🔬 physics

Do All Wood Bats Perform Identically?

Despite having identical inertial properties, wood baseball bats made from ash, birch, and maple do not perform identically, with variations in performance for off-center impacts being driven by differences in bending stiffness rather than wood species.

Original authors: Patrick Drane, Alan M. Nathan, Daniel Russell, Blake Campshure

Published 2026-10-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Patrick Drane, Alan M. Nathan, Daniel Russell, Blake Campshure

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of baseball, the collision between a ball and a bat is a moment of pure physics, a split-second event that determines whether a batter reaches base or strikes out. For decades, scientists have understood the mechanics of this crash, particularly for modern metal and composite bats, which are engineered to perform within strict, regulated limits. However, the wooden bat, the traditional tool of the professional game, remains a mystery in comparison. While manufacturers craft these bats to look and feel the same, the wood itself is a natural material, grown by trees with unique histories of soil, sun, and growth rings. This raises a simple but profound question for any player or fan: if two wooden bats have the exact same length, weight, and shape, do they actually hit the ball with the same force? The answer lies in how the wood vibrates. When a ball strikes a bat, the wood does not just sit still; it bends and shudders. Some of the energy from the pitch is lost to these vibrations, meaning less energy is returned to the ball. The stiffer the wood, the less it bends, and the more energy is preserved for the hit.

A team of researchers from universities and a major sporting goods company set out to test this idea with a collection of eighteen wooden bats. They did not grab random bats off a shelf; instead, they worked with a manufacturer to create eighteen custom bats that were as identical as possible on paper. Six were made of ash, six of birch, and six of maple, the three most common woods used by professional players. Every single bat was cut to the same length of 0.861 meters and weighed exactly 0.897 kilograms. They shared the same balance and the same outer shape. If you held them, they would feel indistinguishable. The researchers wanted to see if, despite these perfect similarities, the bats would behave differently when a ball hit them. To find out, they first measured how each bat vibrated when tapped, listening for the specific pitch of its lowest bending note. Then, they fired baseballs at the stationary bats at a speed of 44.7 meters per second, striking them at various points along the barrel to see how fast the ball bounced back.

The results revealed that even when bats are built to be twins, they are not identical in performance. The key difference was found in the stiffness of the wood, which showed up as a difference in the pitch of the bat's vibration. The researchers found that bats with a higher vibration frequency, indicating stiffer wood, returned the ball faster than those with a lower frequency. However, this difference did not happen everywhere on the bat. When the ball struck the "sweet spot," the area near the center of the barrel where the bat vibrates the least, all the bats performed almost the same, regardless of their wood type or stiffness. The variation was tiny. But when the ball struck the bat just a few inches closer to the handle, away from that sweet center, the differences became clear. At these locations, the stiffer bats, which vibrated at a higher frequency, sent the ball flying faster. The less stiff bats absorbed more energy into their own bending, leaving less energy to propel the ball.

The study also looked closely at the three different types of wood to see if ash, birch, or maple had a natural advantage. The data showed no systematic difference between the species. A maple bat did not inherently outperform an ash or birch bat. Instead, the performance depended entirely on the specific stiffness of that individual piece of wood. A stiff piece of ash performed better than a soft piece of maple, and a soft piece of ash performed worse than a stiff piece of maple. The type of tree the wood came from mattered far less than the specific structural integrity of the bat itself. This means that a professional player holding a bat that feels perfect in their hands might still be holding a bat that is slightly less efficient than another one sitting right next to it, simply because the wood inside vibrates differently.

The researchers used computer simulations to confirm these findings, modeling the collision to understand the physics behind the energy loss. The simulations matched the real-world tests, showing that the energy lost to vibration is the primary reason for the performance gap. When a ball hits the bat away from the sweet spot, the wood bends significantly. If the wood is less stiff, it bends more, soaking up more of the impact energy. If the wood is stiffer, it resists bending, keeping more energy for the ball. The study concluded that while the differences in performance are real, they are subtle and depend heavily on where the ball hits. For a player, this suggests that the quest for the "perfect" bat is not about finding a specific brand or wood type, but about finding the specific piece of wood that happens to be the stiffest among the options available. In the end, the paper proves that nature does not produce identical twins, even when the blueprint is the same, and that in the high-speed world of baseball, those small natural variations can change the outcome of a hit.

Technical Summary: "Do All Wood Bats Perform Identically?"

