Evaporative cooling is a process that is essential in creating Bose-Einstein condensates in dilute atomic gasses. This process has often been simulated based on a model using a truncated Boltzmann distribution. This model assumes that the energy distribution up to the threshold energy can still be described by a Boltzmann distribution: it assumes detailed balance up to the threshold energy. However, the evolution of the distribution function in time is not taken into account. Here we solve the kinetic Boltzmann equation for a gas undergoing evaporative cooling in a harmonic and linear trap in order to determine the evolution of the energy distribution. The magnitude of the discrepancy with the truncated Boltzmannmodel is calculated by including a polynomial expansion of the distribution function. We find that up to 35% fewer particles are found in the high-energy tail of the distribution with respect to the truncated Boltzmann distribution and up to 15% more collisions are needed to reach quantum degeneracy. Supported by a detailed investigation of the particle loss rate at different energies, we conclude that the limited occupation of high-energy states during the evaporation process causes the lowering of the evaporation speed and efficiency.