Energy spectra of ring current protons are crucial to understanding the ring current dynamics. Based on high-quality Van Allen Probes RBSPICE measurements, we investigate the global distribution of the reversed proton energy spectra using the 2013-2016 RBSPICE datasets. The reversed proton energy spectra are characterized by the distinct flux minima around 50 - 100 keV and flux maxima around 200 - 400 keV. Our results show that the reversed proton energy spectrum is prevalent inside the plasmasphere, with the occurrence rates > 90% at L ~ 2 - 4 during geomagnetically quiet periods. Its occurrence also manifests a significant decrease trend with increasing L-shell and enhanced geomagnetic activity. It is indicated that the substorm-associated processes are likely to lead to the disappearances of the reversed spectra. These results provide important clues for exploring the underlying physical mechanisms responsible for the formation and evolution of reversed proton energy spectra.