This Pitiless Storm

Poor naked wretches, whereso’er you are,
That bide the pelting of this pitiless storm,
How shall your houseless heads and unfed sides,
Your loop’d and window’d raggedness, defend you,
From seasons such as these?
The Tragedy of King Lear Act III, Scene 4

“Whenever people talk to me about the weather,” the Irish writer Oscar Wilde once remarked, “I always feel quite certain that they mean something else.” As it happens, the weather at this year’s British Open has been delayed by high winds and will not be finished with the regulation 72 holes until Monday at the earliest. Which raises a question: why does the Open need to finish all 72 holes? The answer concerns something called a “Simpson’s Paradox”—an answer that also demonstrates just how talk about the weather at the British Open is in fact talk about something else. Namely, the 2016 American presidential election.

To see how, it’s first necessary to see the difference between the British Open and other professional golf tournaments, which are perfectly fine with shortening themselves. Take for instance the 2005 Northern Trust Open in Los Angeles: Adam Scott won in a playoff against Chad Campbell after the tournament was shortened to 36 holes due to weather. In 2013, the Tournament of Champions at Kapalua in Hawaii was “first cut to 54 holes because of unplayable conditions over the first two days,” according to Reuters, and was under threat of “being further trimmed to 36 holes.” The same story also quoted tour officials as saying “the eventual champion would wind up with an ‘unofficial win’” were the tournament to be shortened to 36 holes. (As things shook out they did end up completing 54 holes, and so Dustin Johnson’s win officially counted.) In a standard PGA tournament then, the “magic number” for an “official” tournament is 54 holes. But if so, then why does the Open need 72?

To answer that, let’s take a closer look at the standard professional golf tournament. Most such tournaments are conducted according to what the Rules of Golf calls “stroke play”: four rounds of golf, or 72 holes, at the end of which the players who have made it that far add up their scores—their number of strokes. The player with the lowest score, it may seem like it goes without saying, wins. But it does need to be said—because that isn’t the only option.

Many amateur tournaments after all, such as the United States Amateur, use the rules format known as “match play.” Under this format, the winner of the contest is not necessarily the player who shoots the lowest overall score, as in stroke play. Instead, as John Van der Borght has put the matter on the website of the United States Golf Association, in match play the “winner is the player who wins the most holes.” It’s a seemingly minor difference—but in fact it creates such a difference that match play is virtually a different sport than stroke play.

Consider, for instance, the Accenture Match Play tournament—the only tournament on the PGA Tour to be held under match play rules. The 2014 edition (held at the Dove Mountain course near Tucson, Arizona), had some results that demonstrate just how different match play is than stroke play, as Doug Ferguson of the Associated Press observed. “Pablo Larrazabal shot a 68 and was on his way back to Spain,” Ferguson noted about the first day’s results, while “Ernie Els shot 75 and has a tee time at Dove Mountain on Thursday.” In other words, Larrazabal lost his match and Els won his, even though Larrazabal was arguably the better player at this tournament—at least, if you consider the “better player” to be the one who puts his ball in the hole most efficiently.

Such a result might seem unfair—but why? It could be argued that while shooting a lower number might be what stroke play golf is, that isn’t what match play golf is. In other words, Larrazabal obviously wasn’t better at whatever it was that this tournament measured: if Larrazabal couldn’t beat his opponent, while Els could, then clearly Els deserved to continue to play while Larrazabal did not. While you might feel that, somehow or other, Larrazabal got jobbed, that’s merely a sentimental reaction to what ought to be a hardhearted calculation: maybe it’s true that under stroke play rules Larrazabal would have won, but that wasn’t the rules of the contest at Dove Mountain. In other words, you could say that golfing ability was, in a sense, socially constructed: what matters isn’t some “ahistorical” ability to golf, but instead how it is measured.

Here’s the $64,000 question a guy named Bill James might ask in response to such an argument, however (couched in terms of baseball players): “If you were trying to win a pennant, how badly would you want this guy?” In other words, based on the evidence presented, what would you conclude about the respective golf ability of Els and Larrazabal? Wouldn’t you conclude that Larrazabal is better at the task of putting his ball in the hole, and that the various rule systems that could be constructed around that task are merely different ways of measuring that ability—an ability that pre-existed those systems of measurement?

“We’re not trying to embarrass the best players in the game,” said Sandy Tatum at the 1974 U.S. Open, the so-called Massacre at Winged Foot: “We’re trying to identify them.” Scoring systems in short should be aimed at revealing, not concealing, ability. I choose Bill James to make the point not just because the question he asks is so pithy, but because he invented an equation that is designed to discover underlying ability: an equation called the Pythagorean Expectation. That equation, in turn, demonstrates just why it is so that match play and stroke play are not just different—yet equally valid—measures of playing ability. In so doing, James also demonstrates just why it is that the Open Championship requires that all 72 holes be played.

So named because it resembles so closely that formula, fundamental to mathematics, called the Pythagorean Theorem, what the Pythagorean Expectation says is that the ratio of a team’s (or player’s) points scored to that team’s (or player’s) points allowed is a better predictor of future success than the team’s (or player’s) ratio of wins to losses. (James used “runs” because he was dealing with baseball.) More or less it works: as Graham MacAree puts it on the website FanGraphs, using James’ formula makes it “relatively easy to predict a team’s win-loss record”—even in sports other than baseball. Yet why is this so—how can a single formula predict future success at any sport? It might be thought, after all, that different sports exercise different muscles, or use different strategies: how can one formula describe underlying value in many different venues—and thus, incidentally, demonstrate that ability can be differentiated from the tools we use to measure it?

The answer to these questions is that adding up the total points scored, rather than the total games won, gives us a better notion of the relative value of a player or a team because it avoids something called the “Simpson’s Paradox”—which is what happens when, according to Wikipedia, it “appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.” Consider what happens for example when we match Ernie Els’ 75 to Pablo Larrazabal’s 68: if we match them according to who won each hole, Els comes out the winner—but if we just compared raw scores, then Larrazabal would. Simpson’s Paradoxes appear, in short, when we draw the boundaries around the raw data differently: the same score looks different depending on what lens is used to view it—an answer that might seem to validate those who think that underlying ability doesn’t exist, but only the means used to measure it. But what Simpson’s Paradox shows isn’t that all boundaries around the data are equal—in fact, it shows just the opposite.

What Simpson’s Paradox shows, in other words, is that drawing boundaries around the data can produce illusions of value if that drawing isn’t done carefully—and most specifically, if the boundaries don’t capture all of the data. That’s why the response golf fans might have to the assertion that Pablo Larrazabal is better than Ernie Els proves, rather than invalidates, the argument so far: people highly familiar with golf might respond, “well, you haven’t considered the total picture—Els, for instance, has won two U.S. Opens, widely considered to be the hardest tournament in the world, and Larrazabal hasn’t won any.” But then consider that what you have done just demonstrates the point made by Simpson’s Paradox: in order to say that Els is better, you have opened up the data set; you have redrawn the boundaries of the data in order to include more information. So what you would have conceded, were you to object to the characterization of Larrazabal as a better golfer than Els on the grounds that Els has a better overall record than Larrazabal, is that the way to determine the better golfer is to cast the net as wide as possible. You have demanded that the sample size be increased.

That then is why a tournament contested over only 36 holes isn’t considered an “official” PGA tournament, while 54 holes isn’t enough to crown the winner of a major tournament like the Open Championship (which is what the British Open is called when it’s at home). It’s all right if a run-of-the-mill tournament be cut to 54 holes, or even 36 (though in that case we don’t want the win to be official). But in the case of a major championship, we want there to be no misunderstandings, no “fluky” situations like the one in which Els wins and Larrazabal doesn’t. The way to do that, we understand, is to maximize chances, to make the data set as wide as possible: in sum, to make a large sample size. We all, I think, understand this intuitively: it’s why baseball has a World Series rather than a World Championship Game. So that is why, in a major championship, it doesn’t matter how long it takes—all the players qualified are going to play all 72 holes.

Here I will, as they say in both golf and baseball, turn for home. What all of this about Simpson’s Paradoxes means, at the end of the day, is that a tournament like the Open Championship is important—as opposed to, say, an American presidential election. In a presidential election as everyone knows, what matters isn’t the total numbers of votes a candidate wins, but how many states. In that sense, American presidential elections are conducted according to what, in golf, would be considered match play instead of stroke play. Now, as Bill James might acknowledge, that begs the question: does that process result in better candidates being elected?

