Football’s Confounding Physics

Research Blogging / by Dave Munger /

Why is it that soccer goalkeepers sometimes have more trouble stopping long-range shots than shots from up close? Physics and the limits of human perception provide the answers.

Credit: Flickr user gt8073a

In 1997, in a key international soccer matchup with France, Brazilian wingback Roberto Carlos placed a ball 35 meters away from the goal to prepare for a free kick. The score was tied 0-0. At this distance, he was unlikely to score. The French team lined up a wall of players between their opponent and the goal. The only way to score would be to curve a ball over or around the wall, and even then, the goalkeeper should have ample time to react to the shot. Roberto Carlos ran hard at the ball, kicking it with the outside of his left foot, aiming at least a meter to the right of the wall, and well outside the mouth of the goal. But his foot contacted the ball to the right of center, causing it to spin rapidly to the left as it hurtled through the air. This made the shot bend leftward, and when it neared the goal, it appeared to bend even faster. As the shot glanced off the right goalpost and in for a score, the French goalkeeper stood two meters away, completely flummoxed, still expecting that Roberto Carlos’s shot would pass far wide of the goal (here’s a video of the shot, and another, similar goal that perplexed the goalkeeper even more).

Professional soccer players are well aware that shooters can spin the ball and cause its trajectory to bend. So why are goalkeepers, who are paid millions of dollars to stop shots, sometimes utterly baffled by curving balls? Part of the answer comes from the particular physics of a soccer ball. Michael Gutbrod, who blogs at A Scientific Nature, discussed an article published last week that showed how the curving path of a spinning ball changes as it slows down. The researchers, led by Guillaume Dupeux, recorded the path of balls shot into water at high speed. As you’d expect, when the balls were spinning, they curved in a smooth arc in the direction of the spin. But as the speed of the balls slowed, they began to curve even more dramatically.

Dupeux’s team then looked at various sports involving spinning balls, considering the size of the ball and the distances involved, to see when this secondary, more dramatic curve might begin to affect game play. Baseball pitches, they found, were not affected—the distance between the pitcher’s mound and home plate was too short for the ball to slow sufficiently. But in soccer, with a large, relatively lightweight ball, this sharp, unexpected curve could actually occur in a game. That may be exactly what we are seeing in the case of Roberto Carlos’s kick. So even if goalkeepers are aware of the potential for balls to curve, they may not expect the drastic, extra-sharp curve at the end of the shot. The research was published in the New Journal of Physics.

But goalkeepers see hundreds of free kicks in practice on a daily basis. Surely they’d eventually adapt to bending shots, wouldn’t they? I wrote about a similar problem on my blog earlier this year: How baseball fielders track fly balls. Researchers found that even when the ball is not spinning, outfielders don’t follow the optimum path to the ball—instead they constantly update their position in response to the ball’s motion. So an unusual bend to the ball’s motion might indeed throw off even an expert.

In 2008, Dan Peterson of “Sports are 80% Mental” uncovered a study on how soccer players respond to bending free kicks. Elite professionals from some of the top soccer clubs in the world were shown simulations of straight and bending free kicks, which disappeared from view 10 to 12.5 meters from the goal. They then had to predict the path of the ball. The players were accurate for straight kicks, but they made systematic errors on bending shots. Instead of taking the curve into account, players tended to assume the ball would continue straight along the path it was following when it disappeared. Even more surprisingly, goalkeepers were no better at predicting the path of bending balls than other players. Since this report predates the 2010 study showing that soccer balls bend more dramatically than the earlier models predict, players would probably do even worse with more accurate models of ball trajectories. The research was published in Naturwissenschaften.

So both physics and the limits of the human perceptual system combine to make these long, curving shots almost impossible for goalkeepers to react to. Fortunately for the keepers, the shots are rarely well-executed, or we’d see many more videos like the now-infamous Roberto Carlos free kick.

Dave Munger is editor of, where you can find thousands of blog posts on this and myriad other topics. Each week, he writes about recent posts on peer-reviewed research from across the blogosphere. See previous Research Blogging columns »


Originally published September 16, 2010

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