This paper presents an optimization model to complete the missing data in the energy matchup matrix which compares different players’ energy. The optimization model searched for the solutions that can make the eigenvalue of the energy matrix the biggest that should be the principle one. To test the model, we built a Bayesian matrix of energy matchup which mixes the judgments of energy in a matchup between players given by experts and the statistical data gotten from each game in different positions. The proposed method can complete the probabilities given by the Bayesian matrix. Finally, an implementation shows the effectiveness and rationality of the model.