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.

 

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