A new summation method model of the reactor antineutrino energy spectrum is presented. It is updated with the most recent evaluated decay databases and with our total absorption gamma-ray spectroscopy measurements performed during the last decade. For the first time, the spectral measurements from the Daya Bay experiment are compared with the antineutrino energy spectrum computed with the updated summation method without any renormalization. The results exhibit a better agreement than is obtained with the Huber-Mueller model in the 2-5 MeV range, the region that dominates the detected flux. A systematic trend is found in which the antineutrino flux computed with the summation model decreases with the inclusion of more pandemonium-free data. The calculated flux obtained now lies only 1.9% above that detected in the Daya Bay experiment, a value that may be reduced with forthcoming new pandemonium-free data, leaving less room for a reactor anomaly. Eventually, the new predictions of individual antineutrino spectra for the ^{235}U, ^{239}Pu, ^{241}Pu, and ^{238}U are used to compute the dependence of the reactor antineutrino spectral shape on the fission fractions.