The physics of baseball’s sticky situation

In the first inning of a 21 June baseball game between the New York Mets and the Atlanta Braves, umpires checked the Mets’ fireballing righthander Jacob deGrom for sticky substances in his hat, glove, and uniform. He was judged clean. The inspection was the first under a new crackdown from Major League Baseball (MLB) that came in response to reports that pitchers routinely use grip-enhancing substances to increase the spin rate—and thus the divergence from the anticipated trajectory—of their pitches.

Pitchers’ alleged use of tacky materials, which reportedly range from sunscreen to adhesive pastes, seems to be an open secret in the league , much like the widespread use of steroids was in the 1990s. Although the league has long banned the use of unauthorized foreign substances, it has barely enforced the rule until now. And similar to how steroid use hastened record-setting offensive seasons, there is general agreement that the application of grip enhancers is contributing to hitters’ nearly unprecedented futility in recent years. At the end of June the world’s best baseball players had a batting average of .239 for the season. If that mark holds through season’s end, it would be the lowest since 1968. After that “Year of the Pitcher,” MLB leveled the playing field by lowering the mound from 15 inches above the rest of the diamond to 10 inches.

From a physics perspective, the relationship between a baseball’s spin and its trajectory has been tested extensively over the past few decades, and it’s clear that even a small change in spin rate can affect hitters’ chances of success. However, quantifying the advantage of grip-enhancing substances is a stickier proposition. “There are lots of opportunities to give opinions,” says Washington State University sports scientist Lloyd Smith , “but no one knows the real impact of these substances.”

Maximizing the Magnus force

Once thrown, a baseball is subject to three forces: gravity; drag, which opposes the velocity vector; and lift, which acts perpendicularly to the ball’s trajectory. Although both drag and lift depend on the speed v and angular velocity ω of the ball, lift is of the most interest because it causes a pitch to deviate from the path expected by the hitter.

The deviation stems from the Magnus effect. As a pitched baseball streaks toward the plate, air molecules slam into the ball’s leading face, and a boundary layer of air that is moving slowly relative to the ball wraps partly around the ball. The ball’s spin determines where that boundary layer separates from the trailing face of the ball. For a ball thrown with topspin, the boundary layer stretches farther back on the bottom side of the ball than it does on the top side, which redirects the wake upward and creates a net force downward. The Magnus effect also explains how soccer players can curl the ball around a wall of defenders and how tennis players can clobber the ball over the net without sending it sailing off the court .

Over baseball’s more than 150-year history, pitchers have mastered the generation of spin by applying force tangential to the surface of the ball as they throw. That spin creates the lift—or in baseball parlance, the movement or break—that fools hitters. The Magnus force acts in the direction ω × v, so pitchers can apply different spin axes to their pitches to vary the direction of movement. The four-seam fastball, the fastest and most reliable pitch for many hurlers, is usually thrown with backspin. The boundary layer separates farther back on the top side of the ball, which creates a net upward force. Although the displacement isn’t nearly enough to overcome the vertical drop due to gravity, a high-spin fastball can induce hitters to swing under the ball. A curveball, on the other hand, is generally thrown with topspin so that as it approaches home plate it tumbles out of the strike zone toward the dirt. Other pitches have a component of sidespin, which causes the ball to break toward or away from the hitter.

The magnitude of the Magnus force F_M is determined by

where ρ is the air density and A is the cross-sectional area of the ball. Over the past few decades, University of Illinois physicist Alan Nathan and other researchers have subjected baseballs to laboratory and wind tunnel tests to home in on C_L, the dimensionless lift coefficient. Those experiments suggest that C_L is proportional to the spin rate. Thus, increasing spin rates leads to greater Magnus forces and pitch movement.

“We’ve made very accurate measurements of the lift coefficient as a function of spin magnitude,” says Smith, the director of Washington State’s Sports Science Laboratory. “It’s certainly possible to accurately measure the trajectory of a pitched ball for a few feet and then know where it’s going to go.” Each additional 100 rpm of spin on a fastball leads to about 0.43 inches of movement by the time the ball reaches home plate, he says, which is significant when hitters are trying to square up a roughly 2⅝-inch barrel of the bat with a 3-inch-diameter ball.

Since 2015, when MLB began tracking the spin rate of every pitch with the tracking equipment installed at every stadium, pitchers have been imparting more spin to the ball. The average spin rate of a four-seam fastball has risen from 2238 rpm in 2015 to 2307 rpm in 2020. The spin rates of some pitchers’ offerings have increased 300 rpm or more, which translates to over an inch more rise on a fastball or drop on a curveball.

Major league fastballs can reach 100 mph, meaning the hitter has precious little time to perceive the location and movement of the pitch. Leaguewide, the combination of blazing pitch speeds, high spin rates, and other trends—including hitters’ tendency to swing for the fences rather than just try to make contact—has led to the pitcher-dominated state of the game today and MLB’s motivation to adjust the balance of power.

Getting a grip on friction

It’s clear that increasing the ball’s angular velocity offers a benefit to the pitcher. And both on-field measurements and anecdotal evidence support the idea that pitchers have been getting a lot better at spinning the ball, perhaps due at least in part to grip-enhancing substances. (One such substance is legal: Behind the mound is a bag of rosin, which pitchers combine with sweat to get a better handle on the ball.)

What’s more difficult for baseball-minded physicists is identifying the mechanism and quantifiable advantage of an improved grip for generating more spin. The connection may make sense intuitively, Smith says, but dig into the mechanics of pitching and it gets a bit more complicated. For much of the duration of a pitcher’s delivery to the plate, the grip on the ball—the coefficient of friction between fingers and ball—is irrelevant to the spin magnitude of the impending throw. As the arm moves forward to release the ball, the ball rolls from the pitcher’s palm toward the fingers and then, finally, slides off the fingers at the release point. A sticky substance aids in boosting spin only during that final moment of contact when sliding occurs.

Given how fleeting that frictional interaction is, plus the fact that a baseball isn’t particularly slippery to begin with, Smith wonders how much a tacky material actually enhances spin. Working that out with theory is maddening, he says. This is not undergraduate physics friction with a box sliding along a ramp; the surface area of the hand, the sweat on the fingers, and the duration of the sliding action all factor into the magnitude of the frictional force as a pitcher snaps off a nasty curveball.

Smith and colleague Jeff Kensrud plan to explore the question experimentally with a pitching machine. Unlike most such contraptions, which propel baseballs using two rapidly rotating cylinders, the Washington State version is a cradle attached to the end of a piston, which better simulates a throw from a pitcher’s hand. By applying sticky substances to the cradle, the researchers hope to compare the effects of different degrees of tackiness.

Other clues will emerge on the field. Nathan says he is examining MLB’s spin-rate measurements to look for changes following MLB’s early-June announcement of its on-field inspection edict and the 21 June implementation of the policy. He says preliminary data suggest that the average spin rate of four-seam fastballs has fallen about 5% since 1 June and that hitters are swinging and missing less frequently.