Reconfigurable intelligent surfaces (RISs) have received extensive concern to improve the performance of wireless communication systems. In this paper, a subarray-based scheme is investigated in terms of its effects on ergodic spectral efficiency (SE) and energy efficiency (EE) in RIS-assisted systems. In this scheme, the adjacent elements divided into a subarray are controlled by one signal and share the same reflection coefficient. An upper bound of ergodic SE is derived and an optimal phase shift design is proposed for the subarray-based RIS. Based on the upper bound and optimal design, we obtain the maximum of the upper bound. In particular, we analytically evaluate the effect of the subarray-based RIS on EE since it reduces SE and power consumption simultaneously. Numerical results verify the tightness of the upper bound, demonstrate the effectiveness of the optimal phase shift design for the subarray-based RIS, and reveal the effects of the subarray-based scheme on SE and EE.