In soccer, quantitatively evaluating the performance of players and teams is essential to improve tactical coaching and players’ decision-making abilities. To achieve this, some methods use predicted probabilities of shoot event occurrences to quantify player performances, but conventional shoot prediction models have not performed well and have failed to consider the reliability of the event probability. This paper proposes a novel method that effectively utilizes players’ spatio-temporal relations and prediction uncertainty to predict shoot event occurrences with greater accuracy and robustness. Specifically, we represent players’ relations as a complete bipartite graph, which effectively incorporates soccer domain knowledge, and capture latent features by applying a graph convolutional recurrent neural network (GCRNN) to the constructed graph. Our model utilizes a Bayesian neural network to predict the probability of shoot event occurrence, considering spatio-temporal relations between players and prediction uncertainty. In our experiments, we confirmed that the proposed method outperformed several other methods in terms of prediction performance, and we found that considering players’ distances significantly affects the prediction accuracy.