A STATISTICAL ANOMALY
A STATISTICAL ANOMALY
by William H. Benson
June 10, 2010
Vikas Swarup of India published his debut novel, Q & A, in 2005. Told in first person, the story is that of Ram Mohammad Thomas, an eighteen-year-old waiter who survived a multitude of misfortunes—abandonment, child abuse, destitution, and the witness to several murders—while growing up alone on the streets of Mumbai and Delhi in India.
Suddenly, he is selected to appear on the television game show Who Will Win a Billion. The show’s host, Prem Kumar, chose Ram because he assumed that an uneducated street lad would answer only a few questions. He astonishes everyone by answering all twelve questions correctly, and winning the billion rupees. But, Kumar calls the police, who proceed to torture Ram, wanting to know how he had cheated.
It is, they assume, statistically impossible for Ram to know the answers to twelve random questions. But to his attorney Smita Shah, Ram explains, “Well, wasn’t I lucky that they only asked those questions to which I knew the answers?”
Ram then tells about his life, how he had lived it, and how at various points, he had learned the answers to each of the dozen questions, and he had an incredible story behind each question. Ram argued that the questions only tested his memory, not his knowledge.
The book Q & A was then made into the movie Slumdog Millionaire, and although names and details were radically changed, the movie won a host of Oscars two years ago.
Aside from the trifling nature of Ram’s dozen questions, the more significant issue that Q & A brings up is the question of probability: that it is statistically unlikely for anyone in Ram’s station in life—uneducated, a waiter, without home or family, a street urchin—to answer correctly 12 random questions in a row, in a streak.
Stephen Jay Gould, the writer and Harvard professor, wrote in his article “The Streak of Streaks,” that, “the rules of probability govern our universe,” especially winning streaks. Game shows, the state lotteries, as well as the Las Vegas gambling casinos operate their businesses upon those rules of probability, and when someone actually wins, such as Ram on a quiz show, or a lottery or a casino winner, we are all astounded.
Gould argued, and I think quite correctly, that there was one statistical anomaly in the history of sports, once considered unachievable, and that is that “Joe DiMaggio got at least one hit in each of 56 consecutive games in the 1941 season.” It is one of the most cherished of all baseball’s records. His streak began on May 15 and ended on July17 when a third baseman for the Indians caught two of DiMaggio’s hits.
In 1978, Pete Rose hit at least once in 44 successive games in the 1978 season, good enough for third place in the record books, and Ty Cobb hit in 40 games in 1911, earning him the sixth place. No one else in professional baseball has come close to DiMaggio.
In a toss of 100 coins, chances are more than 75% that you will see a streak of 6 or more heads (or tails), and almost a 10% chance that you will produce a streak of 10 or more. But a streak of 56 is far beyond 10 or even 15 heads (or tails) in a row.
Gould wrote, “a streak of this nature must be absolutely exceptionless; you are not allowed a single day of subpar play, or even bad luck. You bat only four or five times in an average game. Sometimes two or three of these efforts yield walks, and you get only one or two shots at a hit. . . . DiMaggio’s streak is the most extraordinary thing that ever happened in American sports.”
Ed Purcell, a winner of a Nobel in physics and a baseball fan, agreed and said that, “Nothing ever happened in baseball above and beyond the frequency predicted by coin-tossing models. The longest runs of wins or losses are as they should be.” His one major exception was DiMaggio’s 56-game hitting streak, the “one sequence so many standard deviations above the expected distribution that it should never have occurred at all.”
Gould said, “Detractors can argue forever about the general tenor of your life and work, but they can never erase a great event.” For Joe DiMaggio, his singular great event was 56 games and a hit in each one in 1941, and for Ram Mohammed Thomas, albeit a fictional character, it was answering twelve trivia questions correctly, in a row.