Abstract
The current metrics used for player evaluation in basketball have the problem of making it difficult to obtain information on the reliability of the evaluation values and to evaluate the synergy effects among players. In this study, we propose a model that considers the abilities of players playing simultaneously, such as teammates and opponents, as well as synergy effects with teammates. We derive the posterior distributions of players' offensive and defensive abilities, as well as those Bayesian credible intervals in closed form, after developing a Bayesian model. Additionally, we calculated Bayesian credible intervals for the indices derived from affine transformations of those capabilities and evaluated the uncertainty in estimating capability values. The computational cost of the proposed method is lower than Markov chain Monte Carlo methods. Using real data from the National Basketball Association (NBA), the proposed method is validated against the existing method, and it is confirmed that the proposed method provides more valid player evaluations than the existing method.