As James might ask in response: would you like to bet?

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Mr. Tatum’s Razor

Arise, awake, and learn by approaching the exalted ones, for that path is sharp as a razor’s edge, impassable, and hard to go by, say the wise.
Katha Upanishad 1-III-14

Plurality is never to be posited without necessity.
—William of Ockham. Questions on the Sentences of Peter Lombard. (1318).

“The United States had lost. And won.” So recently wrote the former European and present naturalized American John Cassidy when Team USA advanced out of the “group stage” in the World Cup soccer tournament despite losing its last game of that stage. (To Germany, 1-0.) So even though they got beat, it’s the first time the U.S. has advanced out of the group stage in back-to-back Cups. But while the moment represented a breakthrough by the team, Cassidy warns it hasn’t been accompanied by a breakthrough in the fandom: “don’t ask [Americans] to explain how goal difference works,” he advises. He’s right that most are unfamiliar with the rule that allowed the Americans to play on, but he’s wrong if he’s implying that Americans aren’t capable of understanding it: the “sabermetric revolution”—the statistical study of the National Pastime—begins by recognizing the same principle that also backs goal difference. Yet while thus there’s precedent to think that Americans could understand goal difference—and, maybe, accept soccer as a big-time sport—there’s one reason to think America can’t: the American political system. And, though that might sound wacky enough for any one piece of writing, golf—a sport equally at home in America and Europe—is ideally suited to explain why.

Goal difference is a procedure that applies at the opening stage of the World Cup, which is organized differently than other large sporting tournaments. The NCAA college basketball tournament, for instance, is an “elimination” type tournament: sorts each of its 64 teams into four different brackets, then seeds each bracket from a #1 ranked team to a #16 ranked team. Each team then plays the team on the opposite side of the bracket, so that the the best team plays the lowest ranked team, and so on. Winning allows a team to continue; losing sends that team home, which is what makes it an “elimination” type of tournament.

The World Cup also breaks its entrants into smaller groups, and for the same reason—so that the best teams don’t play each other too early—but that’s where the similarities end. The beginning, “group” stage of the tournament is conducted in a round-robin format: each team in a group plays every other team in a group. Two teams from each group then continue to the next part of the competition.

Because the group stage is played under a round-robin, rather than elimination, structure losing a game doesn’t result necessarily in exiting the tournament—which is not only how the United States was not eliminated from competition by losing to Germany, but also is what makes the World Cup un-American in Cassidy’s estimation. “Isn’t cheering a team of losers,” Cassidy writes, “an un-American activity?” But there’s at least two questionable ideas packed into this sentence: one is that a team that has lost—a “loser”—is devoid of athletic ability, or what we might call value, and secondly that “losers” are un-American, or anyway that cheering for them is.

The round-robin format of the group stage after all just means that the tournament does not think a loss of a game necessarily reveals anything definitive about the value of a team: only a team’s record against all the other teams in its group does that. If the tournament is still unsure about the value of a team—that is, if two or more teams are tied for best, or second-best (two teams advance) record—then the tournament also looks at other ways to determine value. That’s what “goal difference,” or differential, is: as Ken Boehlke put it on CBSports website (“Understanding FIFA World Cup Procedures”), goal difference is “found by simply subtracting a team’s goals against from its goals scored.” What that means is that by the way the World Cup reckons things, it’s not only important whether a team lost a close game, but it’s also important if that team wins a blow-out.

Goal difference was, as Cassidy says, the reason why the American team was able to be one of the two teams of each group to advance. It’s true that the Americans were tied by win-loss record with another team in their group, Portugal. But the Americans only lost to Germany by one goal, while earlier in the stage the Portuguese lost 4-0. That, combined with some other results, meant that the United States advanced and Portugal did not. What the World Cup understands, is that just winning games isn’t necessarily a marker of a team’s quality, or value: what also matters is how many goals a team allows, and scores.

Now, John Cassidy appears to think that this concept is entirely foreign to Americans, and maybe he’s right—except for any of the Americans who happen to have seen the movie Moneyball, which not only grossed over $75 million dollars in the United States and was nominated for six Oscars but also starred Brad Pitt. “What are you really worth?” was the film’s tagline, and in the speech that is the centerpiece of the movie, the character Peter Brand (played by Jonah Hill, another fairly well-known actor) says to his boss—general manager of the Oakland A’s Billy Beane (played by Pitt)—that “Your goal … should be to buy wins. And in order to buy wins, you need to buy runs.” And while Moneyball, the film, was released just a few years ago, the ideas that fuel it have been around since the 1970s.

To be sure, it’s hardly news that scoring points results in winning games—the key insight is that, as Graham MacAree put it on the website FanGraphs, it is “relatively easy to predict a team’s win-loss record using a simple formula,” a formula that was invented a man named Bill James in the 1970s. The formula resembled the classic Pythagorean Theorem that James called it the Pythagorean Expectation: what it expressed was that the ratio of a team’s past runs scored to runs allowed is a better predictor of future success (i.e., future wins and losses) than that team’s past ratio of wins to losses. What it meant was that, to quote MacAree again, “pure pythagorean expectancy is probably a better way of gauging a team than actual wins and losses.” Or to put it another way, knowing how many runs a team scored versus how many that team’s opponents scored is more valuable than knowing how many games it won.

What the Pythagorean Expectation model and the goal difference model do, then, concentrate focus on what is the foundational act of their respective sports: scoring goals and scoring runs. Conversely, both weaken attention on winning and losing. That might appear odd: isn’t the point of playing a game to win, not (just) to score? But what both these methods realize is that a focus on winning and losing, instead of scoring, is vulnerable to a particular statistical illusion called a Simpson’s Paradox.

As it happens, an episode of the television series Numb3rs used a comparison of the batting averages of Derek Jeter and David Justice in the middle 1990s to introduce the idea of what a Simpon’s Paradox is, which seems tailor-made for the purpose. Here is a table—a more accurate one than the television show used—that shows those averages during the 1995, 1996, and 1997 seasons:

1995

1996

1997

Totals

Derek Jeter

12/48

.250

183/582

.314

190/654

.291

385/1284

.300

David Justice

104/411

.253

45/140

.321

163/495

.329

312/1046

.298

Compare the year-by-year averages: Jeter, you will find, has a worse average than Justice in every year. Then compare the two players’ totals: Jeter actually has a slightly better average than Justice. A Simpson’s Paradox results, as the Stanford Encyclopedia of Philosophy puts it, a when the “structures that underlie” a set of facts “invalidate … arguments that many people, at least initially, take to be intuitively valid.” Or as the definition on Wikipedia describes it, a bit more elegantly, the paradox occurs when “appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.” In this case, if we consider the data year-by-year, it seems like Justice is a better hitter than Jeter—but when we consolidate all of the data, it supports the notion that Jeter is better than Justice.

There’s at least two ways we can think that the latter hypothesis is the more likely: one is the simple fact that 1995 was Derek Jeter’s first appearance in the major leagues, because he was born in 1974, whereas Justice was already a veteran player who was born eight years earlier. Jeter is younger. Quite obviously then from the perspective of a general manager looking at these numbers after the 1997 season, buying Jeter is a better move because more of Jeter’s career is available to be bought: since Jeter is only retiring this year (2014), that means that in 1997 there was 17 seasons of Derek Jeter available, whereas since David Justice retired in 2002, there were only 5 more seasons of David Justice available. Of course, none of that information would have been available in 1997—and injuries are always possible—but given the age difference it would have been safe to say that, assuming you valued each player relatively equally on the field, Jeter was still more valuable. In one sense though that exercise isn’t very helpful, because it doesn’t address just what Simpson’s Paradox has to do with thinking about Derek Jeter.

In another though it has everything to do with it. The only question that matters about a baseball player, says Bill James, is “If you were trying to win a pennant, how badly would you want this guy?” Or in other words, don’t be hypnotized by statistics. It sounds like a simple enough lesson, which in a way it is—but it’s terribly difficult to put into practice. In this case, it is terribly easy to become mystified by the two players’ batting averages, but what James might advise is to look at the events that these numbers represent: instead of looking at the averages, look at the components of those averages.

