The objective of this work is to advance the understanding of helicopter accidents by examining and quantifying the association between helicopter-specific configurations (number of main rotor blades, number of engines, rotor diameter, and takeoff weight) and the likelihood of accidents. We leverage a dataset of 8,338 turboshaft helicopters in the U.S. civil fleet and 825 accidents from 2005 to 2015. We use the dataset to develop a logistic regression model using the method of purposeful selection, which we exploit for inferential purposes and highlight the novel insights it reveals. For example, one important question for the design and acquisition of helicopters is whether twin-engine turboshaft helicopters exhibit a smaller likelihood of accidents than their single-engine counterparts, all else being equal. The evidence-based result we derive indicates that the answer is contingent on other covariates, and that a tipping point exists in terms of the rotor diameter beyond which the likelihood of accidents of twin-engines is higher (worse) than that of their single-engine counterparts. Another important result derived here is the association between the number of main rotor blades and likelihood of accidents. We found that for single-engine turboshaft helicopters, the four-bladed ones are associated with the lowest likelihood of accidents. We also identified a clear coupling between the number of engines and the rotor diameter in terms of likelihood of accidents. In summary, we establish important relationships between the different helicopter configurations here considered and the likelihood of accident, but these are associations, not causal in nature. The causal pathway, if it exists, may be confounded or mediated by other variables not accounted for here. The results provided here lend themselves to a rich set of interpretive possibilities, and because of their significant safety implications they deserve careful attention from the rotorcraft community.