Are heavier baseball players better hitters? Basically, no, says physics

If you’re following major league baseball this season, you’re watching a game that has gotten more powerful recently.

After the MLB put its foot down on performance enhancing drugs in the early 2000s, the league saw a serious drop in the number of home runs hit, but the power hitter seems to be back: players hit a lot more home runs than usual this season. And the rise of the power pitcher continues: pitchers have continued to throw faster on average since the early 2000s.

Simultaneously, it seems, players have gotten bigger. Researchers from Penn State University recently analyzed (paywall) the self-reported heights and weights of baseball players, and found that baseball players are, on average, a lot heavier than they had been in the previous century. From 1991 to 2015, 70% of players had body mass indexes (BMIs) that classified them as overweight or obese. In the preceding decades, those averages hovered between 30% and 40%. “Professional athletes are not immune from the growing obesity crisis and may not provide optimal role models of health,” the authors write.

Granted, BMI is often considered a flawed measure of assessing whether or not a person is at risk of the negative health consequences that can sometimes come with being bigger, like heart disease, diabetes, and cancer. “You don’t know the distribution of muscle versus fat,” said Jayatri Das, a bioscientist who led the development of the Franklin Institute in Philadelphia’s Sports Zone, which showcases the science of sports. Many people who are overweight according to BMI don’t have the markers in their blood, like high cholesterol, associated with carrying extra fat. Athletes in particular may have deceptively high BMIs because of their larger muscles.

 “Baseball favors strength and power training.” Still, there’s no doubt baseball players have been getting bigger, especially in recent years. Both body mass and BMI increased significantly between 1990 and 2010—and, researchers found in a 2014 study (paywall), major league leaders in hitting stats were particularly likely to be huge.

“Baseball…favors strength and power training,” Men’s Health pointed out in 2014. As a result, some baseball players may not have the lean muscular build characteristic of other sportsmen.

It seems intuitive: larger bodies should be able to hit a baseball harder. But do the physics and physiology agree that increased size yields better performance?

The goal of hitters—from a physiological perspective—is to transfer as much of their own energy into the moving the ball forward through hitting it with the bat, explains Thomas Karakolis, a kinesiologist and author of the 2014 paper. It’s all about kinetic energy, the kind of energy used in motion. It’s described by the formula k = (1/2)mv2, where m is the mass of the system—here, the weight of the hitter and the bat—and v is the velocity, or speed, which here accounts for the movement of hitter and bat.

 “In theory, if a bigger guy is just as fast or strong as another guy, he should be able to hit the ball further.” To increase the kinetic energy transferred to the ball, you have to increase the mass and/or the velocity—without decreasing the other—and ensure no energy is lost when your bat makes contact with the ball. So, “in theory, if a bigger guy is just as fast or strong as another guy, he should be able to hit the ball further,” Karakolis says.

Larger muscles probably help. In 2009, Alan Nathan, a retired physicist formerly at the University of Illinois at Urbana-Champaign and long-time baseball enthusiast, authored a paper (pdf—and, notably, not published in a peer-reviewed journal) in which he calculated that if you assume a baseball player starts out with about 50% of their weight as muscle, every 10% of muscle mass he gains will translate into a roughly 3.6% to 3.9% increase in bat speed.

The trouble is, if a player gets bigger—even if he is also getting stronger—he might start to move his bat through the zone more slowly. This happens because of another aspect of physics: momentum.

Momentum is the tendency of things that are moving to keep moving. It’s calculated two ways: first, it’s the product of mass and velocity (p=mv). But “the flip side of momentum is that it’s also equal to force times time,” Das explains.

Hold onto your hats: Force equals mass multiplied by acceleration, or how quickly speed is increasing. Momentum, then, can be defined as: mass x acceleration x time—where in this case, “time” is the duration it takes to complete a swing of the bat.

It’s a lot easier to get something smaller moving than something bigger. Larger players have more to move. They could, therefore, get less momentum because they’re getting less acceleration in the same amount of time—meaning they don’t reach as high a final speed that smaller players do if they’re expending the same amount of energy. “If you’re moving slower and the whole thing takes longer, then that can lower the force you’re applying,” Das says. It’s a lot easier to get something smaller moving than something bigger. 

In other words, even if players increase their mass, they could be decreasing their speed. And because velocity is squared in the kinetic energy formula, it likely has a larger effect than mass.

This is why it’s critical for athletes to not only increase their strength, but also their power, which is a combination of force and speed, explains Karakolis.

The speed in that handy energy equation—k = (1/2)mv2—comes from our bodies. “As biomechanists, we call it the ‘kinematic chain,’” he says. “That’s how motion moves from the ground, all the way up through your body.” When players use their whole bodies to swing, by rotating their hips, torsos, and shoulders, they get a larger total angular velocity, which moves through the bat and then—assuming they make contact—the ball.

In physics, there’s something called the “coefficient in restitution,” which Karakolis explains as “the efficiency of the energy getting transferred from one object to another in a collision.” This number, which can be used to calculate how fast objects will move after they collide, is a fraction between zero and one. In baseball, players want their coefficient in restitution to be close to one, implying that all of the energy from their bodies and the bat goes into the ball. This scenario would be what physicists call a perfectly elastic collision.

In order to do this, players need to hit the ball at the place on the bat where they get the most energy transfer—the “sweet spot”—for the longest amount of time, so that the ball shoots off in the proper direction. “If you can follow through in the same direction as the ball,” Das says. “You’re maintaining the longest contact with the ball and maximizing that transfer of energy.”

Don’t forget, the ball is also coming in really hot at this point. “When pitchers throw the ball harder, that energy comes in with the ball and can be turned around to go faster,” Karakolis says. The trick for players, he explained, is being able to make themselves perfectly stiff at the moment of impact. “Any lack of stiffness leads to energy losses.” This is why it’s really important that players have strong arms and legs and powerful cores, so they can hold themselves steady at the moment of impact.

There are two other variables in play: the ball and the bat. But as FiveThirtyEight reported earlier this year, we can assume the baseballs, at least in the MLB, are all the same.

That leaves the stick. The wood used in bats isn’t totally solid, Karakolis says. It crumples, ever so slightly, when it’s swung and comes into contact with a ball hurdling through the air, which is why are usually dents in a well-used bat. Some of the swing’s kinetic energy can be lost here, too—which is why players may resort to something called “bat boning” to make them even harder. There are fancy ways to do this with vacuums, but it can also be done by rubbing really hard objects, like animal bones, on the bat. In theory, rubbing harder objects on the bat makes the bat harder by pre-condensing the wood, so the ball doesn’t do so when it’s hit.

There are coatings now in use that may achieve the same thing. Steve Phillips, former general manager of the New York Mets, told the New York Times that he felt the bats in use today are a lot shinier than they used to be. “When you look at these bats now, they are so lacquered,” he said. “You don’t even see the grains anymore.” What’s more plausible is what’s really causing more power in the sport is simply that hitters are getting better 

If—and only if—players can keep their speed constant while making perfect contact with the ball on a perfectly hard bat, they would be able to hit the ball harder if they’re bigger.

That, of course is unlikely. What’s more plausible is what’s really causing more power in the sport is simply that hitters are getting better: more skillful at hitting that sweet spot and following through while keeping still to transfer as much of that energy as possible.

“That’s why baseball is so fascinating,” Das says. “There are just so many variables at play that when you do see that home run, it’s like the stars align. It’s a thing of beauty.”

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