Read Triumph and Tragedy in Mudville Online
Authors: Stephen Jay Gould
Joe DiMaggio singles against the Cleveland Indians on July 16, 1941, in the fifty-sixth game of his consecutive hitting streak.
Credit: AP/Wide World Photos
With apologies to Seidel (for he was probably sandbagged by his publishers on this), I must mention one funny error. The caption to a photo reads: “Ted Williams as he looked in 1941 when he hit .406.” But the picture, unless I need a very peculiar pair of glasses, shows Phil Rizzuto. Now you couldn’t find two more different people. Williams was tall, thin, taciturn, cold, the finest hitting machine since Ty Cobb, but not exactly perfect in the outfield. Rizzuto was just the opposite: short, stocky, convivial, not much with the stick, but the finest shortstop in the league. Moreover, Rizzuto played with DiMaggio on the Yankees, Williams for their archrivals, the Boston Red Sox. But then, an even more amusing mix-up once appeared in the “errata” section of th
e New York Times
: “The photo that appeared yesterday on page forty-one, labeled as the sun, was the moon.”
Seidel’s book will
help us to treasure DiMaggio’s achievement by bringing together the details of a genuine legend. But a larger issue lies behind basic documentation and simple appreciation. For we don’t understand the truly special character of DiMaggio’s record because we are so poorly equipped, whether by habits of culture or by our modes of cognition, to grasp the workings of random processes and patterning in nature.
That old Persian tentmaker, Omar Khayyám, understood the quandary of our lives:
Into this Universe, and
Why
not knowing,
Nor
Whence,
like Water willy-nilly flowing; And out of it, as Wind along the Waste,
I know not
Whither,
willy-nilly blowing.
But we cannot bear these conclusions. We must have comforting answers. We see pattern, for pattern surely exists, even in a purely random world. (Only a highly nonrandom universe could possibly cancel out the clumping that we perceive as pattern. We think we see constellations because the stars are dispersed at random in the heavens, and therefore clump in our sight.) Our error lies not in the perception of pattern but in automatically imbuing pattern with meaning, especially with meaning that can bring us comfort, or dispel confusion. Again, Omar took the more honest approach:
Ah, love! could you and I with Fate conspire
To grasp this sorry Scheme of Things entire, Would not we shatter it to bits—and then
Re-mould it nearer to the Heart’s Desire!
We, instead, have tried to impose that “heart’s desire” on the actual earth and its largely random patterns:
All Nature is but Art, unknown to thee;
All Chance, Direction, which thou canst not see;
All Discord, Harmony not under-stood;
All partial Evil, universal Good.
(Alexander Pope,
Essay on Man
, end of Epistle 1)
Sorry to wax so poetic and tendentious about something that leads back to DiMaggio’s hitting streak (pointyheadedness in action, I suppose), but this broader setting is the source of our misinterpretation. We believe in “hot hands” because we must impart meaning to a pattern—and we like meanings that tell stories about heroism, valor, and excellence. We believe that long streaks and slumps must have direct causes internal to the sequence itself, and we have no feel for the frequency and length of sequences in random data. Thus, while we understand that DiMaggio’s hitting streak was the longest ever, we don’t appreciate its truly special character because we view all the others as equally patterned by cause, only a little shorter. We distinguish DiMaggio’s feat merely by quantity along a continuum of courage; we should, instead, view his fifty-six-game hitting streak as a unique assault on the otherwise unblemished record of Dame Probability.
Amos Tversky, who
studied “hot hands,” has performed a series of elegant psychological experiments with Daniel Kahneman. These long-term studies have provided our finest insight into “natural reasoning” and its curious departure from logical truth. To cite an example, they construct a fictional description of a young woman: “Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.” Subjects are then given a list of hypothetical statements about Linda: they must rank these in order of presumed likelihood, most to least probable. Tversky and Kahneman list eight statements, but five are a blind, and only three make up the true experiment:
Linda is active in the feminist movement.
Linda is a bank teller.
