Baseball has been called the “thinking man’s game,” and for good reason. Unlike the other major professional sports, baseball is a mental game with dozens of strategic decisions that must be made before every pitch is thrown. Pitchers must decide whether to throw a fastball or breaking ball, and which part of the strike zone to target. Hitters must anticipate which pitch is coming toward them based on the count and multiple other factors. Fielders position themselves according to where they think the ball will be hit, relying on the hitter’s “spray chart.”
Every pitch thrown produces a dizzying array of data. Pitch speed, batted ball location, fielder position, exit velocity and fielder movement. All that data has helped create a new frontier—the age of analytics. Front offices, managers and players go to the ballpark each day armed with terabytes of data to run through their statistical models and come up with a strategy for every possible matchup that could occur in the game.
The intersection of baseball and data was made popular in the 2011 movie Moneyball, where Jonah Hill plays a data-crunching nerd who helps propel the 2002 Oakland A’s to a division title despite their rock-bottom payroll and a roster made up of scrap-heap players. Over the past two decades, analytics has gone from an obscure part of the game, reserved for nerds in the front office and barely understood by fans, to a full-blown movement. Fans can tell you about launch angle, exit velocity, spin rate or catch probability. While the players may never have taken a class in physics, it is physics that governs every pitch, swing or play on the field.
The Pitch: Why Spin Matters
The play doesn’t start until the pitcher and catcher agree, with coded hand signals hidden from prying eyes, on a pitch. Now, things get interesting. Unlike the ball used in other major sports, a baseball is not particularly aerodynamic. It has an irregular surface and will refuse to move in a straightforward fashion at the speeds in which it will be propelled. A baseball is stitched together. Pitchers can manipulate the ball with a flick of the wrist, their finger placement resulting in “movement” of the ball, either with rotation or a complete lack of it (as we’ll see later) that causes pressure across the ball’s seams. Let’s skip, for now, to the more creative—aka forbidden—ways to make the ball “move.”
At these raised seams with their prominent stitches, unique aerodynamic forces act on the ball as it rockets toward home plate. It’s a study in aerodynamics.
After a pitcher releases the ball, it travels toward the plate. With all but one type of pitch (the infamous knuckleball), the ball leaves the pitcher’s hand spinning. At any instant, one side of the ball will be moving in the same direction as the air and the other side will be moving against the air. The side of the ball moving in the same direction as the air will have a region of air at higher velocity, and therefore less pressure (Bernoulli’s principle) than the opposite side, which is moving into the air and creating higher pressure. This results in a net force from the high-pressure side to the low pressure side that is known as the Magnus effect (after the German physicist Heinrich Gustav Magnus, who ran experiments on spinning cylinders to explain the unpredictable behavior of spinning artillery shells in 1852).
Michael Richmond, physics professor at the Rochester Institute of Technology, explains the Magnus force (with the following equation.
Where:
- CL= lift coefficient (variable and influenced by spin rate, direction of rotation and velocity)
- ρ= density of air
- A = cross sectional area of baseball
- v= velocity
- The final component of the equation in the brackets is a unit vector cross product that establishes the direction of the force (perpendicular to the axis of rotation and the ball’s velocity).
When a pitcher throws a fastball, his goal is to impart as much force onto the ball. The pitcher’s whole body plays a role, acting like a whip, or more accurately, a multi-link rigid body mechanism. The motion starts from the pitcher’s foot on the rubber (the top of the pitcher’s mound), goes through the leg, the body, upper arm, forearm, the hand and, finally, the fingers, with each part adding velocity to the part before it. With a fastball, the pitcher’s two fingers on the pitching hand will hang on to the ball until the last possible moment, pushing the ball toward the plate, but at the same time, with a last little flip, the pitcher’s fingertips impart a downward force on the back of the ball, rotating the it about the horizontal axis, creating backspin. The backspin causes high pressure to develop on the bottom of the ball. If the pitcher generates enough speed and spin, the ball will fight gravity. Baseball players say a fastball will rise, though it may be more accurate to say that it falls less.
Pitchers refer to the erratic movement of the baseball as “pop,” or “life.” With enough spin, the ball will appear to almost hop up over its final few feet of flight to the plate, making it almost impossible for the batter to hit. Curveballs, meanwhile, are thrown with a flick of the wrist, with the motion imparting a rotation about the vertical axis of the ball, causing it to break to the left of a right-handed pitcher or to the right of a left-handed pitcher.
Below, you can see the Magnus effect in full effect as two-time Cy Young Award winner Jacob deGrom just absolutely blows away batter Mark Teixeira with a rising fastball.
Physicists like Lyman Briggs have been researching the airflow around a spinning baseball for decades, but the science has only recently been embraced by coaches and players. Now, any pitcher whose name is worth knowing spends hours and hours studying and tracking his spin rate—because a higher spin rate could be the difference between making millions of dollars in the big leagues or riding a bus for peanuts in the minors. If you watch a bullpen session, especially during Spring Training, it’s not uncommon to see each pitcher step off the mound and consult with an iPad after every pitch. He’s checking his spin rate.
You could devote an entire decade’s worth of research to studying the physics of pitching. There are an infinite number of variables that go into every pitch—arm slot, finger placement and pressure and temperature—but thanks to the new age of analytics, we’re collecting more data related to spin rate and pitch movement than ever before. If you’re interested in learning more or seeing the pitch data of your favorite pitcher, the MLB’s Statcast powered by Baseball Savant or Brooks Baseball and the PITCHf/x tool are excellent resources.
