Superbeam experiments can, in principle, achieve impressive sensitivities for CP violation in neutrino oscillations for large θ 13 . We study how those sensitivities depend on assumptions about systematical uncertainties. We focus on the second phase of T2K, the so-called T2HK experiment, and we explicitly include a near detector in the analysis. Our main result is that even an idealised near detector cannot remove the dependence on systematical uncertainties completely. Thus additional information is required. We identify certain combinations of uncertainties, which are the key to improve the sensitivity to CP violation, for example the ratio of electron to muon neutrino cross sections and efficiencies. For uncertainties on this ratio larger than 2%, T2HK is systematics dominated. We briefly discuss how our results apply to a possible two far detector configuration, called T2KK. We do not find a significant advantage with respect to the reduction of systematical errors for the measurement of CP violation for this setup.