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.”

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Please let me know what you think! Also, if you are having trouble with posting a comment, please feel free to email me personally at djmedinah@yahoo.com. Thanks for reading!

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