 What looking at the raw numbers reveals is that Jeter had more hits than Justice over the three seasons: 385 to 312. That difference matters because—unlike the difference in batting average over the same period, which is only a couple of points—78 more hits is a lot more hits, and as James wrote in The New Bill James Historical Baseball Abstract, the “essential measure of a hitter’s success is how many runs he has created.” Further, without getting too far into the math of it, smart people who’ve studied baseball have found that a single hit is worth nearly half a run. (Joe Posnanski, former Senior Writer at Sports Illustrated and one of those people, has a nice post summarizing the point called “Trading Walks For Hits” at joeposnanski.com.) What that would mean is that Jeter may have created more runs than Justice did over the same period: depending on the particular method used, perhaps more than twenty more runs. And since runs create wins (that conversion being calculated as about ten runs to the win) that implies that Jeter likely helped his team to two more wins than Justice did over the same period.

To really know which player contributed more to winning would require a lot more investigation than that, but the point is that following James’ method leads towards the primary events that generate outcomes, and away from the illusions that a focus on outcomes foster. Wins are generated by runs, so focus on runs; runs are created by hits, so focus on hits. So too does goal difference mean that while the World Cup recognizes wins, it also recognizes the events—goals—that produce wins. Put that way, it sounds quite commonsensical—but in fact James was lucky in a sense to stumble upon it: because there are two ways to organize sport, and only one of those types is amenable to this kind of analysis. It was fortunate, both to James and to baseball, that he was a fan of a game that could easily be analyzed this way.

In sports like baseball, there’s a fairly predictable relationship between scoring and winning. In other sports though there isn’t, and that’s why golf is very important. It is a sport that under one way to play it the sport is very amenable to means of analysis like the World Cup’s goal difference or Bill James’ Pythagorean Expectation. Golf however also has another way to play, and that way does not have a predictable relationship between scores and wins. What the evidence will show is that having two different forms to the sport isn’t due to a mistake on the part of the designers’: it’s that each form of the game was designed for a different purpose. And what that will show, I will argue, is that whether a game has one sort of scoring system or the other predicts what the purpose of the design is—and vice versa.

On the PGA Tour, the standard tournament consists of four rounds, or 72 holes, at the end of which the players who have made it that far add up their scores—their number of strokes—and the lowest one wins. In the Rules of Golf, this format is known as “stroke play.” That’s what makes it like the group stage of the World Cup or Bill James’ conception of baseball: play begins, the players attempt some action that produces a “score” (however that is determined), and at the end of play each of those scoring events is added together and compared. The player or team that produces the right amount of these “scoring events” is then declared the winner. In short, under the rules of stroke play—just as to the World Cup’s group stage, or to Bill James’ notion of baseball—there is a direct relationship between the elemental act of the game, scoring, and winning.

But the format most often used by golf’s professionals is not the only method available: many amateur tournaments, such as the United States Amateur, use the rules format known as “match play.” Under this format, the winner of the contest is not necessarily the player who shoots the lowest overall score, as in stroke play. Instead, as John Van der Borght has put the matter on the website of the United States Golf Association, the official rule-making body of the sport, in match play the “winner is the player who wins the most holes.” It’s a seemingly minor difference—but in fact it creates such a difference that match play is virtually a different sport than stroke play.

Consider, for instance, this year’s Accenture Match Play tournament, held at the Dove Mountain course near Tucson, Arizona. (The only tournament on the PGA Tour to be held under match play rules.)  “Factoring in conceded putts,” wrote Doug Ferguson of the Associated Press earlier this season, “Pablo Larrazabal shot a 68 and was on his way back to Spain,” while “Ernie Els shot 75 and has a tee time at Dove Mountain on Thursday.” In other words, Larrazabal lost his match and Els won his, even though Larrazabal played better than Els. Intuitively, Larrazabal was the better player at this tournament, which would lead to thinking Larrazabal continued to play and Els exited—but the actual results conclude the reverse. It’s a Simpson’s Paradox, and unlike stroke play—which cannot generate Simpson’s Paradoxes—match play produces them all the time. That’s why match play golf does not resemble baseball or soccer, as golf does in stroke play, but instead a sport whose most prestigious tournament—Wimbledon—just concluded. And tennis is the High Church of Simpson’s Paradox.

Simpson’s Paradox, for example, is why many people don’t think Roger Federer is not the greatest tennis player who ever lived. That’s because the Swiss has won 17 major championships, a record, among other career accomplishments. “But,” as Michael Steinberger wrote in the New York Times not long ago, “he has a losing record against [Rafael] Nadal, and a lopsided one at that.” (Nadal leads 23-10.) “How can you be considered the greatest player ever if you were arguably not even the best player of your own era?” Steinberger asks. Heroically, Steinberger attempts to answer that question in favor of Federer—the piece is a marvel of argumentation, where the writer sets up a seemingly-insurmountable rhetorical burden, the aforementioned question, then seeks to overcome it. What’s interesting, though—and in several searches through the Internet I discovered many other pieces tackling more or less the same subject—neither Steinberger nor anyone else attempted what an anonymous blogger did in 2009.

He added up the points.

The blog is called SW19, which is the United Kingdom’s postal code for the district Wimbledon is in. The writer, “Rahul,” is obviously young—he (or she) stopped posting in December of 2009, because of the pressures of college—but yet Rahul did something I have not seen any other tennis journalist attempt: in a post called “Nadal vs. Federer: A Pythagorean Perspective,” Rahul broke down “the Federer/Nadal rivalry on a point-by-point basis, just to see if it really is as lopsided as one would expect.” That is, given Nadal’s dominant win-loss record, the expectation would be that Nadal must win an equally-impressive number of points from Federer.

By July of 2009—the time of publication—Nadal led Federer by 13-7 in terms of their head-to-head record, a 65 percent winning percentage. The two champions had played 4,394 total points across those 20 matches—one of them the 2008 French Open, won by Nadal in straight sets, 6-1, 6-3, 6-0. (Nadal has, as of 2014, now won 9 French Opens, a majors record, while Federer has only won the French once—the very next year after Nadal blew him off the court: 2009.) Now, if there was a straightforward relation between points and wins, Nadal’s percentage of those points ought to be at least somewhat similar to his winning percentage of those matches.

But what Rahul found was this: of the total points, Nadal had won 2,221 and Federer 2,173. Nadal had only beaten Federer on 48 points, total, over their careers to that point, including the smackdown at Roland Garros in 2008. It’s less than one percent of all the points. And if you took that match out of the total, Nadal had won a grand total of eight more points than Federer, out of over 4,000 points and 19 other matches. It is not 65 percent. It is not even 55 percent.

Still, it’s the final nugget that Rahul uncovered that is likely of the most relevance. In three of the twenty matches won by Nadal to that moment in their careers, Federer had actually won more points: two matches in 2006, in Dubai and Rome, and once at the Australian Open in 2009. As Rahul points out, “if Federer had won those three matches, the record would sit at 10-10”—and at least in 2009, nobody would have been talking about Federer’s Achilles heel. I don’t know what the current Pythagorean record stands between the two players at the moment, but it’s interesting that nobody has taken up this detail when discussing Federer’s greatness—though nub of it has been taken up as a serious topic concerning tennis as a whole.

In January in The Atlantic, Professor Ryan Rodenberg of the Florida State University noted that not only did Federer have the 17 Grand Slam titles and the 302 weeks ranked No. 1 in the world, but he also held another distinction: “the worst record among players active since 1990 in so-called ‘Simpson’s Paradox’ matches—those where the loser of the match wins more points than the winner.” Federer’s overall record in these matches is like that of his record against Nadal: not good. The Swiss is only 4-24.

To tennis aficionados, it’s a point that must appear irrelevant—at least, no one until Professor Rodenberg appears to have mentioned it online. To be sure, it does seem questionably relevant: Federer has played nearly 1200 matches professionally; 28 is a pittance. But Rodenberg, along with his co-authors, found that matches like the Isner-Mahut match, where the loser out-scored the winner, constituted “about 4.5 percent” of “61,000 men’s ATP and Grand Slam matches dating back to 1990.” That’s over 3,000 matches—and given that, in exactly zero soccer matches or baseball games over that time frame or any other time, did the losing side net more goals or plate more runs than the other, it at the least raises some questions.

How, after all, is it possible for one side of the net to win—despite losing more of the points? The answer, as Rodenberg puts it, is  “tennis’ decidedly unique scoring system.” In sports like baseball, sports psychologist Allen Fox wrote recently on for the website for the magazine Tennis, “score is cumulative throughout the contest … and whoever has the most points at the end wins.” Sports like tennis or match play golf are different however: in tennis, as Fox says, “[i]f you reach game point and win it, you get the entire game while your opponent gets nothing—all the points he or she won in the game are eliminated.” In the same fashion, once a hole is over in match play golf it doesn’t matter what either competitor scored on that hole: each total is struck out, and the match in effect begins again. What that in turn means is that certain points, certain scoring events, have more value than others: in golf, what matters is the stroke that takes a hole, just as in tennis what matters is the point that takes a game, or a set, or a match. Those points are more valuable than other points—a fact of tremendous importance.

