Pitching Science

Engineers who track baseballs catch insights into the game

The pitcher’s action up to the release of the ball is part of the art of pitching; the action of the ball after release . . . is addressed by physics.

–Robert K. Adair,

The Physics of Baseball, 1994

Even in baseball, there’s pure science and there’s applied science. Mechanical engineer LeRoy W. Alaways has been pursuing a bit of both.

On the one hand, he and his colleagues at a biomechanics lab at the University of California, Davis have been helping forge a better understanding of what makes a baseball curve. They’ve been making particularly good headway on one theoretical question that’s stumped baseball researchers for more than 50 years–how the seams of the ball affect the way it flies from the mound to home plate.

On the other hand, Alaways has also recently been working with designers on next-generation machines capable of pitching just like the human big leaguers.

Curving pitches

When it comes to studying why baseballs do what they do, Alaways finds himself part of a long tradition. In 1949, aeronautical engineer Ralph B. Lightfoot used a wind tunnel to collect the first data suggesting that a baseball’s seams have an important role in every pitch. Lightfoot made those measurements to help his boss Igor Sikorsky, inventor of the helicopter, jump into a national baseball debate. An argument was raging on the pages of Look, Life, and other major magazines over this fundamentally important question: Do baseball pitches really curve?

Ultimately, Lightfoot and other investigators proved that the curve is real. They did so by means of both wind-tunnel tests and high-speed photography. For his part, Lightfoot measured force that causes balls to veer sideways and down. Moreover, he found a striking relationship between those forces and the orientation of a pitched ball’s seams as the ball cuts through the air toward a batter.

The results were never published in a scientific journal. But they made it into a 1953 article entitled “The Hell It Don’t Curve,” which sportswriter Joseph F. Drury wrote for the then-popular magazine American Mercury.

That might have been the end of Lightfoot’s data if Alaways hadn’t heard that Sikorsky had dabbled in baseball science. Alaways searched the Web weekly for “Sikorsky” and “baseball.” Finally, after a year, he had a hit. That clue eventually led him to Lightfoot himself, who retrieved his original data from a folder long tucked away in the attic of his Cape Cod home. Now, those old wind-tunnel results are playing a crucial role in bolstering new baseball studies.

Working backwards

Researchers in the UC Davis sports-biomechanics laboratory like to work backwards. To dissect the performance of athletes, they often first view the balls, sticks, or other objects those players use in a sporting contest. The motion of those objects harbors a wealth of information about the performance of the people who handle them.

The raw data for this research are videotapes that capture the trajectories of sports projectiles, including javelins, golf balls, boomerangs, and shuttlecocks. Mont Hubbard, the mechanical engineer who leads the lab, and his students then carefully analyze those objects’ trajectories. The researchers can backtrack to the forces that shaped the flights–and therefore to the performance of the players who applied the forces.

Not until Alaways joined the lab did the Davis team turn its attention to baseballs. Gravity and the specific mechanical conditions experienced by the ball at the moment that it leaves the pitcher’s hand largely determine the ball’s path. Those conditions include how fast the ball is spinning, the orientation of its spin, and the location and initial direction of its release. Alaways created a mathematical model of the baseball pitch from the instant the ball is let go to the instant that it crosses home plate.

Ignoring complicating factors, such as a crosswind, Alaways created a set of equations that closely predicts actual pitch trajectories both in the laboratory and on the field. Conversely, from trajectories recorded simultaneously on up to 10 high-speed video cameras, he reconstructed the likely initial conditions on the ball by means of a mathematical technique known as nonlinear least-squares parameter estimation. Implemented as a computer program, the technique enables someone with accurate data on the trajectory of a pitch to work backwards to the acceleration and spin that the pitcher put on the ball.

The computer plots a three-dimensional trajectory and compares it with the videotaped path. It then adjusts the calculated pitch’s parameters, such as the spatial coordinates of the release point and the spin rate, according to a scheme aimed at minimizing the difference between the plotted trajectory and that of the videotaped original. By repeating the process, the computer calculates a set of release conditions producing a trajectory that closely matches the videotaped one.

The Davis researchers say their system could become useful to coaches as a new tool for tracking their pitchers’ performances. Perhaps, but their work already has scored points in the long-standing debate about the role of baseball seams in curve balls.

Gripping the ball

In bullpen discussions about curve balls, players commonly compare the merits of so-called four-seam pitches and two-seam pitches. Depending on how the pitcher grips the ball, either two or four lines of stitching pass across the face of the spinning ball with each revolution. The popular lore among players is that four-seam pitches curve more than two-seam pitches do.

So far, scientists have been unable to confirm the players’ hypothesis. Yale University’s Robert K. Adair, who was once the official physicist to the National League, considered the issue in the current edition of The Physics of Baseball. He speculates that the effect should be contrary to what players claim. A four-seam pitch makes the air around it more turbulent than a two-seam throw does, so it actually curves less, he surmises.

