, no. 1 (1980): 2-12.

9. Robert Kaplan, The Nothing That Is: A Natural History of Zero (London: Oxford University Press, 1999), pp. 15-17.

10. Cicero, quoted in Morris Kline, Mathematical Thought from Ancient to Modern Times (London: Oxford University Press, 1972), 1:179.

11. Morris Kline, Mathematics in Western Culture (London: Oxford University Press, 1953), p. 86.

12. Kline, Mathematical Thought, pp. 178-79.

13. Cicero, quoted in Warren Weaver, Lady Luck (Mineola, N.Y.: Dover Publications, 1982), p. 53.

14. Cicero, quoted in F. N. David, Gods, Games and Gambling: A History of Probability and Statistical Ideas (Mineola, N.Y.: Dover Publications, 1998), pp. 24-26.

15. Cicero, quoted in Bart K. Holland, What Are the Chances? Voodoo Deaths, Office Gossip, and Other Adventures in Probability (Baltimore: Johns Hopkins University Press, 2002), p. 24.

16. Ibid., p. 25.

17. James Franklin, The Science of Conjecture: Evidence and Probability before Pascal (Baltimore: Johns Hopkins University Press, 2001), pp. 4, 8.

18. Quoted ibid., p. 13.

19. Quoted ibid., p. 14.

20. William C. Thompson, Franco Taroni, and Colin G. G. Aitken, “How the Probability of a False Positive Affects the Value of DNA Evidence,” Journal of Forensic Sciences 48, no. 1 (January 2003): 1-8.

21. Ibid., p. 2. The story is recounted in Bill Braun, “Lawyers Seek to Overturn Rape Conviction,” Tulsa World, November 22, 1996. See also (Durham was released in 1997.)

22. People v. Collins, 68 Calif. 2d 319, 438 P.2d 33, 66 Cal. Rptr. 497 (1968).

23. Thomas Lyon, private communication.

Chapter 3: Finding Your Way through a Space of Possibilities

1. Alan Wykes, Doctor Cardano: Physician Extraordinary (London: Frederick Muller, 1969). See also Oystein Ore, Cardano: The Gambling Scholar, with a translation of Cardano’s Book on Games of Chance by Sydney Henry Gould (Princeton, N.J.: Princeton University Press, 1953).

2. Marilyn vos Savant, “Ask Marilyn,” Parade, September 9, 1990.

3. Bruce D. Burns and Mareike Wieth, “Causality and Reasoning: The Monty Hall Dilemma,” in Proceedings of the Twenty-fifth Annual Meeting of the Cognitive Science Society, ed. R. Alterman and D. Kirsh (Hillsdale, N.J.: Lawrence Erlbaum Associates, 2003), p. 198.

4. National Science Board, Science and Engineering Indicators—2002 (Arlington, Va.: National Science Foundation, 2002); See vol. 2, chap. 7, table 7-10.

5. Gary P. Posner, “Nation’s Mathematicians Guilty of Innumeracy,” Skeptical Inquirer 15, no. 4 (Summer 1991).

6. Bruce Schechter, My Brain Is Open: The Mathematical Journeys of Paul Erdös (New York: Touchstone, 1998), pp. 107-9.

7. Ibid., pp. 189-90, 196-97.

8. John Tierney, “Behind Monty’s Doors: Puzzle, Debate and Answer?” New York Times, July 21, 1991.

9. Robert S. Gottfried, The Black Death: Natural and Human Disaster in Medieval Europe (New York: Free Press, 1985).

10. Gerolamo Cardano, quoted in Wykes, Doctor Cardano, p. 18.

11. Kline, Mathematical Thought, pp. 184-85, 259-60.

12. “Oprah’s New Shape: How She Got It,” O, the Oprah Magazine, January 2003.

13. Lorraine J. Daston, Classical Probability in the Enlightenment (Princeton, N.J.: Princeton University Press, 1998), p. 97.

14. Marilyn vos Savant, “Ask Marilyn,” Parade, March 3, 1996, p. 14.

15. There are four tires on the car, so, letting RF signify “right front,” and so on, there are 16 possible combinations of responses by the two students. If the first response listed represents that of student 1 and the second that of student 2, the possible joint responses are (RF, RF), (RF, LF), (RF, RR), (RF, LR), (LF, RF), (LF, LF), (LF, RR), (LF, LR), (RR, RF), (RR, LF), (RR, RR), (RR, LR), (LR, RF), (LR, LF), (LR, RR), (LR, LR). Of these 16, 4 are in agreement: (RF, RF), (LF, LF), (RR, RR), (LR, LR). Hence the chances are 4 out of 16, or 1 in 4.

