Of Pale Kings and Paris

 

I saw pale kings and princes too …
—John Keats.
“La Belle Dame Sans Merci” (1819).

… and the pale King glanced across the field
Of battle, but no man was moving there …
Alfred Tennyson.
Idylls of the King: The Passing of Arthur (1871).

 

“It’s difficult,” the lady from Boston was saying a few days after the attacks in Paris, “to play other courses when your handicap is established at an easy course like this one.” She was referring to the golf course to which I have repaired following an excellent autumn season at Medinah Country Club: the Chechessee Creek Club, just south of Beaufort, South Carolina—a course that, to some, might indeed appear to be an easy course. Chechessee measures just barely more than 6000 yards from the member tees and, like all courses in the Lowcountry, it is virtually tabletop flat—but appearances are deceptive. For starters, the course is short on the card because it has five par-three holes, not the usual four, and the often-humid and wet conditions of the seacoast mean that golf shots don’t travel as they do in drier and more elevated locations. So in one sense, the lady was right—in precisely the same sense, as I suspect the lady was not aware, that Martin Heidegger, writing at an earlier moment of terror and the movements of peoples, was right.

Golf course architecture of course might be viewed as remote from the preoccupations of Continental theory as the greens of the Myopia Hunt Club, the lady’s home golf course, are from, say, the finish line of the Boston Marathon. Yet, just as Martin Heidegger is known as an exceptionally, even historically, difficult writer, Myopia Hunt Club is justly known to the elect as an exceptionally, even historically, difficult golf course. At the seventh U.S. Open in 1901—the only Open in which no competitor managed to break 80—the course established the record for highest winning score of a U.S. Open: a 331 shot by both Willie Anderson (who died tragically young) and Alex Smith that was resolved by the first playoff in the Open’s history. (Anderson’s 85 just edged Smith’s 86). So the club earned its reputation for difficulty.

The nature of those difficulties are, in fact, the very same ones those who like the Chechessee Creek Club trumpet: the deeper mysteries of angles, of trompe l’oiel, the various artifices by which the architects of golf’s Golden Age created the golf courses still revered today and whose art Coore and Crenshaw, Chechesee’s designers, have devoted their careers to recapture. Like Chechessee, Myopia Hunt isn’t, and never was, especially long: for most of its history, it has played around 6500 yards, which even at the beginning of the twentieth century wasn’t remarkable. Myopia Hunt is a difficult golf course for reasons entirely different than difficult golf courses like Medinah or Butler National are difficult: they are not easily apparent.

Take, for example, the 390-yard fourth: the contemporary golf architect Tom Doak once wrote that it “might be the best hole of its length in the free world.” A dogleg around a wetland, the fourth is, it seems, the only dogleg on a course of straight holes—in other words, slightly but not extraordinarily different from the other holes. However the hole’s green, it seems, is so pitched that a golfer in one of the course’s Opens (there have been four; the last in 1908) actually putted off the green—and into the wetland, where he lost the ball. (This might qualify as the most embarrassing thing that has ever happened to a U.S. Open player.) The dangers at Myopia are not those of a Medinah or a Butler National—tight tee shots to far distant greens, mainly—but are instead seemingly-minor but potentially much more catastrophic.

At the seventh hole, according to a review at Golf Club Atlas, the “members know full well to land the ball some twenty yards short of the putting surface and allow for it to bumble on”—presumably, players who opt differently will suffer an apocalyptic fate. In the words of one reviewer, “one of the charms of the course” is that “understanding how best to play Myopia Hunt is not immediately revealed.” Whereas the hazards of a Butler or Medinah are readily known, those at Myopia Hunt are, it seems, only revealed when it is too late.

It’s for that reason, the reviewer goes on to say, that the club had such an impact on American golf course design: the famed Donald Ross arrived in America the same year Myopia Hunt held its first Open, in 1898, and spent many years designing nearby courses while drawing inspiration by visiting the four-time Open site. Other famous Golden Age architects also drew upon Myopia Hunt for their own work. As the reviewer above notes, George Thomas and A.W. Tillinghast—builders of some of the greatest American courses—“were influenced by the abundant placement and penal nature of the hazards” (like the wetland next to the fourth’s green) at Myopia Hunt. Some of America’s greatest golf courses were built by architects with first-hand knowledge of the design style pioneered and given definition by Myopia Hunt.

Coore and Crenshaw—the pale kings of American golf architecture—like to advertise themselves as champions of this kind of design: a difficulty derived from the subtle and the non-obvious, rather than simply by requiring the golfer to hit the ball really far and straight. “Theirs,” says the Coore and Crenshaw website, “is an architectural firm based upon the shared philosophy that traditional, strategic golf is the most rewarding.” Chechessee, in turn, is meant to be a triumph of their view: according to their statement on Chechesee’s website, Coore and Crenshaw’s goal when constructing it “was to create a golf course of traditional character that would reward thoughtful, imaginative, and precise play,” and above all to build a course—like a book?—whose “nuances … will reveal themselves over time.” In other words, to build a contemporary Myopia Hunt.

Yet in the view of this Myopia Hunt member, Coore and Crenshaw failed: Chechessee is, for this lady, far easier than her nineteenth-century home course. Why is that? My speculation, without having seen Myopia Hunt, is that whereas Coore and Crenshaw design in a world that has seemingly passed by the virtues of the past, the Massachusetts course was designed on its own terms. That is, Coore and Crenshaw work within an industry where much of their audience has internalized standards that were developed by golf architects who themselves were reacting against the Golden Age architects like Tillinghast or Ross. Whereas Myopia Hunt Club can have a hole—the ninth—whose green is only nine yards wide and forty yards deep, the following generation of architects (and golfers) rejected such designs as “unfair,” and worked to make golf courses less “odd” or “unique.” So when Coore and Crenshaw come to design, they must work against expectations that the designer of Myopia Hunt Club did not.

Thus, the Golden Age designers were in the same position that, according to the German philosopher Martin Heidegger, the Pre-Socratic philosophers were: in a “brief period of authentic openness to being,” as the Wikipedia article about Heidegger says. That is, according to Heidegger the Pre-Socratics (the Greek philosophers, like Anaximander and Heraclitus and Parmenides, all of whom predated Socrates) had a relationship to the world, and philosophizing about it, that was unavailable to those who would come afterwards: they were able, Heidegger insinuates, to confront the world itself in a way different from those who came afterwards—after all, the latecomers unavoidably had to encounter the works of those very philosophers first.

Unlike his teacher then, Edmund Husserl—who “argued that all that philosophy could and should be is a description of experience”—Heidegger himself however thought that the Pre-Socratic moment was impossible to return to: hence, Heidegger claimed that “experience is always already situated in a world and in ways of being.” So while such a direct confrontation with the world as Husserl demands may have been possible for the Pre-Socratics, Heidegger is seemingly willing to allow, he also argues that history has long since closed off such a possibility, and thus forbade the kind of direct experience of the world Husserl thought of as philosophy’s object. In the same way, whereas the Golden Age architects confronted golf architecture in a raw state, no such head-on confrontation is now possible.

What’s interesting about Heidegger’s view, as people like Penn State professor Michael Berubé has pointed out, is that it has had consequences for such things as our understanding of, say, astronomical objects. As Berubé says in an essay entitled “The Return of Realism,” at the end of Heidegger’s massive Being and Time—the kind encyclopedic book that really emphasizes the “German” in “German philosophy”—Heidegger’s argument that we are “always already” implicated within previous thoughts implies that, for instance, it could be said that “the discovery of Neptune in 1846 could plausibly be described, from a strictly human vantage point, as the ‘invention’ of Neptune.” Or, to put it as Heidegger does: “Once entities have been uncovered, they show themselves precisely as entities which beforehand already were.” Before Myopia Hunt Club and other courses like it were built, there were no “rules” of golf architecture—afterwards, however, sayings like “No blind shots” came to have the weight of edicts from the Almighty.

For academic leftists like Berubé, Heidegger’s insight has proven useful, in a perhaps-paradoxical way. Although the historical Heidegger himself was a member of the Nazi Party, according to Berubé his work has furthered the project of arguing “the proposition that although humans may not be infinitely malleable, human variety and human plasticity can in principle and in practice exceed any specific form of human social organization.” Heidegger’s work, in other words, aims to demonstrate just how contingent a lot of what we think of as necessary is—which is to say that his work can help us to re-view what we have taken for granted, and perhaps see it with a glimpse of what the Pre-Socratics, or the Golden Age golf architects, saw. Even if Heidegger would also deny that such would ever be possible for us, here and now.

Yet, as the example of the lady from Myopia Hunt demonstrates, such a view has also its downside: having seen the original newness, she denies the possibility that the new could return. To her, golf architecture ended sometime around 1930: just as Heidegger thought that, some time around the time of Socrates, philosophy became not just philosophy, but also the history of philosophy, so too does this lady think that golf architecture has also become the history of golf architecture.

