Before long, I think that we’ll look back on these years of golf and tennis and marvel that two men — Roger Federer and Tiger Woods — were able to utterly dominate their sports. These athletes didn’t just win tournaments; they seemed to expand the possibilities of the game. David Foster Wallace, in his 2006 profile of Federer, summarized the allure of watching a physical genius play a game better than anyone else has ever played it:

Beauty is not the goal of competitive sports, but high-level sports are a prime venue for the expression of human beauty. The relation is roughly that of courage to war.

The human beauty we’re talking about here is beauty of a particular type; it might be called kinetic beauty. Its power and appeal are universal. It has nothing to do with sex or cultural norms. What it seems to have to do with, really, is human beings’ reconciliation with the fact of having a body.

But now comes the inevitable denouement, as both Woods and Federer struggle to maintain their supremacy. Woods, of course, has his personal melodrama and bum leg to blame, while Federer (and this is why his arc is so poignant) seems to be undone by the ordinary effects of aging. (And he’s not even 30!) Although it’s clear that both men aren’t playing at the exalted level of their peak — and that their competition has gotten better — I think there’s an additional phenomenon that accelerates their decline: Both Federer and Woods have lost their superstar status. And that turns out to be a significant competitive loss.

Let me explain. A few years ago, Jennifer Brown, a professor of Management and Strategy at Northwestern University, published an interesting paper on what she calls “the superstar effect.” The effect occurs when competitors are so intimidated by the presence of a certain player, such as Woods and Federer, that they start playing far worse. As a result, the success of the star becomes a self-fulfilling prophecy. (I wrote about the superstar effect last year in the WSJ.)

To demonstrate the benefits of being a superstar, Brown analyzed data from every player in every PGA Tour event from 1999 to 2006. She chose golf for several reasons, from the lack of “confounding team dynamics” to the immaculate statistics kept by the PGA. Most important, however, was the presence of Tiger, who has dominated his sport in a way few others have. Sure enough, the numbers back up the legend: When Woods’ self-imposed exile from golf began, in November 2009, he had a World Golf Ranking score of 16.169, which was nearly twice the total of the next two players. He has more career major wins than any other active golfer and has been awarded PGA Player of the Year a record 10 times.

Such domination appears to be deeply intimidating. Whenever Woods entered a tournament, every other golfer took, on average, 0.8 more strokes. This effect was even observable in the first round, with the presence of Woods leading to an additional 0.3 strokes among all golfers over the initial 18 holes. (While this might sound like an insignificant difference, the average margin between first and second place in PGA Tour events is frequently just a single stroke.) Interestingly, the superstar effect also varied depending on the player’s position on the leaderboard, with players closer to the lead showing a greater drop-off in performance. Based on this data, Brown calculated that the “superstar effect” boosted Mr. Woods’s PGA earnings by nearly $5 million.

What’s causing the superstar effect? There are two competing explanations. The first is that, when playing against a superstar, opponents simply give up. Instead of trying their best, they accept the inevitability of defeat. They assume that the superstar will win, so why chase after meaningless scraps?

The second explanation is that the presence of the superstar leads to a mild form of choking. Because competitors know they need to play their best to beat Woods or Federer, they become extra anxious about not making mistakes. (They also don’t want to look bad on national television.) And so they obsess over their swing or serve. Unfortunately, such thoughts almost always backfire: We’re so worried about hitting the ball straight that we send it careening into the weeds.

Sian Beilock, a professor of psychology at the University of Chicago, has helped illuminate the cascade of mental events that lead professional athletes to choke. She uses golf as her experimental paradigm. When people are learning how to putt, it can seem like a daunting activity: There’s just so much to think about. Novice golfers need to hold the putter properly and keep their shoulders square. Then, they have to make sure that they hit the little white ball with a smooth stroke, making contact at the center of the putter head and letting the club move to the inside after impact. For an inexperienced player, a golf putt can seem like an endless checklist of do’s and don’ts.

But the mental exertion pays off, at least at first. Beilock has shown that novices hit better putts when they consciously reflect on their actions. The more time they spend thinking about the putt, the more likely they are to avoid beginner’s mistakes and sink the ball in the hole.

A little experience, however, changes everything. After golfers have learned how to putt — once they have memorized the necessary movements — analyzing the stroke is a dangerous waste of time. Beilock has found, for instance, that when experienced golfers are forced to think about their putts, they hit significantly worse shots. All those conscious thoughts erase their years of practice; the grace of talent disappears. And this is why it’s dangerous to compete against a superstar: Players end up thinking up too much.

While Brown limited her data set to golf, I bet that Federer also benefited from the superstar effect. Like golf, tennis is a game of precision and inches, requiring mental toughness and resilience. I can’t help but wonder if, a few years ago, Jo-Wilfried Tsonga would have wilted in the face of two-set deficit on center court at Wimbledon. He would have been so intimidated by Federer’s talent that his game would have collapsed, undone by a lack of motivation and the jitter of nerves. But now everyone knows that Federer is mortal, that he can even be beaten on grass. And because Federer is no longer a unique superstar — he’s just an incredibly gifted player, playing against other gifted players — his competition can rise to the challenge.

And this is why it’s so sad watching the slow fade of a superstar. Yes, they have lost a smidgen of their physical genius. But what’s perhaps even more important is the loss of their invincible aura, that mental advantage which makes them look even better than they are.

Image: Roger Federer after losing the 2011 Wimbledon quarterfinals match to Jo Wilfried Tsonga. (AP)