16. Martin Gardner, “Mathematical Games,” Scientific American, October 1959, pp. 180-82.

17. Jerome Cardan, The Book of My Life: De Vita Propia Liber, trans. Jean Stoner (Whitefish, Mont.: Kessinger, 2004), p. 35.

18. Cardano, quoted in Wykes, Doctor Cardano, p. 57.

19. Cardano, quoted ibid.

20. Cardano, quoted ibid., p. 172.

Chapter 4: Tracking the Pathways to Success

1. Bengt Ankarloo and Stuart Clark, eds., Witchcraft and Magic in Europe: The Period of the Witch Trials (Philadelphia: University of Pennsylvania Press, 2002), pp. 99-104.

2. Meghan Collins, “Traders Ward Off Evil Spirits,” October 31, 2003,

3. Henk Tijms, Understanding Probability: Chance Rules in Everyday Life (Cambridge: Cambridge University Press, 2004), p. 16.

4. Ibid., p. 80.

5. David, Gods, Games and Gambling, p. 65.

6. Blaise Pascal, quoted in Jean Steinmann, Pascal, trans. Martin Turnell (New York: Harcourt, Brace & World, 1962), p. 72.

7. Gilberte Pascal, quoted in Morris Bishop, Pascal: The Life of a Genius (1936; repr., New York: Greenwood Press, 1968), p. 47.

8. Ibid., p. 137.

9. Gilberte Pascal, quoted ibid., p. 135.

10. See A.W.F. Edwards, Pascal’s Arithmetical Triangle: The Story of a Mathematical Idea (Baltimore: Johns Hopkins University Press, 2002).

11. Blaise Pascal, quoted in Herbert Westren Turnbull, The Great Mathematicians (New York: New York University Press, 1961), p. 131.

12. Blaise Pascal, quoted in Bishop, Pascal, p. 196.

13. Blaise Pascal, quoted in David, Gods, Games and Gambling, p. 252.

14. Bruce Martin, “Coincidences: Remarkable or Random?” Skeptical Inquirer 22, no. 5 (September/October 1998).

15. Holland, What Are the Chances? pp. 86-89.

Chapter 5: The Dueling Laws of Large and Small Numbers

1. Tijms, Understanding Probability, p. 53.

2. Scott Kinney, “Judge Sentences Kevin L. Lawrence to 20 Years Prison in Znetix/HMC Stock Scam,” Washington State Department of Financial Institutions, press release, November 25, 2003;

3. Interview with Darrell Dorrell, August 1, 2005.

4. Lee Berton, “He’s Got Their Number: Scholar Uses Math to Foil Financial Fraud,” Wall Street Journal, July 10, 1995.

5. Charles Sanders Peirce, Max Harold Fisch, and Christian J. W. Kloesel, Writings of Charles S. Peirce: A Chronological Edition (Bloomington: Indiana University Press, 1982), p. 427.

6. Rand Corporation, A Million Random Digits with 100,000 Normal Deviates (1955; repr., Santa Monica, Calif.: Rand, 2001), pp. ix-x. See also Lola L. Lopes, “Doing the Impossible: A Note on Induction and the Experience of Randomness,” Journal of Experimental Psychology: Learning, Memory, and Cognition 8, no. 6 (November 1982): 626-36.

7. The account of Joseph Jagger (sometimes spelled Jaggers) is from John Grochowski, “House Has a Built-in Edge When Roulette Wheel Spins,” Chicago Sun-Times, February 21, 1997.

8. For details about the Bernoulli family and Jakob’s life, see E. S. Pearson, ed., The History of Statistics in the 17th and 18th Centuries against the Changing Background of Intellectual, Scientific and Religious Thought: Lectures by Karl Pearson Given at University College, London, during the Academic Sessions 1921-1933 (New York: Macmillan, 1978), pp. 221-37; J. O. Fleckenstein, “Johann und Jakob Bernoulli,” in Elemente der Mathematik, Beihefte zur Zeitschrift, no. 6 (Basel, 1949); and Stephen Stigler, “The Bernoullis of Basel,” Journal of Econometrics 75, no. 1 (1996): 7-13.

9. Quoted in Pearson, The History of Statistics in the 17th and 18th Centuries, p. 224.

10. Stephen Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge, Mass.: Harvard University Press, 1986), p. 65.

11. Pearson, The History of Statistics in the 17th and 18th Centuries, p. 226.

12. William H. Cropper, The Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking (London: Oxford University Press, 2001), p. 31.

