  A physical model is developed, which suggests a pathway to determining the
optimal release conditions for a basketball free throw. Theoretical framework
is supported by Monte Carlo simulations and a series of free throws performed
and analysed at Southbank International School. The model defines a
smile-shaped success region in angle-velocity space where a free throw will
score. A formula for the minimum throwing angle is derived analytically. The
optimal throwing conditions are determined numerically by maximising the
expected number of successful shots given the error pattern inherent to the
player. This approach is fully quantified by the model presented and suggests a
reliable way for individual free throw improvement. The model also explains
recent NBA data showing that some of the most successful free throwers bear
completely different conditions to the average player.
