The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple input-multiple output (MIMO) detection to overcome the two main drawbacks of the original sphere decoder (SD), namely its variable complexity and sequential structure. As such, the FSD is highly suitable for hardware implementation and has shown remarkable performance through simulations. Herein, we explore the theoretical aspects of the algorithm and prove that the FSD achieves the same diversity order as the maximum likelihood detector (MLD). Further, we show that the coding loss can be made negligible in the high signal to noise ratio (SNR) regime with a significantly lower complexity than that of the MLD.