13. Johann Bernoulli, quoted in Pearson, The History of Statistics in the 17th and 18th Centuries, p. 232.

14. This depends, of course, on what you identify as “the modern concept.” I am using the definition employed by Hankel’s 1871 history of the topic, described in great detail in Gert Schubring, Conflicts between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany (New York: Springer, 2005), pp. 22-32.

15. David Freedman, Robert Pisani, and Roger Purves, Statistics, 3rd ed. (New York: W. W. Norton, 1998), pp. 274-75.

16. The Hacking quote is from Ian Hacking, The Emergence of Probability (Cambridge: Cambridge University Press, 1975), p. 143. The Bernoulli quote is from David, Gods, Games and Gambling, p. 136.

17. For a discussion of what Bernoulli actually proved, see Stigler, The History of Statistics, pp. 63-78, and Ian Hacking, The Emergence of Probability, pp. 155-65.

18. Amos Tversky and Daniel Kahneman, “Belief in the Law of Small Numbers,” Psychological Bulletin 76, no. 2 (1971): 105-10.

19. Jakob Bernoulli, quoted in L. E. Maistrov, Probability Theory: A Historical Sketch, trans. Samuel Kotz (New York: Academic Press, 1974), p. 68.

20. Stigler, The History of Statistics, p. 77.

21. E. T. Bell, Men of Mathematics (New York: Simon & Schuster, 1937), p. 134.

Chapter 6: False Positives and Positive Fallacies

1. The account of the Harvard student is from Hastie and Dawes, Rational Choice in an Uncertain World, pp. 320-21.

2. I was told a variant of this problem by Mark Hillery of the Physics Department at Hunter College, City University of New York, who heard it while on a trip to Bratislava, Slovakia.

3. Quoted in Stigler, The History of Statistics, p. 123.

4. Ibid., pp. 121-31.

5. U.S. Social Security Administration, “Popular Baby Names: Popular Names by Birth Year; Popularity in 1935,”

6. Division of HIV/AIDS, Center for Infectious Diseases, HIV/AIDS Surveillance Report (Atlanta: Centers for Disease Control, January 1990). I calculated the statistic quoted from the data given but also had to use some estimates. In particular, the data quoted refers to AIDS cases, not HIV infection, but that suffices for the purpose of illustrating the concept.

7. To be precise, the probability that A will occur if B occurs is equal to the probability that B will occur if A occurs multiplied by a correction factor that equals the ratio of the probability of A to the probability of B.

8. Gerd Gigerenzer, Calculated Risks: How to Know When Numbers Deceive You (New York: Simon & Schuster, 2002), pp. 40-44.

9. Donald A. Barry and LeeAnn Chastain, “Inferences About Testosterone Abuse Among Athletes,” Chance 17, no. 2 (2004): 5-8.

10. John Batt, Stolen Innocence (London: Ebury Press, 2005).

11. Stephen J. Watkins, “Conviction by Mathematical Error? Doctors and Lawyers Should Get Probability Theory Right,” BMJ 320 (January 1, 2000): 2-3.

12. “Royal Statistical Society Concerned by Issues Raised in Sally Clark Case,” Royal Statistical Society, London, news release, October 23, 2001;,%20October%2023rd%202001.pdf.

13. Ray Hill, “Multiple Sudden Infant Deaths—Coincidence or beyond Coincidence?” Paediatric and Perinatal Epidemiology 18, no. 5 (September 2004): 320-26.

14. Quoted in Alan Dershowitz, Reasonable Doubts: The Criminal Justice System and the O. J. Simpson Case (New York: Simon & Schuster, 1996), p. 101.

15. Federal Bureau of Investigation, “Uniform Crime Reports,”

16. Alan Dershowitz, The Best Defense (New York: Vintage, 1983), p. xix.

17. Pierre-Simon de Laplace, quoted in James Newman, ed., The World of Mathematics (Mineola, N.Y.: Dover Publications, 1956): 2:1323.

Chapter 7: Measurement and the Law of Errors

1. Sarah Kershaw and Eli Sanders, “Recounts and Partisan Bickering Bring Election Fatigue to Washington Voters,” New York Times, December 26, 2004; and Timothy Egan, “Trial for Governor’s Seat Set to Start in Washington,” New York Times, May 23, 2005.

2. Jed Z. Buchwald, “Discrepant Measurements and Experimental Knowledge in the Early Modern Era,” Archive for History of Exact Sciences 60, no. 6 (November 2006): 565-649.

3. Eugene Frankel, “J. B. Biot and the Mathematization of Experimental Physics in Napoleonic France,” in Historical Studies in the Physical Sciences, ed. Russell McCormmach (Princeton, N.J.: Princeton University Press, 1977).