Linda is a bank teller and is active in the feminist movement.
Now it simply must be true that the third statement is least likely, since any conjunction has to be less probable than either of its parts considered separately. Everybody can understand this when the principle is explained explicitly and patiently. But all groups of subjects, sophisticated students who ought to understand logic and probability as well as folks off the street corner, rank the last statement as more probable than the second. (I am particularly fond of this example because I know that the third statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me—“but she can’t just be a bank teller; read the description.”)
Why do we so consistently make this simple logical error? Tversky and Kahneman argue, correctly I think, that our minds are not built (for whatever reason) to work by the rules of probability, though these rules clearly govern our universe. We do something else that usually serves us well, but fails in crucial instances: we “match to type.” We abstract what we consider the “essence” of an entity, and then arrange our judgments by their degree of similarity to this assumed type. Since we are given a “type” for Linda that implies feminism, but definitely not a bank job, we rank any statement matching the type as more probable than another that only contains material contrary to the type. This propensity may help us to understand an entire range of human preferences, from Plato’s theory of form to modern stereotyping of race or gender.
We might also understand the world better, and free ourselves of unseemly prejudice, if we properly grasped the workings of probability and its inexorable hold, through laws of logic, upon much of nature’s pattern. “Matching to type” is one common error; failure to understand random patterning in streaks and slumps is another—hence Tversky’s study of both the fictional Linda and the 76ers’ baskets. Our failure to appreciate the uniqueness of DiMaggio’s streak derives from the same unnatural and uncomfortable relationship that we maintain with probability. (If we understood Lady Luck better, Las Vegas might still be a roadstop in the desert, and Nancy Reagan might not have a friend in San Francisco.)
My favorite illustration of this basic misunderstanding, as applied to DiMaggio’s hitting streak, appeared in a recent article by baseball writer John Holway, “A Little Help from His Friends,” and subtitled “Hits or Hype in ’41” (
Sports Heritage
, November/December 1987). Holway points out that five of DiMaggio’s successes were narrow escapes and lucky breaks. He received two benefits of the doubt from official scorers on plays that might have been judged as errors. In each of two games, his only hit was a cheapie. (In game sixteen, a ball dropped untouched in the outfield and had to be ruled a hit, even though the ball could have been caught, had it not been misjudged; in game fifty-four, DiMaggio dribbled one down the third baseline, easily beating the throw because the third baseman, expecting the usual, was playing far back.) The fifth incident is an ofttold tale, perhaps the most interesting story of the streak. In game thirty-eight, DiMaggio was 0 for 3 going into the last inning. Scheduled to bat fourth, he might have been denied a chance to hit at all. Johnny Sturm popped up to begin the inning, but Red Rolfe then walked. Slugger Tommy Henrich, up next, was suddenly swept with a premonitory fear: suppose I ground into a double play and end the inning? An elegant solution immediately occurred to him: why not bunt (an odd strategy for a power hitter)? Henrich laid down a beauty; DiMaggio, up next, promptly drilled a double to left.
Holway’s account is interesting, but his premise is entirely, almost preciously, wrong. First of all, none of the five incidents represents an egregious miscall. The two hits were less than elegant, but they were undoubtedly legitimate; the two boosts from official scorers were close calls on judgment plays, not gifts. As for Henrich, I can only repeat manager Joe McCarthy’s comment when Tommy asked him for permission to bunt: “Yeah, that’s a good idea.” Not a terrible strategy either—to put a man into scoring position for an insurance run when you’re up 3–1.
