Centrality categorization for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:math>in high-energy collisions

High-energy proton- and deuteron-nucleus collisions provide an excellent tool for studying a wide array of physics effects, including modifications of parton distribution functions in nuclei, gluon saturation, and color neutralization and hadronization in a nuclear environment, among others. All of these effects are expected to have a significant dependence on the size of the nuclear target and the impact parameter of the collision, also known as the collision centrality. In this article, we detail a method for determining centrality classes in $p(d)+A$ collisions via cuts on the multiplicity at backward rapidity (i.e., the nucleus-going direction) and for determining systematic uncertainties in this procedure. For $d+\text{Au}$ collisions at $\sqrt{{s}_{{}_{NN}}}=200$ GeV we find that the connection to geometry is confirmed by measuring the fraction of events in which a neutron from the deuteron does not interact with the nucleus. As an application, we consider the nuclear modification factors ${R}_{p(d)+A}$, for which there is a bias in the measured centrality-dependent yields owing to auto correlations between the process of interest and the backward-rapidity multiplicity. We determine the bias-correction factors within this framework. This method is further tested using the hijing Monte Carlo generator. We find that for $d+\text{Au}$ collisions at $\sqrt{{s}_{{}_{NN}}}=200$ GeV, these bias corrections are small and vary by less than 5% (10%) up to ${p}_{T}=10$ (20) GeV/$c$. In contrast, for $p+\text{Pb}$ collisions at $\sqrt{{s}_{{}_{NN}}}=5.02$ TeV we find that these bias factors are an order of magnitude larger and strongly ${p}_{T}$ dependent, likely attributable to the larger effect of multiparton interactions.