4. Charles Coulston Gillispie, ed., Dictionary of Scientific Biography (New York: Charles Scribner’s Sons, 1981), p. 85.

5. For a discussion of the errors made by radar guns, see Nicole Weisensee Egan, “Takin’ Aim at Radar Guns,” Philadelphia Daily News, March 9, 2004.

6. Charles T. Clotfelter and Jacob L. Vigdor, “Retaking the SAT” (working paper SAN01-20, Terry Sanford Institute of Public Policy, Duke University, Durham, N.C., July 2001).

7. Eduardo Porter, “Jobs and Wages Increased Modestly Last Month,” New York Times, September 2, 2006.

8. Gene Epstein on “Mathemagicians,” On the Media, WNYC radio, broadcast August 25, 2006.

9. Legene Quesenberry et al., “Assessment of the Writing Component within a University General Education Program,” November 1, 2000;

10. Kevin Saunders, “Report to the Iowa State University Steering Committee on the Assessment of ISU Comm-English 105 Course Essays,” September 2004; (accessed 2005; site now discontinued).

11. University of Texas, Office of Admissions, “Inter-rater Reliability of Holistic Measures Used in the Freshman Admissions Process of the University of Texas at Austin,” February 22, 2005;

12. Emily J. Shaw and Glenn B. Milewski, “Consistency and Reliability in the Individualized Review of College Applicants,” College Board, Office of Research and Development, Research Notes RN-20 (October 2004): 3;

13. Gary Rivlin, “In Vino Veritas,” New York Times, August 13, 2006.

14. William James, The Principles of Psychology (New York: Henry Holt, 1890), p. 509.

15. Robert Frank and Jennifer Byram, “Taste-Smell Interactions Are Tastant and Odorant Dependent,” Chemical Senses 13 (1988): 445-55.

16. A. Rapp, “Natural Flavours of Wine: Correlation between Instrumental Analysis and Sensory Perception,” Fresenius’ Journal of Analytic Chemistry 337, no. 7 (January 1990): 777-85.

17. D. Laing and W. Francis, “The Capacity of Humans to Identify Odors in Mixtures,” Physiology and Behavior 46, no. 5 (November 1989): 809-14; and D. Laing et al., “The Limited Capacity of Humans to Identify the Components of Taste Mixtures and Taste-Odour Mixtures,” Perception 31, no. 5 (2002): 617-35.

18. For the rosé study, see Rose M. Pangborn, Harold W. Berg, and Brenda Hansen, “The Influence of Color on Discrimination of Sweetness in Dry Table-Wine,” American Journal of Psychology 76, no. 3 (September 1963): 492-95. For the anthocyanin study, see G. Morrot, F. Brochet, and D. Dubourdieu, “The Color of Odors,” Brain and Language 79, no. 2 (November 2001): 309-20.

19. Hilke Plassman, John O’Doherty, Baba Shia, and Antonio Rongel, “Marketing Actions Can Modulate Neural Representations of Experienced Pleasantness,” Proceedings of the National Academy of Sciences, January 14, 2008;

20. M. E. Woolfolk, W. Castellan, and C. Brooks, “Pepsi versus Coke: Labels, Not Tastes, Prevail,” Psychological Reports 52 (1983): 185-86.

21. M. Bende and S. Nordin, “Perceptual Learning in Olfaction: Professional Wine Tasters Versus Controls,” Physiology and Behavior 62, no. 5 (November 1997): 1065-70.

22. Gregg E. A. Solomon, “Psychology of Novice and Expert Wine Talk,” American Journal of Psychology 103, no. 4 (Winter 1990): 495-517.

23. Rivlin, “In Vino Veritas.”

24. Ibid.

25. Hal Stern, “On the Probability of Winning a Football Game,” American Statistician 45, no. 3 (August 1991): 179-82.

26. The graph is from Index Funds Advisors, “Index Take the Risk Capacity Survey,”, where it is credited to Walter Good and Roy Hermansen, Index Your Way to Investment Success (New York: New York Institute of Finance, 1997). The performance of 300 mutual fund managers was tabulated for ten years (1987-1996), based on the Morningstar Principia database.

27. Polling Report, “President Bush—Overall Job Rating,”

28. “Poll: Bush Apparently Gets Modest Bounce,” CNN, September 8, 2004,

29. “Harold von Braunhut,” Telegraph, December 23, 2003;

30. James J. Fogarty, “Why Is Expert Opinion on Wine Valueless?” (discussion paper 02.17, Department of Economics, University of Western Australia, Perth, 2001).