Among the “literary people” of his own day, the novelist and journalist Tom Wolfe once complained, could be found a similar snobbishness: “it is one of the unconscious assumptions of modern criticism,” Wolfe wrote, “that the raw material is simply ‘there,’” and from such minds the only worthy question is “Given such-and-such a body of material, what has the artist done with it?” What mattered to these critics, in other words, wasn’t the investigatory reporting done by such artists as Balzac or Dickens, Tolstoy or Gogol, but rather the techniques each artist applied to that material. The human misery each of those writers witnessed and reported, this view holds Wolfe says, is irrelevant to their work; rather, what matters is how artfully that misery is arranged.

It’s a conflict familiar both to literary people and the people that invented golf. The English poets, like Keats and Tennyson, who invented the figure of the Pale King were presumably drawing upon a verse well-known to King James’ translators; literary folk who feared the cost of seeing anew. The relevant verse, imaginably the source of both Keats and Tennyson, is from the James translation of the Book of Revelations (chapter 6, verse 8):

And I looked, and behold a pale horse:
and his name that sat on him was Death,
and Hell followed with him.

But opponents of the Auld Enemy saw the new differently; as novelist John Updike once reported, according the “the old Scots adage,”

We should be conscious of no more grass …
than will cover our own graves.

To the English, both heirs to and inventors of a literary tradition, the Pale King was a terrible symbol of the New, the Young, and the Unknown. But to their ancient opponents, the Scots, the true fear was to be overly aware of the past, at the expense of welcoming in the coming age. As another Celt from across the sea, W. B. Yeats, once put the same point:

Be not inhospitable to strangers,
lest they be angels in disguise.

Parisians put the same point in the aftermath of the shootings and bombings that Friday evening on Twitter by using the hashtag “#PorteOuverte”—a slogan by which, in the aftermath of the horror, thousands of Parisians offered shelter to strangers from whatever was still lurking in the darkness. To Parisians, like the Scots before them, what matters is not whether the Pale King arrives, but our reaction when he does.

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At Play In The Fields Of The Lord

Logo for 2015 US Amateur at Olympia Fields Country Club
Logo for 2015 US Amateur at Olympia Fields Country Club

 

Behold, I send you forth as sheep in the midst of wolves:
be ye therefore wise as serpents, and harmless as doves.
—Matthew 10:16

Now that the professional, Open tournaments are out of the way, the U.S. Amateur approaches. A tournament that has always been a symbol of wealth and discrimination—the Amateur was a tournament invented specifically to keep out the riff-raff of professional golfers—the site of this year’s edition might be considered particularly unfortunate considering that this year the tournament will fall just more than a year after the Michael Brown shooting in Ferguson, Missouri: Olympia Fields, in Chicago’s south suburbs, is a relatively wealthy enclave among a swath of exceedingly poor villages and towns very like the terrain of the St. Louis suburbs just a few hundred miles away. Yet there’s a deeper irony at work here that might be missed even by those who’d like to point out that similarity of setting: the format of the tournament, match-play, highlights precisely what the real message of the Brown shooting was. That real message, the one that is actually dangerous to power, wasn’t the one shouted by protestors—that American police departments are “racist.” The really dangerous message is the one echoed by the Amateur: a message that, read properly, tells us that our government’s structure is broken.

The later rounds of U. S. Amateur are played under golf’s match play, rather than stroke play, rules—a difference that will seem arcane to those unfamiliar with the sport, but is a very significant difference nevertheless. In stroke play, competitors play whatever number of holes are required—in professional tournaments, usually 72 holes—and count up however many strokes each took: the player with the fewest strokes wins. Match play however is not the same: in the first place, because in stroke play each golfer is effectively playing against every other player in the field, because all the strokes of every player count. But this is not so in match play.

In the first place, match play consists of, as the name suggests, matches: that is, once the field is cut to the 64 players with the lowest score after an initial two-day stroke play tournament, each of those 64 contestants plays an 18-hole match against one other contestant. The winner of each of these matches then proceeds to move on, until there is a champion—a single-elimination tournament that is exactly like the NCAA basketball tournament held every year in March. The winner of each match in turn, as John Van der Borght says on the website of the United States Golf Association, “is the player who wins the most holes.” That is, what matters on every hole is just whether the golfer has shot a lower score than the opponent for that hole, not overall. Each hole starts the competition again, in other words—like flipping coins, what happened in the past is irrelevant. It’s a format that might sound hopeful, because on each hole whatever screw-ups a player commits are consigned to the dustbin of history. In fact, however, it’s just this element that makes match-play the least egalitarian of formats—and ties it to Ferguson.

Tournaments conducted under match play rules are always subject to a kind of mathematical oddity called a Simpson’s Paradox: such a paradox occurs when, as the definition on Wikipedia says, it “appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.” For example, as I have mentioned in this blog before, in the first round of the PGA Tour’s 2014 Accenture Match Play tournament in Tucson, an unknown named Pedro Larrazabal shot a 68 to Hall-of-Famer Ernie Els’ 75—but because they played different opponents, Larrazabal was out of the tournament and Els was in. Admittedly, even with such an illustration the idea might still sound opaque, but the meaning can be seen by considering, for example, the tennis player Roger Federer’s record versus his rival Rafael Nadal.

Roger Federer has won 17 major championships in men’s tennis, a record—and yet many people argue that he is not the Greatest Of All Time (G.O.A.T.). The reason those people can argue that is because, as Michael Steinberger pointed in the New York Times not long ago, Federer “has a losing record against Nadal, and a lopsided one at that.” Steinberger then proceeded to argue why that record should be discarded and Federer should be called the “GOAT” anyway. But weirdly, Steinberger didn’t attempt—and neither, so far as I can tell, has anyone else—what an anonymous blogger did in 2009: a feat that demonstrates just what a Simpson’s Paradox is, and how it might apply both to the U.S. Amateur and Ferguson, Missouri.

What that blogger did, on a blog entitled SW19—a reference to the United Kingdom’s postal code for Wimbledon, the great tennis arena—was he counted up the points.

Let me repeat: he counted up the points.

That might sound trivial, of course, but as the writer of the SW19 blog realized, tennis is a game that abounds in Simpson’s Paradoxes: that is, it is a game in which it is possible to score fewer points than your opponent, but still win the match. Many people don’t realize this: it might be expected, for example, that because Nadal has an overwhelmingly-dominant win-loss record versus Federer, he must also have won an equally-dominant number of points from the Swiss champion. But an examination of the points scored in each of the matches between Federer and Nadal demonstrates that in fact the difference between them was miniscule.

The SW19 blogger wrote his post in 2009; at that time Nadal led Federer by 13 matches to 7 matches, a 65 percent winning edge for the Spaniard, Nadal. Of those 20 matches, Nadal won the 2008 French Open—played on Nadal’s best surface, clay—in straight sets, 6-1, 6-3, 6-0. In those 20 matches, the two men played 4,394 total points: that is, where one player served and the two volleyed back and forth until one player failed to deliver the ball to the other court according to the rules. If tennis had a straightforward relationship between points and wins—like golf’s stroke play format, in which every “point” (stroke) is simply added to the total and the winner has the fewest points—then it might be expected that Nadal has won about 65 percent of those 4,394 points played, which would be about 2,856 points. In other words, to get a 65 percent edge in total matches, Nadal should have about a 65 percent edge in total points: the point total, as opposed to the match record, between the two ought to be about 2,856 to 1,538.

Yet this, as the SW19 blogger realized, is not the case: the real margin between the two players was Nadal, 2,221, and Federer, 2,173. In other words, even including the epic beating at Roland Garros in 2008, Nadal had only beaten Federer by a total of 48 points over the course of their careers–a total of less than one percent of all the points scored. Not merely that, but if that single match at the 2008 French Open is excluded, then the margin becomes eight points.  The mathematical difference between Nadal and Federer, thus, is the difference between a couple of motes of dust on the edge of a coin while it’s being flipped—if what is measured is the act that is the basis of the sport, the act of scoring points. In terms of points scored, Nadal’s edge is about a half of percentage point—and most of that percentage was generated by a single match. But Nadal had a 65 percent edge in their matches.

How did that happen? The answer is that the structure of tennis scoring is similar to that of match play in golf: the relation between wins and points isn’t direct. In fact, as the SW19 blogger shows, of the twenty matches Nadal and Federer had played to that moment in 2009, Federer had actually scored more points than Nadal in three of them—and still lost the match. If there were a direct relation between points and wins in tennis, that is, the record between Federer and Nadal would actually stand even, at 10-10, instead of what it was in reality, 13-7—a record that would have accurately captured the real point differential between them. But because what matters in tennis isn’t—exactly—the total number of points you score, but instead the numbers of games and sets you win, it is entirely possible to score more points than your opponent in a tennis match—and still lose. (Or, the converse.)

