# Game Theory and Business Strategy

## Common Knowledge and Rationality:

Optimal Angle to Hit a Baseball

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 threads which make it not a perfect sphere, and other factors, influence the precise angle that correctly answers the question.
Yet, baseball players seem to naturally adjust 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.

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 on this issue, including: