[Mike Maffie is on a “thesis-defense vacation” this week, so we’re re-running one of his most popular columns from last year. Note new research at conclusion.]

I was reading an article about Rafa Nadal and the unbelievable topspin he generates on his forehand. Another player described the feeling of returning Rafa’s forehand as “like ripping your shoulder out of its socket.” For those who don’t follow tennis, Nadal can hit a tennis ball with about 500 more rotations per minute than the next best tennis player. Naturally I asked Google how many rotations per minute a curveball has.

Here’s the answer. It turns out the average Major League curve ball rotates at 2,450 RPM. Aces like Justin Verlander, can take that number all the way above 3,000 RPM. File this away as yet another reason why you would never want to get in the batter’s box against a big league pitcher.

Yet, RPMs ultimately don’t tell us a whole lot. How do curveballs work? Why do they actually curve? Why do hitters say that curveballs “jump”? Why did Amy Adams take a leading role in the worst baseball movie since, well, um….?

The answer to most of these questions (well, not the Amy Adams’ one) was given to us a long time ago, in a galaxy far, far away: Our eyes can deceive us.

Like much of baseball’s early history, the origin of the curveball is a bit murky. Some believe the curveball was invented by a guy named Candy Cummings around the time of the American Civil War. Others claim the first  curveball was thrown by Clinton Scollard for Hamilton College in the 1880s. In 1884, an article entitled “How Science Won the Game” written by George Harvey, told the story of a pitcher who learned to throw a curveball to defeat a superior team.

[The key line in this story, repeated in both the introduction and in the conclusion, could be right out of a Society for American Baseball Research meeting: “You have the strength,” he used to say to them, “but I tell you, ‘science’ is the thing that wins!” Walter White would be proud.]

According to people who understand physics, a curveball travels in the continuous shape of a parabola, with no sharp break. Yet many hitters say they see the ball radically alter its path as it crosses the hitting zone. This has set off a debate in the scientific community to explain why so many professional hitters say that a curveball suddenly jolts as it approaches the plate.

A recent study by Arthur Shapiro et al (2010) offers a pretty good explanation. Without getting too deep into the science of the study, here is an outline of their findings:

Back in 2004, scientists (Bahill and Baldwin) argued there are two different approaches to hitting: the optimal learning strategy and the optimal hitting strategy. Hitters, they argue, have a choice between watching the ball as it travels into the hitting zone or moving their eyes to where they think the ball will cross the plate. The first strategy (optimal learning) allows the hitter to learn the flight of the ball, but the hitter’s eyes will fall behind the flight of the ball as it crosses the plate (and therefore it will be very difficult to make contact). The alternative strategy requires the batter to quickly recognize the spin on the ball and then move his eyes to the point of contact. If the hitter correctly identified the pitch, this strategy maximizes the chances he will actually make contact with the ball. Hitters alternate between the two strategies to learn different pitches during a game.

So, why does the ball appear to jump? Shapiro and his colleagues tell us that people’s eyes do not give equal treatment to all images within our field of view. The authors explain that because of the concentration of photoreceptors and cells in the central 2 degrees of our field of view, the brain is better able to interpret information from our central view than our periphery. They believe that a curveball appears to “jump” because our peripheral vision is less capable of projecting the flight path of a curveball than our central vision.

Our brain interprets two signals from the ball: the local motion of the ball (the spin) and the global motion (the direction). If hitters adopt an “optimal hitting strategy”, they rely on their peripheral vision to track a ball to the contact point. When a hitter does this his peripheral vision creates a different interpretation of the baseball and causes him to see the ball “jump” as it re-enters their central vision.

Check out Shapiro’s really cool illustration. But be prepared to not believe your eyes. Seriously.

[Note: Mike’s article talks about the importance of spin rates. That’s an issue on the cutting edge of understanding pitching. New research has shown an interesting connection between spin rate and pitching effectiveness. Spin rates are one of the measurements the new cameras are finding in all MLB parks. Data hasn’t been released to the public yet. Here are a couple related articles: Examples of pitchers helped by spin rates; Technical study for fans of scientific journals.]