As artificial intelligence spreads out to numerous fields, the application of AI to sports analytics is also in the spotlight. However, one of the major challenges is the difficulty of automated acquisition of continuous movement data during sports matches. In particular, it is a conundrum to reliably track a tiny ball on a wide soccer pitch with obstacles such as occlusion and imitations. Tackling the problem, this paper proposes an inference framework of ball trajectory from player trajectories as a cost-efficient alternative to ball tracking. We combine Set Transformers to get permutation-invariant and equivariant representations of the multi-agent contexts with a hierarchical architecture that intermediately predicts the player ball possession to support the final trajectory inference. Also, we introduce the reality loss term and postprocessing to secure the estimated trajectories to be physically realistic. The experimental results show that our model provides natural and accurate trajectories as well as admissible player ball possession at the same time. Lastly, we suggest several practical applications of our framework including missing trajectory imputation, semi-automated pass annotation, automated zoom-in for match broadcasting, and calculating possession-wise running performance metrics.