Image: Curveball study
Scientists analyzed the actual motion of pitches thrown by professional baseball players to determine that optical illusion have a lot to do with the curve of a curveball.
updated 10/13/2010 5:28:30 PM ET 2010-10-13T21:28:30

When those curveballs from playoff pitchers like Phillies ace Roy Halladay near the plate, their sudden drop may be a mirage, scientists say.

It doesn't really matter, though, because most people still can't hit them.

That movement is called a "break," when the ball suddenly seems to drop sharply, usually resulting in the batter swinging above or below it.

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The ball actually follows a smooth arc from pitcher to catcher, but seems to break when it moves from one part of the batter's vision to another, according to researchers Arthur Shapiro of American University and Zhong-Lin Lu of the University of Southern California.

The solution, they agree, has been the mantra of dads and coaches for decades: "Keep your eye on the ball."

And, as batters from Little League to the majors can attest, "Easier said than done."

"The argument been going on forever about whether (curveballs) break or not," observed Rob Gray, a psychology professor at Arizona State University who was not part of Shapiro and Lu's research team.

Scientists will tell you the ball follows a smooth curve, he said, while baseball players use terms like "falls off the table."

"We tell players to keep their eye on the ball, but you just can't," Gray said. "It is physically impossible to follow a major league baseball all the way to the plate."

"The curveball does curve, but the curve has been measured and shown to be gradual," Shapiro said. "It's always going to follow a parabolic path. But from a hitter's point of view, an approaching ball can appear to break, drop or do a whole range of unusual behaviors."

The problem is that how you see the ball differs depending on whether the eye is focused on it or if the peripheral vision at the side of the eye is being used, Lu and Shapiro report in a research paper published online Wednesday in the journal PLoS ONE.

Batters focus on the ball as it leaves the pitcher, Lu explained, but when it's about 20 feet from home plate they often switch to peripheral vision, then go back to central vision as the ball arrives at the plate.

That can cause the ball to appear to break as much as a foot, the researchers said.

It also explains the apparent rise of some fastballs, they added.

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Indeed, in their research they won a prize for an illusion illustrating their theory demonstrating how an object falling in a straight line can seem to change direction.

Lu said he and Shapiro began studying the subject because they realize the "break" of a curve is inconsistent with physics.

Since then, he said, sports researchers have approached them for help in finding ways to defeat a curveball.

He said fans watching games on television also say a curveball appears to break when observed from behind home plate.

That is a geometric illusion, he said, caused by the fact that for the first part of a pitch, the viewer sees little or no vertical drop. Because the pitcher throws the ball at a slight upward angle, the first part of the pitch appears more or less flat. Then the drop seen near home plate surprises the eye.

Asked who throws the best curve, Lu had no hesitation in naming Dodgers' Hall of Famer Sandy Koufax.

Their findings aren't limited to baseball, Lu added.

"When we look at a scene, most of the images fall on the visual periphery, which has much lower resolution, although we don't normally notice the difference between central and peripheral vision," he said.

"We often confuse different signals in peripheral vision. For example, if we see a moving car with our peripheral vision, we may confuse the movement of the car with any movement in its immediate background.

Copyright 2010 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

Explainer: The math and science of baseball

  • Image: Fenway Park
    Adam Hunger  /  Reuters
    Fans take their seats for the MLB American League baseball game between the Boston Red Sox and the Tampa Bay Rays at Fenway Park in Boston, Massachusetts, September 8, 2008. This was the 456th consecutive sell out at Fenway Park which set a new MLB record.

    Baseball is well-known as America's pastime. For many mathematicians and scientists, it also passes as class time. Batting average is just an appetizer on the menu of number-crunching options for the avid fan. Statistical models exist to determine everything from the winner of the Cy Young award, pitching's grand prize, to a manager's contribution to the team.

    Scientists, too, have a blast on game day. They've used the laws of physics, for example, to explain why a head-first slide is faster than going for the bag feet-first. To prepare yourself for the Fall Classic, click the “Next” label and take some math and science out to the ballgame.

  • Why the best team doesn't always have the best record

    Alan Diaz  /  AP
    Florida Marlins' Josh Beckett pitches against the Washington Nationals in the third inning Friday, July 29, 2005, in Miami.

    Major-league baseball teams play 162 games in the regular season. While that may sound like a lot, it isn't nearly enough to ensure that the best team in the league ends the season with the best record. For the 16-team National League, that would require teams to play 256 games per season, a pair of physicists from the Los Alamos National Laboratory calculated.

    Their statistical analysis indicates that for the best team of any league to be assured of having the best win-loss record, the number of games on the schedule should be roughly the number of teams cubed. A schedule with that many games overcomes the randomness that permits a lesser team to prevail in any given matchup, according to the physicists.

