When is randomization advantageous in quantum simulation?

We investigate which Hamiltonians benefit from randomized quantum simulation methods, focusing on product formulas and the \ac{qsvt}. We propose a sparse QSVT method based on composite stochastic decompositions, where the bulk of the Hamiltonian is treated deterministically and the tail is sampled stochastically and analyze how the resulting stochastic errors propagate through the block-encoding and QSVT procedures. To evaluate the approach, we construct ensembles of random Hamiltonians with varying variance, locality, and number of terms, and benchmark the improvement due to randomization. We find that in regimes with a large number of terms and high coefficient variance, randomization can reduce the required gate count by an order of magnitude. Interestingly, this regime is similar to that of second-quantized Hamiltonians in quantum chemistry. A drawback is that deterministic methods eventually catch up as the target error decreases. In practice, for target errors below roughly $10^{-3}$, deterministic methods become more efficient.