Golf, Baseball and Biomechanics: The Underlying Science of Sports

It's Game Six of the 2013 World Series. St. Louis Cardinals starting pitcher Michael Wacha steps up to the mound, winds up and smoothly delivers a pitch on its way to meet the Boston Red Sox Shane Victorino's bat. The bat makes contact with a "whack," delivering a game-changing, three-run double to give Boston a lead they would never relinquish. Had more balls smacked into the catcher's mitt instead, the Cardinals could have held off the Red Sox from clinching the Series win. The answer to achieving the elusive, seamlessly delivered pitch could lie in a scientific equation, combining biomechanics and physics.

Convergent Science, a company based in Middleton, Wisc., analyzed the St. Louis Cardinals pitcher Adam Wainwright's curveball. They examined one of the best pitchers in baseball to find that his 12-6 curveball spins at 93-94 mph about an axis perpendicular to the ground at 1800 revolutions per minute of top spin. The combination of these factors creates the 11.1-inch drop for Wainwright and his knee-buckling curveball.

For a regular curveball thrown by a right-handed pitcher, the ball naturally travels in a path that draws it down and to the left. The 12-6 curveball is more difficult to hit because it sinks straight down -- there is no left or right movement on the ball. To throw an effective 12-6 curveball, a pitcher must create top spin that spins straight towards the ground as well. The down-force is at its peak during the initial release of the ball and at its lowest as the ball reaches the catcher's mitt.

"This software is generally not used in baseball -- but we took it and are using it," said Rob Kaczmarek, the director of marketing at Convergent Science. "To use it for a sport is new terrain."

The company began solving for the Navier-Stokes equation with this particular computer application of computational fluid dynamics. This technology has many uses from internal combustion engine and green technology to wind technology and wind farm optimization.

Though typically used for commercial operations, a few Convergent Science staff members were watching the World Series and arguing over who was a better pitcher.

"We don't normally do this type of analysis," Kaczmarek said. "But after the analysis was done, we thought it was interesting that we were able to do it and predict it."

No one in the sports realm is currently using this software to help predict or help fine-tune a pitcher. The company began marketing the product in November after they realized the power of the analysis, Convergent Science said. The software's design of simulating how the ball moves within a domain opens up the path to other applications, such as replicating conditions of different stadiums.

"If a stadium was dusty or windy, we could see how that affects a batted ball," Kaczmarek said. "Would a ball in California behave differently than one inside Fenway Park in Boston? You can predict which stadiums have the best likelihood of getting home runs depending on weather conditions."

In addition to improving a pitcher's curveball, the company cites other potential uses in baseball, including determining how to achieve better breaking curveballs and how to save a pitcher's arm by reducing the spin and force while maintaining the same drop. For example, a pitch thrown at 85 mph with 1800 rpm spin on the ball will result in a very different looking curveball than if the ball had been thrown at 95 mph with the same rpm.

"The ability to tweak the curveball is there with 1-2 mph changes in speed going toward the catcher with a few hundred rpm change," Kaczmarek said. "This may key up people to start thinking about analyzing this type of stuff."

The software was developed over the course of six years and is still evolving in terms of adding features, functions and models, he said.

As of this fall, Convergent Science is the only company to claim to have found the equation to track the ball's movement through time and space. Others use software that simply spins the ball to figure out the type of force at work.

"There are other people in companies that do this type of software, but ours is unique in the sense that the ball actually moves throughout the domain -- meaning we simulate ball from pitchers hand to catcher's mitt," Kaczmarek said.

In the past, baseball training technology has primarily focused on how the bat meets the ball rather than the ball's release from the pitcher. Cade Donaldson, a sophomore at Beavercreek High School in Beavercreek, Ohio, has been playing ball since the age of three and was introduced to the ProBatter Pitching Simulator at age 12 with the Dayton Dynasty. His former club team reserved an evening slot with the simulation machine twice a week.

The ProBatter program Donaldson used could train hitters for four pitches: the two-seam fastball, the four-seam fastball, the curveball and the change-up. The machine has a large screen with a video of a pitcher winding up and going through the motions of a throw. However, the screen has a hole from which the ball is released and delivered to the hitter. The latest ProBatter PX2 Pitching Simulator includes nine pre-programmed pitches.

"I felt more prepared when the season started that year because I got used to seeing different pitchers... both left and right," he said.