The reason why that is possible, as Florida State University professor Ryan Rodenberg put it in The Atlantic not long ago, is due to “tennis’ decidedly unique scoring system.” (Actually, not unique, because as might be obvious by now match play golf is scored similarly.) In sports like soccer, baseball, or stroke play golf, as sports psychologist Allen Fox once wrote in Tennis magazine, “score is cumulative throughout the contest … and whoever has the most [or, in the case of stroke play golf, least] points at the end wins.” But in tennis things are different: “[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.” Just in the same way that what matters in tennis is the game, not the point, in match play golf all that matters is the hole, and not the stroke.

Such scoring systems breed Simpson’s Paradoxes: that is, results that don’t reflect the underlying value a scoring system is meant to reflect—we want our games to be won by the better player, not the lucky one—but instead are merely artifacts of the system used to measure. The point (ha!) can be shown by way of an example taken from a blog written by one David Smith, head of marketing for a company called Revolution Analytics, about U.S. median wages. In that 2013 post, Smith reported that the “median US wage has risen about 1%, adjusted for inflation,” since 2000. But was that statistic important—that is, did it measure real value?

Well, what Smith found was that wages for high school dropouts, high school graduates, high school graduates with some college, college graduates, and people with advanced degrees all fell over the same period. Or, as Smith says, “within every educational subgroup, the median wage is now lower than it was in 2000.” But how can it be that “overall wages have risen, but wages within every subgroup have fallen?” The answer is similar to the reason why Rafael had a 65 percent winning margin against Federer: although there are more college graduates now than in 2000, the wages of college graduates haven’t fallen (1.2%) as far as, say, high school dropouts (7.9%). So despite the fact that everyone is poorer—everyone is receiving lower wages, adjusted for inflation—than in 2000, mendacious people can say wages are actually up. Wages are up—if you “compartmentalize” the numbers in just the way that reflects the story you’d like to tell.

Now, while the story about American wages might suggest a connection to Ferguson—and it does—that isn’t the connection between the U.S. Amateur and Ferguson, Missouri, I’d like to discuss. That connection is this one: if the trouble about the U.S. Amateur is that it is conducted under match play—a format that permits Simpson’s Paradox results—and Simpson’s Paradoxes are, at heart, boundary disputes—arguments about whether to divide up the raw data into smaller piles or present them as one big pile—then that suggests the real link to Ferguson because the real issue behind Darren Wilson’s shooting of Michael Brown then isn’t racism—or at least, the way to solve it isn’t to talk about racism. Instead, it’s to talk borders.

After Ferguson police officer Darren Wilson shot Michael Brown last August, the Department of Justice issued a report that was meant, as Zoë Carpenter of The Nation wrote this past March, to “address the roots of the police force’s discriminatory practices.” That report held that those practices were not “simply the result of racist cops,” but instead stemmed “from the way the city preys on residents financially, relying on the fines that accompany even minor offenses to balance its budget.” The report found an email from Ferguson’s finance director to the town’s police chief that, Carpenter reported, said “unless ticket writing ramps up significantly before the end of the year, it will be hard to significantly raise collections next year.” The finance director’s concerns were justified: only slightly less than a quarter of Ferguson’s total budget was generated by traffic tickets and other citations. The continuing operation of the town depends on revenue raised by the police—a need, in turn, that drives the kind of police zealotry that the Department of Justice said contributed to Brown’s death.

All of which might seem quite far from the concerns of the golf fans watching the results of the matches at the U.S. Amateur. Yet consider a town not far from Ferguson: Beverly Hills, Missouri. Like Ferguson, Beverly Hills is located to the northwest of downtown St. Louis, and like Ferguson it is a majority black town. But where Ferguson has over 20,000 residents, Beverly Hills has only around 600 residents—and that size difference is enough to make the connection to the U.S. Amateur’s format of play, match play, crystalline.

Ferguson after all is not alone in depending so highly on police actions for its revenues: Calverton Park, for instance, is another Missouri “municipality that last fiscal year raised a quarter of its revenue from traffic fines,” according to the St. Louis Post-Dispatch. Yet while Ferguson, like Calverton Park, also raised about a quarter of its budget from police actions, Beverly Hills raised something like half of its municipal budget on traffic and other kinds of citations, as a story in the Washington Post. All these little towns, all dependent on traffic tickets to meet their budgets; “Most of the roughly ninety municipalities in St. Louis County,” Carpenter reports in The Nation, “have their own courts, which … function much like Ferguson’s: for the purpose of balancing budgets.” Without even getting into the issue of the fairness of property taxes or sales taxes as a basis for municipal budgeting, it seems obvious that depending on traffic tickets as a major source of revenue is poor planning at best. Yet without the revenue provided by cops writing tickets—and, as a result of Ferguson, the state of Missouri is considering limiting the percentage of a town’s budget that can be raised by such tickets, as the St. Louis Dispatch article says—many of these towns will simply fail. And that is the connection to the U.S. Amateur.

What these towns are having to consider in other words is, according to the St. Louis Post-Dispatch, an option mentioned by St. Louis County Executive Steve Stenger last December: during an interview, the official said that “the consolidation of North County municipalities is what we should be talking about” in response to the threat of cutting back reliance on tickets. Small towns like Beverly Hills may simply be too small: they create too little revenue to support themselves without a huge effort on the part of the police force to find—and thus, in a sense, create—what are essentially taxable crimes. The way to solve the problem of a “racist” police department, in other words, might not be to conduct workshops or seminars in order to “retrain” the officers on the frontline, but instead to redrawn the political boundaries of the greater St. Louis metropolitan area.

That, at least, is a solution that our great-grandparents considered, as an article by writer Kim-Mai Cutler for Tech Crunch this past April remarked. Examining the historical roots of the housing crisis in San Francisco, Cutler discovered that in “1912, a Greater San Francisco movement emerged and the city tried to annex Oakland,” a move Oakland resisted. Yet as a consequence of not creating a Bay-wide government, Cutler says, “the Bay Area’s housing, transit infrastructure and tax system has been haunted by the region’s fragmented governance” ever since: the BART (Bay Area Regional Transit) system, for example, as originally designed “would have run around the entire Bay Area,” Cutler says, “but San Mateo County dropped out in 1961 and then Marin did too.” Many of the problems of that part of Northern California could be solved, Cutler thusly suggests via this and other instances—contra the received wisdom of our day—by bigger, not smaller, government.

“Bigger,” that is, in the sense of “more consolidated”: by the metric of sheer numbers, a government built to a larger scale might not employ as many people as do the scattered suburban governments of America today. But what such a government would do is capture all of the efficiencies of economies of scale available to a larger entity—thus, it might be in a sense smaller than the units it replaced, but definitely would be more powerful. What Missourians and Californians—and possibly others—may be realizing then is that the divisions between their towns are like the divisions tennis makes around its points, or match play golf makes around its strokes: dividing a finite resource, whether points or strokes or tax dollars (or votes), into smaller pools creates what might be called “unnatural,” or “artificial,” results—i.e., results that inadequately reflect the real value of the underlying resource. Just like match play can make Ernie Els’ 75 look better than Pedro Larrazabal’s 68, or tennis’ scoring system can make Rafael Nadal look much better than Federer—when in reality the difference between them is (or was) no more than a sliver of a gnat’s eyelash—dozens of little towns dissipate the real value, economic and otherwise, of the people that inhabit a region.

That’s why when Eric Holder, Attorney General for the United States, said that “the underlying culture” of the police department and court system of Ferguson needs to be reformed, he got it exactly wrong. The problems in St. Louis and San Francisco, the evidence suggests, are created not because government is getting in the way, but because government isn’t structured correctly to channel the real value of the people: scoring systems that leave participants subject to the vagaries of Simpson’s Paradox results might be perfectly fine for games like tennis or golf—where the downsides are minimal—but they shouldn’t be how real life gets scored, and especially not in government. Contra Holder, the problem is not that the members of the Ferguson police department are racists. The problem is that the government structure requires them, like occupying soldiers or cowboys, to view their fellow citizens as a kind of herd. Or, to put the manner in a pithier way: A system that depends on the harvesting of sheep will turn its agents into wolves. Instead of drowning the effects of racism—as a big enough government would through its very size—multiplying struggling towns only encourages racism: instead of diffusing racism, a system broken into little towns focuses it. The real problem of Ferguson then—the real problem of America—is not that Americans are systematically discriminatory: it’s that the systems used by Americans aren’t keeping the score right.

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.

