From Prior Beliefs to Lineup Truths: Bayesian Inference for Lineup Performance

One of the key responsibilities of a team's coach is to identify the lineups that provide the best chance of winning a game. Traditional metrics such as offensive and defensive ratings summarize past performance, but they are inherently noisy and not predictive. To address this limitation, we adopt a fully Bayesian approach to estimate the posterior predictive distribution of each lineup's offensive and defensive rating. Specifically, we assume a normal prior for these ratings, while the observed points scored and allowed per possession for each lineup serve as our evidence. Given the normal likelihood and the conjugacy of the normal model, the posterior predictive distribution is also normal, with updated mean and variance reflecting both prior beliefs and observed data. Our out-of-sample evaluations show that forecasts based on the posterior predictive distribution outperform the baseline model considering only the past lineup performance observed. The performance gap also increases as the observation lineup samples get smaller. In addition to the prediction improvements, the proposed Bayesian framework naturally quantifies uncertainty in lineup performance, enabling the generation of different rankings, including probabilistic comparisons that better reflect the inherent variability in basketball outcomes.