Caveman Logic: The Persistence of Primitive Thinking in a Modern World (23 page)

The nice thing about statistics is that they let you calculate the actual probability of each of these outcomes occurring by chance. It’s useful to look at these values because they match up surprisingly well with our intuitions. Even if you’re not a statistician, you probably knew the probability of the first toss coming up heads was .5, or one in two. When you toss the coin again, the probability of getting a second head in a row by chance was one in 2
²
, or 1/4. Toss the coin again and the chance of three consecutive heads are one in 2
³
, or 1/8 And so it goes, with the probability of consecutive heads having happened by chance getting progressively smaller as the number of tosses increases. The probabilities associated with a run of between one and nine consecutive heads by chance are .5, .25, .125, .062, .031, .015, .0075, .0037, and .0018, respectively. By the time you reach a string of ten consecutive heads, the probability of that event having occurred by chance is less than .001, or less than one in a thousand. In short, don’t hold your breath for ten consecutive heads to occur by chance with an unbiased coin. If you see it happen, something else is probably going on. That “something else” in this case is the fact that we’re using a trick coin.

It is important to note that science does not usually require such rigorous standards of proof. Plainly, scientists want to know that experimental outcomes are unlikely to have occurred by chance, but in general they do not expect the likelihood of chance to have been reduced to .001. Most experiments in the social sciences require what is called a
.05 significance level
—that is, the outcome would occur by chance no more than 1 in 20 times. That’s unlikely enough so we can conclude that our results reflect something
other than
chance.

Most people may understand “chance” at an intuitive level, but they are a little fuzzy about how it translates into real outcomes. If you don’t understand the sort of things that can happen by chance, you’re likely to overestimate the significance of outcomes that require no explanation at all. In fact, often they lie well within the range of what can and does happen by chance.

Here are a couple of examples from two unrelated areas: sports and ESP. ESP is the more obvious case. Persons with so-called psychic abilities such as telepathy are supposed to be able to determine outcomes when no conventional sensory information is available to them. The only way we know they’re doing impressive things is when the accuracy of their performance exceeds what we’d expect to happen by chance. That means we’d better have a clear understanding of the ways in which chance expresses itself. Just how probable are these “paranormal” outcomes? Many people will tell you that the “science” involved in testing ESP has to do with how well the blindfold is fastened or whether the sender and receiver are adequately isolated from each other. Granted, those things are important, but it’s just as important to understand chance and probability.

In slightly different ways, understanding chance is also important to our appreciation of most sports. It doesn’t come into play when we are watching a race, where individual performance is evaluated against the performance of other athletes on the field or, in some cases, the “personal best” of the runner. But, more often than not, team sports reduce themselves into a labyrinth of statistics. My own experience as a baseball fan led me to calculate batting averages for each player on my favorite team well before my tenth birthday. It was my first real experience with any form of mathematics and probably did much to immunize me against later numerical traumas associated with a university education. Baseball is a game awash in quantification. Nobody can debate the merits of their favorite player or team for very long without turning to on-base percentages, won-lost records, batting or earned run averages, and so on. Indeed, a whole new generation of baseball fans has evolved what is known as a
sabrmetric
approach to the game (a term derived from Society for American Baseball Research),
¹
with reference to all kinds of numerical exotica such as secondary averages, OPS percentages, range factors, and so on. Yet, for all this statistical sophistication, we often misinterpret what we see on the field because of deeper shortcomings in how we reason statistically.

For example: any fan knows what clutch hitting is, but has anyone ever identified a clutch
hitter
? The last I looked, the search was still on for a player who reliably performed better in “clutch situations” than he did when the stakes weren’t high. Players who do well in so-called clutch situations are usually players who do well in general. And so, the search continues for a player who reliably performs better under the gun. With over a century of organized baseball behind us, there is still no evidence of such differential abilities. That, however, has not stopped managers, coaches, sportscasters, and fans from describing someone as a “clutch hitter” with little trace of uncertainty in their voices. Why does this happen? Obviously, if we observe a player hit a game-winning home run in the bottom of the ninth with two outs, we are likely to remember that event. Often, it’s transformed into a hypothesis about that player that gets further supported by future positive outcomes. But can this hypothesis be as easily disconfirmed by future (or past) negative performance? The answer is probably no. Again, it is the salience of positive cases and our inability to disconfirm that renders this conclusion illogical. We simply don’t keep track of baselines adequately, and we tend to emphasize occasional “hits” disproportionately.

In most sports there is a pervasive idea of a “hot hand” or a streak. Players are described as being “in the zone.” During these elusive periods, their performance, we are told, reaches nearly Herculean proportions and they can do little wrong. They score more goals, sink more baskets, catch more passes, hit more home runs, or strike out more hitters than anyone expects. We’ve all witnessed such “streaks” although we can’t quite explain what causes them. In fact, the streak often becomes an explanation of itself. He’s hitting this way because he’s on a streak. “He’s a streaky hitter,” we are told by the announcer. “You don’t want to face him when he’s hot like this.” Hardly anyone, from players and managers and coaches to sports commentators and journalists, seems to doubt the existence of the streak.

Psychologist Thomas Gilovich and his colleagues published a detailed investigation of sports streaks and concluded that, at least in the realm they studied, streaks were illusory.
²
Gilovich and his colleagues examined NBA performance and reported that while basketball players occasionally run up impressive strings of “hits” (e.g., four or five baskets in a row), these clusters do not exceed what one might expect by chance alone. Gilovich et al. used each player’s own performance as a baseline. For example, if a player sank 60 percent of his free throws that season, how often might he be expected to sink five in a row? What is the probability associated with this outcome happening by chance over the course of a season? Whatever the answer, you’d better have that information available before you start talking about the psychological, perceptual, or motivational reasons for a “hot hand.” If the performance in question doesn’t lie outside the boundaries of chance, what’s the point of trying to explain it?

