A Part of the Main

We may be confident that the Great American Poem will not be written, no matter what genius attempts it, until democracy, the idea of our day and nation and race, has agonized and conquered through centuries, and made its work secure.

But the Great American Novel—the picture of the ordinary emotions and manners of American existence … will, we suppose, be possible earlier.
—John William De Forest. “The Great American Novel.” The Nation 9 January 1868.

Things refuse to be mismanaged long.
—Theodore Parker. “Of Justice and the Conscience.” 1853.

 

“It was,” begins Chapter Seven of The Great Gatsby, “when curiosity about Gatsby was at its highest that the lights in his house failed to go on one Saturday night—and, as obscurely as it began, his career as Trimalchio was over.” Trimalchio is a character in the ancient Roman novel The Satyricon who, like Gatsby, throws enormous and extravagant parties; there’s a lot that could be said about the two novels compared, and some of it has been said by scholars. The problem with comparing the two novels however is that, unlike Gatsby, The Satyricon is “unfinished”: we today have only the 141, not-always-continguous chapters collated by 17th century editors from two medieval manuscript copies, which are clearly not the entire book. Hence, comparing The Satyricon to Gatsby, or to any other novel, is always handicapped by the fact that, as the Wikipedia page continues, “its true length cannot be known.” Yet, is it really true that estimating a message’s total length based only on a part of the whole is impossible? Contrary to the collective wisdom of classical scholars and Wikipedia contributors, it isn’t, which we know due to techniques developed at the behest of a megalomaniac Trimalchio convinced Shakespeare was not Shakespeare—work that eventually become the foundation of the National Security Agency.  

Before getting to the history of those techniques, however, it might be best to describe first what they are. Essentially, the problem of figuring out the actual length of The Satyricon is a problem of sampling: that is, of estimating whether you have, like Christopher Columbus, run up on an island—or, like John Cabot, smacked into a continent. In biology, for instance, a researcher might count the number of organisms in a given area, then extrapolate for the entire area. Another biological technique is to capture and tag or mark some animals in an area, then recapture the same number of animals in the same area some time later—the number of re-captured previously-tagged animals provides a ratio useful for estimating the true size of the population. (The fewer the numbers of re-captured, the larger the size of the total population.) Or, as the baseball writer Bill James did earlier this year on his website (in “Red Hot Start,” from 16 April), of forecasting the final record of a baseball team based upon its start: in this case, the “true underlying win percentage” of the Boston record given that the team’s record in its first fifteen games was 13-2. The way that James did it is, perhaps, instructive about possible methods for determining the length of The Satyricon.

James begins by noting that because the “probability that a .500 team would go 13-2 or better in a stretch of 15 games is  … one in 312,” while the “probability that a .600 team would go 13-2 in a stretch of 15 games is … one in 46,” it is therefore “much more likely that they are a .600 team than that they are a .500 team”—though with the caveat that, because “there are many more .500 teams than .600 teams,” this is not “EXACTLY true” (emp. James). Next, James finds the standard statistical measure called the standard deviation: that is, the amount by which actual team records distribute themselves around the .500 mark of 81-81. James finds this number for teams in the years 2000-2015 to be .070, a low number; meaning that most team records in that era bunched closely around .500. (By comparison, the historical standard deviation for “all [major league] teams in baseball history” is .102, meaning that there used to be a wider spread between first-place teams and last-place teams than there is now.) Finally, James arranges the possible records of baseball teams according to what mathematicians call the “Gaussian,” or “normal” distribution: that is, how team records would look were they to follow the familiar “bell-shaped” curve, familiar from basic statistical courses, in which most teams had .500 records and very few teams had either 100 wins—or 100 losses. 

If the records of actual baseball teams follow such a distribution, James finds that “in a population of 1,000 teams with a standard deviation of .070,” there should be 2 teams above .700, 4 teams with percentages from .675 to .700, 10 teams from .650 to .675, 21 teams from .625 to .650, and so on, down to 141 teams from .500 to .525. (These numbers are mirrored, in turn, by teams with losing records.) Obviously, teams with better final records have better chances of starting 13-2—but at the same time, there are a lot fewer teams with final records of .700 than there are of teams going .600. As James writes, it is “much more likely that a 13-2 team is actually a .650 to .675 team than that they are actually a .675 to .700 team—just because there are so many more teams” (i.e., 10 teams as compared to 4). So the chances of each level of the distribution producing a 13-2 team actually grows as we approach .500—until, James says, we approach a winning percentage of .550 to .575, where the number of teams finally gets outweighed by the quality of those teams. Whereas in a thousand teams there are 66 teams who might be expected to have winning percentages of .575 to .600, thereby meaning that it is likely that a bit better than one of those teams might have start 13-2 (1.171341 to be precise), the chance of one of the 97 teams starting at 13-2 is only 1.100297. Doing a bit more mathematics, which I won’t bore you with, James eventually concludes that it is most likely that the 2018 Boston Red Sox will finish the season with .585 winning percentage, which is between a 95-67 season and a 94-68 season. 

