The key to more discerning sports intuition is understanding this simple fact of life: Random sequences seldom look random, be- cause they contain more streaks than people expect. Many, many years ago, some people excelled at perceiving rainfall patterns, game- at-the-water-hole patterns, crop cycle patterns. We are the descen- dants of these skilled pattern-detectors. True to our legacy, we look for order, for meaningful patterns—even in random data.
Consider a random coin flip: If someone flipped a coin six times, which of the following sequences of heads (H) and tails (T) would seem most likely: HHHTTT or HTTHTH or HHHHHH?
Daniel Kahneman and Amos Tversky report that most people be- lieve HTTHTH would be the most likely random sequence. (Ask someone to predict six coin tosses and they will likely tell you a
sequence like this.) Actually, all are equally likely (or, you might say, equally unlikely). To demonstrate this phenomenon for myself (as you can do), I flipped a coin fifty-one times, with these results:
HTTTHHHTTTTHHTTHTTHHTTHTTTHTHTTTTTTHTTHTHHHHTHHTTTT
Looking over the sequence, patterns jump out: Underlined tosses 10 to 22 provided an almost perfect pattern of pairs of tails followed by pairs of heads. On the boldfaced tosses, 30 to 38, I had a ‘‘cold hand,’’ with only one head in nine tosses. But my fortunes shortly thereafter reversed with a hot hand—six heads out of seven tosses.
Why these patterns? Was I exercising paranormal control over my coin? Did I snap out of my tails funk and get in a heads groove? No such explanations are needed, for these are the sorts of streaks found
in any random sequence. Comparing each toss outcome to the next,
twenty-four of the fifty comparisons yielded a changed result—just the sort of near 50 percent alternation we expect from coin tossing. Despite the seeming patterns in these data, the outcome of one toss gives no clue to the outcome of the next toss.
The ‘‘Bible code’’ craze of the late 1990s offers an example of what
Celestine Prophecy author James Redfield called ‘‘seemingly ‘Chance
Coincidences’—strange occurrences that feel like they were meant to happen.’’ If one turns the Hebrew text into a long string of letters minus spaces, computers can then find certain words turning up, formed of every nth letter going vertically, horizontally, or diagonally. For example, the letters spelling the name of Israel’s assassinated prime minister, Yitzhak Rabin, were found close to ‘‘assassination.’’ After the fact, however, one can find all sorts of words (unspecified in advance) seemingly encoded in all kinds of text. One NBA basketball fan, shortly before the Chicago Bulls won the 1998 title, used the ‘‘equidistant letter sequence’’ technique and found ‘‘Chicago’’ in
War and Peace. Shall we say the ‘‘Tolstoy code’’ predicted the Bulls’
sixth championship? Given enough random strings of letters tracked in enough directions, some words—some patterns—will become apparent.
Consider: Which of these patterns on a ten-by-ten grid appears to offer the most random placement of its fifty white and fifty black cells?
In a random pattern, the color of any cell would give us no clue to the color of the next one. It would be a toss-up. That’s true of the pattern on the left. The right-hand pattern looks more random to most people, report Ruma Falk and Clifford Konold. But it’s not, because it has a too-high (63 percent) rate of color change when moving either vertically or horizontally. The more complex and diffi- cult to remember a pattern is, the more random people think it is. When attempting to generate random sequences, people overpro- duce alternations and underproduce the streaks and clusters that we see on the left.
A mathematician friend of mine once tried to create a brick wall inside her home using a table of random numbers to place the red, white, and black bricks. Alas, she had to discard the table, because she found herself with a big area with nothing but black bricks. The random placement just didn’t look random.
Wartime Londoners experienced this tendency to see clusters in random patterns—and thus to think that the clusters were not really random. For example, seeing German bombs falling disproportion- ately in certain areas of the city prompted them to theorize that the working-class East Enders received more than their fair share because the Germans were trying to alienate the poor from the rich. After the war, a statistical analysis revealed merely a random bomb dispersion. The German V-1 buzz bombs and V-2 rocket bombs could find London but were just not accurate enough to spot particular areas.
More recently, Americans have suffered clusters of shark attacks and have found neighborhood clusters of cancer or leukemia. In one example—among thousands of clusters that have been reported to public health officials—a McFarland, California (population 6,400),
woman, whose child developed cancer, found four other cases within a few blocks, and then doctors found six more cases. This led to lawsuits against the manufacturers of pesticides that were believed to have contaminated groundwater wells and to have caused the cancer. As miners stricken with black lung disease remind us, environments can be toxic. But to the disbelief of ‘‘stricken’’ communities, environ- mental causes have not been found to explain recent cancer clusters. California’s chief environmental health investigator concluded that, given the many tens of thousands of cancers registered, some census tracts are bound to have random elevations. If yours does, he notes, ‘‘it almost certainly won’t mean a thing.’’
My father once called from his Seattle retirement home, where about twenty-five people die each year. He was wondering about a curious phenomenon: ‘‘The deaths seem to come in bunches. Why is that?’’ How odd of God that folks should pass en masse.
The moral: More than we suppose, random sequences are streaky. And thanks to the nearly inevitable streaks in random sequences, we see order and pattern where there is none.