The model for the cuprates based on the modified electron-phonon pairing mechanism has been tested. For this purpose, the superconductors with high value of the critical temperature have been taken into consideration. In particular: YBa2Cu3O7−y, HgBa2CuO4+y, HgBa2Cu1−xZnxO4+y, and HgBa2Ca2Cu3O8+y. It has been shown that the dependence of the ratio R1 ≡ 2∆ (0) tot /kBTC on the doping (p) can be properly predicted in the framework of the presented theory; the symbol ∆ (0) tot denotes the energy gap amplitude at the temperature of zero kelvin, and TC is the critical temperature. The numerical results have been supplemented by the formula which describes the function R1(p).