Using Physics Simulations to Find Targeting Strategies in Competitive Tenpin Bowling
Academic Background
Bowling is one of the most popular sports in the United States, with over 45 million people regularly participating as of 2017. With millions of dollars at stake in national competitions each year, improving player scores has become a research focus. However, due to the complexity of calculations and the numerous variables affecting the ball’s trajectory, most studies rely on statistical analysis of empirical data rather than theoretical modeling. For example, the 2018 United States Bowling Congress (USBC) Equipment Specifications Report used data from 37 bowlers rather than a computer model.
Quantitative analysis of bowling physics has been rare, primarily due to the many parameters involved. Researchers such as Fröhlich, Hopkins, and Huston have attempted to establish mathematical models over the past few decades, considering the effects of internal weight blocks in bowling balls and providing simulation results for a small set of parameter values. However, these models assumed simple friction profiles and could not fully reflect the complexities of actual competition conditions.
This study aims to explore targeting strategies in competitive bowling through physics simulations, helping players improve their scores in matches. Specifically, the research team developed a system of six coupled differential equations to simulate the trajectory of a bowling ball on the lane and analyzed the ball paths under different initial conditions to determine optimal targeting strategies.
Source of the Paper
This paper was co-authored by S. S. M. Ji, S. Yang, W. Dominguez, C. G. Hooper, and C. S. Bester, affiliated with Princeton University, Massachusetts Institute of Technology, The University of New Mexico, Loughborough University, and Swarthmore College, respectively. The paper was published on April 15, 2025, in the journal AIP Advances, titled “Using Physics Simulations to Find Targeting Strategies in Competitive Tenpin Bowling.”
Research Process and Results
1. Derivation of the Equations of Motion
The research team derived a system of six coupled differential equations based on Euler’s equations to describe the rotation of a bowling ball. The equations accounted for the ball’s moment of inertia, initial angular velocity, and the friction effects of the lane. Specifically, the direction of the friction force was determined by the velocity at the contact point between the ball and the lane, with its magnitude proportional to the friction coefficient μ.
By numerically solving these equations, the team was able to simulate the trajectory of the bowling ball on the lane and analyze its different motion phases (sliding and rolling). The sliding phase typically occurs when friction is low, while the rolling phase begins when the contact point velocity between the ball and the lane becomes zero.
2. Oil Patterns and Strike Rate Analysis
In competitive bowling, oil is applied to the lanes in specific patterns to create complex friction profiles. The team simulated two typical oil patterns (flat and short) and analyzed the strike rates under different initial conditions.
The results showed that the strike rate is closely related to the ball’s entry position and entry angle. The ideal entry position is 4 to 12 cm offset from the center of the lane, while the ideal entry angle is approximately 6 degrees. By combining simulation results with empirical data from the USBC, the team was able to calculate strike rates for various initial conditions.
3. Miss Room for an Imperfect Bowler
In actual competition, bowlers cannot hit their targets with perfect accuracy. The team modeled the initial angle error using a Gaussian distribution and analyzed its impact on strike rates. The results revealed that certain targeting strategies create greater “miss room,” allowing bowlers to maintain high strike rates even with slight deviations.
4. Determining the Optimal Targeting Strategy
By simulating ball paths for different initial positions and launch angles, the team identified the optimal targeting strategy. For the short oil pattern, the optimal initial position is board 28, with a launch angle of 1.8 degrees. This strategy ensures the ball enters the ideal region even with minor deviations, thereby increasing the strike rate.
Conclusion and Significance
This study proposes optimal targeting strategies for competitive bowling through physics simulations, providing scientific insights for players and coaches. The results demonstrate that selecting targeting strategies that align with the oil pattern characteristics can significantly improve strike rates. Additionally, the study highlights the concept of miss room for imperfect bowlers, offering greater adjustment flexibility in actual matches.
The scientific value of this research lies in its systematic analysis of bowling ball trajectories and strike rates through a theoretical model, filling a gap in the field. Its practical value is reflected in the provision of actionable targeting strategies for players and coaches, as well as offering references for tournament organizers to design more challenging oil patterns.
Research Highlights
- Innovative Methodology: The development of a system of six coupled differential equations enabled precise simulation of bowling ball trajectories for the first time.
- Practical Applications: The proposed targeting strategies can significantly enhance players’ strike rates, offering substantial practical value.
- Miss Room Analysis: By modeling initial angle errors using a Gaussian distribution, the study revealed the error tolerance of different targeting strategies.
- Multi-Oil Pattern Analysis: Simulations of flat and short oil patterns provided tailored strategies for players under various competition conditions.
Future Research Directions
The research team noted that future studies could further consider factors such as lane topography and bowling ball hardness on ball paths. Additionally, more accurate friction coefficients could be measured experimentally to improve model precision. These enhancements will provide more comprehensive theoretical support and practical guidance for the sport of bowling.
Through physics simulations, this study offers scientifically grounded targeting strategies for competitive bowling, holding significant academic and practical importance.