Using 52 gamma-ray bursts observed and localized by BeppoSAX and HETE-2, a comprehensive analysis of the correlation between the properties of prompt emissions and the brightness of the afterglows was performed. We found a highly significant correlation between the isotropic total energy of prompt emission and luminosity of optical afterglow. There is also a correlation between the fluence in prompt emission and the magnitude of the optical afterglow. We then investigated the energy conversion efficiency in prompt emissions of gamma-ray bursts using 24 bursts with the known redshift. We calculated the kinetic energy of relativistic shells from the luminosities of the optical afterglows. The energy-conversion efficiency, as estimated by comparing this kinetic energy with the total radiated energy of prompt emission, is distributed between about 1% and 40%. This result suggests that the ratio of the Lorentz factor of two colliding shells is large, or the fraction of shock energy that goes into the electrons is small for the internal shock scenario.
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