31. Stigler, The History of Statistics, p. 143.

Chapter 8: The Order in Chaos

1. Holland, What Are the Chances? p. 51.

2. This is only an approximation, based on more recent American statistics. See U.S. Social Security Administration, “Actuarial Publications: Period Life Table.” The most recent table is available at

3. Immanuel Kant, quoted in Theodore Porter, The Rise of Statistical Thinking: 1820-1900 (Princeton, N.J.: Princeton University Press, 1988), p. 51.

4. U.S. Department of Transportation, Federal Highway Administration, “Licensed Drivers, Vehicle Registrations and Resident Population,”

5. U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, “Motor Vehicle Safety Data,”

6. “The Domesday Book,” History Magazine, October/November 2001.

7. For Graunt’s story, see Hacking, The Emergence of Probability, pp. 103-9; David, Gods, Games and Gambling, pp. 98-109; and Newman, The World of Mathematics, 3:1416-18.

8. Hacking, The Emergence of Probability, p. 102.

9. Theodore Porter, The Rise of Statistical Thinking, p. 19.

10. For Graunt’s original table, see Hacking, The Emergence of Probability, p. 108. For the current data, see World Health Organization, “Life Tables for WHO Member States,” The figures quoted were taken from abridged tables and rounded.

11. Ian Hacking, The Taming of Chance (Cambridge: Cambridge University Press, 1990), p. vii.

12. H. A. David, “First (?) Occurrence of Common Terms in Statistics and Probability,” in Annotated Readings in the History of Statistics, ed. H. A. David and A.W.F. Edwards (New York: Springer, 2001), appendix B and pp. 219-28.

13. Noah Webster, American Dictionary of the English Language (1828; facsimile of the 1st ed., Chesapeake, Va.: Foundation for American Christian Education, 1967).

14. The material on Quételet is drawn mainly from Stigler, The History of Statistics, pp. 161-220; Stephen Stigler, Statistics on the Table: The History of Statistical Concepts and Methods (Cambridge, Mass.: Harvard University Press, 1999), pp. 51-66; and Theodore Porter, The Rise of Statistical Thinking, pp. 100-9.

15. Louis Menand, The Metaphysical Club (New York: Farrar, Straus & Giroux, 2001), p. 187.

16. Holland, What Are the Chances? pp. 41-42.

17. David Yermack, “Good Timing: CEO Stock Option Awards and Company News Announcements,” Journal of Finance 52, no. 2 (June 1997): 449-76; and Erik Lie, “On the Timing of CEO Stock Option Awards,” Management Science 51, no. 5 (May 2005): 802-12. See also Charles Forelle and James Bandler, “The Perfect Payday—Some CEOs Reap Millions by Landing Stock Options When They Are Most Valuable: Luck—or Something Else?” Wall Street Journal, March 18, 2006.

18. Justin Wolfers, “Point Shaving: Corruption in NCAA Basketball,” American Economic Review 96, no. 2 (May 2006): 279-83.

19. Stern, “On the Probability of Winning a Football Game.”

20. David Leonhardt, “Sad Suspicions about Scores in Basketball,” New York Times, March 8, 2006.

21. Richard C. Hollinger et al., National Retail Security Survey: Final Report (Gainesville: Security Research Project, Department of Sociology and Center for Studies in Criminal Law, University of Florida, 2002-2006).

22. Adolphe Quételet, quoted in Theodore Porter, The Rise of Statistical Thinking, p. 54.

23. Quételet, quoted in Menand, The Metaphysical Club, p. 187.

24. Jeffrey Kluger, “Why We Worry about the Things We Shouldn’t…and Ignore the Things We Should,” Time, December 4, 2006, pp. 65-71.

25. Gerd Gigerenzer, Empire of Chance: How Probability Changed Science and Everyday Life (Cambridge: Cambridge University Press, 1989), p. 129.

26. Menand, The Metaphysical Club, p. 193.

27. De Vany, Hollywood Economics; see part IV, “A Business of Extremes.”

28. See Derek William Forrest, Francis Galton: The Life and Work of a Victorian Genius (New York: Taplinger, 1974); Jeffrey M. Stanton, “Galton, Pearson, and the Peas: A Brief History of Linear Regression for Statistics Instructors,” Journal of Statistics Education 9, no. 3 (2001); and Theodore Porter, The Rise of Statistical Thinking, pp. 129-46.

29. Francis Galton, quoted in Theodore Porter, The Rise of Statistical Thinking, p. 130.

30. Peter Doskoch, “The Winning Edge,” Psychology Today, November/ December 2005, pp. 44-52.

31. Deborah J. Bennett, Randomness (Cambridge, Mass.: Harvard University Press, 1998), p. 123.

32. Abraham Pais, The Science and Life of Albert Einstein (London: Oxford University Press, 1982), p. 17; see also the discussion on p. 89.