Problem Statement
Despite extensive research into the physics of baseball-bat collisions, particularly regarding non-wood bats and the regulation of their performance (e.g., BBCOR standards), the performance variability of nominally identical wood bats remains unaddressed. The central question posed is whether two wood bats with identical inertial properties (length, weight, moment of inertia, and shape) perform identically in game situations. Specifically, the study investigates if differences in wood species (ash, birch, maple) or inherent material variations lead to measurable differences in exit velocity, and if so, what physical mechanisms drive these differences.

Methodology
The study utilized a controlled experimental and computational approach involving 18 specially constructed wood bats: six each of ash, birch, and maple. All bats shared nominally identical dimensions (0.861 m length, 0.897 kg weight) and shape profiles.

Modal Analysis: Each bat underwent experimental modal analysis to determine natural frequencies and mode shapes of the lowest bending vibrations. The bats were suspended via rubber bands to simulate free-free boundary conditions (approximating hand-held conditions). An impact hammer and a roving accelerometer were used to measure frequency response functions, yielding the frequencies of the first four bending modes ( $f_1$ through $f_4$ ).
High-Speed Impact Studies: A high-speed air cannon fired baseballs at a stationary bat at 44.7 m/s (100 mph). Impacts were recorded at various locations along the barrel, ranging from the sweet spot (approx. 15.2 cm from the tip) to locations 5 cm further toward the handle. The Ball-Bat Coefficient of Restitution (BBCOR, denoted as $e$ ) was calculated from the ratio of outgoing to incoming ball speeds.
Computer Simulations: A physics-based simulation, utilizing Timoshenko beam equations modified for non-uniform bat profiles, was employed. The model adjusted the Young's modulus ( $E$ ) and shear modulus ( $S$ ) for each bat to match the experimentally measured bending frequencies ( $f_1$ and $f_4$ ). These parameters were then used to simulate ball-bat collisions and predict BBCOR values across the barrel.

Key Contributions and Results
The study establishes that nominally identical wood bats do not perform identically, with performance variations primarily driven by differences in bending stiffness rather than wood species.

Variability in Stiffness: Despite identical dimensions, the fundamental bending frequency ( $f_1$ ) varied significantly across the sample set, ranging from 122 Hz to 160 Hz. This variation was observed within and across wood species, indicating that stiffness is a property of the individual piece of wood rather than the species itself.
Location-Dependent Performance: The impact of stiffness on performance is highly dependent on the impact location:
- At the Sweet Spot: Differences in BBCOR among the bats were minimal (approx. 2.1% spread). The data and simulations confirm that at the sweet spot, where vibrational energy is minimized, the dependence of BBCOR on bending stiffness is weak.
- Off the Sweet Spot: Significant performance differences emerged at impact locations further from the barrel tip (specifically 5 cm or 2 inches beyond the sweet spot). Here, the spread in BBCOR values increased to approximately 4.9%. A strong positive correlation was found between the fundamental bending frequency ( $f_1$ ) and BBCOR: stiffer bats (higher $f_1$ ) exhibited higher BBCOR values.
Wood Species: The study found no systematic performance differences attributable to the wood species (ash, birch, or maple). When controlling for bending stiffness, the three species performed indistinguishably.
Physical Mechanism: The performance difference is explained by energy dissipation. At locations off the sweet spot, the vibrational amplitude is higher. The study demonstrates that the energy dissipated in bending modes is a function of the collision time relative to the vibrational period ( $\omega\tau$ ). Bats with lower stiffness (lower $f_1$ ) dissipate more kinetic energy into bending vibrations (specifically higher-order modes) during off-center impacts, resulting in a lower exit velocity (lower BBCOR).

Significance and Claims
The paper concludes that while professional players often select bats based on wood species, the primary determinant of performance variability among nominally identical bats is the specific bending stiffness of the individual bat, not the species. The research clarifies that:

Performance differences are negligible at the sweet spot but become significant at impact locations common in actual gameplay (off the sweet spot).
Stiffer bats (higher bending frequency) generally perform better in these off-center scenarios.
There is no inherent performance advantage to ash, birch, or maple when inertial properties and stiffness are accounted for.

The authors note a discrepancy between experimental data and simulation at off-center locations, where the observed dependence on stiffness was weaker than predicted, suggesting other unknown factors contribute to performance variability. However, the core finding remains that bending stiffness is a critical, measurable variable in wood bat performance.

More like this