The underlying problem is that most of us don’t really know what chance looks like. Worse yet, we
think
we do. Most undergraduates will tell you that the purest example of chance in a
p
= .5 binary situation like a coin toss is an outcome that looks like H-T-H-T-H-T-H-T. Back and forth and back and forth: 50-50 on the nose. We expect some deviation from pure alternation but the question is, how much? It is here that many observers run into trouble; they underestimate the amount of streaklike clusters that are likely to occur under a truly random distribution. Any but the mildest deviations from regularity is likely to trigger our suspicion. We are very quick to see biased coins or streaks or hot hands, when in fact we are looking at nothing more than chance. As Gilovich points out, there is a 25 percent chance of seeing five consecutive heads if a normal coin is tossed twenty times. Most observers have great difficulty reconciling five consecutive anythings with the idea of chance. And so we are quick to reject chance in favor of more exotic alternatives.

Taking this back to the basketball court, it is easy to see how a cluster of five baskets in a row might send us running for the record books. Our impoverished sense of the many faces of chance leads us on a pointless quest for explanation. Call in the color commentators to ramble on about the player being “locked in” or “in the zone.” My colleague Scott Parker has devised a humorous tale to illustrate this point in reverse, namely, a case in which ignorance of chance leads us to
minimize
a truly exceptional feat. A man billed as the “World’s Greatest Coin Tosser” steps before an audience and produces five hundred consecutive heads. He then takes the same coin and produces five hundred consecutive tails. The audience sits in silence until someone stands and says, “Big deal. Fifty-fifty—anyone can do that!”

Our problems with chance would be far less troublesome if they were confined to the basketball court. Obviously, they aren’t. Whether talking about sports or gambling or the stock market, the stage is set whenever a binary set of outcomes (e.g., heads/tails, win/lose) lies outside our control. Our explanatory skills, needlessly dragged into play, do not often reflect what is brightest and best about our species. Whether invoking cycles of the moon, karma, or curses, we attempt to explain what needs no explaining. This is not to deny that
something
caused that head or tail on the coin toss. Of course, it did. But the issue here is not to account for the physical and psychological forces that cause every event on Earth. Our concern is with the
sequence
of events and whether
it
lies beyond the random fluctuations we can expect as the universe unfolds. More often than not, it does not.

Just how much knowledge of science is out there? It’s not an easy thing to measure. In the last year or so, I’ve run an informal survey using what is often termed an “opportunistic” or “convenience sample.” In short, I’ve asked just about everyone with whom I came into contact. That might have been a disastrous approach if I were a more typical academic or shy about talking to strangers. Fortunately, I am neither. And so I asked this question of literally hundreds of people: “What do you think science is?” These six words usually produce a pause, which I immediately fill with the easier question, “What do you think of when you think of science?” That question intimidates fewer people since there is plainly no wrong answer. If someone says, “The
Mona Lisa
” or “Elvis Presley,” then so be it.

But nobody has. Their answers are all far more relevant, and surprisingly consistent. I’ve talked to undergraduate students; gas station attendants; baseball fans; grad students; colleagues; folk, jazz, and rock musicians; food and hardware store sales people; financial advisors; servers in restaurants and pubs; ex-girlfriends; and my housekeeper. The list is actually quite a bit longer and more varied, and many people in my sample are difficult to classify since they fit multiple categories. Their education ranges from some high school through PhD degrees.

With the exception of most of my colleagues and a few grad students, this informal census has yielded a surprisingly consistent pattern. Because what I report isn’t about being right or wrong, it doesn’t shed light on the issue of scientific literacy. But it does address the public perception of science. Most people think about the
results
of science, rather than its
methods
. More than 95 percent of the people I spoke with mentioned things like “space travel,” “medical cures,” and “wonder drugs.” Some people said “E=MC
²
” or mentioned Einstein. People talked about computers, and a few included plasma screen TVs and iPods. Cloning was a popular response and a few referred to stem cell research. And that was basically it. This is what most people I spoke with think about when they think of science.

As much as anything, this is essentially a “Science’s Greatest Hits” list, as reflected by media coverage. Conspicuous by its absence is any reference to the
methods
of science. The idea of gathering evidence, formulating or testing hypotheses, and building theories appeared in a very small percentage of responses, almost all of them coming from my colleagues or graduate students, all of whom are in the business of
being
scientists. This should surprise no one, but it is a sobering thought. For most people, the methods of science consist of hardware rather than logic. Perform your own survey and you will find that most people think that scientists go about their business using exotic instruments like particle accelerators or electron microscopes, and then they share their discoveries with the rest of us, who either accept them (if we can understand them) or stay clear of them. But if we accept them, it is on faith or through appeal to authority. (“Scientists report that . . .”)

The scary part of this is that the fundamental methods of science, which lie well within the grasp of the average person, are not widely taught or appreciated. It is this lack of critical thinking, not the failure to do gene splicing or run an MRI unit, that dooms the average person to vulnerability at the hands of charlatans and purveyors of quackery and mysticism.

Most people believe that training in the scientific method confers some kind of immunity to the sorts of mental errors we are concerned with in this book. People with no scientific training, indeed people with little formal education, often misunderstand why this is so. They assume that scientists are less likely to hold irrational beliefs because scientists have learned
things
that contradict such widely held nonsense.