Can a corked bat truly enhance hitting distance?

Ranked No. 33 on ESPN's compilation of The 100 Most Unforgettable Moments from the Last 25 Years: Sammy Sosa, facing the Devil Rays on June 4, 2003, breaks his bat during a hit against pitcher Jeremi Gonzalez. Umpire Tim McClelland, upon inspecting the shattered bat, discovers cork embedded in the barrel. This incident embarrassed Sosa and reignited a major debate in baseball: Are corked bats providing hitters with an undue benefit?

To explore this issue, it's essential to delve into the mechanics of corked bats. A standard Major League baseball bat is crafted from a single piece of wood, usually ash or maple. For instance, Derek Jeter uses a 34-inch, 32-ounce ash Louisville Slugger. Imagine modifying Jeter's bat by drilling a 1-inch wide, 10-inch deep hole along the barrel, filling it with a light substance like cork or Styrofoam, or even shredded Super Balls, and then sealing it with wood filler to conceal the alteration. This creates a corked bat. But what's the purpose behind such modifications?

By removing wood from the barrel, the bat becomes lighter. The weight reduction can be calculated using the dimensions of the drilled hole. The volume of a cylinder is determined by the following formula:

V = πrh

For instance, a 1-inch-wide hole drilled 10 inches deep into a bat would have a volume of:

V = (3.14)(0.5 inches)(0.5 inches)(10 inches) = 7.85 cubic inches = 0.0045 cubic feet = 0.00013 cubic meters

Using the density formula (d = m/V) and referencing the density of white ash wood, which is 670 kilograms/cubic meter [source: SI Metric], we can determine the mass of the removed wood.

m = dv = (670 kilograms/cubic meter)(0.00013 cubic meters) = 0.0871 kilograms = 3.07 ounces

If you were to hollow out Derek Jeter's bat, it would weigh approximately 29 ounces (822 grams). However, since the hole is filled with cork, you must consider its weight. Assuming the cork fills the same volume as the hole and using the density of solid cork, which is 240 kilograms/cubic meter, the weight of the cork can be calculated [source: SI Metric]:

m = dv = (240 kilograms/cubic meter)(0.00013 cubic meters) = 0.0312 kilograms = 1.1 ounces

Thus, a corked bat is roughly 2 ounces (nearly 57 grams) lighter than a standard bat. For Derek Jeter, this translates to using a 30-ounce (850-gram) bat instead of a 32-ounce (907-gram) one. Additionally, inserting cork alters the bat's center of gravity, moving it closer to the batter's hands. These combined effects make the bat easier to swing, allowing for greater speed.

Is this significant? Absolutely, and we'll explain why next.

Put a Cork in It (or Don't Actually)

The distance a baseball travels after being hit is determined by its speed upon leaving the bat, referred to as batted ball speed or BBS. Higher BBS translates to greater distances. BBS is influenced by two key factors: the speed of the swing and the bat's weight. While a corked bat increases swing speed, potentially boosting BBS, its lighter weight reduces the power transferred during impact, which can lower BBS.

In 2011, physicists Alan Nathan and Daniel Russell, known for their studies on the science behind baseball, explored how corked bats impact batted ball velocity. They examined collision efficiency, or q, which measures a bat's effectiveness in converting pitch speed into hit power. Their findings showed an unmodified bat had a q value of 0.214, while a corked bat had a q value of 0.193 [source: Nathan et al.]. They used the following formula to calculate batted ball speed:

BBS = (q)(pitch speed) + (1 + q)(bat speed)

For a standard bat, the math would appear as follows:

BBS = (0.214)(94 mph) + (1.214)(70 mph) = 20.116 mph + 84.98 mph = 105 mph

For a corked bat, the calculation appears as follows (note that the 3-mph increase is an estimated assumption):

BBS = (0.193)(94 mph) + (1.193)(73 mph) = 18.142 mph + 87.089 mph = 105 mph

Interestingly, the batted ball speed remains identical for both bats. The study indicates that the benefits of faster bat speed are offset by the drawbacks of reduced bat weight. In essence, a corked bat has no net effect on batted ball speed or the distance the ball travels.

However, the debate doesn't end here, as corked bats may offer another benefit. A skilled hitter can not only swing a corked bat faster but also accelerate it more quickly, enabling them to reach top speed in less time. This allows the batter to delay their swing, track the pitch more effectively, and adjust their swing accordingly. While home runs may not increase, consistent solid contact and a higher batting average are likely outcomes.