Shot Management

There are many decisions which require choosing an optimal mix of several goods. Throw in some uncertainty and you have a classic portfolio problem. The portfolio problem answers this question:
What is the optimal mixture of securities (stocks and bonds) which optimizes a portfolio’s return, given an investor’s risk preference?

Recently, I’ve been wondering if the same techniques can be used to analyze basketball shot selection. Basketball teams choose to take a two or three point shot. The likelihood of making either shot should determine the optimal ratio of two to three point shots. In the next few days I’ll provide a simple model and derive conditions for optimal shot ratios.