What, however, does all of this have to do with The Satyricon, much less with the National Security Agency? In the specific case of the Roman novel, James provides a model for how to go about estimating the total length of the now-lost complete work: a model that begins by figuring out what league Petronius is playing in, so to speak. In other words, we would have to know something about the distribution of the lengths of fictional works: do they tend to converge—i.e., have a low standard deviation—strongly on some average length, the way that baseball teams tend to converge around 81-81? Or, do they wander far afield, so that the standard deviation is high? The author(s) of the Wikipedia article appear to believe that this is impossible, or nearly so; as the Stanford literary scholar Franco Moretti notes, when he says that he works “on West European narrative between 1790 and 1930,” he “already feel[s] like a charlatan” because he only works “on its canonical fraction, which is not even one percent of published literature.” There are, Moretti observes for instance, “thirty thousand nineteenth-century British novels out there”—or are there forty, or fifty, or sixty? “[N]o one really knows,” he concludes—which is not even to consider the “French novels, Chinese, Argentinian, [or] American” ones. But to compare The Satyricon to all novels would be to accept a high standard deviation—and hence a fairly wide range of possible lengths. 

Alternately, The Satyricon could be compared only to its ancient comrades and competitors: the five ancient Greek novels that survive complete from antiquity, for example, along with the only Roman novel to survive complete—Apuleius’ The Metamorphoses. Obviously, were The Satyricon to be compared only to ancient novels (and of those, only the complete ones) the standard deviation would likely be higher, meaning that the lengths might cluster more tightly around the mean. That would thereby imply a tighter range of possible lengths—at the risk, since the six ancient novels could all differ in length from The Satyricon much more than all the novels written likely would, of making a greater error in the estimate. The choice of which set (all novels, ancient novels) to use thereby is the choice between a higher chance of being accurate, and a higher chance of being precise. Either way, Wikipedia’s claim that the length “cannot be known” is only so if the words “with absolute certainty” are added. The best guess we can make can either be nearly certain to contain the true length within it, or be nearly certain—if it is accurate at all—to be very close to the true length, which is to say that it is entirely possible that we could know what the true length of The Satyricon was, even if we were not certain that we did in fact know it. 

That then answers the question of how we could know the length of The Satyricon—but when I began this story I promised that I would (eventually) relate it to the foundations of the National Security Agency. Those, I mentioned, began with an eccentric millionaire convinced that William Shakespeare did not write the plays that now bear his name. The millionaire’s name was George Fabyan; in the early 20th century he brought together a number of researchers in the new field of cryptography in order to “prove” Fabyan’s pet theory that Francis Bacon was the true author of the Bard’s work Bacon having been known as the inventor of the code system that bears his name; Fabyan thusly subscribed to the proposition that Bacon had concealed the fact of his authorship by means of coded messages within the plays themselves. The first professional American codebreakers thereby found themselves employed on Fabyan’s 350-acre estate (“Riverbank”) on the Fox River just south of Geneva, Illinois, which is still there today—and where American military minds found them on the American entry into World War One in 1917. 

Specifically, they found Elizabeth Smith and William Friedman (who would later marry). During the war the couple helped to train several federal employees in the art of codebreaking. By 1921, they had been hired away by the War Department, which then led to spending the 1920s breaking the codes of gangsters smuggling liquor into the dry United States in the service of the Coast Guard. During World War Two, Elizabeth would be employed in breaking one of the Enigma codes used by the German Navy; meanwhile, her husband William had founded the Army’s Signal Intelligence Service—the outfit that broke the Imperial Japanese Navy’s “Purple” code (itself based on Enigma machines), and was the direct predecessor to the National Security Agency. William had also written the scientific papers that underlay their work; he had, in fact, even coined the word cryptanalysis itself.          

Central to Friedman’s work was something now called the “Friedman test,” but then called the “kappa test.” This test, like Bill James’ work, compared two probabilities: the first being the obvious probability of which letter a coded one is likely to be, which in English is in one in 26, or 0.0385. The second, however, was not so obvious, that being the chance that two randomly selected letters from a source text will turn out to be the same letter, which is known in English to be 0.067. Knowing those two points, plus how long the intercepted coded message is, allows the cryptographer to estimate the length of the key, the translation parameter that determines the output—just as James can calculate the likely final record of a team that starts 13-2 using two different probabilities. Figuring out the length of The Satyricon, then, might not be quite the Herculean task it’s been represented to be—which raises the question, why has it been represented that way? 

The answer to that question, it seems to me, has something to do with the status of the “humanities” themselves: using statistical techniques to estimate the length of The Satyricon would damage the “firewall” that preserves disciplines like Classics, or literary study generally, from the grubby no ’ccount hands of the sciences—a firewall, we are eternally reminded, necessary in order to foster what Geoffrey Harpham, former director of the National Institute for the Humanities, has called “the capacity to sympathize, empathize, or otherwise inhabit the experience of others” so “clearly essential to democratic citizenship.” That may be so—but it’s also true that maintaining that firewall allows law schools, as Sanford Levinson of the University of Texas remarked some time ago, to continue to emphasize “traditional, classical legal skills” at the expense of “‘finding out how the empirical world operates.’” And since that has allowed (in Gill v. Whitford) the U.S. Supreme Court the luxury of considering whether to ignore a statistical measure of gerrymandering, for example, while on the other hand it is quite sure that the disciplines known as the humanities collect students from wealthy backgrounds at a disproportionate rate, it perhaps ought to be wondered precisely in what way those disciplines are “essential to democratic citizenship”—or rather, what idea of “democracy” is really being preserved here. If so, then—perhaps using what Fitzgerald called “the dark fields of the republic”—the final record of the United States can quite easily be predicted.

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Noble Lie

With a crew and good captain well seasoned,
They left fully loaded for Cleveland.
—“The Wreck of the Edmund Fitzgerald.” 1976.

The comedian Bill Maher began the “panel” part of his show Real Time the other day—the last episode before the election—by noting that virtually every political expert had dismissed Donald Trump’s candidacy at every stage of the past year’s campaign. When Trump announced he was running, Maher observed, the pundits said “oh, he’s just saying that … because he just wants to promote his brand.” They said Trump wouldn’t win any voters, Maher noted—“then he won votes.” And then, Maher went on, they said he wouldn’t win any primaries—“then he won primaries.” And so on, until Trump became the Republican nominee. So much we know, but what was of interest about the show was the response one of Maher’s guests: David Frum, a Canadian who despite his immigrant origins became a speechwriter for George W. Bush, invented the phrase “axis of evil,” and has since joined the staff of the supposedly liberal magazine, The Atlantic. The interest of Frum’s response was not only how marvelously inane it was—but also how it had already been decisively refuted only hours earlier, by men playing a boy’s game on the Lake Erie shore.

Maybe I’m being cruel however: like most television shows, Real Time with Bill Maher is shot before it is aired, and this episode was released last Friday. Frum then may not have been aware, when he said what he said, that the Chicago Cubs won the World Series on Wednesday—and if he is like most people, Frum is furthermore unaware of the significance of that event, which goes (as I will demonstrate) far beyond matters baseball. Still, surely Frum must have been aware of how ridiculous what he said was, given that the conversation began with Maher reciting the failures of the pundit class—and Frum admitted to belonging to that class. “I was one of those pundits that you made fun of,” Frum confessed to Maher—yet despite that admission, Frum went on to make a breathtakingly pro-pundit argument.

Trump’s candidacy, Frum said, demonstrated the importance of the gatekeepers of the public interest—the editors of the national newspapers, for instance, or the anchors of the network news shows, or the mandarins of the political parties. Retailing a similar  argument to one made by, among others, Salon’s Bob Cesca—who contended in early October that “social media is the trough from which Trump feeds”—Frum proceeded to make the case that the Trump phenomena was only possible once apps like Facebook and Twitter enabled presidential candidates to bypass the traditional centers of power. To Frum, in other words, the proper response to the complete failure of the establishment (to defeat Trump) was to prop up the establishment (so as to defeat future Trumps). To protect against the failure of experts Frum earnestly argued—with no apparent sense of irony—that we ought to give more power to experts.

There is, I admit, a certain schadenfreude in witnessing a veteran of the Bush Administration tout the importance of experts, given that George W.’s regime was notable for, among other things, “systematically chang[ing] and supress[ing] … scientific reports about global warming” (according to the British Broadcasting Corporation)—and not even to discuss how Bush cadres torpedoed the advice of the professionals of the CIA vis á vis the weapons-buying habits of a certain Middle Eastern tyrant. But the larger issue, however, is that the very importance of “expert” knowledge has been undergoing a deep interrogation for decades now—and that the victory of the Chicago Cubs in this year’s World Series has brought much of that critique to the mainstream.

What I mean can be demonstrated by a story told by the physicist Freeman Dyson—a man who never won a Nobel Prize, nor even received a doctorate, but nevertheless was awarded a place at Princeton’s Institute of Advanced Study at the ripe age of thirty by none other than Robert Oppenheimer (the man in charge of the Manhattan Project) himself. Although Dyson has had a lot to say during his long life—and a lot worth listening to—on a wide range of subjects, from interstellar travel to Chinese domestic politics, of interest to me in connection to Frum’s remarks on Donald Trump is an article Dyson published in The New York Review of Books in 2011, about a man who did win the Nobel Prize: the Israeli psychologist Daniel Kahneman, who won the prize for economics in 2002. In that article, Dyson told a story about himself: specifically, what he did during World War II—an experience, it turns out, that leads by a circuitous path over the course of seven decades to the epic clash resolved by the shores of Lake Erie in the wee hours of 3 November.

Entitled “How to Dispel Your Illusions,” Dyson there tells the story of being a young statistician with the Royal Air Force’s Bomber Command in the spring of 1944—a force that suffered, according to the United Kingdom’s Bomber Command Museum, “a loss rate comparable only to the worst slaughter of the First World War trenches.” To combat this horror, Dyson was charged with discovering the common denominator between the bomber crews that survived until the end of their thirty-mission tour of duty (about 25% of all air crews). Since they were succeeding when three out of four of their comrades were failing, Dyson’s superiors assumed that those successful crews were doing something that their less-successful colleagues (who were mostly so much less successful that they were no longer among the living) were not.

Bomber Command, that is, had a theory about why some survived and some died: “As [an air crew] became more skillful and more closely bonded,” Dyson writes that everyone at Bomber Command thought, “their chances of survival would improve.” So Dyson, in order to discover what that something was, plunged in among the data of all the bombing missions the United Kingdom had run over Germany since the beginning of the war. If he could find it, maybe it could be taught to the others—and the war brought that much closer to an end. But despite all his searching, Dyson never found that magic ingredient.

It wasn’t that Dyson didn’t look hard enough for it: according to Dyson, he “did a careful analysis of the correlation between the experience of the crews and their loss rates, subdividing the data into many small packages so as to eliminate effects of weather and geography.” Yet, no matter how many different ways he looked at the data, he could not find evidence that the air crews that survived were any different than the ones shot down over Berlin or lost in the North Sea: “There was no effect of experience,” Dyson’s work found, “on loss rate.” Who lived and who died while attempting to burn Dresden or blow up Hamburg was not a matter of experience: “whether a crew lived or died,” Dyson writes, “was purely a matter of chance.” The surviving crews possessed no magical ingredient. They couldn’t—perhaps because there wasn’t one.

Still, despite the conclusiveness of Dyson’s results his studies had no effect on the operations of Bomber Command: “The crews continued to die, experienced and inexperienced alike, until Germany was overrun and the war finally ended.” While Dyson’s research suggested that dying in the stratosphere over Lübeck had no relation to skill, no one at the highest levels wanted to admit that the survivors weren’t experts—that they were instead just lucky. Perhaps, had the war continued, Dyson’s argument might eventually have won out—but the war ended, fortunately (or not) for the air crews of the Royal Air Force, before Bomber Command had to admit he was right.

All of that, of course, might appear to have little to do with the Chicago Cubs—until it’s recognized that the end of their century-long championship drought had everything to do with the eventual success of Dyson’s argument. Unlike Bomber Command, the Cubs have been at the forefront of what The Ringer’s Rany Jazayerli calls baseball’s “Great Analytics War”—and unlike the contest between Dyson and his superiors, that war has had a definite conclusion. The battle between what Jazayerli calls an “objective, data-driven view” and an older vision of baseball “ended at 48 minutes after midnight on November 3”—when the Cubs (led by a general manager who, like Dyson, trusted to statistical analysis) recorded the final out of the 2016 season.

That general manager is Theo Epstein—a man who was converted to Dyson’s “faith” at an early age. According to ESPN, Epstein, “when he was 12 … got his first Bill James historical abstract”—and as many now recognize, James pioneered applying the same basic approach Dyson used to think about how to bomb Frankfurt to winning baseball games. An obscure graduate of the University of Kansas, after graduation James took a job as a night security guard at the Stokely-Van Camp pork and beans cannery in Kansas City—and while isolated in what one imagines were the sultry (or wintry) Kansas City evenings of the 1970s, James had plenty of time to think about what interested him. That turned out to be somewhat like the problem Dyson had faced a generation earlier: where Dyson was concerned with how to win World War II, James was interested in what appeared to be the much-less portentous question of how to win the American League. James thereby invented an entire field—what’s now known as sabermetrics, or the statistical study of baseball—and in so doing, the tools James invented have become the keys to baseball’s kingdom. After all, Epstein—employed by a team owner who hired James as a consultant in 2003—not only used James’ work to end the Cubs’ errand in baseball’s wilderness but also, as all the world knows, constructed the Boston Red Sox championship teams of 2004 and 2007.

What James had done, of course, is shown how the supposed baseball “experts”—the ex-players and cronies that dominated front offices at the time—in fact knew very little about the game: they did not know, for example, that the most valuable single thing a batter can do is to get on base, or that stolen bases are, for the most part, a waste of time. (The risk of making an out, as per for example David Smith’s “Maury Wills and the Value of a Stolen Base,” is more significant than the benefit of gaining a base.) James’ insights had not merely furnished the weaponry used by Epstein; during the early 2000s another baseball team, the Oakland A’s, and their manager Billy Beane, had used James-inspired work to get to the playoffs four consecutive years (from 2000 to 2003), and won twenty consecutive games in 2002—a run famously chronicled by journalist Michael Lewis’ book, Moneyball: The Art of Winning an Unfair Game, which later became a Hollywood movie starring Brad Pitt. What isn’t much known, however, is that Lewis has noticed the intellectual connection between this work in the sport of baseball—and the work Dyson thought of as similar to his own work as a statistician for Bomber Command: the work of psychologist Kahneman and his now-deceased colleague, Amos Tversky.

The connection between James, Kahneman, and Tversky—an excellent name for a law firm—was first noticed, Lewis says, in a review of his Moneyball book by University of Chicago professors Cass Sunstein, of the law school, and Richard Thaler, an economist. When Lewis described the failures of the “old baseball men,” and conversely Beane’s success, the two professors observed that “Lewis is actually speaking here of a central finding in cognitive psychology”: the finding upon which Kahneman and Tversky based their careers. Whereas Billy Beane’s enemies on other baseball teams tended “to rely on simple rules of thumb, on traditions, on habits, on what other experts seem to believe,” Sunstein and Thaler pointed out that Beane relied on the same principle that Dyson found when examining the relative success of bomber pilots: “Statistics and simple arithmetic tell us more about ourselves than expert intuition.” While Bomber Command in other words relied on the word of their “expert” pilots, who perhaps might have said they survived a run over a ball-bearing plant because of some maneuver or other, baseball front offices relied for decades on ex-players who thought they had won some long-ago game on the basis of some clever piece of baserunning. Tversky and Kahneman’s work, however—like that of Beane and Dyson—suggested that much of what passes as “expert” judgment can be, for decades if not centuries, an edifice erected on sand.

That work has, as Lewis found after investigating the point when his attention was drawn to it by Sunstein and Thaler’s article, been replicated in several fields: in the work of the physician Atul Gawande, for instance, who, Lewis says, “has shown the dangers of doctors who place too much faith in their intuition.” The University of California, Berkeley finance professor Terry Odean “examined 10,000 individual brokerage accounts to see if stocks the brokers bought outperformed stocks they sold and found that the reverse was true.” And another doctor, Toronto’s Donald Redelmeier—who studied under Tversky—found “that an applicant was less likely to be admitted to medical school if he was interviewed on a rainy day.” In all of these cases (and this is not even to bring up the subject of, say, the financial crisis of 2007-08, a crisis arguably brought on precisely by the advice of “experts”), investigation has shown that “expert” opinion may not be what it is cracked up to be. It may in fact actually be worse than the judgment of laypeople.