April Cruel

“Well now that’s done: and I’m glad it’s over”
—T.S. Eliot
The Wasteland

According to a friend whose golfer narrowly missed the cut and, thus, spent Friday staring at the leaderboard as it clicked and clacked, sometime as that drowsy south Georgia afternoon drawled on toward sundown my golfer had been tied for ninth, and perhaps even as high as seventh. It may, for all I know, be possible to reconstruct events using tee times and the full leaderboard, but in the event I slept pretty well with the knowledge that, as Friday slipped into Friday night, we stood at tied for eleventh. Part of the myth of golf is that underdogs and unknowns can suddenly leap up from nowhere—a century ago near Boston, at the Country Club in Brookline, the former caddie Francis Ouimet beat the two British champions Harry Vardon and Ted Ray. But in pro golf, Friday afternoon is about as far from Sunday night as Galveston is from El Paso.

Still, if Sunday’s a week from Friday, Friday is a month from Monday, which is when professional tournaments hold their “qualifying tournaments.” These are 18 hole shootouts open to anybody with 450 bucks and the requisite USGA-certified handicap. Usually they consist of around 80 brave souls willing to wager their money against the chance of shooting low enough to get one of the five or six or so tee times assigned to “qualifiers.” Those “tournaments before the tournament” last all day, because everyone’s spending forever on their putts and so on, and then end with some kind of playoff for the last tee time available in the tournament proper: often there are four or more guys playing for one or more of the last remaining slots.

Qualifiers are thus always the last to be looking for a caddie. They show up to the tournament golf course on Tuesday morning with haunted and hunted looks, furtively searching out the faces of the loopers hanging out in the parking lots and wondering if one of those guys might be the final piece of the puzzle that might enable them to escape from the hell of Monday qualifying forever—the only way for a player without status (that is, a player without a “tour card” gained by his past performance) to get into a tournament without Monday qualifying is by finishing in the top twenty-five places in the previous week’s tournament. Conversely, the Monday qualifier is the time-honored way for a new caddie to learn his trade and break into the business—the “Mondayer,” as they’re called, gets you out of the parking lot and onto the golf course, where you can be seen by other, better-established, players.

I’d picked up my player in said time-honored fashion, in the parking lot on Tuesday. “Hey,” I said to the golfer carrying (as opposed to the light carry bags most Monday qualifiers have) a technicolor tour staff bag, “Are you set for the week?” No, the guy replied. But he wanted to look around a bit first. After this initial encounter, my guru Mullet told me what would happen: “He’s going to go around and see that all the quality experienced guys are already locked up for the week. Then he’s going to come right back to you.” And that is what happened.

My player was, as his tour golf bag signified, an actual touring professional: he had, in fact, not only won on what was now called the Web.com Tour (formerly the Nationwide Tour, and before that the Nike and Hogan Tours) but had also won on the PGA Tour itself. It’s a small piece of knowledge, but it contained worlds about the realities of life on tour: another chunk would reveal itself when I learned that our playing partners on Thursday, when the tournament finally began, were Rich Beem, winner of the 2002 PGA Championship, and Len Mattiace, who lost the Masters to Mike Weir in a playoff in 2003. Both Beem and Mattiace had, once, been ranked in the top 50 of the world rankings; life on tour could go sidewise at any time.

As, in fact, things had for my pro: after winning on the PGA Tour, he’d fallen on hard times lately—as his financial guy, Tom (who looked remarkably like the best-friend-turned-manager character on Entourage) told me on the eve of the tournament’s start Wednesday night. He’d gotten a divorce and—though the causality appeared unclear—had played only twice since October of last year. Making it into the field for the South Georgia Classic, in other words, meant at least one more week avoiding going into the shirt-folding trade. A top twenty-five finish in this tournament, in turn, would ensure dodging that fate for yet another week.

His showing in the tournament, in sum, was terribly important to his future. Every shot hit was one step closer either to the life and security he’d felt as a tour winner, or one step farther away: which is to say, one step closer to the life he’d been dreaming of from childhood, or one step farther away. Rolling off the eighth tee box—a par three—that Wednesday, we were discussing baseball. I asked him what team he followed, given that he was from the South: the Braves, or some other team, for some idiosyncratic reason. He was not. He liked football; baseball, he said, had too many games. He attended the games of his state’s university, a large member of the SEC; they gave him access to the sidelines, apparently. No, he didn’t donate to the university. He didn’t appear to think of this as unusual; or rather, there was something about him that seemed to dare you to find something unusual about it.

Ever since Francis Ouimet, American golfers have participated in what Tom Wolfe, speaking about the original seven Project Mercury astronauts in The Right Stuff, calls the “magical” practice of single combat: where “the mightiest soldier of one army would fight the mightiest soldier of the other army as a substitute for pitched battle.” Wolfe notes one curious fact about the practice: “the honor and glory” granted to these warriors “were in many cases rewards before the fact; on account, as it were.” Golfers, like other athletes, participate in this economy: that’s why mine had access to the sidelines for every home game of his hometown college team (which wasn’t his alma mater). He’d been riding a gravy train with biscuit wheels ever since he was a teenager, in short, and now somebody was threatening to take it away.

It wasn’t then the ideal situation to be introduced to someone, much less to work for, and whether it was that circumstance, or some quirk to his personality, I quickly realized he wasn’t the most personable guy. He was curt: on Wednesday, I waited for him to come out of the clubhouse at the appointed time—he wasn’t there. I eventually found him on the opposite side of the practice range from most of the players: his first remark to me was a snide “I don’t think anyone practices at the clubhouse.” During our practice round, while I adjusted to the fact that he stood on the opposite side of the ball (he’s a lefty), he continually reminded me that he’d been a golf pro since 1997; I fought the urge to note that I’ve been looping since 1995.

Along about then, when I realized what sort of person I was dealing with, I approached an experienced caddie about my situation: the problem, I told him, was that I had not had a conversation about payment immediately. “You got to get your money straight right away,” he said, after listening to my story. He told me that not getting the money straight was unprofessional, “on both your parts”—but that the burden fell more heavily on the pro, who should have known better. That was an egg that would remain broken however, because if I tried to approach him now about it, I could easily end up fired because there were still caddies available.

With that kind of smoothly-functioning working relationship established, then, we went to battle on the longest golf course played by the Web.com Tour: Kinderlou Forest, outside Valdosta, Georgia. Designed by Davis Love III, it’s a strange track: in addition to a punishing length, the par-fives in particular have the peculiar feature of being both ridiculously long but also absurdly penal toward long hitters, through the use of contrived angles and forced perspectives. One of them actually called upon the players to hit away from the fairway. Not a single golfer I talked to had much praise for the course, other than to say that the maintenance was good: drolly, the eventual winner would afterwards observe that “You won’t see par fives like this anywhere else in the world.” The course, oblivious to the obvious irony, immediately put that up on the website.

Throughout the spring the Southeast had suffered heavy rains, which was good for Georgia farmers (Georgia has been undergoing a drought that some think may be related to global warming) but not so good for golfers. Due to the wet conditions, the already-monster long Kinderlou track was playing even longer: a tee shot that might, on a dry course, run out twenty yards or more was more or less staying where it landed. And in another way the course played slightly differently than its design: because of the need for grandstands and such as befitting a tour stop, the nines of the course were reversed, so that what was the first hole for normal play was the tenth for the tournament, and so on.

The history of our week is recorded, somewhere, in the servers of the PGA Tour’s ShotLink system, which records every shot hit by every golfer in every sanctioned tournament worldwide. That record will reflect a one-under par first round, a fine three-under second round (which launched us up the leaderboard, since birdies on such a golf course were as scarce as anti-smoking laws in Georgia), and then a one-over par third round—a setback, but not terribly so given how hard scoring was. Although his ballstriking was sometimes not the best, he had an excellent short game that papered over a lot. Everything appeared set for a nice Sunday walk that would nail down my player’s entry into the next week’s tournament and (perhaps) begin a heartwarming story of professional redemption.

Sunday was another sunny Georgia peach of a day, foretelling the oceans of heat that come in summer. We set off just inside the top twenty-five cutline that was our implicit objective—which, given how things had gone the past three days, translated into a sense that an under-par score would lock up next week. And he seemed to respond: on the first hole, where he’d missed an ideal fairway lie each of the three previous rounds, he striped one down the middle. In fact, he played his best golf of the week: by the time his putt fell on the eighth hole, he was three-under for the round, and six-under for the tournament. We weren’t just looking at getting into the next tournament, we just might have been about to make some serious money.

What—predictably—followed was perhaps the worst hour I’ve ever spent on a golf course. At the ninth, a badly-pushed drive ended up on the inside of the dogleg-left, blocked by trees that rejected his first recovery shot. The bogey save appeared to right the ship, but missing the tenth green from the fairway less than 150 yards from the pin augured poorly. And then came the eleventh.

The eleventh at Kinderlou (the second on its standard scorecard) is a monster par-five that, on tour, begins with a tee shot over a massive ravine. That accomplished, a long downhill second shot can reach the front of an elongated green canted at an angle to the fairway. Behind the green is a lateral water hazard (a swampy forest) while another sits eighty yards short and right. The fairway itself is hugely wide, but aside from those two hazards it’s lined by both forest and tall grass. Still, for a professional none of those potential dangers exist: the longest club most professionals would be considering these days might be a five-wood, which generally speaking is a remarkably easy club to hit.

Par-fives on the professional circuit, though, can take forever to play because each group has to wait for the previous one to clear the green. We waited next to the ball as the golfers in front of us putted out. And waited. As we did my player debated his options: perhaps he should hit a soft five wood to the front of the green, allowing for a simple chip up to the hole. Or a hard three iron that might chase on to the green itself. The downhill slope and hazard beyond the hole precluded hitting a three wood, though maybe he could choke it up a bit … and so forth. In the event, he chose the five wood. And pulled it into the hazard short and right of the green.

Just barely, however, as we discovered when eventually we found the ball. It was less than a foot inside the hazard line, facing the green, with no obstacles in the path of a swing. Admittedly, the ball was sitting on bare earth, but that also meant that there was nothing to get between the ball and the club—it was, in sum, about as good an outcome as was possible given the previous shot. Which is why it was such a surprise when he bladed the ball (hit it with the leading edge of the club, instead of the face of the club) over the green and into the hazard beyond.

The tragicomedy that followed isn’t worth rehearsing, other than to note that he missed a three-footer to save double-bogey. The tee shot on the next hole, apologetically yet inevitably, sailed into the forest on the right side of the fairway. Yelling at the marshall whose duty it was to find the ball had its cathartic properties, but didn’t help us locate it. The rest of the round passed by in a stew of anger, regret, and ugly emotions that went, in large part though not completely, unexpressed. In other words, it was a like a lot of golf rounds, only with the added spice of being able to calculate precisely how much money got spent by each futile swing.

Afterward, we walked in silence towards the Range Rover (!) that the player used to transport himself. I took a last look at the clubs I’d carried for what had been nearly a week now, checking to make sure there was no grass or red clay of southern Georgia still remaining. There was nothing. I put them into the back of the truck. There was nothing more to do than to get paid. Which was when my player said, “I’m going to have to get your information …”

In the moment, I froze: I didn’t particularly know what to do. I was getting stiffed. Nothing in my experience had prepared me for this: in club caddieing, no matter how much they don’t like you, they still have to pay you something. And the worst of it was that—golf being so individualistic—there would be no recourse. At a club, you can go to the caddiemaster, or the head pro. But in this situation, there didn’t appear to be any higher authority. I thought for a moment.

Immediately after leaving the parking lot, I went to a tour official and told him substantially the story I just relayed. The man I spoke with in Valdosta asked me if I was going to Athens, Georgia, the tour’s next stop; I said I was. He said that if I hadn’t heard from my player by Friday that week I should contact a certain higher official with the professional circuit’s bureaucracy, which I did after I had no word that week. That official told me the tour would be “all over it”—and, in fact, they were. I’ve never met people who were quite so concerned about whether I’d gotten payed properly.

Over the next couple of weeks I got several phone calls from the main office of the PGA Tour in Ponte Vedre, Florida. There was quite some to do about the whole thing; at one point it slipped that the phrase “conduct unbecoming” had become part of the conversation between the tour officials and the player. Apparently the tour frowns on players stiffing caddies—a concern that was really surprising, and not a little touching. It shouldn’t have been, I suppose, since presumably the motive was to protect the tour: if it became a widely accepted notion that professional golfers are not fine and upstanding gentlemen … well, there’s a reason for golf’s self-advertisement as a sport apart from all the others. It was nice of the tour to look out for my interests so rabidly, but I’m not under much illusion that their motives were solely about my well-being.

It was, perhaps more rather than less likely, a part of why, as Tom Wolfe remarks, when it comes to single combat warriors it’s important that “the proper emotion, the seemly sentiment, the fitting moral tone should be established and should prevail.” Part of the role of the single combat warrior is not only performing on the field, naturally, but also (and maybe crucially) performing the act of being the mannerly gentleman—said person must provide the public with “the correct feelings!” Indeed, this might be more important than the on-field part—as perhaps the opposing cases of Tim Tebow (who by all accounts is a perfect gentleman, but whose on-field performance has, on the whole, lacked) and Tiger Woods (pretty much opposite) alternately demonstrate. And my player, whose demeanor already destabilized that balance, threatened it yet further. They were out to get him.

To many, who approached me at various times over the next week, that was as it should be: the tour acted to protect the interests of the majority of, not only its players, but everyone associated with it—all the people whose jobs depend on the seemingly-magical ability of some to put a small white ball into a slightly larger hole in the ground. Others, I suppose, might decry what might be viewed as a kind of interference or intrusion into what is, in mythology, golf’s individualistic purity.

In a recent story about a naval officer who—really—shot down down one of our own planes (an F-4) with an American crew in 1987, but is now up for admiral, the Washingtonian magazine notes that, until recently, the military “endeavored to promote officers whose records were as close to perfect as possible.” “But the effect of the so-called zero-defect culture,” the magazine goes on to say, “was that the services raised up a generation of cautious, risk-averse bureaucrats who were judged on how well they followed procedures and … not for innovation.” The effect of intrusion into players’ affairs is, so the argument might go, detrimental to the tour: it’s no wonder that, as critics have been saying since the 1970s at least, the PGA Tour is full of “mindless drones.” Tiger, you might say, wasn’t right to do what he did—but he did judge correctly that he had to hide it behind that robotic facade.

Tiger’s judgment that, for whatever reason, golfers—and especially him—don’t get to be human, don’t get to make mistakes, ultimately demonstrates just how bankrupt that idea is, in this line of thought: hiding behind such criticism, I suspect, is the notion that there unnameable John Daly-type players who have the potential to WOW us if we’d only let them have the chance. That might, I suppose, be true in some hypothetical sense—but the fact of the matter is that my player, at least, has not really demonstrated that he belongs out on tour, despite the fact that he’s won. Part of the argument against granting people like John Daly second (or third, or sixteenth) chances is that behaving oneself is not a separate thing from playing golf well: part of playing golf well, in this conception, is the ability to continue to play well, which ultimately has to do with not only how one treats one’s body, but also with how one treats others.

What we are left with, in short, is two visions of golf and, perhaps, the world itself: in one vision, each of our skills is separable from the rest of ourselves. In the other, not: we are whole beings, entire to ourselves. Our skills are extensions, or expressions, of our innermost selves—or they are incidental, merely the reflection of time we have devoted (or, as the case may be, not devoted) to their practice. Golf, for the most part, comes down on the former side: “There has always been,” as Jerry Tarde, editor of Golf Digest, wrote recently, “the impression that success in golf was tied to inner character, as in the widespread belief that you can know the measure of a man by simply playing a round of golf with him.” It’s a lovely idea, I suppose. But I suspect that it’s about as far from reality as El Paso from Galveston.

In any case, I just got a check. I don’t know what the tour said to the player, but evidently it worked.

The Mark of Z

“One way to characterize professional golf,” wrote John Cassidy earlier this summer in The New Yorker, “is to say that it has reached parity—there are so many good players, and they all have a roughly equal chance of winning.” Cassidy called it the “random golfer theory,” and has trotted it out after Webb Simpson’s win at Olympic and Ernie Els’ win at Lytham. The idea is that anybody within the top 100 has a shot of winning any major: an idea that is, more or less, borne out by the fact that of the past 17 majors, there has been 17 winners. Until now, which is to say that Rory’s win at the PGA has blown that idea up just as surely as the events of the past five years has blown up both the Black-Scholes formula and the hype of this year’s Ryder Cup at Medinah to what will, especially in the Fleet Street press, be absurd levels.

The cry will be, as it’s been since McIlroy won the U.S. Open at Congressional a year ago, for a Tiger vs. Mac showdown during Sunday’s singles matches, only with an even heightened pitch now that Rory’s won his first two majors at a more rapid clip than Tiger won his first two. And as it happens, Tiger’s second major was also a PGA, and, also, it was at Medinah. Which, as it further happens, was also the first time Tiger faced a competitor who seemed to have all the tools he did, but was from Europe—and younger to boot. And after that PGA, in 1999, Sergio Garcia, like Rory’s fans today, demanded to play Tiger in that year’s Ryder Cup.

Obviously, European fans are hoping for a different outcome this time around: that Ryder Cup was at the Country Club in Brookline, and the Euros got smoked in singles; that was the year that the American captain, Ben Crenshaw, said the night before the finale, “I got a good feeling about this.” It was also the year of the “excessive celebration” after Justin Leonard made his putt on the 17th hole of regulation—which came before Jose Olazabal had a chance to make his putt, which would have at least continued the match, a point that, if you believe the London papers, all of Europe has been brooding about for the past nearly-decade-and-a-half. Not that Europeans are well-known to carry around centuries-long grudges or anything.

