  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.
