This Pitiless Storm

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


Darth Looper

The putt came screaming down the hill—carrying with it my golfer’s hopes of a win and my hopes of a decent payday—like Luke Skywalker’s torpedo flew down the Death Star’s trench and, given the condition of the greens, the speed of it was a surprise. It’s been an unfortunate fact that the last two major championships at Medinah have been PGAs, traditionally played in August. August is usually a poor month for Medinah’s grass; the heat of a Chicago summer has never agreed well with Course 3. Medinah has been lucky that Tiger won both of them; if he hadn’t, the course’s condition during play would probably have been a bigger story. In 1999 for instance the green on the 16th hole, where on Sunday Sergio Garcia nearly made what would have been an epic birdie that would have tied Tiger for the lead, had almost no grass on it by Sunday. Things weren’t as bad in 2006, but they were slow; and this summer, even despite all the changes made (Sub-Air systems, entirely new grass, and this year even giant fans), there’s still a chance that Medinah might lose the greens entirely sometime in August.

All that lies in the future now, as we wait for the high furnace winds of August to arrive,  and the golf world awaits the final selections for the Ryder Cup teams, which won’t happen until after the PGA. As of this writing, the only thing to talk about in golf is Adam Scott’s Via Dolorosa over the final four holes of the Open Championship, known to us colonials as the British Open. There’s very little as agonizing as caddying for somebody experiencing such a collapse, as I found—again—at about the same time on that Sunday that Scott wandered through the stages of his stations of the cross at Royal Lytham.

My patron was an anxious little guy, a member playing a match for the President’s Cup—a ladder match tournament played through the season—ahead of the club championship, which would start later in the morning. (My loop for the championship had canceled 15 minutes before his tee time for reasons that are still unclear.) He’d asked for somebody who could read the greens, so I got sent.

His nerves were apparent from the very first tee, when he made some kind of forgettable and ridiculously bad joke about something or other. Having honors, he hit his ball a moderate way down the fairway, followed shortly by his opponent, who hit it about the same amount. The two were, by handicap indexes, exactly matched, even though you might not think it to look at them: my guy was in his fifties, perhaps; his adversary, perhaps in his early 40s, and far more athletic-looking. Yet the way they hit their golf balls betrayed an equality: neither could hit it much more than 240 yards with their drivers, though my guy made slightly better contact with his pull-slice kind of action than the other guy was with his. My guy hit the green in two shots; the other guy missed and after two putts from our hero, the Adversary was one down.

That lead didn’t last long—my guy hit it in the water on the second hole, after a pull job that didn’t get high enough to the elevated green. And after winning the third with a two-putt par to go up again—me having called for a six-iron, rather than the five my player thought was necessary—my guy three-putted to the Opponent’s one-putt for another push. On the sixth, we were on regulation, while the other guy was ten yards short of the green. He used his putter to advance the ball to the front part of the green—with a pin on the back, atop a tier whose steep approaches not only threatened to stop anything not well-struck, but actually Elvis them: “Return to Sender.”

Naturally, the guy sent his ball through the swale in front of the green, then up those slopes—and sank it. Just as naturally, my guy missed his par putt, despite it only being a few feet away and on the same tier. The match was shaping up to be the classic “ball-striking vs. putting” contest; which, to my mind, favored my player, considering the condition of the greens.

After all, if your game depends on putting, burned-out and slow greens, create so many obstacles that even a good putter can’t depend on making many. It changes the dynamic of the traditional structure of the tortoise-vs.-hare joust, which usually is the difference between, say, taking your life-savings, driving to Vegas, and putting it all down on the roulette wheel’s black, and putting a quarter of your paycheck into a savings account every month. Or in other words, betting on your putting against the other guy’s ball-striking is essentially saying that the value of your putt outweighs the value of all the strokes made by the other guy. It’s possible, sure, but on slow greens, a game based around putting isn’t just roulette but roulette with a broken wheel.