In any case, this year’s Ryder Cup is shaping up, at least from the wrong end of the Atlantic, to be a kind of revanchist’s dream, only without soaking the fields of Flanders in blood. In place of Sergio, they have Rory, who actually wins tournaments, and even majors, without regripping his club twenty-five times or casually insulting entire states. And most alarmingly, at least from this side of the Atlantic, our main guy not only has never made a big deal out of these kinds of team events—Tiger is on record as saying he doesn’t regard the Ryder Cup as being the same as one of the four majors—but he hasn’t won a major in four years. Or, in other words, since their kid starting winning them. Which is where the Black-Scholes point comes in.

“If Capital One was trading at $30 a share,” says Michael Lewis in The Big Short: Inside the Doomsday Machine, the Black-Scholes model for pricing options—those obscure financial instruments that have had so much say in our lives recently— “assumed that, over the next two years, the stock was more likely to get to $35 a share than to $40, and more likely to get to $40 than to $45, and so on.” This makes sense to us, intuitively: we like to think that “slow and steady wins the race,” for instance. But the real world does not always behave in that slow and incremental way: everyone would have bet that dinosaurs would be the dominant species on the planet for eons, until a meteorite crashed in southern Mexico. Sometimes things can change quite suddenly—and not reach any intermediate stops. Once, there were billions of dinosaurs. Then, there weren’t.

Once, there was a Tiger, and now there’s a Rory. In between there’s been a collection of Keegan Bradleys and Webb Simpsons, a collection that has largely made the golf press uneasy at best and, at worst, spooked. Golf is, after all, one of the few sports—the other that I can think of at the moment being horse racing—where nobody likes an underdog, at least until the point where it seems like the underdog can actually win; or, in short, become the overdog. Rory, with his eight-shot win at the PGA, might just have reached that point: a point that, as it happens, the wonks over at Grantland have quantified using a measure they call “Z-Score,” which is apparently a standard part of the average mathematician’s toolbag.

“Z-Score” is calculated by taking the winner’s score and subtracting the average score of all the players who finished the tournament, then dividing that against “the variance between the scores and the average performance,” as Grantland’s resident golf stat-head, Bill Barnwell, says. In other words, a tournament where the winner shot “20-under-par and the last-place finisher shot 20-over-par” would have a higher value than a tournament “in which the winner shot 3-under-par and the duffer in last shot 4-over.” Of the top ten scores ever figured, Tiger Woods and Jack Nicklaus have three apiece, with Tiger Woods’ performance at the 2000 U.S. Open, where he blew away the field by fifteen shots, achieving the highest “Z-Score” ever recorded at -4.12 (meaning that he was more than four standard deviations better than the average performance in the tournament.

It’s a good methodology in that it factors out things like weather (everyone plays in similar conditions, within reason) and so on, and to a degree allows us to compare performances across the generations. For instance, it’s now arguable that Jack Nicklaus’ performance at the 1965 Masters might be better than Woods’ win in 1997, even though Woods broke Nicklaus’ scoring record (271, or -11 to par, versus 270, or -12 to par), because while Woods’ “Z-Score” in 1997 was -3.24 Nicklaus’ “Z-Score” was -3.48. Or in other words, Woods was only a bit more than three times better than his competitors in 1997, while Nicklaus was nearly three-and-a-half times better. Obviously, this doesn’t really matter much (though Davis Love’s win at the 1997 PGA, which he took by five shots and produced a Z-Score of 3.54, looks a lot better after running it through this formula), but it’s fun to compare scores across eras.

Like, for instance, the scores Tiger Woods produced in his prime versus the scores Rory McIlroy has produced in his two major wins: last year’s U.S. Open at Congressional and this year’s PGA. McIlroy won both tournaments by eight shots, which is the kind of performance necessary to place on the Z-Score leaderboard, but Z-Score isn’t factored by how much the second-place guy shot, but rather by how much the field as a whole shot. Rory’s Z-Score for the tournaments places him comfortably within the top twenty Z-Scores ever recorded, but his -3.07 score for Congressional, together with his -3.15 score for Kiawah, aren’t enough to place him very close to Tiger’s epic win in 2000. The Congressional score, in fact, doesn’t even place Rory close to Jack Nicklaus’ -3.22 at Turnberry in 1977—you know, the “Duel In The Sun” Jack lost to Tom Watson.

Rory’s wins, that is, have been big—but they haven’t been that big, at least by comparison to Jack and Tiger. The win at Congressional, at least as measured by Z-Score, isn’t even as good as Padraig Harrington’s British Open win in 2008, which the Irishman won at 3-OVER par, only four shots better than his nearest competitor—Harrington rang up a -3.09 Z-Score during what was a famously-windblown tournament. Still, Rory’s fans might cite Barnwell’s observation that through “his first nine majors, McIlroy has put up an average Z-Score 0.97 standard deviations below the mean,” an average only exceeded by Seve Ballesteros (-1.04) and Ernie Els (-1.25) in anyone’s first nine majors. Rory is, obviously, still very young; it’s quite possible we still haven’t seen his best stuff.

Still, what the Z-Score tale tells us is that while Rory is a very, very good golfer, he doesn’t go to the same dimension-bending, dinosaur-slaying, places Tiger Woods could go in his prime. But if we haven’t yet seen Rory’s best, there are few places Rory could demonstrate that to better effect than Medinah, the course Tiger has tamed twice for two of his fourteen major titles and a membership in the club itself. It’s no honorary membership, either: Tiger has the same rights as any other full member, an honor the club presented him with after his second win in 2006, which is to say that, in a sense perhaps more real than any other course, Medinah really is Tiger’s home turf. For Rory to beat Tiger there would be, one suspects, a grievous blow to the competitive Tiger—all the implacable laws of sport, which are even more inflexible than any mathematical model, thus demand that there is only one possible final match for the Ryder Cup’s finale at the end of September: Woods v. McIlroy, for all the stakes that there are. May the best Z-Score win—and to hell with the “random golfer theory.”

Dolorous Strokes

I looked to you as it fell
And now you’re in my way.
“Call Me Maybe.”
Carly Rae Jepsen.

 

“Move!” Paulie was yelling at me the whole time, but after that story about J.R. he’d told earlier I figured he was screwing with me. In the story Paul had told early in the round, about J.R., both of them were out on a loop and forecaddieing one hole when a mishit drive came hurtling toward them. J.R. was either taking a piss, or in some other way distracted, and didn’t see the incoming missile. And when Paul tried to warn him, J.R. ignored the advice—Paul has such a reputation as a clown that most people have learned to ignore what he says. The same scenario played out again during this round—Paul warned me repeatedly, but I ignored him, in part precisely because of the story he’d already told.

As it turns out, it wasn’t so bad for me (the lady couldn’t hit it that hard), though it seems it was for J.R., who ended up with an ugly bruise. When caddieing, as with other things, we ignore others at our peril. Women don’t often play Course 3, with good reason—the carries over water alone are awful—but this was the lady’s most important client, from out of state, and he’d already turned down an invite to another club just to play this year’s Ryder Cup host site. She meant business, and if it meant occasionally whacking a caddie—specifically, the caddie she’d asked the head pro to set up for her—along the way, well, she was prepared to make sacrifices.

What I didn’t realize until later was just how far those sacrifices were going to go. Already, the group had missed the Ryder Cup itself by a few days, which arrived at Medinah last week in order to be photographed in front of the clubhouse for television purposes. I was interested to learn that the cup’s entourage is quite small by big-time trophy standards: only one guy, assigned just for this trip, stood watch over it while a photographer and his assistant took shots of it in front of the clubhouse. This differentiates it from, say, the Stanley Cup, which has its own full-time minder as well as its own room in the Hockey Hall of Fame. Also, the Stanley Cup is a behemoth compared to the Ryder Cup, which is only a bit more than a foot tall.

Of course, the Stanley Cup long ago sold out to the pro racket, while the Ryder Cup is perhaps the last major sporting event played by professionals simply, as Medinah member Michael Jordan’s old contract put it, “for the love of the game.” The Cup’s own PR makes a big deal out of this; it’s actually one last ideological bit of the ancien regime—that infrastructure of knights and feudal lords—still hanging on even now, early in the twenty-first century.

Golf is a sport of the bourgeois, not the aristos; Queen Mary might have played the game, but it’s horse racing that’s the sport of kings, and Scotland never had the money that could support the kind of polo-playing idlers a proper nobility requires. For all that the Ryder Cup might aspire to that kind of ludicrous display of foppery, in other words—and the official website is something to be read—golf is the sport of business people, not blood-lusting armored goons or dandyish fashion-crazed aesthetes. Golf is, in the end, about money.

