The restoring (or re-centring) capability is an important feature of any isolation system and a fundamental requirement of current standards and guideline specifications for the design of seismically isolated structures. In this paper, the restoring capability of spherical sliding isolation systems, often referred to as friction pendulum systems (FPSs), is investigated through an extensive parametric study involving thousands of non-linear response history analyses of SDOF systems. The dynamic behavior of the isolation system is described with the visco-plastic model of Constantinou et al. (J Struct Eng 116(2):455–474, 1990), considering the variability of the friction coefficient with sliding velocity and contact pressure. Numerical analyses have been carried out using a set of approximately three hundred natural seismic ground motions recorded during different earthquakes and differing in seismic intensity, frequency content characteristics, magnitude, epicentral distance and soil characteristics. Regression analysis has been performed to derive the dependency of the residual displacement from the parameters governing the dynamic response of FPS. The influence of near-fault earthquakes and the accumulation of residual displacements due to real sequences of seismic ground motions have been also investigated. Finally, the restoring compliance criteria proposed in this study are compared to the lateral restoring force requirements of current seismic codes. Based on the results of this study, useful recommendations for a (more) rational design of FPSs are outlined