It’s this scoring mechanism that is what allows tennis and match play golf to produce Simpson’s Paradox games: a system whereby the competition as a whole is divided into smaller competitions that function independently of the others. In order to get Simpson’s Paradox results, having a system like this is essential. The $64,000 question however is: just who would design a system like that, a system that can in effect punish a player who does the thing that defines the sport better than the other player more often than the player who doesn’t? It isn’t enough just to say that results like that are uncommon, because why allow that to happen at all? In virtually every other sport, after all, no result like these would ever come up. The only serious answer must be that tennis and match play golf were specifically designed to produce Simpson’s Paradoxes—but why? The only way to seek that answer, I’d say, is to search back through history.

The game we today call tennis in reality is correctly termed “lawn tennis,” which is why the formal name of the organization that sponsors the Wimbledon tournament is the “All England Lawn Tennis and Croquet Club.” The sport is properly called that in order to distinguish it from the older game known as “real tennis” or, in French, Jeu de Paume. Whereas our game of tennis, or lawn tennis, is generally played outdoors and on a single plane, Jeu de Paume is played indoors, in unique, non-standardized courts where strange bounces and funny angles are the norm. And while lawn tennis only came into existence in 1874, Jeu de Paume goes well back into the Middle Ages. “World titles in the sport were first competed in 1740,” as Rolf Potts noted in a piece about the game in the online magazine, The Smart Set, “and have continued to the present day, making Jeu de Paume men’s singles the oldest continuous championship event in sport.” Jeu de Paume, thus, is arguably the oldest sport in the world.

Aside from its antiquity, the game is also, and not unrelatedly, noted for its roots in the ancien regime: “Nearly all French royalty were familiar with the sport from the 13th century on,” as Rolf Potts notes. And not just French royalty: Henry VIII of England is regularly described as a great player by historians. These are not irrelevant facts, because the status of the players of Jeu de Paume in fact may be directly relevant to how tennis is scored today.

“When modern tennis,” writes Potts, “was simplified into its popular form in 1874, it appropriated the scoring system of the ancient French game.” So our game of tennis did not invent its own method of scoring; it merely lifted another game’s method. And that game’s method may be connected to the fact that it was played by aristocrats in the fact that so much about Jeu de Paume is connected to gambling.

“In October of 1532,” Potts reports, Henry VIII lost 50 pounds on tennis matches: “about a thousand times the sum most Englishmen earned in a week.” Anne Boleyn, Henry’s second wife, by some accounts “was betting on a tennis game when Henry’s men arrested her in May of 1536,” while others say that her husband received the news of her execution while he himself was playing a match. Two centuries earlier, in 1355, King John II of France had been recorded paying off a bet with “two lengths of Belgian cloth.” And in Rob Lake’s academic paper, “Real Tennis and the Civilising Process,” published in the academic journal Sport in History, Lake claims that “the game provided opportunities for nobles to engage in conspicuous consumption … through gambling displays.”

So much so, in fact, that Potts also reports that “some have speculated that tennis scoring was based on the gros denier coin, which was said to be worth 15 deniers.” Be that as it may, two facts stand out: the first is that the game’s “gradual slide into obscurity began when fixed games and gambling scandals sullied its reputation in the late 17th century,” and the second that “games are still regulated by a complicated handicapping system … so that each player begins the game with an equal expectation of winning.” So elaborate is that handicap system, in fact, that when Rolf Potts plays the first match of his life, against a club professional who is instructing him, he “was able to play a close game.” Gambling, in seems, was—as Potts says—“intrinsic to Jeu de Paume.” And since the sport still has a handicap system, which is essential to gambling, so it still is.

We can think about why that is by comparing Jeu de Paume to match play golf, which also has an early connection both to feudalism and gambling. As Michael Bohn records in Money Golf: 600 Years Of Bettin’ On Birdies, the “earliest record of a golf bet in Scotland was in 1503,” when on February 3 King James IV paid out 42 shillings to the Earl of Bothwell in “play at the golf.” And as John Paul Newport of the Wall Street Journal writes, “historically all the early recorded competitions—King James IV in 1503, for example, or the Duke of York, later King James II [of England], in 1681—were match play.” That is likely not a coincidence, because the link between the aristocracy, gambling, and match play is not difficult to explain.

In the first place, the link between the nobility and gambling is not difficult to understand since aristocrats were virtually the only people with both money and the time for sport—the opportunity, as a prosecutor would say. “With idle people amusement is the business of life,” as  the London magazine The Spectator noted in 1837; and King James’ bet with the Earl of Bothwell—42 shillings, or a little over £2—would have bought roughly six month’s work from a laborer during the sixteenth century. Not merely that: the aristocracy were practically the only people who, legally speaking, could gamble in during the Renaissance: as Nicholas Tosney notes in a paper for the University of Nevada, Las Vegas in 2010—“Gaming in Britain and America: Some Historical Comparisons”—gambling in England was outlawed in 1541 for anyone not at least a gentleman.

Yet just having the ability does not carry a case. It’s also required to be able to posit a reason—which of course isn’t all that hard to find when it comes to gambling. Aside from the obvious financial inducement, though, aristocratic men had something extra pushing them toward gaming. As the same 1837 Spectator article noted, gambling was widely thought to be “a necessary accomplishment of a young man in fashionable circles.” After all, what better way to demonstrate belonging to the upper classes by that form of conspicuous consumption that buys—nothing? The literature on the subject is so extensive as to not need bothering with trolling out in its entirety: nobles had both the means and the motive to gamble, so it therefore seems reasonable to suppose that a game adopted by gamblers would be ideal for gambling.

And examined closely, match play does have such features. Gambling after all would best explain why match play consists of what John Van der Borght calls “18 one-hole contests.” According to John Paul Newport, that’s so “an awful hole here or there doesn’t spoil the day”—but a better explanation is likely because doing things that way allows the previous hole’s loser to bet again. Multiplying contests obviously increases the opportunity to bet—and thus for a sucker to lose more. And that’s why it is significant that the match play format should have a link to the nobility and gambling: because it helps to demonstrate that the two formats of golf are not just different versions of the same game, but in fact have two different purposes—purposes that are so different they are virtually different sports.

That difference in purpose is likely why, as Newport observes, it isn’t “until the mid-18th century are there records of stroke-play competitions.” One reason for the invention of the stroke play format was, Newport tells us, “to make tournaments involving larger numbers of golfers feasible.” The writer for the Wall Street Journal—make of that connection what you will—presents the new format as simply demanded by the increasing number of players (a sign, though Newport does not mention it, that the game was spreading beyond the boundaries of the nobility). But in reality stroke play was invented to serve a different purpose than match play, a purpose even now recognized by the United States Golf Association.

About the best definition of the purpose of stroke play—and thus, it’s difference from match play—can be found in the reply Sandy Tatum, then the executive director of the United States Golf Association, gave to a reporter at the 1974 U.S. Open at Winged Foot. That tournament would become known as “the Massacre at Winged Foot,” because even the winner, Hale Irwin, finished over par (+7). So when the extent of how tough the golf course was playing became obvious, one reporter asked Tatum if the USGA was trying to embarrass the best players in the world. What Tatum said in reply to the reporter is about as succinct an explanation of the purpose of the U.S. Open, and stroke play, as is possible.

“Our objective is not to humiliate the best golfers in the world,” Tatum said in response to the question: “It’s to identify them.”And identifying the greatest golfers is still the objective of the USGA: That’s why, when Newport went to interview the current executive director of the USGA, Mike Davis, about the difference between stroke play and match play for his article, Davis said “If all you are trying to do is determine who is playing the best over a relatively short period of time, [then] 72 holes of stroke play is more equitable [than match play].” The position of the USGA is clear: if the purpose of the competition is to “identify,” as Tatum said, or “determine,” as Davis said, the best player, then the best format for that purpose is stroke play, and not match play.

