This paper describes analyses of single-degree-of-freedom structures with different spacing, coefficients of restitution, structural periods, and both linear and nonlinear cases, to a suite of earthquake records with equivalent probability of occurrence. A methodology to relate the probability of impact, and the probability of different levels of percentage peak, spectral displacement increase over a suite of events with equivalent probability of occurrence. Thus, both analyses provide a design risk assessed for these different design parameters, which provides a framework for risk analysis and design that is developed and illustrated. It is shown that smaller gaps between structures and greater difference between structural periods independently lead to greater probabilities of impact. Also, smaller gaps, greater coefficients of restitution and structural linearity (i.e. less yielding) lead to increases of structural displacement as a result of impact. The overall results provide significant insight into the design parameters and their sensitivity around structural impact, and provide these results within a risk based framework amenable to designers and the profession. The approach developed may be generalized to other cases with more degrees of freedom, different masses or damping values.