Transient enhanced diffusion of dopants in silicon is frequently modeled using the "+ 1" approximation of implantation damage. Using a more realistic model predicts somewhat more transient diffusion than the +1 model. For many purposes, the +1 model can be improved by a simple scaling factor, which we call the effective plus factor. In this work we study the dose, energy, and ion species dependence of the effective plus factor. The simulation model is based on binary collision simulations to obtain point defect concentrations after ion implantation and a continuum model that includes the effect of spatial correlations of the defects to describe diffusion and recombination. This approach is shown to agree well with atomistic simulations. Results are presented in the energy range of 1 keV to 1 MeV, for doses between 0 and 3 x 10(14) cm(-2) and the ion species B, Si, P, and As. In the high-dose limit deviations from the +1 model are considerable for heavy ions and/or low energies with a maximum of approximately 4 for 1 keV As. The plus factor also increases with decreasing dose. However, the increase is not significant for doses above 10(13) cm(-2) and only moderate (less than a factor of two) for doses above 10(12) cm(-2). The results agree with transient enhanced diffusion data over a range of energies and doses, with some anomalous exceptions at very low dose.