One reason why the USGA can know this is that it is obviously not in the interest of gamblers to identify themselves as great players. Consider, for instance, a photo printed along with Golf magazine’s excerpt of Kevin Cook’s book, Titanic Thompson: The Man Who Bet On Everything. The photo depicts one Alvin “Titanic Thompson” Thomas, swinging a club late in life. Born in 1892, Cook says that “Titanic was the last great player to ignore tournament golf”—or stroke play golf, anyway. Not because he couldn’t: Cook says that Byron Nelson, who among other exploits won 11 tournaments on the PGA Tour in a row in the summer of 1945, and thus seems an excellent judge, said “there was ‘no question’ that Titanic could have excelled on Tour, ‘but he didn’t have to.’”—because Titanic “‘was at a higher level, playing for $25,000 a nine while we [Tour players] played for $150.’” Thomas, or Thompson was the greatest of golf gamblers; hence the caption of the photo: “Few golf photos exist of Thompson,” it reads, “for obvious reasons.” Being easily identifiable as a great golfer, after all, is not of much use to a gambler—so a format designed for gambling would have little incentive to “out” better players.

To put it simply then the game of tennis today has the structure that it does today because it descends from a different game—a game whose intent was not to identify the best player, but rather to enable the best player to maximize his profits. Where the example of tennis, or match play golf, should then lead specifically, is to the hypothesis that any point-driven competition that has non-continuous scoring—which is to say divided into sub-competitions whose results are independent of all the others—and where some parts of the competition have a higher value than other parts, ought to raise doubt, at the least, as to the validity of the value of the competition’s results.

The nature of such structures make it elementary to conceal precisely that which the structure is ostensibly designed to reveal: the ultimate value that underlies the whole operation, whether that is the athletic ability of an individual or a team—or something else entirely. Where goal difference and Pythagorean Expectation and stroke play all consolidate scores in order to get at the true value those scoring events represent, tennis’ method and match play divide scores to obscure value.

That’s why match play is so appealing to golf gamblers—it allows the skilled player to hide his talent, and thus maximize income. Conversely, that’s why the U.S. Open uses stroke play: because the USGA wants to reveal the best player. Some formats of play lend themselves to one purpose or the other—and what that leads to is a kind of thought experiment. If the notion advanced here is correct, then there are two kinds of ways a given sport may score itself, and concurrently two different purposes those different means of scoring may serve. If a sport is more like golf’s match play than it is like golf’s stroke play, in short, it can be predicted that it’s likely to be vulnerable to gamblers.

As it happens, it’s widely believed that professional tennis has a gambling problem. “Everyone knows,” said last year’s Wimbledon winner, Andy Murray, “that match-fixing takes place in professional tennis”—all the way back in October of 2007. A story in the Guardian that year summed up the scandal that broke over the sport that August, which began when the world’s largest online betting exchange, Betfair, reported “irregular gambling patterns” on a match between Nikolay Davydenko—once ranked as high as #3 in the world—and Martin Arguello—at the time ranked #87—at the Polish Open. At the end of September 2007, Novak Djokovic—this year’s Wimbledon champion—said “he was offered £10,000 to lose in a tournament in St. Petersburg” the previous year. In late October of 2007—after Murray’s comment to the press—“French undercover police” were “invited into the Paris Masters amid suspicions of match-fixing in tennis.” But what Simpson’s Paradox would tell the police—or tennis’ governing bodies—is that looking for fixed matches is exactly what the cunning gambler would want the authorities to do.

“The appeal of tennis to gamblers,” wrote Louisa Thomas for Grantland earlier this year, “makes total sense” for a number of reasons. One is that “tennis is played everywhere, all the time”: there’s likely a tournament, somewhere in the world, any time anyone feels the urge to bet, unlike a lot of other sports. That ubiquity makes tennis vulnerable to crooked gamblers: as Thomas observes, there are “tens of thousands of professional matches, hundreds of thousands of games, millions of points”—a spread of numbers so wide that the volume alone discourages detection by any authority.

Another reason why tennis should be appealing to gamblers is that “bettors can make wagers during play itself”: you can get online while watching a match and lay down some action. As The Australian reported this year—when a young man was arrested at the Australian Open with an electronic device designed to transmit scores quicker than the official tournament did—there are “websites that allow bets to be laid on individual events such as whether a player faults on serve.” Now, essentially the scam that the man at the Australian Open was arrested for is the same con as depicted in the film The Sting, which itself tells something of a tale about the sport.

But the real scandal of tennis, though perhaps Thomas does not emphasize this enough, is that it is vulnerable to manipulation simply because  “broken into discrete points, games, sets, matches, and tournaments.” It’s a point, however, that one of Professor Rodenberg’s students understands.

What Benjamin Wright—a graduate student in Rodenberg’s department at the Florida State University—knows is that because of tennis’ scoring system, the sport doesn’t need to have crooked players throwing matches to be corrupt. “Governing bodies must be aware,” says Wright—in his master’s thesis, “Best of N Contests: Implications of Simpson’s Paradox in Tennis”—“that since tennis does not use a running score like other sports intentionally losing points, games, and sets is plausible since such acts may not have long-term implications.” In other words, “a player would not need to lose an entire match intentionally.” All that’s necessary—especially since it’s possible to bet on tennis in real time—is for a player to lose “points during specific periods of a match.” All a gambler needs to know, that is, is that a player will throw the second point of the fourth game of the second set—knowledge that is nearly undetectable because under the rules of the game it is entirely possible for a player to shave points without risking a loss.

“Who’s to say,” says Thomas about the undetectability of corruption, a player is “not just having a really rotten day?” But what Thomas doesn’t appear to grasp fully is that the actual disgrace is the question of how a player could be accused of corruption if she has won her match? That’s the real scandal: how even apparently well-trained journalists can miss the point. “Although tennis is perceived as a genteel sport,” wrote Joe Drape of the New York Times about the Davydenko scandal in 2007, “it has always confronted the same problem as other contests based on individual competition like boxing.” That problem, Drape said, is that a “fixer needs to sway only one person, and taking a dive is hard to detect.” Drape is, to be sure, right about what he says—so far as that goes. But Drape does not point out—I think likely because he does not understand—why “taking a dive” is so difficult to unmask in tennis: because it’s possible to throw a point—or a game, or a set—without affecting the outcome of the match.

Now, this is so obviously crooked that the gall of it is simply breathtaking. Yet the reality is simply that, aside from a few very naive people who could probably stand to have a few dollars taken from them by shrewd, and likely Russian, mobsters, no one really loses much by this arrangement. There are far worse scams in the world, and people who bet on tennis are probably not very sympathetic victims. But what knowing what we now know about tennis, and match play golf, allows us to now do is to evaluate all competitions: any contest which has the characteristics we have isolated (non-cumulative scoring, unequal points) will necessarily produce Simpson’s Paradox results. Further, any contest that produces Simpson’s Paradox results does so by design: there’s no reason to add an extra layer of complexity to a competition unless it’s in somebody’s interests. Lastly, since the only reason to add that layer of complexity, and thus produce Simpson’s Paradoxes, is to conceal value, it’s more likely than not that those interests are not entirely legitimate.

Now, it so happens that there is a competition that has those two characteristics and has demonstrably produced at least one paradoxical result: one where the “winner” lost and the “loser” won.

That competition is called an American presidential election.

The End of Golf?

And found no end, in wandering mazes lost.
Paradise Lost, Book II, 561

What are sports, anyway, at their best, but stories played out in real time?
Grantland “Home Fields” Charles P. Pierce

We were approaching our tee shots down the first fairway at Chechessee Creek Golf Club, where I am wintering this year, when I got asked the question that, I suppose, will only be asked more and more often. As I got closer to the first ball I readied my laser rangefinder—the one that Butler National Golf Club, outside of Chicago, finally required me to get. The question was this: “Why doesn’t the PGA Tour allow rangefinders in competition?” My response was this, and it was nearly immediate: “Because that’s not golf.” That’s an answer that, perhaps, appeared clearer a few weeks ago, before the United States Golf Association announced a change to the Rules of Golf in conjunction with the Royal and Ancient of St. Andrews. It’s still clear, I think—as long as you’ll tolerate a side-trip through both baseball and, for hilarity’s sake, John Milton.

Throughout the rest of this year, any player in a tournament conducted under the Rules of Golf would be subjected to disqualification should she or he take out their cell phone during a round to consult a radar map of incoming weather. But on the coming of the New Year, that will be permitted: as the Irish Times wonders, “Will the sight of a player bending down to pull out a tuft of grass and throwing skywards to find out the direction of the wind be a thing of the past?” Perhaps not, but the new decision certainly says where the wind is blowing in Far Hills. Technology is coming to golf, as, it seems, to everything.