If so, might I suggest, then David Frum’s “expert” suggestion about what to do to avoid a replay of the Trump candidacy—reinforce the rule of experts, a proposition that itself makes several questionable assumptions about the nature of the events of the past two years, if not decades—stops appearing to be a reasonable proposition. It begins, in fact, to appear rather more sinister: an attempt by those in Frum’s position in life—what we might call Eastern, Ivy League-types—to will themselves into believing that Trump’s candidacy is fueled by a redneck resistance to “reason,” along with good old-fashioned American racism and sexism. But what the Cubs’ victory might suggest is that what could actually be powering Trump is the recognition by the American people that many of the “cures” dispensed by the American political class are nothing more than snake oil proffered by cynical tools like David Frum. That snake oil doubles down on exactly the same “expert” policies (like freeing capital to wander the world, while increasingly shackling labor) that, debatably, is what led to the rise of Trump in the first place—a message that, presumably, must be welcome to Frum’s superiors at whatever the contemporary equivalent of Bomber Command is.

Still, despite the fact that the David Frums of the world continue to peddle their nonsense in polite society, even this descendant of South Side White Sox fans must allow that Theo Epstein’s victory has given cause for hope down here at the street-level of a Midwestern city that for has, for more years than the Cubs have been in existence, been the plaything of Eastern-elite labor and trade policies. It’s a hope that, it seems, now has a Ground Zero.

You can see it at the intersection of Clark and Addison.

Striking Out

When a man’s verses cannot be understood … it strikes a man more dead than a great reckoning in a little room.
As You Like It. III, iii.

 

There’s a story sometimes told by the literary critic Stanley Fish about baseball, and specifically the legendary early twentieth-century umpire Bill Klem. According to the story, Klem is working behind the plate one day. The pitcher throws a pitch; the ball comes into the plate, the batter doesn’t swing, and the catcher catches it. Klem doesn’t say anything. The batter turns around and says (Fish tells us),

“O.K., so what was it, a ball or a strike?” And Klem says, “Sonny, it ain’t nothing ’till I call it.” What the batter is assuming is that balls and strikes are facts in the world and that the umpire’s job is to accurately say which one each pitch is. But in fact balls and strikes come into being only on the call of an umpire.

Fish is expressing here what is now the standard view of American departments of the humanities: the dogma (a word precisely used) known as “social constructionism.” As Fish says elsewhere, under this dogma, “what is and is not a reason will always be a matter of faith, that is of the assumptions that are bedrock within a discursive system which because it rests upon them cannot (without self-destructing) call them into question.” To many within the academy, this view is inherently liberating: the notion that truth isn’t “out there” but rather “in here” is thought to be a sub rosa method of aiding the political change that, many have thought, has long been due in the United States. Yet, while joining the “social construction” bandwagon is certainly the way towards success in the American academy, it isn’t entirely obvious that it’s an especially good way to practice American politics: specifically, because the academy’s focus on the doctrines of “social constructionism” as a means of political change has obscured another possible approach—an approach also suggested by baseball. Or, to be more precise, suggested by the World Series of 1904 that didn’t happen.

“He’d have to give them,” wrote Will Hively, in Discover magazine in 1996, “a mathematical explanation of why we need the electoral college.” The article describes how one Alan Natapoff, a physicist at the Massachusetts Institute of Technology, became involved in the question of the Electoral College: the group, assembled once every four years, that actually elects an American president. (For those who have forgotten their high school civics lessons, the way an American presidential election works is that each American state elects a number of “electors” equal in number to that state’s representation  in Congress; i.e., the number of congresspeople each state is entitled to by population, plus two senators. Those electors then meet to cast their votes in what is the actual election.) The Electoral College has been derided for years: the House of Representatives introduced a constitutional amendment to abolish it in 1969, for instance, while at about the same time the American Bar Association called the college “archaic, undemocratic, complex, ambiguous, indirect, and dangerous.” Such criticisms have a point: as has been seen a number times in American history (most recently in 2000), the Electoral College makes it possible to elect a president without a majority of the votes. But to Natapoff, such criticisms fundamentally miss the point because, according to him, they misunderstood the math.

The example Natapoff turned to in order to support his argument for the Electoral College was drawn from baseball. As Anthony Ramirez wrote in a New York Times article about Natapoff and his argument, also from 1996, the physicist’s favorite analogy is to the World Series—a contest in which, as Natapoff says, “the team that scores the most runs overall is like a candidate who gets the most popular votes.” But scoring more runs than your opponent is not enough to win the World Series, as Natapoff goes on to say: in order to become the champion baseball team of the year, “that team needs to win the most games.” And scoring runs is not the same as winning games.

Take, for instance, the 1960 World Series: in that contest, as Lively says in Discover, “the New York Yankees, with the awesome slugging combination of Mickey Mantle, Roger Maris, and Bill ‘Moose’ Skowron, scored more than twice as many total runs as the Pittsburgh Pirates, 55 to 27.” Despite that difference in production, the Pirates won the last game of the series (in perhaps the most exciting game in Series history—the only one that has ever ended with a ninth-inning, walk-off home run) and thusly won the series, four games to three. Nobody would dispute, Natapoff’s argument runs, that the Pirates deserved to win the series—and so, similarly, nobody should dispute the legitimacy of the Electoral College.

