For typical microscopic systems, the SM approach is the only one possible. Indeed, a typical macroscopic body contains a number of molecules of the order of Avogadro's number, $N_A \approx 6 \cdot 10^{23}$. If we wanted to predict the trajectory of each particle of a system of $N$ particles exactly, we would need to solve $3 \cdot N \approx 10^{24}$ coupled equations, which is infeasible even for modern computers. Moreover, even if a computer was able to solve such a large number of equations in a short time, we would need to write the $6 \cdot N \approx 10^{24}$ initial conditions, which is definitely infeasible. Therefore, we renounce to a complete knowledge of the system and try to get an average knowledge, by applying the tools of statistics and probability theory.