At some point, and it isn’t likely that far away, all relevant information will likely be available to a player in real time: wind direction, elevation, humidity, and, you know, yardage. The question will be, is that still golf? When the technology becomes robust enough, will the game be simply a matter of executing shots, as if all the great courses of the world were simply your local driving range? If so, it’s hard to imagine the game in the same way: to me, at least, part of the satisfaction of playing isn’t just hitting a shot well, it’s hitting the correct shot—not just flushing the ball on the sweet spot, but seeing it fly (or run) up toward the pin. If everyone is hitting the correct club every time, does the game become simply a repetitive exercise to see whose tempo is particularly “on” that day?

Amateur golfers think golf is about hitting shots, professionals know that golf is selecting what shots to hit. One of the great battles of golf, to my mind, is the contest of the excellent ball-striker vs. the canny veteran. Bobby Jones vs. Walter Hagen, to those of you who know your golf history: since Jones was perhaps known for the purity of his hits while Hagen, like Seve Ballesteros, for his ability to recover from his impure ones. Or we can generalize the point and say golf is a contest between ballstriking and craftiness. If that contest goes, does the game go with it?

That thought would go like this: golf is a contest because Bobby Jones’ ability to hit every shot purely is balanced by Walter Hagen’s ability to hit every shot correctly. That is, Jones might hit every shot flush, but he might not hit the right club; while Hagen might not hit every shot flush, but he will hit the correct club, or to the correct side of the green or fairway, or the like. But if Jones can get the perfection of information that will allow him to hit the correct club more often, that might be a fatal advantage—paradoxically ending the game entirely because golf becomes simply an exercise in who has the better reflexes. The idea is similar to the way in which a larger pitching mound became, in the late 1960s, such an advantage for pitchers that hitting went into a tailspin; in 1968 Bob Gibson became close to unhittable, issuing 268 strikeouts and possessing a 1.12 ERA.

As it happens, baseball is (once again) wrestling with questions very like these at the moment. It’s fairly well-known at this point that the major leagues have developed a system called PITCH/fx, which is capable of tracking every pitch thrown in every game throughout the season—yet still, that system can’t replace human umpires. “Even an automated strike zone,” wrote Ben Lindbergh in the online sports magazine Grantland recently, “would have to have a human element.” That’s for two reasons. One is the more-or-less obvious one that, while an automated system has no trouble judging whether a pitch is over the plate or not (“inside” or “outside”) it has no end of trouble judging whether a pitch is “high” or “low.” That’s because the strike zone is judged not only by each batter’s height, but also by batting stance: two players who are the same height can still have different strike zones because one might crouch more than another, for instance.

There is, however, a perhaps-more rooted reason why umpires will likely never be replaced: while it’s true that major league baseball’s PITCH/fx can judge nearly every pitch in every game, every once in (a very great) while the system just flat out doesn’t “see” a pitch. It doesn’t even register that a ball was thrown. So all the people calling for “robot umpires” (it’s a hashtag on Twitter now) are, in the words of Dan Brooks of Brooks Baseball (as reported by Lindbergh), “willing to accept a much smaller amount of inexplicable error in exchange for a larger amount of explicable error.” In other words, while the great majority of pitches would likely be called more accurately, it’s also so that the mistakes made by such a system would be a lot more catastrophic than mistakes made by human umpires. Imagine, say, Zack Greinke was pitching a perfect game—and the umpire just didn’t see a pitch.

These are, however, technical issues regarding mechanical aids, not quite the existential issues of the existence of what we might term a perfectly transparent market. Yet they demonstrate just how difficult such a state would, in practical terms, be to achieve: like arguing whether communism or capitalism are better in their pure state, maybe this is an argument that will never become anything more than a hypothetical for a classroom. The exercise however, like seminar exercises are meant to, illuminates something about the object in question: since a computer doesn’t know the difference between the first pitch of April and the last pitch of the World Series’ last game—and we do—that I think tells us something about what we value about both baseball and golf.

Which is what brings up Milton, since the obvious (ha!) lesson here could be the one that Stanley Fish, the great explicator of John Milton, says is the lesson of Milton’s Paradise Lost: “I know that you rely upon your senses for your apprehension of reality, but they are unreliable and hopelessly limited.” Fish’s point refers to a moment in Book III, when Milton is describing how Satan lands upon the sun:

There lands the Fiend, a spot like which perhaps
Astronomer in the Sun’s lucent Orb
Through his glaz’d optic Tube yet never saw.

Milton compares Satan’s arrival on the sun to the sunspots that Galileo (whom Milton had met) witnessed through his telescope—at least, that is what the first part of the thought appears to imply. The last three words, however—yet never saw—rip away that certainty: the comparison that Milton carefully sets up between Satan’s landing and sunspots he then tells the reader is, actually, nothing like what happened.

The pro-robot crowd might see this as a point in favor of robots, to be sure—why trust the senses of an umpire? But what Fish, and Milton, would say is quite the contrary: Galileo’s telescope “represents the furthest extension of human perception, and that is not enough.” In other words, no matter how far you pursue a technological fix (i.e., robots), you will still end up with more or less the problems you had before, only they might be more troublesome than the ones you have now. And pretty obviously, a system that was entirely flawless for every pitch of the regular season—which encompasses, remember, thousands of games just at the major league level, not even to mention the number of individual pitches thrown—and then just didn’t see a strike three that (would have) ended a Game 7 is not acceptable. That’s not really what I meant by “not golf” though.

What I meant might best be explained by reference to (surprise, heh) Fish’s first major book, the one that made his reputation: Surprised by Sin: The Reader in Paradise Lost. That book set out to hurdle what had seemed to be an unbridgeable divide, one that had existed for nearly two centuries at least: a divide between those who read the poem (Paradise Lost, that is) as being, as Milton asked them, intended to “justify the ways of God to men,” and those who claimed, with William Blake, that Milton was “of the Devil’s party without knowing it.” Fish’s argument was quite ingenious, which was in essence was that Milton’s technique was true to his intention, but that, misunderstood, could easily explain how some could mis-read him so badly. Which is rather broad, to be sure—as in most things, the Devil is in the details.

What Fish argued was that Paradise Lost could be read as one (very) long instance of what are now called “garden path” sentences, which are grammatical sentences that begin in a way that appear to direct the reader toward one interpretation, only to reveal their true meaning at the end. Very often, they require the reader to go back and reread the sentence, such as in the sentence, “Time flies like an arrow; fruit flies like a banana.” Another example is Emo Philips’ line “I like going to the park and watching the children run around because they don’t know I’m using blanks.” They’re sentences, in other words, where the structure implies one interpretation at the beginning, only to have that interpretation snatched away by the sentence’s end.

Fish argued that Paradise Lost was, in fact, full of these moments—and, more significantly, that they were there because Milton put them there. One example Fish uses is just that bit from Book III, where Satan gets compared, in detail, with the latest developments in solar astronomy—until Milton jerks the rug out with the words “yet never saw.” Satan’s landing is just like a sunspot, in other words … except it isn’t. As Fish says,

in the first line two focal points (spot and fiend) are offered the reader who sets them side by side in his mind … [and] a scene is formed, strengthened by the implied equality of spot and fiend; indeed the physicality of the impression is so persuasive that the reader is led to join the astronomer and looks with him through a reassuringly specific telescope (‘glaz’d optic Tube) to see—nothing at all (‘yet never saw’).

The effect is a more-elaborate version of that of sentences like “The old man the boats” or “We painted the wall with cracks”—typical examples of garden-path sentences. Yet why would Milton go to the trouble of constructing the simile if, in reality, the things being compared are nothing alike? It’s Fish’s answer to that question that made his mark on criticism.

Throughout Paradise Lost, Fish argues, Milton again and again constructs his language “in such a way that [an] error must be made before it can be acknowledged by the surprised reader.” That isn’t an accident: in a sense, it takes the writerly distinction between “showing” and “telling” to its end-point. After all, the poem is about the Fall of Man, and what better way to illustrate that Fall than by demonstrating it—the fallen state of humanity—within the reader’s own mind? As Fish says, “the reader’s difficulty”—that is, the continual state of thinking one thing, only to find out something else—“is the result of the act that is the poem’s subject.” What, that is, were Adam and Eve doing in the garden, other than believing things were one way (as related by one slippery serpent) when actually they were another? And Milton’s point is that trusting readers to absorb the lesson by merely being told it is just what got the primordial pair in trouble in the first place: why Paradise Lost needs writing at all is because our First Parents didn’t listen to what God told them (You know: don’t eat that apple).

