In this paper, we provide a theoretical analysis on the performance of the famous Gradient-based Tone-Reservation PAPR reduction algorithm. To that end, we study the amplitude statistical distribution of the time domain OFDM signals to which PAPR reduction has been applied. Such distribution is then integrated into a generic EVM expression in order to provide a closed form expression of this latter, which is validated and analyzed through numerical simulations. Thanks to this work, we provide theoretical tools to analytically assess the performance of the Gradient method relatively to the optimal TR algorithm, and hence allow further analysis about the complexity-PAPR reduction efficiency trade-off of TR PAPR reduction algorithms, which could be useful for the optimization of the power efficiency of any multicarrier system. © 2020 IEEE.