Donaldson spent one season training with the ProBatter program. He said that becoming accustomed to the different pitches improved his hitting overall and greatly improved hitting a curveball and hitting off of a lefty pitcher.

"The delivery is different with a lefty, and I was having trouble hitting off of one," he said. "When it's just a batting machine, it's repetitive. When it's the pitcher, you kind of feel like you're being pitched to, and it is better practice with a live pitcher -- but the batting machine certainly simulated one."

The cost of the program was included in the $1,200 fee to play on the team -- much of this went towards the simulation batting training. On top of the cost, there's a certain inconvenience factor since there are only a handful of these in existence, Donaldson said.

"I'm not sure if my new coaches even know about it," he said. "If there was one at the batting cages, they would probably use it."

The machine can be set up in two different ways. The hitter can either run it himself, in which case he'd know which pitch would be thrown in advance, or the hitter can emulate a game setting by having another player or coach operate the machine.

"It really helped me with the curveball just by exposing me to the pitch more -- and I became much better with hitting them," the 15-year-old said.

If a team isn't within a reasonable distance to travel for a machine, coaches make do with videotapes and iPads.

With Donaldson's current team, the Tipp City Flames, coaches videotape pitches and review the motions on an iPad, from which players can re-watch and fix mistakes, he said.

The type of technology that Convergent Science claims to have invented could be groundbreaking for baseball and golf -- two sports in which the shape of the ball and other conditions, such as weather, contact of the club or bat, and speed, dictate performance.

Calculating the trajectory of a sphere using this technique is a problem people have been working on for an extended period of time, said Alan Nathan, a physics professor at the University of Illinois at Urbana-Champaign. Nathan's area of expertise is in the physics of baseball, a specialization he has studied for 14 years.

"I've been to conferences where people give talks about this, and the usual word is that they haven't succeeded... They may be close, but they just aren't there yet," Nathan said.
"They are trying to solve very complicated equations."

Another major area in which science directly affects the game of baseball concerns bats. Non-wooden bats are typically used in college baseball because of an already-understood scientific issue: Aluminum bats outperform wooden bats.

"Learning how to regulate performance is a real physics problem," Nathan said. "It's an area where physics can have a dramatic impact on baseball at an amateur level -- it can, and it has."

These calculations in sports demand the same computer codes that airplanes use to design wings and auto manufacturers use to create aerodynamic cars. Nathan said that the benefits of cracking this technique would extend well beyond sports since its use is widespread across industries and "this particular problem is a hard problem."

"The golf ball has dimples, and the baseball has seams -- and those things matter," Nathan said. "You have to take these into account when doing those types of equations."

Most touring professionals or top level golfers use a technology called TrackMan. This radar detection system tracks the club path, face angle and club head speed. Using these figures, it estimates the impact between club face and ball, producing up to 50 different calculations, including spin rates, ball speed and launch angle.

"It puts science behind the ball flight principles that have been around for generations," said Jonathan Balyeat, a Golf Pro at Sycamore Hills Golf Club in Fort Wayne, Ind. "It can use scientific figures and numbers to show you a reason for the reactions the golf ball produces based on various angles and characteristics of each individual golf swing."

In the context of the computational fluid dynamics equation developed by Convergent Science, Balyeat agrees with Nathan that this software would be invaluable to golf. The program picks up where TrackMan leaves off -- after the golf ball leaves the club face.

TrackMan is a system that allows golfers to understand how the ball reacts up until the club strikes to create the flight it travels in, he said. TrackMan will detect the side spin, back spin, the face angle, launch angle and speeds up until the club makes contact with the ball. Following this, the radar system tracks the trajectory of the golf ball to provide the carry distance and total distance based on monitored statistics.

"It seems like the team has solved the second half of this equation -- which in turn could definitely be revolutionary as far as golf ball characteristics and how you make a golf ball become more efficient," Balyeat said.

However, the differences between the games of golf and baseball may come into play regarding how -- or even if -- this type of technology could be used as an effective training device.

"Unlike in golf, you can't restrict how fast or how much movement a pitcher can throw a ball in baseball," Balyeat said.

The U.S. Golf Association and R&A, the two governing bodies of golf, set limits on what golf balls can do and how they can perform.

"It'll be interesting to see in terms of what you can do as far as improvement within the limitations," Balyeat said.

CORRECTION: A previous version of this post incorrectly described a feature of the TrackMan system. The post has been updated to correct this.