Tell You Wrong

I embrace my rival, but only to strangle him.
Jean Racine. Britannicus, Act IV, iii.

“Joe Frazier, I’ll tell the world right now, brings out the best in me,” Muhammed Ali said after the “Thrilla in Manila” in 1975, the third and final fight between the two: the one that “went the distance” of 15 rounds in the searing tropical heat of a Third World dictatorship, the one that nearly killed both men and did land them both in the hospital. Phil Mickelson wasn’t as lyrical after giving Tiger Woods an eleven-shot beating at Pebble Beach a few weeks ago: “Although I feel like he brings out the best in me,” Mickelson observed, “it’s only been the past five years.” (Since 2007 Mickelson’s been 8-3-1 when playing against Tiger, bringing the overall record to 13-13-4 in the thirty times they’ve been paired together.) For years, golf writers have lamented the fact that there have been no Tom Watsons or Lee Trevinos around to challenge Tiger as those players did Jack Nicklaus; as it turns out, it seems that rival—Phil—has been there for five years. But are rivals only recognizable in retrospect, and if so what does that mean for the “rivalry” theory?

I take it for granted that anyone reading this will be familiar with the complaint that Tiger has not faced any worthy rivals; as an example, I will cite a story from Yahoo Sports from nearly four years ago. It’s simply entitled “Tiger Misses What Arnie, Jack Had: Rivals.” “Tiger has no true rival,” wrote Dan Wetzel then, “no one familiar face just as cold-blooded, talented and intelligent to push him to perhaps even greater heights.” The complaints implicitly voiced here are longstanding, going back at least to the excitement surrounding the PGA at Medinah in 1999, when Sergio Garcia appeared to many about to challenge Tiger. Such complaints appear much like the usual sportswriter’s fantasies, like the “clutch” player—so far as I know, no player has ever been shown to perform better than his career numbers might indicate in particular situations, in any sport—or that running and defense wins football games. A contrarian might reply, for instance, that Tiger’s run was fueled by a number of breaks: the fact that David Duval essentially fell off the planet after 2001 might be the first item on that list.

Phil’s record with Tiger might suggest that simply because only a few of Phil’s and Tiger’s matchups have come on the final day of a major that one of them ended up winning (which disqualifies, for instance, the electric final day of the 2009 Masters, when Phil shot a 30 on the front nine but didn’t win), they have in fact been “rivals” the whole time—which in turn might suggest that a further combing of the data might discover other “rivals” whose presence had been undiscovered because they had not appeared at widely-televised moments. It’s kind of a silly argument, but as it turns out someone’s taken it seriously and quantified the difference between Tiger and his fellow competitors—and it’s really true: Tiger, in his heyday, didn’t have anyone who remotely approached him.

In 2008, as it happens, a paper published in the Journal of Political Economy by one Jennifer Brown entitled “Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars,” found that in general players not named Woods took an additional .8 more shots in every tournament Tiger entered. The effect was even more pronounced in the first round of tournaments, where Woods was effectively conceded another third of a shot by the field, and yet more so among “elite” players: those close to the top of the leaderboard gave away nearly two shots to Tiger. Although these margins seem thin, the difference between first and second on the PGA Tour is usually one shot; what that’s meant, according to Brown, is that meant the rest of the tour players have conceded something on the order of $6 million to Tiger over the course of Tiger’s career.

Still, while that does I think prove the “no rivals” theory it doesn’t actually provide any causation: one possible explanation, for instance, might be found in the way that Tiger himself plays. According to his former coach, Butch Harmon, Tiger has methods to confound his playing partners: in an interview with Steve Elling of, Harmon said that Tiger for instance will “often putt out first” (which means that galleries will often be moving to the next hole while whoever he’s playing with is putting); that Woods will try to get to the tee box last, so the crowd will give him its biggest cheers; change his pace of play to play “fast” with slow players and vice versa; and hit three-wood instead of driver on some holes, so as to hit his approach first—thereby making his opponent wait to hit his shot. None of these methods are against the rules, of course—but they don’t win friends in the locker room either.

Yet Brown’s paper found no evidence that players playing with Tiger are more affected than those not playing with him. Joel Waldfogel reported in Slate that Brown’s work found that “being in Tiger’s foursome [sic] has no additional negative impact on performance.” In other words, even if Tiger was practicing gamesmanship—and it was successful—it didn’t show up in the statistics. Playing with Tiger or not playing with Tiger, all that seems to matter is that the other players know he’s there.

One way to test for that is to see if the other players have been “attempting longer, riskier shots to try to keep up with Tiger.” A website called notes that Brown’s account does this: if players were trying such a strategy, there would likely be what financial professionals would call “volatility”: there’d be more eagles—and double bogeys—when Tiger played than in other tournaments. In reality though, there “were significantly fewer eagles and double bogeys when Woods played.” Tiger’s presence wasn’t causing the other players to adopt a “high-risk, high-reward” strategy. Instead, it seems that he really just caused them not to throw things into some higher gear that, possibly, might have been available to them.

What’s interesting about this is that what it suggests that Tiger’s dominance was, in fact, the effect of something within his opponents’ craniums, not just a statistical anomaly caused in part by Tiger’s skillfulness but also by chance. But what it also suggests is that the nature of that dominance didn’t lie in something sportswriters ascribed to Tiger’s “aura” or his vaunted “Zen-like” mental discipline: the potential mechanism that Brown theorizes to explain the effect is quite different.

