Recently, angle-resolved photoemission spectroscopy has been used to highlight an anomalously large band renormalization at high binding energies in cuprate superconductors: the high energy "waterfall" or high energy anomaly (HEA). The anomaly is present for both hole-and electron-doped cuprates as well as the half-filled parent insulators with different energy scales arising on either side of the phase diagram. While photoemission matrix elements clearly play a role in changing the aesthetic appearance of the band dispersion, i.e. creating a "waterfall"-like appearance, they provide an inadequate description for the physics that underlies the strong band renormalization giving rise to the HEA. Model calculations of the single-band Hubbard Hamiltonian showcase the role played by correlations in the formation of the HEA and uncover significant differences in the HEA energy scale for hole-and electron-doped cuprates. In addition, this approach properly captures the transfer of spectral weight accompanying doping in a correlated material and provides a unifying description of the HEA across both sides of the cuprate phase diagram. We find that the anomaly demarcates a transition, or cross-over, from a quasiparticle band at low binding energies near the Fermi level to valence bands at higher binding energy, assumed to be of strong oxygen character. Advancements in angle-resolved photoemission spectroscopy, an important probe of electronic structure, [1] have impacted significantly the study of strongly correlated materials. High resolution experiments, at binding energies up to 1 eV and higher, made possible by these advances, have revealed the presence of a "waterfall"-like structure with a characteristic kink at intermediate binding energies -the high energy anomaly (HEA) -in the dispersion of high T c superconductors. [2-12] Found universally in hole-doped compounds, the characteristic HEA energy scale is ∼ 300 meV with a similar dispersion anomaly observed in the half-filled parent insulators.[13] In contrast to earlier low energy studies focusing on dispersion kinks under ∼ 100 meV, [14] interpreted as signatures of coupling to low energy bosonic modes, [15-17] the extrapolated band bottom has a value larger than that obtained from band structure calculations [2, 3] and the energy scale associated with the anomaly would tend to rule-out coupling to similar bosonic modes as the origin of the HEA.More recently, anomalies have been found in electrondoped compounds at approximately twice the energy scale.[9-12] Taken together with results from hole-doped and half-filled parent materials, these findings raise questions about the origin or mechanism of the HEA, given the ap- Photoemission matrix elements clearly play a role in modifying the appearance of the HEA, complicating the analysis. The kink-or "waterfall"-like structure found in the first Brillouin zone (BZ) in experiments performed using synchrotron sources appears instead in newer experiments performed using low photon energy, laser sources as a ban...