    Playing fewer games, of course, gives underdogs more of a chance to reach the playoffs and sometimes win the World Series, as the wild-card Florida Marlins did in 2003.

  • Mathematical model judges fielding ability

    Alex Rodriguez
    Kathy Willens  /  AP
    New York Yankees third baseman Alex Rodriguez commits an error on Boston Red Sox David Ortiz's third inning grounder during the third inning of their baseball game, Tuesday, May 9, 2006, at Yankee Stadium in New York. Ortiz was safe at first on the play.

    Should Alex Rodriguez, the New York Yankees third baseman, go back to playing shortstop as he did for the Texas Rangers? According to a mathematical model developed by Shane Jensen at the Wharton School at the University of Pennsylvania … yes, he should.

    The model measures factors such as how many runs a fielder saved or cost his team. It ranked Rodriguez as the best shortstop in the league before he was switched to third base to accommodate Derek Jeter, the Yankees' longtime shortstop. According to the model, Jeter is one of the worst shortstops in the majors.

  • The statistics of managerial style

    ALCS: Los Angeles Angels of Anaheim v Chicago White Sox - Game 2
    Jed Jacobsohn  /  Getty Images
    Mike Scioscia of Los Angeles Angels of Anaheim argues with home plate umpire Doug Eddings (L) and Jerry Crawford after the controversial play in the ninth inning of Game Two of the American League Championship Series allowing the Chicago White Sox to win 3-1.

    Stats let managers keep close tabs on the performance of their players. Steve Wang, a statistician at Swarthmore College and avid Yankees fan, has devised a statistical means to keep tabs on managers as well.

    He examined data on everything from how often a manager goes to the bullpen, to the number of lineups used in a season. Such factors went into an algorithm to determine managerial style. Certain styles, he notes, might be more effective with certain kinds of teams.

    "A manager who prefers to stay with his starters might be best-suited for a team with veteran starting pitching, whereas a team with fragile young arms might do best with a manager who uses his bullpen aggressively," he said in a news release.

  • Head-first slide is faster

    Image: Sliding head first
    Alan Diaz  /  AP file
    Florida Marlins' Alfredo Amezaga slides safely into third base after hitting a triple against Washington Nationals' Collin Balester in the seventh inning of a baseball game in Miami, Sunday, Sept. 14, 2008.

    Every fraction of a second counts when a player rounds third and races to beat the throw at home plate, which raises the question: is it faster to slide feet or head first?

    According to David Peters, a physicist at Washington University in St. Louis, head first has the edge. For one, arms are lighter than legs, which means as the body rotates, arms extend out a bit farther than the legs. For another thing, the feet give an extra push.

    That said, many players still prefer a foot-first slide. They can pop up easier, instead of sliding by the bag, for starters. They also face less risk of an injury to their hands that could keep them out of the batting lineup for months.

  • To catch a fly ball, keep an eye on it

    Running at top speed with his back to the plate, New York Giants center fielder Willie Mays gets under a 450-foot blast off the bat of Cleveland first baseman Vic Wertz to pull the ball down in front of the bleachers wall in the eighth inning of the World Series opener at the Polo Grounds in New York on September 29, 1954. In making the miraculous catch with two runners on base, Willie came within a step of crashing into the wall. The Giants won 5-2.

    It may be the most repeated advice in all of ball sports: "Keep your eye on the ball." It's also what outfielders do to catch a pop-up fly, according to researchers at Brown University, who watched student ballplayers catch virtual fly balls in a virtual reality lab.

    The researchers found that good players position themselves so that it appears the fly ball is neither speeding up nor slowing down. If the ball seems to be speeding up, the player should move back. If it’s slowing down, they should head in closer.

    The findings, however, fail to explain Willie Mays’ famous grab in Game 1 of the 1954 World Series, shown here. He caught the ball over his shoulder and without even looking at it.

  • Why hitters take a few pitches

    Image: Albert Pujols
    Jeff Roberson  /  AP
    St. Louis Cardinals Albert Pujols watches his second home run of the night against the Arizona Diamondbacks during the sixth inning of a baseball game Friday, July 17, 2009, in St. Louis. Pujols hit his first home of the game during the fourth inning.

    Often the world's best sluggers will watch a pitch or two pass over home plate and into the catcher’s mitt. Some of them are fastballs that could have easily been smacked out of the park. Why do they do it? To calibrate the ball’s track, explained Ken Fuld, a psychologist at the University of New Hampshire.

    “The batter purposely leaves eye contact midway through a pitch and makes an anticipatory saccade (an eye movement) to the point just in front of where the ball crosses the plate. If the ball seems to rise (which it physically can't if it was thrown overhand), it is traveling faster than the batter initially thought, but now the batter has calibrated it," he explained in a news release.

    The next time the same type of pitch is thrown, the slugger has an advantage and just may knock it out to the cheap seats.


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