33. On Brown and the history of Brownian motion, see D. J. Mabberley, Jupiter Botanicus: Robert Brown of the British Museum (Braunschweig, Germany, and London: Verlag von J. Cramer / Natural History Museum, 1985); Brian J. Ford, “Brownian Movement in Clarkia Pollen: A Reprise of the First Observations,” Microscope 40, no. 4 (1992): 235-41; and Stephen Brush, “A History of Random Processes. I. Brownian Movement from Brown to Perrin,” Archive for History of Exact Sciences 5, no. 34 (1968).

34. Pais, Albert Einstein, pp. 88-100.

35. Albert Einstein, quoted in Ronald William Clark, Einstein: The Life and Times (New York: HarperCollins, 1984), p. 77.

Chapter 9: Illusions of Patterns and Patterns of Illusion

1. See Arthur Conan Doyle, The History of Spiritualism (New York: G. H. Doran, 1926); and R. L. Moore, In Search of White Crows: Spiritualism, Parapsychology, and American Culture (London: Oxford University Press, 1977).

2. Ray Hyman, “Parapsychological Research: A Tutorial Review and Critical Appraisal,” Proceedings of the IEEE 74, no. 6 (June 1986): 823-49.

3. Michael Faraday, “Experimental Investigation of Table-Moving,” Athenaeum, July 2, 1853, pp. 801-3.

4. Michael Faraday, quoted in Hyman, “Parapsychological Research,” p. 826.

5. Faraday, quoted ibid.

6. See Frank H. Durgin, “The Tinkerbell Effect: Motion Perception and Illusion,” Journal of Consciousness Studies 9, nos. 5-6 (May-June 2002): 88-101.

7. Christof Koch, The Quest for Consciousness: A Neurobiological Approach (Englewood, Colo.: Roberts, 2004), pp. 51-54.

8. The study was D. O. Clegg et al., “Glucosamine, Chondroitin Sulfate, and the Two in Combination for Painful Knee Osteoarthritis,” New England Journal of Medicine 354, no. 8 (February 2006): 795-808. The interview was “Slate’s Medical Examiner: Doubts on Supplements,” Day to Day, NPR broadcast, March 13, 2006.

9. See Paul Slovic, Howard Kunreuther, and Gilbert F. White, “Decision Processes, Rationality, and Adjustment to Natural Hazards,” in Natural Hazards: Local, National, and Global, ed. G. F. White (London: Oxford University Press, 1974); see also Willem A. Wagenaar, “Generation of Random Sequences by Human Subjects: A Critical Survey of Literature,” Psychological Bulletin 77, no. 1 (January 1972): 65-72.

10. See Hastie and Dawes, Rational Choice in an Uncertain World, pp. 19-23.

11. George Spencer-Brown, Probability and Scientific Inference (London: Longmans, Green, 1957), pp. 55-56. Actually, 10 is a gross underestimate.

12. Janet Maslin, “His Heart Belongs to (Adorable) iPod,” New York Times, October 19, 2006.

13. Hans Reichenbach, The Theory of Probability, trans. E. Hutton and M. Reichenbach (Berkeley: University of California Press, 1934).

14. The classic text expounding this point of view is Burton G. Malkiel, A Random Walk Down Wall Street, now completely revised in an updated 8th ed. (New York: W. W. Norton, 2003).

15. John R. Nofsinger, Investment Blunders of the Rich and Famous—and What You Can Learn from Them (Upper Saddle River, N.J.: Prentice Hall, Financial Times, 2002), p. 62.

16. Hemang Desai and Prem C. Jain, “An Analysis of the Recommendations of the ‘Superstar’ Money Managers at Barron’s Annual Roundtable,” Journal of Finance 50, no. 4 (September 1995): 1257-73.

17. Jess Beltz and Robert Jennings, “Wall $treet Week with Louis Rukeyser’s Recommendations: Trading Activity and Performance,” Review of Financial Economics 6, no. 1 (1997): 15-27; and Robert A. Pari, “Wall $treet WeekRecommendations: Yes or No?” Journal of Portfolio Management 14, no. 1 (1987): 74-76.

18. Andrew Metrick, “Performance Evaluation with Transactions Data: The Stock Selection of Investment Newsletters, Journal of Finance 54, no. 5 (October 1999): 1743-75; and “The Equity Performance of Investment Newsletters” (discussion paper no. 1805, Harvard Institute of Economic Research, Cambridge, Mass., November 1997).

19. James J. Choi, David Laibson, and Brigitte Madrian, “Why Does the Law of One Price Fail? An Experiment on Index Mutual Funds” (working paper no. W12261, National Bureau of Economic Research, Cambridge, Mass., May 4, 2006).

