  In this paper we present a new theoretical model to find out an optimal
weight associated with a soccer player under the presence of a stochastic goal
dynamics by using Feynman path integral method, where the action of a player is
on $\sqrt{8/3}$-Liouville Quantum Gravity surface. Before determine the optimal
weight we first establish an Infinitary logic which can deal with infinite
variables on the strategy space then, a quantum formula of this logic has been
developed and finally, based on this we are able show the existence of a
Lefschetz-Hopf fixed point of this game. As in a competitive tournament, all
possible standard strategies to score goals are known to the opposition team, a
player's action is stochastic in nature and they would have some comparative
advantage to score goals. Furthermore, conditions like uncertainties due to
rain, dribbling and passing skill of a player, whether the match is a day match
or a day-night match, advantages of having home crowd and asymmetric
information of action profiles have been considered on the way to determine the
optimal weight.