No MLB pitcher has embraced the science and physics behind pitching more than Trevor Bauer, who is constantly tinkering with his grips and essentially “designing” his pitch arsenal every year. “That’s the power of understanding the principles and what’s actually going on at that critical moment,” Bauer said. “Because I understand and did all the studying and designing of it, it makes it very easy to make adjustments because you know all the different control parameters.”
Embracing the physics of pitching certainly paid off in a big way for Bauer last year. He won the National League Cy Young Award with a 1.73 ERA and is set to cash a big check this winter as a free agent.
The Swing: Launch Angle, the Hitter’s Answer to Spin Rate
Spin rate has revolutionized (see what I did there) pitching, but on the hitter side, launch angle and exit velocity are having their own moment. Many of the same principles of physics that govern pitching also apply to hitting. The way a ball spins off the bat will contribute to how far it goes. If a hitter really squares up a ball and strikes it perfectly, he will generate backspin. As with a fastball thrown with backspin, a ball hit with backspin will sail farther than it would otherwise. It’s a thing of beauty to see a home run clear the fence while appearing to rise. At least that’s true for the batter.
A batted baseball generally follows a parabolic flight path, as governed by the rules of physics related to projectile motion. Initial velocity and launch angle are the two biggest drivers of the total distance traveled.
D = v2 * sin(2ϴ)/g
The hitter can control the angle at which his batted ball begins its flight, but he is also fighting the spin put on the ball by the pitcher to generate an ideal launch angle and high exit velocity. A hitter wants to swing up on the ball to make contact at a quality launch angle, but doesn’t want a complete uppercut, which will send the ball 50 feet high but not very far.
The bat itself is a key component in how far the ball will travel. Newton’s law of conservation of momentum requires that the total momentum in a system must be preserved after a collision. The pitched ball has its own momentum, as does the swinging bat. After the bat makes contact with the ball, most of the energy is transferred to the ball. How far the ball will go depends on how well the hitter centered the ball in the sweet spot of his bat.
As energy from the collision between the ball and bat is transferred into the wooden bat, the bat begins to vibrate. If the ball is struck with the bat’s sweet spot, the thick part (aka the barrel), the bat vibrates closer to its fundamental frequency, causing more energy to be transferred to the ball. When a hitter strikes the ball too close to the end of the bat or the handle of the bat, the bat vibrates at a frequency that is farther away from its fundamental frequency, sending more energy back into the batter’s hands. Showing that there’s no limit to what the numbers can tell you, statisticians have developed a method of measuring well-struck baseballs using Statcast data called “barrels.” Fernando Tatis Jr. led the league in barrels last year and nearly won the MVP Award at the age of 21.
The exit velocity that a hitter can generate depends on how much energy he is able to put into his swing. The author, 5'-10" and 155 pounds soaking wet, could hit baseballs all day at the perfect launch angle and never hit one out of an MLB ballpark. Sadly, I lack the physical strength to produce enough bat speed.
Luckily for most MLB players, physical strength isn’t an issue. Just watch them line up and hit dinger after dinger in batting practice. It’s muscles and training that let them swing at the proper angle to maximize the value of their contact. They’re able to do this in batting practice where they’re being fed 75-mph “meatballs,” but all bets are off at game time, when the pitcher is going for a win—a pitcher who will force the batter to decide, in the blink of an eye, whether a pitch is a strike or a ball, a fastball or slider, where the ball is located (on the inside or outside of the plate), and whether to swing. To make contact with a 100-mph fastball, a hitter has roughly 0.4 seconds to decide whether to swing or not—truly the blink of an eye. Every kernel of data they’re able to stuff into their heads or use to fine-tune their swing could be the difference between a starting job in the big leagues or riding the bus in the minor leagues.
Analytics: The Future of the Game—Like it or Not
A popular backlash against the surge of analytics has erupted. Twitter is awash with reasons why analytics-based baseball is ruining the national pastime. While whether analytics are good or bad is debated, the way they have changed the game is unmistakable. Armed with a statistical profile for each hitter, pitchers are getting better at attacking weak spots and holes in batters’ swings, resulting in rapidly growing strikeout rates. Hitters, in contrast, have adopted the idea that a ball hit on the ground is almost worthless. Fielders are being shifted all over the field, leading to a vanishing number of pitches being thrown to fielders symmetrically positioned in the playing field.
Some fans might not like analytics, but the teams that have been quicker to embrace them are contending for titles, while teams that have been slower to adapt have been left in the basements of their divisions. Those same Moneyball A’s have been to the playoffs 11 times since 2000, despite having a roster that is constantly turning over as star players price themselves out of Oakland. More recently, with a miniscule budget, the Tampa Bay Rays came within two games of winning the 2020 World Series before eventually being defeated by the wealthy Los Angeles Dodgers. Both the Oakland and Tampa Bay franchises rely heavily on analytics.
Players also benefit from the rise of analytics and science in sports. Just ask Trevor Bauer, who’s set to make north of $25 million next year, or Nicholas Castellanos, who parlayed excellent batted ball data and improved numbers into a $64 million deal. The players who embrace and understand the physics of the game, or who at least do more than brush it off as “the nerds upstairs ruining the game,” will have more successful careers.
And so, science remains undefeated. This time in baseball.