If Fish is right, then Milton concluded that just to tell readers, whether of his time or ours, isn’t enough. Instead, he concocted a fantastic kind of riddle: an artifact where, just by reading it, the reader literally enacts the Fall of Man within his own mind. As the lines of the poem pass before the reader’s eyes, she continually credits the apparent sense of what she is reading, only to be brought up short by a sudden change in sense. Which is all very well, it might be objected, but even if that were true about Paradise Lost (and not everyone agrees that it is), it’s something else to say that it has anything to do with baseball umpiring—or golf.

Yet it does, and for just the same reason that Paradise Lost applies to wrangling over the strike zone. One reason why we couldn’t institute a system that could possibly just not see one pitch over another is because, while certainly we could take or leave most pitches—nobody cares about the first pitch of a game, for instance, or the middle out of the seventh inning during a Cubs-Rockies game in April—there are some pitches that we must absolutely know about. And if we consider what gives those pitches more value than other pitches—and surely everyone agrees that some pitches have more worth than others—then what we have to arrive at is that baseball doesn’t just take place on a diamond, but also takes place in time. Baseball is a narrative, not a pictorial, art.

To put it another way, what Milton does in his poem is just what a good golf architect does for the golf course: it isn’t enough to be told you should take a five-iron off this tee, while on another a three wood. The golfer has to be shown it: what you thought was one state of affairs was in fact another. And not merely that—because that, in itself, would only be another kind of telling—but that the golfer—or, at least, the reflective golfer—must come to see the point as he traverses the course. If a golf hole, in short, is a kind of sentence, then the assumptions with which he began the hole must be dashed by the time he reaches the green.

As it happens, this is just what the Golf Club Atlas says about the fourth at Chechessee Creek, where a “classic misdirection play comes.” At the fourth tee, “the golfer sees a big, long bunker that begins at the start of the fairway and hooks around the left side.” But the green is to the right, which causes the golfer to think “‘I’ll go that way and stay away from the big bunker.’” Yet, because there is a line of four small bunkers somewhat hidden down the right side, and bunkers to the right near the green, “the ideal tee ball is actually left center.” “Standing behind the hole”—that is, once play is over—“the left to right angle of the green is obvious and clearly shows that left center of the fairway is ideal,” which makes the fourth “the cleverest hole on the course.” And it is, so I’d argue, because it uses precisely the same technique as Milton.

That, in turn, might be the basis for an argument for why getting yardages by hand (or rather, foot) so necessary to the process of professional golf at the highest level. As I mentioned, amateur golfers think golf is about hitting shots while professionals know that golf is selecting what shots to hit. Amateurs look at a golf hole and think, “What a pretty picture,” while a professional looks at one and thinks of the sequence of shots it would take to reach the goal. That’s why it is so that, even though so much of golf design is mostly conjured by way of pretty pictures, whether in oils or photographic, and it might be thought that pictures, since they are “artistic,” are antithetical to the mechanistic forces of computers, it might be thought that it is the beauty of golf courses that make the game irreducible to analysis—an idea that, in fact, gets things precisely wrong.

Machines, that is, can paint a picture of a hole that can’t be beat: just look at the innumerable golf apps available for smart phones. But computers can’t parse a sentence like “Time flies like an arrow; fruit flies like a banana.” While computers can call (nearly) every pitch over the course of a season, they don’t know why a pitch in the seventh inning of a World Series game is more important than a spring training game. If everything is right there in front of you, then computers or some other mechanical aids are quite useful; it’s only when the end of a process causes you to re-evaluate everything that came before that you are in the presence of the human. Working out yardages without the aid of a machine forces the kind of calculations that can see a hole in time, not in space—to see a hole as a sequence of events, not (as it were) a whole.

Golf isn’t just the ability to hit shots—it’s also, and arguably more significantly, the ability to decide what the best path to the hole is. One argument for why further automation wouldn’t harm the game in the slightest is the tale told by baseball umpiring: no matter how far technological answers are sought, it’s still the case that human beings must be involved in calling balls and strikes, even if not in quite the same way as now. Some people, that is, might read Milton’s warning about astronomy as saying that pursuing that avenue of knowledge is a blind alley, when what Milton might instead be saying is just that the mistake is to think that there could be an end to the pursuit: that is, that perfect information could yield perfect decision-making. We extend “human perception” all we like—it will not make a whit of difference.

Milton thought that was because of our status as Original Sinners, but it isn’t necessary to take that line to acknowledge limitations, whether they are of the human animal in general or just endemic to living in a material universe. Some people appear to take this truth as a bit of a downer: if we cannot be Gods, what then is the point? Others, and this seems to be the point of Paradise Lost, take this as the condition of possibility: if we were Gods, then golf (for example) would be kind of boring, as merely the attempt to mechanically re-enact the same (perfect) swing, over and over. But Paradise Lost, at least in one reading, seems to assure us that that state is unachievable. As technology advances, so too will human cleverness: Bobby Jones can never defeat Walter Hagen once and for all.

Yet, as the example of Bob Gibson demonstrates, trusting to the idea that, somehow, everything will balance out in the end is just as dewy-eyed as anything else. Sports can ebb and flow in popularity: look at horse racing or boxing. Baseball reacted to Gibson’s 13 shutouts and Denny McLaine’s 31 victories in 1968, as well as Carl Yastrzemski’s heroic charge to a .301 batting average, the lowest average ever to win the batting crown. Throughout the 1960s, says Bill James in The New Bill James Historical Abstract, Gibson and his colleagues competed in a pitcher’s paradise: “the rules all stacked in their favor.” In 1969, the pitcher’s mound was lowered from 15 to 10 inches high and the strike zone was squeezed too, from the shoulders to the armpits, and from the calves to the top of the knee. The tide of the rules began to swing the other way, until the offensive explosion of the 1990s.

Nothing, in other words, happens in a vacuum. Allowing perfect yardages, so I would suspect, advantages the ballstrikers at the expense of the crafty shotmakers. To preserve the game then—a game which, contrary to some views, isn’t always the same, and changes in response to events—would require some compensating rule change in response. Just what that might be is hard, for me at least, to say at the moment. But it’s important, if we are to still have the game at all, to know what it is and is not, what’s worth preserving and why we’d like to preserve it. We can sum it up, I think, in one sentence. Golf is a story, not a picture. We ought to keep that which allows golf to continue to tell us the stories we want—and, perhaps, need—to hear.

The Weight We Must Obey

The weight of this sad time we must obey,
Speak what we feel, not what we ought to say.
King Lear V,iii

There’s a scene in the film Caddyshack that at first glance seems like a mere throwaway one-liner, but that rather neatly sums up what I’m going to call the “Kirby Puckett” problem. Ted Knight’s Judge Smails character asks Chevy Chase’s Ty Webb character about how if Webb doesn’t, as he claims, keep score, then how does he measure himself against other golfers? “By height,” Webb replies. It’s a witty enough reply on its own of course. But it also (and perhaps there’s a greater humor to be found here) raises a rather profound question: is there a way to know someone is a great athlete—aside from their production on the field? Or, to put the point another way, what do bodies tell us?

I call this the “Kirby Puckett” problem because of something Bill James, the noted sabermetrician and former , once wrote in his New Historical Baseball Abstract: “Kirby Puckett,” James observed, “once said that his fantasy was to have a body like Glenn Braggs’.” Never heard of Glenn Braggs? Well, that’s James’ point: Glenn Braggs looked like a great ballplayer—“slender, fast, very graceful”—but Kirby Puckett was a great ballplayer: a first-ballot Hall of Famer, in fact. Yet despite his own greatness—and surely Kirby Puckett was aware he was, by any measure, a better player than Glenn Braggs—Puckett could not help but wish he appeared “more like” the great player he, in reality, was.

What we can conclude from this is that a) we all (or most of us) have an idea of what athletes look like, and b) that it’s extremely disturbing when that idea is called into question, even when you yourself are a great athlete.
This isn’t a new problem, to be sure. It’s the subject, for instance, of Moneyball, the book (and the movie) about how the Oakland A’s, and particularly their general manager Billy Beane, began to apply statistical analysis to baseball. “Some scouts,” wrote Michael Lewis in that book, about the difference between the A’s old and the new ways of doing things, “still believed they could tell by the structure of a young man’s face not only his character but his future in pro ball.” What Moneyball is about is how Beane and his staff learned to ignore what their eyes told them, and judge their players solely on the numbers.

