  This paper studies the relationship between basketball teams' four factors
and efficiency ratings as defined by Oliver (2004). The paper introduces an
equation showing how a team's four factors in conjunction with its field goal
and free throw percentages can be used to calculate its offensive rating.
Moreover, the substitution of defensive four factors into the equation allows
for the calculation of defensive and net ratings. To incorporate recent trends
in the NBA, the paper updates the estimation for the relative frequency of
possession-ending free throws which are needed to estimate the number of
possessions from box score data. Sensitivity analysis of the offensive rating
is performed in order to better understand the relative importance of the four
factors. By examining partial derivatives of the offensive rating, the paper
quantifies the marginal impact of small changes in the offensive and defensive
four factors on offensive, defensive, and net ratings. Most importantly it is
observed that the relationship between the four factors and efficiency ratings
is non-linear and the individual factors' effect on the ratings depends on the
values of the other factors. The paper also includes examples from NBA seasons
spanning 1996-97 through 2022-23.