On the seventh, I reminded my player to tee his ball on the right side of the tee box, to accomodate his cutty kind of pull shape shot, which was fortunate because he started his ball well left of the fairway but it ended up dead center. After trading wins and pushes on the next three holes things started looking up at the beginning of the back nine. Sticking it to less than two feet in regulation on the tenth hole was great, though somehow the Adversary managed a par after getting lost in the woods off his drive. Thankfully, my guy made his birdie. Then came the eleventh, which appeared to be a kind of turning point.

My player hit a good drive down the center of the fairway, while the Adversary found the forest and its trees again. He had to play out, ending up about fifty yards away from the green. Meanwhile, I and my player were locked in a bit of a dilemma. The actual distance to the pin appeared to dictate a six-iron, but it was far towards the back of the green beyond which grew a thick stand of pine trees from which it’s impossible to recover. In addition, the green on the eleventh is slightly below the level of the fairway where we were, and the wind was slightly helping the kind of cut my player favored. I therefore advocated he use the seven-iron.

Thus far, I pointed out, we had played conservative golf: I had consistently pushed for the club that would put us near the center of the green without much trouble. And thus far we’d been rewarded: sure, the other guy had made some miraculous recoveries—but the point was that he’d had to make them. On every hole, even those when we’d missed the fairway somehow, we had been threatening to make bogey or better. Therefore I argued that while the seven-iron might not reach all the way back to the hole, it also wouldn’t reach the pines beyond, and so we’d not risk anything worse than a bogey. My player saw the point—and immediately hit it into the front right bunker.

And just after that, the Adversary hit his fifty-yard approach to bounce in front of the green and then roll up the green as if it were a judiciously-struck putt, eventually ending up not more than four feet from the hole … and on the same tier. So things certainly looked bad. Still when we reached our ball it appeared that the ball would have fallen from the sky at least as far as the green’s front, had it only been a yard or two more left, and, more significantly, had a very good lie in the bunker’s center.

The bunker shot came out okay—okay, but not great, right in the center of the green. I underlined the importance of hitting it firmly, he hit the par putt three feet by the whole, so seemingly we’d lost the hole. Until the sweet-putting Adversary had put his par putt about the same distance from the hole as he’d started—and then did it again. And again. My guy managed to make his bogey, and the Adversary actually picked up his ball and threw it into the pine trees near the green. Thing were looking up.

On the twelfth, I counseled a three-wood on the approach, despite the yardage seeming to dictate the hybrid he carried—which, he said, he didn’t hit particularly well—and my player found the green. (His comment was that he’d only hit the green in two once before.) Still, we were a long way from the pin, and above it, though the Opponent was also in a precarious position above the hole—and he was there in three. The line of putt I thought should be played was probably too high—though the breaks on the twelfth hole on Course 3 can be enormous—and my player didn’t hit it firmly enough considering how slow the greens were, so we ended up just slightly inside our Opponent’s ball. Luckily enough, he missed, but we ended up with another push on a hole that we could easily have won.

Still, after a two-putt par on the par-five fourteenth, we found ourselves three up with four holes to play. And after some bad Adversary shots on the fifteenth, followed by another miracle Adversary downhill putt from nearly off the green to make bogey, we merely had to two-putt for a par that would win the match. Of course, my guy hit the first one slightly too hard, which left him a three-foot putt for par. Which he pulled, missed on the low side, and never even sniffed the cup.

You already know what happened next. The Adversary hit a ridiculous third shot on the par-four sixteenth to inches from the cup; we missed our par (I possibly misread it slightly). On the seventeenth, I reminded my guy to place his ball on the right side of the box, especially on account of a tree that slightly overhangs the tee box there; naturally, he pulled his tee shot into the tree and failed to clear the water, which meant that we couldn’t take advantage of our Adversary’s wildly-overclubbed approach that left him twenty yards over the green. On the eighteenth, the Opponent hit another bad drive to our solid hit down the middle. His punch-out left him well short of the green. And so we had a dilemma.

