The historically renowned original treatments of Avrami predicted the continuous change in the Avrami index between 3 and 4 with a time-dependent effective nucleation rate I for the nucleation and subsequent linear growth process of spherical domains under isothermal conditions. The nucleation rate I is determined by the number density N-0 of tiny germ-nuclei at t = 0 and the transformation rate r of a germ nucleus to the active nucleus. This model is applied to the crystallization of poly(butylene terephthalate) (PBT), which reveals a continuous change in the Avrami index with temperature when a nucleating agent (NA) talc is added. In particular, for crystallization with NA, N-0 corresponds to the number density of NA particles, and the rate r represents the formation rate of an active nucleus from an NA particle. The product of N-0 and crystal growth rate G, i.e., N(0)(1/3)G, and the rate r are independently evaluated from the time-dependent behavior of crystallization with the Avrami index between 3 and 4. The efficiency of NA is evaluated from the rate r and its temperature dependence, which is determined by the thermal activation barrier for the transformation and is characterized by an excess surface free energy Delta sigma evaluable using the current analysis method. The dispersibility of NA is assessed by the relative increase of N-na/N-wo in N-0, with the addition of NAs N-na from the number density without agents N-wo. The applicability and usability of the analysis method were confirmed for PBT crystallization with talc, using fast-scanning calorimetry. The evaluated rate r exhibited a stronger temperature dependence than the crystal growth rate G, and the relative increase N-na/N-wo was more than 100 times in the sample with well-dispersed talc.