The synthesis of superheavy nuclei (SHN) through fusion reactions is a critical area of nuclear physics, offering insights into nuclear stability and the limits of the periodic table. However, theoretical predictions of evaporation residue cross sections ${\sigma }_{\mathrm{ER}}$ remain challenging due to large uncertainties arising from complex reaction mechanisms and sensitive model parameters. In this work, the average production probabilities of SHN with atomic number $Z\ge 110$ are systematically analyzed, based on the barrier tunneling concept. Together with the empirical barrier distribution method for describing capture, a phenomenological formula, EBD3, is proposed, which reproduces 58 measured ${\sigma }_{\mathrm{ER}}$ within one order of magnitude, with a root-mean-square deviation of 0.369. The formula successfully captures key quantities in the fissionlike process, including fission barrier height, mass asymmetry, depth of the capture pocket, and the effective fusion barrier height. Predictions for the synthesis of element 119 are presented, identifying promising projectile-target combinations such as ${}^{50}\mathrm{Ti}+{}^{249}\mathrm{Bk}$ with a maximum cross section of $54.9_{-29.0}^{+61.3}$ fb at the excitation energy of 36.5 MeV. The maximum cross section falls to $3.2_{-1.7}^{+3.6}$ fb for ${}^{54}\mathrm{Cr}+{}^{243}\mathrm{Am}$ at the optimal incident energy of 244 MeV.

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• Low & intermediate energy heavy-ion reactions
• Nuclear fusion
• Nuclear reactions
• Synthesis of new superheavy elements
• A ≥ 220