Why? Because if, as Lively writes, in the World Series “[r]uns must be grouped in a way that wins games,” in the Electoral College “votes must be grouped in a way that wins states.” Take, for instance, the election of 1888—a famous case for political scientists studying the Electoral College. In that election, Democratic candidate Grover Cleveland gained over 5.5 million votes to Republican candidate Benjamin Harrison’s 5.4 million votes. But Harrison not only won more states than Cleveland, but also won states with more electoral votes: including New York, Pennsylvania, Ohio, and Illinois, each of whom had at least six more electoral votes than the most populous state Cleveland won, Missouri. In this fashion, Natapoff argues that Harrison is like the Pirates: although he did not win more votes than Cleveland (just as the Pirates did not score more runs than the Yankees), still he deserved to win—on the grounds that the total numbers of popular votes do not matter, but rather how those votes are spread around the country.

In this argument, then, games are to states just as runs are to votes. It’s an analogy that has an easy appeal to it: everyone feels they understand the World Series (just as everyone feels they understand Stanley Fish’s umpire analogy) and so that understanding appears to transfer easily to the matter of presidential elections. Yet, while clever, in fact most people do not understand the purpose of the World Series: although people think it is the task of the Series to identify the best baseball team in the major leagues, that is not what it is designed to do. It is not the purpose of the World Series to discover the best team in baseball, but instead to put on an exhibition that will draw a large audience, and thus make a great deal of money. Or so said the New York Giants, in 1904.

As many people do not know, there was no World Series in 1904. A World Series, as baseball fans do know, is a competition between the champions of the National League and the American League—which, because the American League was only founded in 1901, meant that the first World Series was held in 1903, between the Boston Americans (soon to become the Red Sox) and the same Pittsburgh Pirates also involved in Natapoff’s example. But that series was merely a private agreement between the two clubs; it created no binding precedent. Hence, when in 1904 the Americans again won their league and the New York Giants won the National League—each achieving that distinction by winning more games than any other team over the course of the season—there was no requirement that the two teams had to play each other. And the Giants saw no reason to do so.

As legendary Giants manager, John McGraw, said at the time, the Giants were the champions of the “only real major league”: that is, the Giants’ title came against tougher competition than the Boston team faced. So, as The Scrapbook History of Baseball notes, the Giants, “who had won the National League by a wide margin, stuck to … their plan, refusing to play any American League club … in the proposed ‘exhibition’ series (as they considered it).” The Giants, sensibly enough, felt that they could not gain much by playing Boston—they would be expected to beat the team from the younger league—and, conversely, they could lose a great deal. And mathematically speaking, they were right: there was no reason to put their prestige on the line by facing an inferior opponent that stood a real chance to win a series that, for that very reason, could not possibly answer the question of which was the better team.

“That there is,” writes Nate Silver and Dayn Perry in Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong, “a great deal of luck involved in the playoffs is an incontrovertible mathematical fact.” But just how much luck is involved is something that the average fan hasn’t considered—though former Caltech physicist Leonard Mlodinow has. In Mlodinow’s book, The Drunkard’s Walk: How Randomness Rules Our Lives, the scientist writes that—just by virtue of doing the math—it can be concluded that “in a 7-game series there is a sizable chance that the inferior team will be crowned champion”:

For instance, if one team is good enough to warrant beating another in 55 percent of its games, the weaker team will nevertheless win a 7-game series about 4 times out of 10. And if the superior team could be expected to beat its opponent, on average, 2 out of each 3 times they meet, the inferior team will still win a 7-game series about once every 5 matchups.

What Mlodinow means is this: let’s say that, for every game, we roll a one-hundred sided die to determine whether the team with the 55 percent edge wins or not. If we do that four times, there’s still a good chance that the inferior team is still in the series: that is, that the superior team has not won all the games. In fact, there’s a real possibility that the inferior team might turn the tables, and instead sweep the superior team. Seven games, in short, is just not enough games to demonstrate conclusively that one team is better than another.

In fact, in order to eliminate randomness as much as possible—that is, make it as likely as possible for the better team to win—the World Series would have to be much longer than it currently is: “In the lopsided 2/3-probability case,” Mlodinow says, “you’d have to play a series consisting of at minimum the best of 23 games to determine the winner with what is called statistical significance, meaning the weaker team would be crowned champion 5 percent or less of the time.” In other words, even in a case where one team has a two-thirds likelihood of winning a game, it would still take 23 games to make the chance of the weaker team winning the series less than 5 percent—and even then, there would still be a chance that the weaker team could still win the series. Mathematically then, winning a seven-game series is meaningless—there have been just too few games to eliminate the potential for a lesser team to beat a better team.

Just how mathematically meaningless a seven-game series is can be demonstrated by the case of a team that is only five percent better than another team: “in the case of one team’s having only a 55-45 edge,” Mlodinow goes on to say, “the shortest statistically significant ‘world series’ would be the best of 269 games” (emp. added). “So,” Mlodinow writes, “sports playoff series can be fun and exciting, but being crowned ‘world champion’ is not a very reliable indication that a team is actually the best one.” Which, as a matter of fact about the history of the World Series, is simply a point that true baseball professionals have always acknowledged: the World Series is not a competition, but an exhibition.