20. Leonard Koppett, “Carrying Statistics to Extremes,” Sporting News, February 11, 1978.

21. By some definitions, Koppett’s system would be judged to have failed in 1970; by others, to have passed. See CHANCE News 13.04, April 18, 2004-June 7, 2004,

22. As touted on the Legg Mason Capital Management Web site,

23. Lisa Gibbs, “Miller: He Did It Again,” CNNMoney, January 11, 2004,

24. Thomas R. Gilovich, Robert Vallone, and Amos Tversky, “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Cognitive Psychology 17, no. 3 (July 1985): 295-314.

25. Purcell’s research is discussed in Gould, “The Streak of Streaks.”

26. Mark Hulbert, “Not All Stocks Are Created Equal,”, January 18, 2005, accessed March 2005 (site now discontinued).

27. Kunal Kapoor, “A Look at Who’s Chasing Bill Miller’s Streak,” Morningstar, December 30, 2004,

28. Michael Mauboussin and Kristen Bartholdson, “On Streaks: Perception, Probability, and Skill,” Consilient Observer (Credit Suisse-First Boston) 2, no. 8 (April 22, 2003).

29. Merton Miller on “Trillion Dollar Bet,” NOVA, PBS broadcast, February 8, 2000.

30. R. D. Clarke, “An Application of the Poisson Distribution,” Journal of the Institute of Actuaries 72 (1946): 48.

31. Atul Gawande, “The Cancer Cluster Myth,” The New Yorker, February 28, 1998, pp. 34-37.

32. Ibid.

33. Bruno Bettelheim, “Individual and Mass Behavior in Extreme Situations,” Journal of Abnormal and Social Psychology 38 (1943): 417-52.

34. Curt P. Richter, “On the Phenomenon of Sudden Death in Animals and Man,” Psychosomatic Medicine 19 (1957): 191-98.

35. E. Stotland and A. Blumenthal, “The Reduction of Anxiety as a Result of the Expectation of Making a Choice,” Canadian Review of Psychology 18 (1964): 139-45.

36. Ellen Langer and Judith Rodin, “The Effects of Choice and Enhanced Personal Responsibility for the Aged: A Field Experiment in an Institutional Setting,” Journal of Personality and Social Psychology 34, no. 2 (1976): 191-98.

37. Ellen Langer and Judith Rodin, “Long-Term Effects of a Control-Relevant Intervention with the Institutionalized Aged,” Journal of Personality and Social Psychology 35, no. 12 (1977): 897-902.

38. L. B. Alloy and L. Y. Abramson, “Judgment of Contingency in Depressed and Nondepressed Students: Sadder but Wiser?” Journal of Experimental Psychology: General 108, no. 4 (December 1979): 441-85.

39. Durgin, “The Tinkerbell Effect.”

40. Ellen Langer, “The Illusion of Control,” Journal of Personality and Social Psychology 32, no. 2 (1975): 311-28.

41. Ellen Langer and Jane Roth, “Heads I Win, Tails It’s Chance: The Illusion of Control as a Function of Outcomes in a Purely Chance Task,” Journal of Personality and Social Psychology 32, no. 6 (1975): 951-55.

42. Langer, “The Illusion of Control.”

43. Ibid., p. 311.

44. Raymond Fisman, Rakesh Khurana, and Matthew Rhodes-Kropf, “Governance and CEO Turnover: Do Something or Do the Right Thing?” (working paper no. 05-066, Harvard Business School, Cambridge, Mass., April 2005).

45. P. C. Wason, “Reasoning about a Rule,” Quarterly Journal of Experimental Psychology 20 (1968): 273-81.

46. Francis Bacon, Novum Organon, trans. by P. Urbach and J. Gibson (Chicago: Open Court, 1994), p. 57 (originally published in 1620).

47. Charles G. Lord, Lee Ross, and Mark Lepper, “Biased Assimilation and Attitude Polarization: The Effects of Prior Theories on Subsequently Considered Evidence,” Journal of Personality and Social Psychology 37, no. 11 (1979): 2098-109.

48. Matthew Rabin, “Psychology and Economics” (white paper, University of California, Berkeley, September 28, 1996).

49. E. C. Webster, Decision Making in the Employment Interview (Montreal: Industrial Relations Centre, McGill University, 1964).

50. Beth E. Haverkamp, “Confirmatory Bias in Hypothesis Testing for Client-Identified and Counselor Self-generated Hypotheses,” Journal of Counseling Psychology 40, no. 3 (July 1993): 303-15.