But these details
do not touch the main point—Holway’s premise is false because he accepts the conventional mythology about long sequences. He believes that streaks are unbroken runs of causal courage—so that any prolongation by hook or crook is an outrage against the deep meaning of the phenomenon. But extended sequences are no such thing. Long streaks always are, and must be, a matter of extraordinary luck imposed upon great skill. Please don’t make the vulgar mistake of thinking that Purcell or Tversky or I or anyone else would attribute a long streak to “just luck”—as though everyone’s chances are exactly the same, and streaks represent nothing more than the lucky atom that kept moving in one direction. Long hitting streaks happen to the greatest players—Sisler, Keeler, DiMaggio, Rose—because their general chance of getting a hit is so much higher than average. Just as Joe Airball cannot match Larry Bird for runs of baskets, Joe’s cousin Bill Ofer, with a lifetime batting average of .184, will never have a streak to match DiMaggio’s with a lifetime average of .325. The statistics show something else, and something fascinating: there is no “causality of circumstance,” no “extra” that the great can draw from the soul of their valor to extend a streak beyond the ordinary expectation of coin-tossing models for a series of unconnected events, each occurring with the characteristic probability for that particular player. Good players have higher characteristic probabilities, hence longer streaks.
Of course DiMaggio had a little luck during his streak. That’s what streaks are all about. No long sequence has ever been entirely sustained in any other way (the Orioles almost won several of those twenty-one games). DiMaggio’s remarkable achievement—its uniqueness, in the unvarnished literal sense of that word—lies in whatever he did to extend his success well beyond the reasonable expectations of random models that have governed every other streak or slump in the history of baseball.
Probability does pervade the universe—and in this sense, the old chestnut about baseball imitating life really has validity. The statistics of streaks and slumps, properly understood, do teach an important lesson about epistemology, and life in general. The history of a species, or any natural phenomenon that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he’s at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor. The best of us will try to live by a few simple rules: do justly, love mercy, walk humbly with thy God, and never draw to an inside straight.
DiMaggio’s hitting streak is the finest of legitimate legends because it embodies the essence of the battle that truly defines our lives. DiMaggio activated the greatest and most unattainable dream of all humanity, the hope and chimera of all sages and shamans: he cheated death, at least for a while.
January 3, 1985
Joe DiMaggio
2150 Beach Street
San Francisco, CA 94123
Dear Joe,
My best wishes to you for a happy 1985. I hope you had a chance to see the
NOVA
show in which you so kindly participated. I have received so many favorable comments, with unanimous agreement that your appearance made the show.
I mentioned to you in San Francisco that my colleague Ed Purcell, a Nobel Laureate and one of the world’s greatest physicists, had determined that your fifty-six-game hit streak was, statistically, the most unusual and unexpected great event in the history of baseball. Ed recently sent me the enclosed note in which he derives the reason for his statement. The mathematical details need not be pursued, but the chart on the back of the second page will give you some idea of how remarkable and unpredictable your achievement was in statistical terms. The top row labeled
b
represents lifetime batting averages of .400, .380, and .300. The first column labeled
n
at the left indicates the number of games in a hitting streak—40, 50, and 60 in this example. The nine numbers in the chart itself give you the probability that a batter with a lifetime batting average of
b
will have a hit streak of number of games
n
over a career of one thousand games. Just consider the .0096 value for a .350 lifetime average and a fifty-game hitting streak. This means that a lifetime .350 batter has only nine chances in a thousand to have a fifty-game hitting streak in a career of one thousand games. To make it more likely than unlikely that such a hitting streak would exist, the number in the chart must be greater than .5—for a probability of greater than one-half. Thus, there would have to be fifty-two lifetime .350 hitters in order to make the probability of a fifty-game hit streak more than likely (.0086 times 52 equals the crucial value of one-half). I don’t have my encyclopedia handy, but I think that only three or four people actually have lifetime averages exceeding .350 (Cobb, Hornsby, perhaps Shoeless Joe Jackson). But your streak went for fifty-six games, a value that would only become more likely to happen than not to happen if baseball included more than one hundred lifetime .350 hitters.
You asked me jokingly if this analysis meant that your record would never be broken. Even us pompous academics wouldn’t dare to make a statement like that. But Ed Purcell’s analysis does suggest that of all baseball records, your hit streak is surely the one least likely to be broken.
Thanks again for your time and, especially, for your kindness to my son Ethan.
Sincerely,
Stephen Jay Gould
/ap
Encl.