Drunkard's Walk - Leonard Mlodinow [94]
I’ve cited some examples of the hot-hand fallacy in the context of sports and the financial world. But in all aspects of our lives we encounter streaks and other peculiar patterns of success and failure. Sometimes success predominates, sometimes failure. Either way it is important in our own lives to take the long view and understand that streaks and other patterns that don’t appear random can indeed happen by pure chance. It is also important, when assessing others, to recognize that among a large group of people it would be very odd if one of them didn’t experience a long streak of successes or failures.
No one credited Leonard Koppett for his lopsided successes, and no one would credit a coin tosser. Many people did credit Bill Miller. In his case, though the type of analysis I performed seems to have escaped many of the observers quoted in the media, it is no news to those who study Wall Street from the academic perspective. For example, the Nobel Prize–winning economist Merton Miller (no relation to Bill) wrote, “If there are 10,000 people looking at the stocks and trying to pick winners, one in 10,000 is going to score, by chance alone, and that’s all that’s going on. It’s a game, it’s a chance operation, and people think they are doing something purposeful but they’re really not.”29 We must all draw our own conclusions depending on the circumstances, but with an understanding of how randomness operates, at least our conclusions need not be naive.
IN THE PRECEDING I’ve discussed how we can be fooled by the patterns in random sequences that develop over time. But random patterns in space can be just as misleading. Scientists know that one of the clearest ways to reveal the meaning of data is to display them in some sort of picture or graph. When we see data exhibited in this manner, meaningful relationships that we would likely have missed are often made obvious. The cost is that we also sometimes perceive patterns that in reality have no meaning. Our minds are made that way—to assimilate data, fill in gaps, and look for patterns. For example, look at the following arrangement of grayish squares in the figure below.
Photo from Frank H. Durgin, “The Tinkerbell Effect,” Journal of Consciousness Studies 9, nos. 5–6 (May to June 2002)
The image does not literally look like a human being. Yet you can make enough sense of the pattern that if you saw in person the baby pictured, you would probably recognize it. And if you hold this book at arm’s length and squint, you might not even perceive the imperfections in the image. Now look at this pattern of Xs and Os:
Here we see rectangular clusters, especially in the corners. I have put them in boldface. If the Xs and Os represented events of interest, we might be tempted to wonder if those clusters signified something. But any meaning we assigned them would be misconceived because these data are identical to the earlier set of 200 random Xs and Os, except for the geometric 5-by-40 arrangement and the choice of which letters to put in boldface.
This very issue drew much attention toward the end of World War II, when V2 rockets started raining down on London. The rockets were terrifying, traveling at over five times the speed of sound, so that one heard them approach only after they had hit. Newspapers soon published maps of the impact sites, which seemed to reveal not random patterns but purposeful clusters. To some observers the clusters indicated a precision in the control of the rockets’ flight path that, given the distance the rockets had to travel, suggested that German technology was much more advanced than anyone had dreamed possible. Civilians speculated that the areas spared were home to German spies. Military leaders worried that the Germans could target crucial military sites, with devastating consequences.
In 1946 a mathematical analysis of the bombing data was published in the Journal of the Institute of Actuaries. Its author, R. D. Clarke, divided the area of interest into