Wind-tunnel studies dating back to Lightfoot’s work in the late 1940s paint a confusing picture. Lightfoot, for one, found a striking difference between two- and four-seam orientations when he gauged the curve-inducing aerodynamic force known as lift. His measurements revealed that lift on four-seam pitches is up to three times as great as on two-seam pitches. But tests by other scientists since then have revealed no such difference.

In their recent experiments, Alaways and Hubbard entered the fray when they detected a small but statistically significant disparity between the two types of pitches. The researchers describe their experiment, which was also the basis for Alaways’ doctoral thesis, in the May issue of the Journal of Sports Science.

Alaways, now at the California Maritime Academy in Vallejo, is confident that there’s a difference between the lifts of the two and four-seam pitches. Moreover, he now also thinks that the new work explains why the results of the various experiments over the years didn’t agree.

In trials using high-speed photography and balls marked with reflective tape, Alaways and Hubbard collected data from pitches thrown by a pitching machine. From trajectory and spin data, Alaways’ software determined the release conditions, including the initial lift on the ball, for nine pitches thrown in the two-seam orientation and eight thrown in the four-seam orientation. The researchers also varied the conditions of spin and initial velocity to cover a range of possible pitches.

Plotted on a graph, the findings bridge a gap in the conflicting wind-tunnel data. At one extreme are the results of Sikorsky and Lightfoot. They measured a large effect of seam orientation while exploring pitches having low values of a ratio known as the spin parameter. It divides an object’s rotation speed by its forward velocity.

At the other extreme are findings from a team led by Robert G. Watts of Tulane University in New Orleans in the late 1980s. His group found no influence from seam orientation at much higher spin parameters.

Without additional data, it had been difficult to come to a conclusion about the role of seams in curve balls. The newer results break the stalemate, Alaways says. Collectively, the data suggest that the distinction between 2- and 4-seam orientations diminishes as the speed at which the seams circulate begins to compare to the speed of the ball itself.

Watts, coauthor of the baseball science book entitled Keep Your Eye on the Ball (2000, W.H. Freeman and Co.), finds the new picture persuasive. “I concluded that the orientation didn’t matter, but it looks like it does,” he comments. Adair also has come around to thinking that the four-seam ball probably curves more, a new perspective that he says will show up in the next edition of his book.

Meanwhile, Alaways and Lightfoot have coauthored a paper that, after 50 years, will finally bring Lightfoot’s pioneering wind-tunnel data into the official literature on baseball science. It’s slated for publication in a forthcoming issue of Sports Engineering.

Besides tracking pitches in the laboratory, the Davis researchers have also been applying their new method to real baseball games. In 1996, Alaways, Hubbard, and Sean P. Mish, now at Credence Systems in Hillsboro, Ore., mounted high-speed video cameras at the Fulton County Stadium in Atlanta.

In the Cuba-versus-Japan contest of the Summer Olympic Games, they used the equipment to track pitches in three dimensions. The paths predicted by their model for 21 pitches deviated by less than 2 centimeters on average from the recorded ones, they reported in the February Journal of Applied Biomechanics.

Their analysis of the videotaped trajectories produced hints of another aerodynamic effect called the drag crisis–a steep decrease in air resistance, or drag, on moving bodies above a certain velocity. If further studies confirm that there is a drag crisis within the ranges of speeds that pitchers can throw, then balls fired above a certain speed wouldn’t lose velocity as fast as balls thrown just a little slower.

Pitching machine

While taking a break from pursuing issues of pure baseball science, Alaways has turned to an application. Last spring, engineers at Fastball Development Corp. in Seattle were searching the Web and discovered Alaways’ dissertation (http://www.geocities.com/baseballdocs/). They then offered him some summer work.

For 3 years, Fastball has been developing a deluxe pitching machine, nicknamed Abner after baseball’s putative inventor, Abner Doubleday. Besides spitting out balls at controlled speeds and nearly any desired orientation of launch and spin, this pitching simulator displays an animation of a pitcher winding up and throwing. What’s more, in the most advanced version of Abner, the ball shoots through the screen at whatever point the pitcher’s hand appears to be letting it go.

That was all well and good, but the designers didn’t understand baseball aerodynamics sufficiently to know where the ball would end up, given the launch settings they fed into the machine. That’s where Alaways’ work came in.

“What he did was of tremendous value to us,” says the company’s sales and marketing chief Michael Kirby. Alaways “gave us the equations and told us what in the hell we needed to program these pitches,” Kirby says.

Now, the machine’s curves, fastballs, sliders, and other styles of pitches reliably cross home plate within a palm’s width of any desired point in the strike zone, Alaways says.

This spring, the Cleveland Indians and the St. Louis Cardinals rented the machines for training. The players have raved about them in ESPN Magazine and other venues. The company is now discussing sales of the $175,000 machines with a handful of Major League teams, Kirby says.

Alaways is about to go into private industry himself, but he won’t be designing pitching machines. Instead, he’ll be applying the same sorts of math and models to the task of recreating, from skid marks and other evidence at a crash site, the trajectories of cars in a collision.

As for the data that gave Alaways the bedrock on which his own work stands, it will never again be so hard to find. The researchers have donated Lightfoot’s data to the Baseball Hall of Fame in Cooperstown, N.Y.

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