  Knowledge of the electronic stopping curve for swift ions, $S_e(v)$,
particularly around the Bragg peak, is important for understanding radiation
damage. Experimentally, however, the determination of such feature for light
ions is very challenging, especially in disordered systems such as liquid water
and biological tissue. Recent developments in real-time time-dependent density
functional theory (rt-TDDFT) have enabled the calculation of $S_e(v)$ along
nm-sized trajectories. However, it is still a challenge to obtain a meaningful
statistically averaged $S_e(v)$ that can be compared to observations. In this
work, taking advantage of the correlation between the local electronic
structure probed by the projectile and the distance from the projectile to the
atoms in the target, we devise a trajectory pre-sampling scheme to select,
geometrically, a small set of short trajectories to accelerate the convergence
of the averaged $S_e(v)$ computed via rt-TDDFT. For protons in liquid water, we
first calculate the reference probability distribution function (PDF) for the
distance from the proton to the closest oxygen atom,
$\phi_R(r_{p{\rightarrow}O})$, for a trajectory of a length similar to those
sampled experimentally. Then, short trajectories are sequentially selected so
that the accumulated PDF reproduces $\phi_R(r_{p{\rightarrow}O})$ to
increasingly high accuracy. Using these pre-sampled trajectories, we
demonstrate that the averaged $S_e(v_p)$ converges in the whole velocity range
with less than eight trajectories, while other averaging methods using randomly
and uniformly distributed trajectories require approximately ten times the
computational effort. This allows us to compare the $S_e(v_p)$ curve to
experimental data, and assess widely used empirical tables based on Bragg's
rule.
