Optimal Angle to Hit a Baseball

Common Knowledge and Rationality

When an introductory physics student is asked "what angle whould one hit a baseball to obtain maximum distance," the most common answer is 45 degrees. This, of course, is true under the simplifying assumptions in introductory physics, but not in general. In particular, the wind, the construction of the bat, the type and spin of the pitch, the compression of the ball at the point of impact, the ball's shape which is not a perfect sphere on account of the threads, and other factors, influence the precise angle that correctly answers the question. Yet, baseball players seem to adjust naturally to these conditions.

We interpret "rationality" not as an assumption about how people make decisions, but as a tool for analyzing how people learn to act. The experienced baseball player does not hit the ball optimally due to a study of physics, but due to experience. If we wanted to predict how a baseball player would hit a ball in a given situation, however, the answer a physicist would give is likely to be very close.

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For those who are very curious, the following physics article provides the calculations involved:

How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories by Sawicki, Hubbard, and Stronge, American Journal of Physics, November 2003.

There is a surprisingly large body of research by physicists on this issue, including:

• The effect of spin on the flight of a baseball
• Tradeoff between speed and spin
• Dynamics of the baseball-bat collision