It was just this, we learned afterwards, that the lady member didn’t understand. I had gotten about what I thought of as a somewhat pedestrian tip—standard hundred dollars for a single bag—but what I thought of as my helpers got screwed. The “A” caddie—one rank less than me—got half what I got, while the two “B” caddies—two ranks lower—got even less. Later, at dinner, I remarked to somebody that it was just this kind of thing that prevents women from rising higher in business: she had specifically asked a favor of the caddiemaster, who’d done what she’d asked—but she hadn’t given out the rewards that such a favor ought to bring.

Now, if she ever brought in that client or some other, and wanted to create the kind of experience a place like Medinah can provide (and brother, what we won’t do for a big tipper is a very short list, indeed), everyone involved will probably, without thinking about it consciously, throw some sand in the wheels: the clubhouse guys might not have the shoes ready to go on time; the valet guys (who she hadn’t parked with) might not have her car ready to bring the client back to the airport quite as efficiently as they might; the pro shop might not get her just the tee time she’d like.

Without even thinking about it, we are all going to be a step slow: not that we’re malicious or anything, but hey, if some big-timer is coming down the block, he’s (and it’s just because of things like this, I’d argue, that are what makes it more likely that “he’s” a he, and not a she) going to get our attention, and she isn’t. But this lady isn’t going to notice any of that—all she’s going to see is that she isn’t getting the attention some other member is getting, and she’ll probably chalk it up to the “old boys’ club” and leave it at that.

That doesn’t mean, of course, that she’ll get bad service; on the contrary, the job she got for her client was really a terrific day for me. I overclubbed the guy on the second hole, as per usual—there’s nowhere to go on that hole, as the green is so shallow; it’s a point to consider during the Ryder Cup matches this fall. But I got him a good read after he hit a good sand shot, and the putt fell. The rest of the day though was followed by poorly-struck approach shots; with some mediocre chipping and so-so putting these led to easy bogies, but still. Towards the end of the round the guest told me he’d just gotten off an airplane that morning after an early flight, which explained the bad iron play to one degree or another; nonetheless he shot an 83 or 84, which isn’t that bad when playing Course 3 for the first time. On this day, in other words, the lady member asked for, and got, the best that Medinah can do for her—and she didn’t reward anybody.

Afterwards, hearing me tell the story, a woman suggested that maybe she just didn’t know what or how to do it. But that’s the whole point: if you’re going to do something like that, you ought to know, or be willing to find out, what the going rate is. Anything else is a category mistake: thinking of an economic question as some other kind of problem. In Arthurian romance, there’s the curious story of the Fisher King—it formed the basis of T.S. Eliot’s The Wasteland, if you’re hip to High Modernism.

In the sources used by Eliot, the king, often called Pelles, has been wounded by what’s called the Dolorous Stroke, which not only has caused this king’s unhealing wound, but also, by some magic or other, caused a kind of environmental catastrophe: it’s as if the land itself has been wounded, through an identification between the country and its leader. The only way to cure the king, and thus the country itself, is to ask the king a question (it’s the opposite of a riddle, in a way), and that question is, according to some sources, something like “Why do you (the king) suffer?” Or in other words, what’s necessary is to have some kind of human identification with the king, to put oneself in the king’s place and ask what that would be like.

In the Arthurian cycle though the knight in question (originally Percival, or in Wagner, Parzifal; in the later poems the role is played by Galahad) is too polite, too courtly, to ask the question the first time the two meet, which is what sets off the Grail Quest and a whole series of adventures that have to take place before the two can meet again. Only by undergoing those experiences can the knight learn enough to know to ignore the conventions of polite society and get at the human experience underneath them: to learn, in short, to ask the question that will heal.

In our own lives, of course, it very often takes a great deal of experience to get to that point; so much of our early lives are taken up with learning how to play our roles that it takes enormous efforts to learn when to ignore them and address the realities of the person, and not the role, that stands before you. And people who are unsure, or don’t know, just what their role is have just that much harder of a time of standing to the side of their roles and making that address.

Which, perhaps, explains something about what New Yorker writer John Cassidy calls the “random winner theory” of golf’s major tournaments, a theory that is even better illustrated by a contrast between two recent majors in two different, but related, sports: golf’s U.S. Open and tennis’ French Open. In tennis, three men—Djokovic, Nadal, and Federer—have won 28 of the last 29 Grand Slam tournaments, going back all the way to 2005. In half of these tournaments, one of those three has played another of them in the final. Jo-Wilfried Tsonga, the man ranked fifth in the world, actually said before the French Open even started that he had no chance to win the tournament.

Such a statement would be ridiculous in golf; Cassidy invites us “to look at this list of the last seventeen major winners, tagged by their world ranking in the week before they won: 29, 1, 3, 3, 69, 72, 33, 110, 4, 37, 54, 13, 29, 8, 111, 108, 16.” These results would be impossible in tennis: “In most individual sports—tennis, sprinting, or skiing, for example—if you put the top six players together,” Cassidy says, “the victor would almost certainly turn out to be one of them.” But not in golf. Cassidy takes the results of this year’s U.S. Open as confirmation of what he’s saying: Webb Simpson, the winner, was ranked 14th in the world before he won at the Olympic Club.

That doesn’t mean that Simpson is a bad player, obviously—he won twice last year, in his breakout season. But it does suggest that the difference between Simpson winning and, say, David Toms (ranked 42nd) winning—or even Michael Thompson (ranked 107th), who ended up tying for second a shot behind Simpson—doesn’t have much to do with how superior Simpson is as a golfer to anybody else who finished high on the leaderboard. Rather, it concerns how much “luck,” or random chance, has to do these days with who wins what in golf. It hasn’t always, certainly, been that way in golf.

Prior to 2008, when Tiger Woods won his last major at Torrey Pines in June of that year at the Open, he’d been golf’s answer to Federer or Lance Armstrong: the dominant player. Tiger at his height used to win about one in every three or four majors, which is astonishing. Since that win, and perhaps more to the point, his gut-wrenching loss to Y.E. Yang at Hazeltine in 2009 (the only time Tiger has spit the bit with the lead in a major) and the subsequent, ahem, domestic issues, major tournaments have been pretty much open to anyone willing to win them.

Maybe what that suggests is that the way to win majors is to behave as Tiger behaved prior to the Thanksgiving incident: singlemindedly, and selfishly, pursuing one’s own goals at the expense of anyone around you. Or, to put it another way, to perform exactly one’s role. This was, it seems, Percival’s understanding of how to go about pursuing the Holy Grail: to ignore anything that did not appear to pertain directly upon that quest. The point of the story, of course, is that Percival does not find the Grail (or more precisely, does not recognize that he’s already found it, because in some versions it turns out that it was in the room with him when he first meets the Fisher King) until he learns, to put it lamely, that Some Things Are More Important.

Certainly, from the point of view of the Tour and the television executives who pay the tour, not having a dominant player is something to be mourned: ratings are always higher when Tiger has a chance of winning. Is this true, though? I certainly could have gotten more out of the guest had I asked him how he was feeling; he would have told me he’d just spent the morning traveling, which would have changed the way I was thinking about what shots he should hit. (Not to mention not getting hit by a golf ball.) The lady member will, more than likely, not get as much out of her membership as she might have had she only asked me. Maybe it’s possible that Tiger can’t ever become the old Tiger he once was: intimidating, unknown, and scary. Maybe all know too much now. But perhaps he isn’t out of options—and maybe neither is golf. At least, there might still be time to duck.

The Razor’s Edge

… for that path is sharp as a razor’s edge, impassable,
and hard to follow, say the wise.
—Katha Upanishad 1.3.14
 

“Never start a ball over a hazard,” said the kid, with a confused look on his face. He was baffled, though he might not have described it this way, because while many might think that the patron saint of golf, if it has one, is Saint Andrew (whose ensign, an “X,” isn’t particularly encouraging for a golfer, and whose feast day, November 30, isn’t a particularly good one for golf, at least in the Northern Hemisphere), it’s actually William of Ockham, whose commemoration date is that ideal day of the 10th of April, and who is best-known for writing “Plurality should not be postulated without necessity,” otherwise known to philosophers as “Occam’s Razor.” Or, to put it in golf terms, the notion that you ought to play a hole in as few shots as possible. What was perplexing the kid was that the hole we were looking at smashed that straight to hell. Sorting it out, in turn—a phraseology not used lightly—necessitates considering Walt Disney, Tiger Woods, the Rules of Golf, long-handled putters and the recent changes regarding Q-School proposed by the PGA Tour, though getting there implies a less-direct route than William might like.