What the New York Giants were saying in 1904 then—and Mlodinow more recently—is that establishing the real worth of something requires a lot of trials: many, many different repetitions. That’s something that, all of us, ought to know from experience: to learn anything, for instance, requires a lot of practice. (Even if the famous “10,000 hour rule” New Yorker writer Malcolm Gladwell concocted for this book, Outliers: The Story of Success, has been complicated by those who did the original research Gladwell based his research upon.) More formally, scientists and mathematicians call this the “Law of Large Numbers.”

What that law means, as the Encyclopedia of Mathematics defines it, is that “the frequency of occurence of a random event tends to become equal to its probability as the number of trials increases.” Or, to use the more natural language of Wikipedia, “the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.” What the Law of Large Numbers implies is that Natapoff’s analogy between the Electoral College and the World Series just might be correct—though for the opposite reason Natapoff brought it up. Namely, if the Electoral College is like the World Series, and the World Series is not designed to find the best team in baseball but instead be merely an exhibition, then that implies that the Electoral College is not a serious attempt to find the best president—because what the Law would appear to advise is that, in order to obtain a better result, it is better to gather more voters.

Yet the currently-fashionable dogma of the academy, it would seem, is expressly-designed to dismiss that possibility: if, as Fish says, “balls and strikes” (or just things in general) are the creations of the “umpire” (also known as a “discursive system”), then it is very difficult to confront the wrongheadedness of Natapoff’s defense of the Electoral College—or, for that matter, the wrongheadedness of the Electoral College itself. After all, what does an individual run matter—isn’t what’s important the game in which it is scored? Or, to put it another way, isn’t it more important where (to Natapoff, in which state; to Fish, less geographically inclined, in which “discursive system”) a vote is cast, rather than whether it was cast? The answer in favor of the former at the expense of the latter to many, if not most, literary-type intellectuals is clear—but as any statistician will tell you, it’s possible for any run of luck to continue for quite a bit longer than the average person might expect. (That’s one reason why it takes at least 23 games to minimize the randomness between two closely-matched baseball teams.) Even so, it remains difficult to believe—as it would seem that many today, both within and without the academy, do—that the umpire can continue to call every pitch a strike.

 

The Oldest Mistake

Monte Ward traded [Willie] Keeler away for almost nothing because … he made the oldest mistake in management: he focused on what the player couldn’t do, rather than on what he could.
The New Bill James Historical Baseball Abstract

 

 

What does an American “leftist” look like? According to academics and the inhabitants of Brooklyn and its spiritual suburbs, there are means of tribal recognition: unusual hair or jewelry; a mode of dress either strikingly old-fashioned or futuristic; peculiar eyeglasses, shoes, or other accessories. There’s a deep concern about food, particularly that such food be the product of as small, and preferably foreign, an operation as possible—despite a concomitant enmity of global warming. Their subject of study at college was at minimum one of the humanities, and possibly self-designed. If they are fans of sports at all, it is either extremely obscure, obscenely technical, and does not involve a ball—think bicycle racing—or it is soccer. And so on. Yet, while each of us has exactly a picture of such a person in mind—probably you know at least a few, or are one yourself—that is not what a real American leftist looks like at the beginning of the twenty-first century. In reality, a person of the actual left today drinks macro-, not micro-, brews, studied computer science or some other such discipline at university, and—above all—is a fan of either baseball or football. And why is that? Because such a person understands statistics intuitively—and the great American political battle of the twenty-first century will be led by the followers of Strabo, not Pyrrho.

Each of those two men were Greeks: the one, a geographer, the other a philosopher—the latter often credited with being one of the first “Westerners” to visit India. “Nothing really exists,” Pyrrho reportedly held, “but human life is governed by convention”—a philosophy very like that of the current American “cultural left,” governed as it is by the notion, as put by American literary critic Stanley Fish, that “norms and standards and rules … are in every instance a function or extension of history, convention, and local practice.” Arguably, most of the “political” work of the American academy over the past several generations has been done under that rubric: as Fish and others have admitted in recent years, it’s only by acceding to some version of that doctrine that anyone can work as an American academic in the humanities these days.

Yet while “official” leftism has prospered in the academy under a Pyrrhonian rose, in the meantime enterprises like fantasy football and above all, sabermetrics, have expanded as a matter of “entertainment.” But what an odd form of relaxation! It’s an bizarre kind of escapism that requires a familiarity with both acronyms and the formulas used to compute them: WAR, OPS, DIPS, and above all (with a nod to Greek antecedents), the “Pythagorean expectation.” Yet the work on these matters has, mainly, been undertaken as a purely amateur endeavor—Bill James spent decades putting out his baseball work without any remuneration, until finally being hired latterly by the Boston Red Sox in 2003 (the same year that Michael Lewis published Moneyball, a book about how the Oakland A’s were using methods pioneered by James and his disciples). Still, all of these various methods of computing the value of both a player and a team have a perhaps-unintended effect: that of training the mind in the principle of Greek geographer, Strabo.