51. David L. Hamilton and Terrence L. Rose, “Illusory Correlation and the Maintenance of Stereotypic Beliefs,” Journal of Personality and Social Psychology 39, no. 5 (1980): 832-45; Galen V. Bodenhausen and Robert S. Wyer, “Effects of Stereotypes on Decision Making and Information-Processing Strategies,” Journal of Personality and Social Psychology 48, no. 2 (1985): 267-82; and C. Stangor and D. N. Ruble, “Strength of Expectancies and Memory for Social Information: What We Remember Depends on How Much We Know,” Journal of Experimental Social Psychology 25, no. 1 (1989): 18-35.

Chapter 10: The Drunkard’s Walk

1. Pierre-Simon de Laplace, quoted in Stigler, Statistics on the Table, p. 56.

2. James Gleick, Chaos: Making a New Science (New York: Penguin, 1987); see chap. 1.

3. Max Born, Natural Philosophy of Cause and Chance (Oxford: Clarendon Press, 1948), p. 47. Born was referring to nature in general and quantum theory in particular.

4. The Pearl Harbor analysis is from Roberta Wohlstetter, Pearl Harbor: Warning and Decision (Palo Alto, Calif.: Stanford University Press, 1962).

5. Richard Henry Tawney, The Agrarian Problem in the Sixteenth Century (1912; repr., New York: Burt Franklin, 1961).

6. Wohlstetter, Pearl Harbor, p. 387.

7. The description of the events at Three Mile Island is from Charles Perrow, Normal Accidents: Living with High-Risk Technologies (Princeton, N.J.: Princeton University Press, 1999); and U.S. Nuclear Regulatory Commission, “Fact Sheet on the Three Mile Island Accident,”

8. Perrow, Normal Accidents.

9. W. Brian Arthur, “Positive Feedbacks in the Economy,” Scientific American, February 1990, pp. 92-99.

10. Matthew J. Salganik, Peter Sheridan Dodds, and Duncan J. Watts, “Experimental Study of Inequality and Unpredictability in an Artificial Cultural Market,” Science 311 (February 10, 2006); and Duncan J. Watts, “Is Justin Timberlake a Product of Cumulative Advantage?” New York Times Magazine, April 15, 2007.

11. Mlodinow, “Meet Hollywood’s Latest Genius.”

12. John Steele Gordon and Michael Maiello, “Pioneers Die Broke,” Forbes, December 23, 2002; and “The Man Who Could Have Been Bill Gates,” BusinessWeek, October 25, 2004.

13. Floyd Norris, “Trump Deal Fails, and Shares Fall Again,” New York Times, July 6, 2007.

14. Melvin J. Lerner and Leo Montada, “An Overview: Advances in Belief in a Just World Theory and Methods,” in Responses to Victimizations and Belief in a Just World, ed. Leo Montada and Melvin J. Lerner (New York: Plenum Press, 1998), pp. 1-7.

15. Melvin J. Lerner, “Evaluation of Performance as a Function of Performer’s Reward and Attractiveness,” Journal of Personality and Social Psychology 1 (1965): 355-60.

16. Melvin J. Lerner and C. H. Simmons, “Observer’s Reactions to the ‘Innocent Victim’: Compassion or Rejection?” Journal of Personality and Social Psychology 4 (1966): 203-10.

17. Lerner, “Evaluation of Performance as a Function of Performer’s Reward and Attractiveness.”

18. Wendy Jean Harrod, “Expectations from Unequal Rewards,” Social Psychology Quarterly 43, no. 1 (March 1980): 126-30; Penni A. Stewart and James C. Moore Jr., “Wage Disparities and Performance Expectations,” Social Psychology Quarterly 55, no. 1 (March 1992): 78-85; and Karen S. Cook, “Expectations, Evaluations and Equity,” American Sociological Review 40, no. 3 (June 1975): 372-88.

19. Lerner and Simmons, “Observer’s Reactions to the ‘Innocent Victim.’”

20. David L. Rosenhan, “On Being Sane in Insane Places,” Science 179 (January 19, 1973): 237-55.

21. Elisha Y. Babad, “Some Correlates of Teachers’ Expectancy Bias,” American Educational Research Journal 22, no. 2 (Summer 1985): 175-83.

22. Eric Asimov, “Spirits of the Times: A Humble Old Label Ices Its Rivals,” New York Times, January 26, 2005.

23. Jonathan Calvert and Will Iredale, “Publishers Toss Booker Winners into the Reject Pile,” London Sunday Times, January 1, 2006.

24. Peter Doskoch, “The Winning Edge,” Psychology Today, November/ December 2005, p. 44.

25. Rosenhan, “On Being Sane in Insane Places,” p. 243.