The kid and I were standing on the tee of one of the weirder holes I’ve ever seen: a sweeping dog-leg 5-par around an oxbow bend in the Buffalo Bayou, Houston’s main river. The tee shot is basically blind: you can see the beginning of the fairway but not the rest of the hole; the dogleg is so severe that hitting the ball that way is too short a distance for a driver. The only way to play that hole, in other words, is to flout deliberately one of those rules professional golfers live by, the rule that you should never intentionally put a hazard into play. But in order to play this hole in the fewest amount of strokes it’s necessary to take the risk of the hazard: the conundrum put the aspiring-tour-pro head of the kid into brain-lock.

On most days, I was the kid’s caddie, on what was then the Adams Tour, a mini-tour based in Texas during the late fall into winter, but since getting to Houston he’d had trouble breaking 90 in the stiff Texas wind, and, in need of cash, we’d both turned to looping like attractive would-be pre-med coeds turn to … well, whatever it is that they do. So there we were, at Houston Country Club, the oldest golf club in Houston and one of the oldest in Texas, and though the golf course isn’t as old as the club (which had moved from its old location in the 1950s), still it was designed by Robert Trent Jones, Sr., one of the giants of golf architecture.

Houston Country Club is a posh joint run by old-time oil swells (one of its founders was Howard Hughes’ father, Howard Hughes, Sr.): all of which is to say that HCC is probably one of the most conservative places in the country, if not the planet. It’s disturbing, in other words, to find such a rebel of a hole at the golf course’s heart: in order to score well on that course a birdie is absolutely necessary there, which is to say that it demands precisely that rule-flouting that the club’s members, presumably, would abhor in their own lives. But you play the golf course as you find it, not how you’d wish it to be—and if the members of Houston Country Club are unaware of the ironies of their own course, then that’s one of the burdens of professional knowledge, I suppose. That doesn’t mean, to be sure, that the swells can’t suddenly re-discover the rules when it’s convenient, though—a point that has a direct bearing on the story that Houston Country Club and its caddie program is best-known for having a tangential connection with these days, since it was there that Taylor Smith completed his back nine on this planet.

Taylor Smith finished his days as a caddie at Houston CC in 2007, at the age of 40, apparently of pancreatitis. He’d never married, never had any children so far as anyone knows. He is, at best, a footnote in golf history: the guy who’d almost had to face down Tiger Woods in a playoff but didn’t and, because he didn’t, handed Tiger his second win on tour. The story of how he didn’t is a story about conflicting rules and how to apply them, and perhaps is instructive about golf and other matters.

The scene of the tale was Walt Disney World in October of 1996, the PGA Tour’s Orlando stop and one of the last chances for a player to make enough money to secure his tour card for the following season. Smith didn’t particularly need that chance: he’d already had two top-five finishes and would finish the season with a comfortable $220,000, which in those days was more than enough to make the top 125. Still, Smith was still looking for a win and at Orlando he not only made the cut, but spent Saturday night sleeping near the lead along with another guy whose career would also be cut short: Payne Stewart. Then there was a kid whose last name was Woods.

Back then Eldrick was still a young golfer trying to solidify his presence on the Big Show: though only a bit before the Disney he’d already won at the Las Vegas Invitational (beating Davis Love in a playoff), which meant his status for the next season wasn’t in doubt, he hadn’t yet become the Tiger Woods of whom other golfers were, for a time, afraid. Smith, in the final round, surely didn’t play scared: he calmly rolled in a putt on the last green to tie Woods at 267 for the tournament, 21 shots under par. And that despite the fact that, even aside from Woods, he had every reason to be anxious during that final round.

Earlier that day, while making the turn, Smith’s playing partner Lennie Clements, noticed something about the putter Smith was using: one of the two grips the long putter had was flat on one side. Clements knew this was a problem, and indeed a rules official confirmed that the putter violated Appendix II, 4-1c(v): “A putter may have more than one grip, provided each is circular in cross-section and the axis of each coincides with the axis of the shaft.” Smith played on anyway under an appeal of the decision and finished the round. But his protest—and the fact that, as many acknowledged then and now, there’s little reason to think that the flat grip could have assisted him any more than the fact that he had a broom-handle putter (perfectly allowable under the rules) already anyway—fell on deaf ears. Woods thereby won by default.

Smith won a lot of plaudits after the tournament though, via what many called the “classy” way he handled his DQ. When it was all over, he said that Clements “did the right thing” by calling over a rules official, and according the Orlando Sentinel a year later, Smith’s “noble handling of the disappointment gained him coast-to-coast style points.” But the same story (“As a Rule of Thumb, Give Smith His Due”) also hints at something darker: “tour insiders,” it says, “say he has had difficulty letting it go.” What Smith “dwelled on,” the story says, was “the revelations about the possibility that Woods, too, had been unknowingly playing Disney with a non-conforming putter.”

The tour got a phone call, it seems, on the Monday after the tournament was over that alleged that Tiger’s Scotty Cameron putter—the same one that he’d also used to win at Las Vegas earlier that fall—did not conform to Rule 4-1b of the Rules of Golf, which mandated that the neck of a putter measure five inches or less from the point of contact with the shaft and the putter’s bottom. The tour called Tiger’s camp immediately—but didn’t actually inspect the putter until two days later, by which time it had already been replaced in Tiger’s bag by another, conforming, putter. Which, as it turns out, was something of a moot point anyway, since as Rule 34-1 holds, “a penalty must not be rescinded, modified or imposed after the competition has closed,” a rule that has something of the same effect as Article I, Section 9 (the rule against ex post facto laws) does in the United States Constitution. Because Smith’s non-conforming putter was discovered at the time, in other words, he suffered a penalty that Tiger, whose putter never did get inspected, escaped.

Almost certainly, of course, that Woods wasn’t subject to the same level of scrutiny as Smith was what bothered Smith—though more certainly Smith isn’t around to be asked about it. Why it’s of anything more than an antiquarian’s interest though is in light of the recent proposal of the PGA Tour to eliminate Q-School as a direct route to the tour. Smith originally got on the Big Show through Q-School, the annual tournament whose final stage is 6 days long and is probably the most grueling competition in golf, while Tiger, of course, never had to play Q-School because he got invited to tournaments through sponsor exemptions—and then he won. Yet the routes of both of these men to the tour would be closed if the tour has its way.

Under a proposal first outlined to PGA Tour players at the annual meeting on the Tuesday before the tour stop at Torrey Pines, Q-School as a route to the PGA Tour would be eliminated. Instead, the Fall Finish tournaments (of which the Disney used to be one) would become a three-event shootout between the top 75 Nationwide players and the 75 Big Show players on the bubble, with 50 PGA Tour cards at stake. The Q-School tournament, whose traditional dates in early December would in any case be disrupted by the new format, would become merely a route to the Nationwide Tour.

Or whatever they will call it, since the PGA Tour has also announced that Nationwide Insurance is pulling out as a title sponsor. One of the consequences of that decision might be that Tiger’s route to the PGA Tour might also be closed: a few potential sponsors of the Fall Finish tournaments have said that they aren’t interested unless their tournaments are part of the FedEx Cup chase, which means that the new PGA Tour season will have to start in October right after the Tour Championship. Instead of being events traditionally skipped by the bigger names on tour, who usually take a break after the Tour Championship—and thus allowing younger guys like Woods to catch some sponsor exemptions and get a chance to compete at a high level without directly facing the best of the best immediately—the change threatens to make the PGA Tour a constant, year-around affair.

And, perhaps solving some headaches for the tour’s staff, would immediately have the effect of dividing professional golfers rather handily into two classes: PGA Tour players and all others. Instead of the fluidity represented by the careers of Tiger and Taylor, we’d have very, very solidly defined career paths: players, even great ones, would have to spend a year on the Nationwide Tour (or whatever it is named in the future) without exception, while there also would be no way for a marginal player to catch lightning in a bottle for a week and ride to a fun (and lucrative) year on the PGA Tour. The new system would act … well, very much like a razor, sharply delineating who is deserving of special treatment and who is not with what is evidently a satisfying clarity to the tour.

It will also have the effect of multiplying the classes of golfers into two: those with access to the rich purses of the PGA Tour and those playing on whatever the Nationwide Tour will become, where the purses are roughly one-tenth as much. It might be worth noting, in this connection, that while generally speaking the kid’s rule about where you should never start your tee shot is valid, it’s also true that there is, in golf architecture, a species of golf hole known as a “Cape hole.” The species is named for the 14th at C.B. Macdonald’s National Golf Links of America, on Long Island; what makes it the archetype for the species is that a water hazard runs along one side of a fairway that curves around it, meaning that the further a tee shot is flown over the hazard the greater the potential reward in terms of distance left to the green. At times, in other words, it’s necessary to hit it directly at a hazard. Houston Country Club’s par-five is an example.

There are, also, others.