“It is proper to derive our explanations from things which are obvious,” Strabo wrote two thousand years ago, in a line that would later be adopted by the Englishman who constructed geology, Charles Lyell. In Lyell’s Principles of Geology (which largely founded the field) Lyell held—in contrast to the mysteriousness of Pyrrho—that the causes of things are likely to those already around us, and not due to unique, unrepeatable events. Similarly, sabermetricians—as opposed to the old-school scouts depicted in the film version of Moneyball—judge players based on their performance on the field, not on their nebulous “promise” or “intangibles.” (In Moneyball scouts were said to judge players on such qualities as the relative attractiveness of their girlfriends, which was said to signify the player’s own confidence in his ability.) Sabermetricians disregard such “methods” of analysis in favor of examination of the acts performed by the player as recorded by statistics.

Why, however, would that methodological commitment lead sabermetricians to be politically “liberal”—or for that matter, why would it lead in a political direction at all? The answer to the latter question is, I suspect, inevitable: sabermetrics, after all, is a discipline well-suited for the purpose of discovering how to run a professional sports team—and in its broadest sense, managing organizations simply is what “politics” is. The Greek philosopher Aristotle, for that reason, defined politics as a “practical science”—as the discipline of organizing human beings for particular purposes. It seems inevitable then that at least some people who have spent time wondering about, say, how to organize a baseball team most effectively might turn their imaginations towards some other end.

Still, even were that so, why “liberalism,” however that is defined, as opposed to some other kind political philosophy? Going by anecdotal evidence, after all, the most popular such doctrine among sports fans might be libertarianism. Yet, beside the fact that libertarianism is the philosophy of twelve-year-old boys (not necessarily a knockdown argument against its success), it seems to me that anyone following the methods of sabermetrics will be led towards positions usually called “liberal” in today’s America because from that sabermetrical, Strabonian perspective, certain key features of the American system will nearly instantly jump out.

The first of those features will be that, as it now stands, the American system is designed in a fashion contrary to the first principle of sabermetrical analysis: the Pythagorean expectation. As Charles Hofacker described it in a 1983 article for Baseball Analyst, the “Pythagorean equation was devised by Bill James to predict winning percentage from … the critical difference between runs that [a team] scores and runs that it allows.” By comparing these numbers—the ratio of a team’s runs scored and runs allowed versus the team’s actual winning percentage—James found that a rough approximation of a team’s real value could be determined: generally, a large difference between those two sets of numbers means that something fluky is happening.

If a team scores a lot of runs while also preventing its opponents from scoring, in other words, and yet somehow isn’t winning as many games as those numbers would suggest, then that suggests that that team is either tremendously unlucky or there is some hidden factor preventing success. Maybe, for instance, that team is scoring most of its runs at home because its home field is particularly friendly to the type of hitters the team has … and so forth. A disparity between runs scored/runs allowed and actual winning percentage, in short, compels further investigation.

Weirdly however the American system regularly produces similar disparities—and yet while, in the case of a baseball team, that would set off alerts for a sabermetrician, no such alarms are set off in the case of the so-called “official” American left, which apparently has resigned itself to the seemingly inevitable. In fact, instead of being the subject of curiosity and even alarm, many of the features of the U.S. constitution, like the Senate and the Electoral College—not to speak of the Supreme Court itself—are expressly designed to thwart what Chief Justice Earl Warren said was “the clear and strong command of our Constitution’s Equal Protection Clause”: the idea that “Legislators represent people … [and] are elected by voters, not farms or cities or economic interests.” Whereas a professional baseball team, in the post-James era, would be remiss if it were to ignore a difference between its ratio of runs scored and allowed and its games won and lost, under the American political system the difference between the will of the electorate as expressed by votes cast and the actual results of that system as expressed by legislation passed is not only ignored, but actively encouraged.

“The existence of the United States Senate”—for example wrote Justice Harlan in his dissent to the 1962 case of Baker v. Carr—“is proof enough” that “those who have the responsibility for devising a system of representation may permissibly consider that factors other than bare numbers should be taken into account.” That is, the existence of the U.S. Senate, which sends two senators from each state regardless of each state’s population, is support enough for those who believe—as the American “cultural left” does—in the importance of factors like “history” or the like in political decisions, as opposed to, say, the will of the American voters as expressed by the tally of all American votes.

As Jonathan Cohn remarked in The New Republic not long ago, in the Senate “predominantly rural, thinly populated states like Arkansas and North Dakota have the exact same representation as more urban, densely populated states like California and New York”—meaning that voters in those rural states have more effective political power than voters in the urban ones do. In sum, the Senate is, as Cohn says, one of Constitution’s “levers for thwarting the majority.” Or to put it in sabermetrical terms, it is a means of hiding a severe disconnect in America’s Pythagorean expectation.

Some will defend that disconnect, as Justice Harlan did over fifty years ago, on the grounds of terms familiar to the “cultural left”: that of “history” and “local practice” and so forth. In other words, that is how the Constitution originally constructed the American state. Yet, attempting (in Cohn’s words) to “prevent majorities from having the power to determine election outcomes” is a dangerous undertaking; as the Atlantic’s Ta Nehisi-Coates wrote recently about certain actions taken by the Republican party designed to discourage voting, to “see the only other major political party in the country effectively giving up on convincing voters, and instead embarking on a strategy of disenfranchisement, is a bad sign for American democracy.” In baseball, the sabermetricians know, a team with a high difference between its “Pythagorean expectation” and its win-loss record will usually “snap back” to the mean. In politics, as everyone since before Aristotle has known, such a “snap back” is usually a bit more costly than, say, the price of a new pitcher—which is to say that, if you see any American revolutionaries around you right now, he or she is likely wearing, not a poncho or a black turtleneck, but an Oakland A’s hat.