Picture for a moment a soccer ball resting in uneasy balance at the top of a hill, primed to roll down into one of two valleys on either side below. But which? That, of course, depends on a number of factors: wind, temperature, the starting position of the ball, maybe some uneven ground or rocks.
It's an example of the so-called butterfly effect, made somewhat famous in pop culture in recent years. At the risk of oversimplifying -- and scandalizing the Ph.D.s in the audience -- it's the notion that outcomes depending on a complex set of variables can be drastically changed by altering even slightly just one of those inputs.
Now, in place of the ball, imagine instead that the object on the brink is the fortune of a national soccer team. The two valleys? Call them success and failure. The line between the two for many teams at this year's World Cup will be that thin, and the factors at work in determining the difference in the final outcome can seem just as random.
Case in point: the 2002 American World Cup squad. Coached by Bruce Arena, that team made U.S. soccer history by reaching the quarterfinals in Korea and Japan. Memorable wins over Portugal and Mexico, and a near miss against Germany when a win would have meant a ticket to the semifinals, cemented its legacy as maybe the greatest American team of all time. So it's easy to forget how close the Americans came to being eliminated in the first round, after a loss to Poland in the final group game.
"In 2002, the difference was in another game that was played, with Portugal missing chances that they usually don't miss," said midfielder Earnie Stewart, who remembers waiting on the field after the loss to Poland for confirmation that South Korea had edged the Portuguese, 1-0, to send the Americans through in second place. "If they had scored a goal we would have been out of the World Cup, and that would have been it. But you get lucky on one hand, and Korea pulls an upset that puts us into the second round."
Had Portugal's usually top-notch finishing, which had produced six goals in its first two games, not gone completely awry that evening; had the Europeans not seen two men sent off, the first in just the 27th minute; had budding star Park Ji-Sung's brilliant goal not found the space between the legs of keeper Vitor Baia -- all this in a match in which the U.S. wasn't even involved -- the triumphant American memories of 2002 would be lost to history, and that now storied team largely forgotten.
Then there's the 2006 version of the U.S. team. With the same coach and many of the same players, the team crashed out in the group round, earning just one point. History now regards that squad as an underachiever, but if a potentially game-winning DaMarcus Beasley goal against Italy had not been disallowed, or a controversial penalty not been whistled for Ghana in the next match, it might be a completely different story.
"There's such a marginal difference, just based on what took place," said Josh Wolff, a member of both teams. "In '02 we were on the upside of it, and in '06 we were on the minus side. In '02, the Poland game, we lost, and we got a good result from Korea. In '06 it's a difficult penalty we take in that Ghana match, and it's a game we're pushing toward getting that result that would have gotten us through."
Of course, there are such defining moments in all of sports. Referees' decisions and inch-thin margins that change everything. The best teams are the ones that put themselves in position to take advantage of those moments on a regular basis, and the law of averages tends to even the breaks out over time.
But not so much at the World Cup, at least for the middle-of-the-pack teams, for which success is usually defined by the ability to finish in the top two of a four-team group. Three group games is all a team has to prove itself, followed by the pressure-packed knockout rounds, played on the brink of elimination, balanced by an ever-growing legacy of accomplishment for the winners.
In the group phase, the difference between qualification for the knockout rounds and early elimination is simply the margin between second and third place, sometimes determined by a single goal from among the six group matches. That makes each potential defining moment that much more definitive -- the referee brings his whistle to his mouth but doesn't call the borderline penalty, or does; a team tacks on a soft added-time goal that turns out to be the defining margin in goal differential.
"With the narrowness of getting through," Wolff said, "the breaks are very defining in a World Cup. Mainly in a tournament format, I don't know that you can duplicate that in baseball or football, those other sports don't have the theme we have. It's such a big deal, and you have three games, and points are so important. It's what makes it so exciting."
There's no doubt the World Cup is all the more exciting for that characteristic: win or wait the equivalent of a sporting eternity for redemption. Perhaps even crueler is the manner in which chance events can lead to an overall verdict of success or failure for a team, and sometimes even an entire generation of national team players.
"It's a very fine line," said longtime U.S. defender Mike Burns. "I look at the '94 team I was on and the '98 team I was on, and there's no way that one team was that much better than the other to advance out of the group, and the other not to get a point and finish last. But that's the way it goes sometimes in tournament play. You look at France in '98 and they win the World Cup, conceding one goal the entire tournament. In 2002 they didn't score a goal and didn't advance. There's no way France in '98 was that much better."
Those observations come from a man who knows about fortune at the World Cup. Not only did Burns play a role in the disastrous 1998 effort, he is widely remembered, somewhat unfortunately amidst a long career, as the man who let a German header find the narrow space between his body and the post -- the first goal against the Americans in that Cup, and the beginning of a downward spiral for the team.
"Soccer is the most subjective game in the world," added Alexi Lalas, Burns' teammate, who had much the opposite World Cup fortune. Lalas became a worldwide symbol of American soccer amid the successes of 1994, but remained glued to the bench for the 1998 World Cup, perhaps to the long-term benefit of his own legacy.
"We call it the simplest [sport], but it is also the most complex," Lalas said. "These moments that end up defining whether you're good or bad, it's real easy to say 'but it's just this moment, so that's not fair.' But that's the whole point. That's what the great teams are, those that find the ability to exploit these moments, and put themselves in position to have these moments."
No doubt, Brazil and Spain will get through the group stages in South Africa, with or without catching the breaks. Not so for a middle-of-the-road team such as the U.S. Like that ball perched atop the hill, on the brink of two valleys, a shift in just one small variable could make all the difference.
"If I could sign up for it right now, I'd want to be the luckiest team in the tournament," Burns said. "Because the team that wins it will certainly have some luck go their way. The good teams usually prevail, but you need to have a little bit of luck on your side, you need to have some balls bounce your way."
There's no telling when it will happen. But at some point this African winter, a referee will blow his whistle, a goal will be scored in a game not involving the team in question, or a linesman will raise his flag in error. And that moment will seal a team's fate, and help define its place in history.
For most of the field, World Cup success is just that capricious. Call it what you want, but the butterfly effect is alive and well in soccer.
Brent Latham covers soccer for ESPN.com. He previously covered sports throughout Africa for Voice of America radio and now works as a soccer commentator for a national television station in Guatemala. He can be reached at email@example.com.