Or in other words, to predict future production only by past production, instead of by what appearances appeared to promise. Now, fairly obviously that doesn’t mean that coaches and general managers of every sport need to ignore their players’ appearances when evaluating their future value. Indisputably, many different sports have an ideal body. Jockeys, of course, are small men, whereas football players are large ones. Basketball players are large, too, but in a different way: taller and not as bulky. Runners and bicyclists have yet a different shape. Pretty clearly, completely ignoring those factors would lead any talent judge far astray quickly.

Still, the variety of successful body types in a given sport might be broader than we might imagine—and that variety might be broader yet depending on the sport in question. Golf for example might be a sport with a particularly broad range of potentially successful bodies. Roughly speaking, golfers of almost any body type have been major champions.

“Bantam” Ben Hogan for example, greatest of ballstrikers, stood 5’7” and weighed about 135 pounds during his prime, and going farther back Harry Vardon, who invented the grip used almost universally today and won the British Open six times, stood 5’9” and weighed about 155 pounds. But alternately, Jack Nicklaus was known as “Fat Jack” when he first came out on tour—a nickname that tells its own story—and long before then Harry Vardon had competed against Ted Ray, who won two majors of his own (the 1912 British and the 1920 U.S. Opens)—and was described by his contemporaries as “hefty.” This is not even to bring up, say, John Daly.

The mere existence of John Daly, however, isn’t strong enough to expand our idea of what constitutes an athlete’s body. Golfers like Daly and the rest don’t suggest that the overweight can be surprisingly athletic; instead, they provoke the question of whether golf is a sport at all. “Is Tiger Woods proof that golf is a sport, or is John Daly confirmation to the contrary?” asks a post on Popular Science’s website entitled “Is Golf a Sport?” There’s even a Facebook page entitled “Golf Is Not a Sport.”

Facebook pages like the above confirm just how difficult it is to overcome our idealized notions of what athletes are. It’s to the point that if somebody, no matter how skillful his efforts, doesn’t appear athletic, then we are more likely to narrow our definition of athletic acts rather than expand our definition of athletic bodies. Thus, Kirby Puckett had trouble thinking of himself as an athlete, despite that he excelled in a sport that virtually anyone will define as one.

Where that conclusion could (and, to some minds, should) lead us is to the notion that a great deal of what we think of as “natural” is, in fact, “cultural”—that favorite thesis of the academic Left in the United States, the American liberal arts professors proclaiming the good news that culture trumps nature. One particular subspecies of the gens is the supposedly expanding (aaannnddd rimshot) field called by its proponents “Fat Studies,” which (according to Elizabeth Kolbert of The New Yorker) holds that “weight is not a dietary issue but a political one.” What these academics think, in other words, is that we are too much the captives of our own ideas of what constitutes a proper body.

In a narrow (or, anti-wide) sense, that is true: even Kirby Puckett was surprised that he, Kirby Puckett, could do Kirby Puckett-like things while looking like Kirby Puckett. To the academics involved in “Fat Studies” his reaction might be a sign of “fatphobia, the fear and hatred of fatness and fat people.” It’s the view of Kirby Puckett, that is, as self-hater; one researcher, it seems, has compared “fat prejudice … to anti-semitism.” In “a social context in which fat hatred is endemic,” this line of thinking might go, even people who achieve great success with the bodies they have can’t imagine that success without the bodies that culture tells them ought to be attached to it.

What this line of work might then lead us to is the conclusion that the physical dimensions of a player matter very little. That would make the success of each athlete largely independent (or not) of physical advantage—and thereby demonstrate that thousands of coaches everywhere would, at least in golf, be able to justify asserting that success is due to the “will to succeed” rather than a random roll of the genetic dice. It might mean that nations looking (in expectation perhaps of the next Summer Olympics, where golf will be a medal sport) to achieve success in golf—like, for instance, the Scandinavian nations whose youth athletics programs groom golfers, or nations like Russia or China with a large population but next to no national golf tradition—should look for young people with particular psychological characteristics rather than particular physical ones.

Yet whereas “Fat Studies” or the like might focus on Kirby Puckett’s self-image, Bill James instead focuses on Kirby Puckett’s body: the question James asks isn’t whether Puckett played well despite his bad self-image, bur rather whether Puckett played well because he actually had a good body for baseball. James asks whether “short, powerful, funny-looking kind of guy[s]” actually have an advantage when it comes to baseball, rather than the assumed advantage of height that naturally allows for a faster bat speed, among the other supposed advantages of height. “Long arms,” James speculates, “really do not help you when you’re hitting; short arms work better.” Maybe, in fact, “[c]ompressed power is more effective than diffuse power,” and James goes on to name a dozen or more baseball stars who all were built something like Honus Wagner, who stood 5’11” and weighed 200 pounds. Which, as it happens, was also about the stat line for Jack Nicklaus in his prime.

So too, as it happens, do a number of other golfers. For years the average height of a PGA Tour player was usually said to be 5’9”; these days, due to players like Dustin Johnson, that stat is most often said to be about 5’11”. Still—as remarked by the website Golf Today—“very tall yet successful golfers are a rarity.”I don’t have the Shotlink data—which has a record of every shot hit by a player on the PGA Tour since 2003—to support the idea that certain-sized guys of one sort or another had the natural advantage, though today it’s possible that it could easily be obtained. What’s interesting about even asking the question, however, is that it is a much-better-than-merely-theoretically-solvable problem—which significantly distinguishes it from that of the question that might be framed around our notions of what constitutes an athletic body, as might be done by the scholars of “Fat Studies.”

Even aside from the narrow issue of allocating athletic resources, however, there’s reason for distrusting those scholars. It’s true, to be sure, that Kirby Puckett’s reaction to being Kirby Puckett might lend some basis for thinking that a critical view of our notions of what bodies are is salutary in an age where our notions of what bodies are and should be are—to add to an already-frothy mix of elements—increasingly driven by an advertising industry that, in the guise of either actors or models, endlessly seeks the most attractive bodies.

It would easier to absorb such warnings, however, were there not evidence that obesity is not remaining constant, but rather a, so to say, growing problem. As Kolbert reports, the federal government’s Centers for Disease Control, which has for decades done measurements of American health, found that whereas in the early 1960s a quarter of Americans were overweight, now more than third are. And in 1994, their results got written up in the Journal of American Medicine: “If this was about tuberculosis,” Kolbert reports about one researcher, “it would be called an epidemic.” Over the decade previous to that report Americans had, collectively, gained over a billion pounds.

Even if “the fat … are subject to prejudice and even cruelty,” in other words, that doesn’t mean that being that way doesn’t pose serious health risks both for the individual and for society as a whole. The extra weight carried by Americans, Kolbert for instance observes, “costs the airlines a quarter of a billion dollars’ worth of jet fuel annually,” and this isn’t to speak of the long-term health care costs that attach themselves to the public pocketbook in nearly unimaginable ways. (Kolbert notes that, for example, doors to public buildings are now built to be fifteen, instead of twelve, feet wide.)

“Fat Studies” researchers might claim in other words, as Kolbert says, that by shattering our expectations of what a body ought to be so thoroughly fat people (they insist on the term, it seems) can shift from being “revolting … agents of abhorrence and disgust” to “‘revolting’ in a different way … in terms of overthrowing authority, rebelling, protesting, and rejecting.” They might insist that “corpulence carries a whole new weight [sic] as a subversive cultural practice.” In “contrast to the field’s claims about itself,” says Kolbert however, “fat studies ends up taking some remarkably conservative positions,” in part because it “effectively allies itself with McDonald’s and the rest of the processed-food industry, while opposing the sorts of groups that advocate better school-lunch programs and more public parks.” In taking such an extreme position, in short, “Fat Studies” ends up only strengthening the most reactionary policy tendencies.

As, logically speaking, it must. “To claim that some people are just meant to be fat is not quite the same as arguing that some people are just meant to be poor,” Kolbert observes, “but it comes uncomfortably close.” Similarly, to argue that our image of a successfully athletic body is tyrannical can, if not done carefully, be little different from the fanatical coach who insists that determination is the only thing separating his charges from championships. Maybe it’s true that success in golf, and other sports, is largely a matter of “will”—but if it is, wouldn’t it be better to be able to prove it? If it isn’t, though, that would certainly enable a more rational distribution of effort all the way around: from the players themselves (who might thereby seek another sport at an earlier age) to recruiters, from national sporting agencies to American universities, who would then know what they sought. Maybe, in other words, measuring golfers by height isn’t so ridiculous at all.