Brown finds the mechanism by analogy to other fields: she “cites the competition among newly hired associates at a law firm as another example of a nonlinear incentive structure,” as another review of her work says. Such a structure might be better known from the practice of the firm in Glengarry Glen Ross—where, as Alec Baldwin’s character Blake said, first place is an Eldorado, second is a set of steak knives, and, anticipating Donald Trump, “third prize is you’re fired.” In a law firm, usually only one associate might be hired from a given group: in law firms as in Ricky Bobby’s NASCAR, “if you’re not first you’re last.”

The mechanism Brown proposes, as described by Jonah Lehrer in an essay on the paper for the Wall Street Journal is therefore that “the superstar effect is especially pronounced when the rewards for the competition are ‘non-linear,’ or there is an extra incentive to finish first.” In such a contest, the rewards for finishing first are so exponentially better that finishes less than first are, by comparison, not as meaningful. “We assume,” as Lehrer puts the point, “that the superstar will win, so why chase after meaningless scraps?” In other words, Brown’s theory is that professional golfers, seeing Woods’ name in the pairing sheets, consciously or not effectively “mail in” their effort. They aren’t expending everything they have because they don’t expect to be rewarded for extra effort.

What that suggests though is that what’s going on in tour players’ heads isn’t a fear of Tiger so much as it is a rational calculation based, ultimately, on some sense of fairness or justice. Isn’t that what we might call a reasonable conclusion in the face of evidence of a “rigged” game? It wouldn’t matter from this point of view (though you might compare my previous work on Taylor Smith) whether the game were “actually” gamed in some fashion or other in Tiger’s favor, merely that players behaved as if it were. Or to put it another way, from an individual tour player’s perspective it wouldn’t matter whether Tiger was who he was from sheer ability or from some shadiness: the player-not-named-Woods’ own abilities would be disturbed in some way in either case.

Now this is extremely interesting because what it suggests is that even the perception of inequality is harmful. Brown suggests that societies that insufficiently spread the wealth, however that is defined, in the long run are inefficient: they fail to get the best out of their people. Unequal societies waste human resources. And worse.

If Brown, for instance, was looking for a society that uses a “nonlinear incentive structure” as its working principle, she might have stopped looking for it on pristine golf courses and started in on the southwest corner of Utah, which is perhaps (and probably not coincidentally) some of the most isolated terrain in the continental United States. In that territory north of the Grand Canyon lie the adjacent towns of Colorado City, Arizona and Hilldale, Utah. What’s noticeable about these two towns is that there are lots of large families headed by “single” women: the product of a polygamous sect, the Fundamentalist Church of Jesus Christ of Latter Day Saints (FLDS). It’s an issue adequately explored elsewhere—Jon Krakauer’s Under the Banner of Heaven is perhaps an excellent beginning—but what’s not usually mentioned is something that has rather a bearing on Jennifer Brown’s research.

“Often,” observed the historian of marriage Stephanie Coontz, “the subordination of women is in fact also a way of controlling men.” Or as Libby Copeland, writing for Slate, puts it: “Rich old guys with lots of wives win twice: They have more women to bear them babies and do household work, and they also gain an advantage over other men.” Since they control access to marriage, any man who wants to get married has to deal with them—and since the rich old guys are taking a surplus, that makes a lot of boys inessential to the society. In a polygamous community, then, we’d expect to see a lot of homeless teenaged boys: in 2007, Time magazine said the number of boys abandoned by their polygamous families in that state may number in the thousands. The results of a “nonlinear incentive structure,” as Ms. Brown calls it, aren’t especially difficult to discern in this case: I don’t think the problem of a surplus of unsupervised and despairing teenagers needs much detailing. Nor, perhaps, do Tiger’s off-course problems appear as inscrutable.

I don’t mean, to be sure, to minimize the sufferings of women and children in such a community, but it is worth noting that such arrangements necessarily burden the whole community and not just particular groups in it. By laying down in front of Tiger, for instance, PGA Tour players effectively ceded him not only today’s purses but tomorrow’s: a tour that had had one or two other guys who could have gone the distance with Tiger in 2001 or 2002 might have gotten an even greater television contract. But by understanding the mechanism by which the trick is done goes a long way toward understanding how to combat it: removing the “nonlinear incentive structure,” rather than, as has been suggested, somehow convincing everyone on the tour that they’re “tougher,” or whatever, than they thought. Or to put it in terms relevant to a larger field, stop working on “raising self-esteem” or the like and more on regularizing pay-scales.

That isn’t, necessarily, to demand that the PGA Tour stop disproportionately rewarding its winners: golf is a sport, and sports aren’t necessarily the same as other parts of life. It can, and has, been argued that pro golf, in particular, needs a dominant, or a few dominant, players in order to make it interesting to the general public: if a different pro won every week, tournaments might come to seem like lotteries for people with the leisure to raise golfers. The regular appearance of some few names, perhaps, creates the possibility of drama.

Drama like that of the last Ali-Frazier fight. Frazier had trained for the fight like a man possessed, knowing that it would be his last shot at the title. Ali, in the midst of domestic turmoil, less so. Sometime in the seventh round, in the early Philippine afternoon—the fight started in the late morning for international television—Ali began to fade from the heat and a relentless assault from Frazier, who would not stop coming despite the furious combinations Ali laid on him. “Joe,” Ali said during a clinch, “they told me you was all washed up.” “They told you wrong, pretty boy,” Frazier replied. It’s arguable that, whatever the medical histories, neither man left that ring whole. For years, golf has wondered how to get that kind of effort out of its players. What evidence suggests is that if golf wants true rivalries, and the drama that results, it might do better to stop catering to the elite—which, despite the fact that it apparently remains unlearned in parts of Utah or the Philippines (or Wall Street), doesn’t appear a difficult lesson.


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