The eighteenth hole on Course 3 had a Redan-style green, meaning that it is elevated above the fairway at a slight angle: the further left you go, the farther the shot must carry to reach home. (Another example of such a green is the fourth at Riviera.) But there is an opening on the right side of the green, between the deep bunkers in front of the green itself and to the left of the opening and the deep bunker to the right of the green, that allows a humbler, less-daring shot. Now, looking at our distance, my player said “The hybrid?” I mentioned that he had said earlier he didn’t like to hit that club, and we hadn’t used it all day. “The four then,” he concluded. And I said no—“The five.”

The idea was that by hitting a five my player would be able to control his shot better (all things being equal, a shorter club is easier) and thereby avoid the bunkers on the left, while at the same time, no matter how well he hit the ball, he would never be able to hit it so far as to carry into the bunker on the right. The golfer saw the virtue of the notion and, striking it well, left his ball in the middle of the opening about thirty yards from the flag. Next, the Opponent put his third shot well past the pin, leaving himself a dangerous twenty-five foot downhill putt for par.

When he hit it, my first thought was that he’d hit too hard—if it missed, there was no way the comeback putt would be any less than six feet, even on the slow green. But it didn’t miss. Instead, it struck the back of the cup, popped into the air a few inches, and dropped back into the center of the cup. We were all stunned, and my patron’s miss a minute or two later was a foregone conclusion. Through eighteen holes, we were now all square.

That raised the question of a playoff. Normally we would merely proceed to the first hole of the golf course and begin again—but with the last groups of the club championship, the members of the top flight of golfers who were really competing for the overall prize, going off, the club pro standing at the first tee told us it was impossible. This piqued my golfer, who had some hard words for the club pro, but as there was nothing to be done we proceeded to the first tee of Medinah’s Course 1, where the Adversary sliced his tee shot into the trees right of the fairway.

The first hole of Course 1 is a short par-five, only about 530 yards. The tee shot’s view is dominated by an enormous bunker that stands immediately beyond a stream that flows through the rest of the course, itself just beyond the edge of the forward tee box. The bunker is usually merely decorative, and is in the shape of a Bactrian camel; apparently this is in homage to Medinah’s connection to the Shriners, who take their club’s trappings from a kind of fantasia of the Arabian Nights—though the Bactrian, or two-humped, camel is from Central Asia, thousands of miles from Arabia. The other feature of the tee box is a couple of trees that cast their shade over the tee in the afternoon; the box faces north, which is to say that the trees stand on the left side as the golfer faces the green off in the distance.

I assume you can discern what happened next.

It did. My patron pulled his drive into the tree on the left, whereupon it ricocheted over the stream, hit another tree, and ended up between the camel’s humps just off the near edge of the bunker. Though it didn’t end up getting wet, we were still in about as impossible a situation as could be: because the edge of the bunker was so close, we needed a short club merely to make contact with the ball, not just to be sure to carry the ball out of the bunker. That done, we were still hitting our third shot from nearly four hundred yards; I won’t bore you with the comedy that followed—even after all that, because of the Adversary’s poor ball-striking we weren’t out of the hole until nearly the final putt—but as amusing as it was in some respect it did nothing to change the final result: my golfer lost.

Afterwards, I went to the caddie shack (actually a rather pleasant room connected to the pro shop) to sit in the air conditioning a bit and clean up. The caddie for the Adversary, who was about 14 years old, was there waiting for his ride, and when a couple of my friends asked me how it went, he piped up. In his telling, his golfer’s victory was a win for the romantic, the impossible, what TV shows like Star Trek call the “human.” When things looked blackest for his golfer, he had “encouraged” him, told him not to give up, and all of the other cliches used in sports movies and, come to think of it, a lot of others: at the end of Star Wars, for instance, Obi-Wan tells Luke to turn off his targeting computer and “trust the Force,” which allows him to get off the shot that scurries into the center of the Death Star’s exhaust port, destroying the evil weapon and winning the day for the good guys. According to this looper, the victory was entirely due to the encouragement he provided for his golfer, just as the Rebels in Star Wars won because of Obi-Wan’s coaching at the crucial moment. Which, I suppose, is itself an encouraging sign: it’s well-known that in these times of resistance to government health-care, or stimulus spending, or for that matter the fact of global warming, what’s really necessary is to inspire a love of irrationality in our youth.