Shapley values are extensively used in explainable artificial intelligence
(XAI) as a framework to explain predictions made by complex machine learning
(ML) models. In this work, we focus on conditional Shapley values for
predictive models fitted to tabular data and explain the prediction
$f(\boldsymbol{x}^{*})$ for a single observation $\boldsymbol{x}^{*}$ at the
time. Numerous Shapley value estimation methods have been proposed and
empirically compared on an average basis in the XAI literature. However, less
focus has been devoted to analyzing the precision of the Shapley value
explanations on an individual basis. We extend our work in Olsen et al. (2023)
by demonstrating and discussing that the explanations are systematically less
precise for observations on the outer region of the training data distribution
for all used estimation methods. This is expected from a statistical point of
view, but to the best of our knowledge, it has not been systematically
addressed in the Shapley value literature. This is crucial knowledge for
Shapley values practitioners, who should be more careful in applying these
observations' corresponding Shapley value explanations.

Shapley value explanations are less precise for observations on the outer region of the training data distribution, which has not been systematically addressed in the Shapley value literature.