The modeling of the laser-induced damage processes can be divided into thermal and electronic processes. Especially, electronic damage seems to be well understood. In corresponding models, the damage threshold is linked to the excitation of valence electrons into the conduction band, and often the damage is obtained if a critical density of free electrons is exceeded. For the modeling of the electronic excitation, rate equation models are applied which can vary in the different terms representing different excitation channels. According to the current state of the art, photoionization and avalanche ionization contribute the major part to the ionization process, and consequently the determination of laser-induced damage thresholds is based on the calculation of the respective terms. For the theoretical description of both, well established models are available. For the quantitative calculation of the photoionization, the Keldysh theory is used most frequently, and for the avalanche processes the Drude theory is often applied. Both, Drude and Keldysh theory calculations depend on the laser frequency and use a monochromatic approach. For most applications the monochromatic description matches very well with the experimental findings, but in the range of few-cycle pulses the necessary broadening of the laser emission spectrum leads to high uncertainty for the calculation. In this paper, a novel polychromatic approach is presented including photo- and avalanche ionization as well as the critical electron density. The simulation combines different ionization channels in a Monte-Carlo procedure according to the frequency distribution of the spectrum. The resulting influence on the wavelength and material dependency is discussed in detail for various pulse shapes and pulse durations. The main focus of the investigation is concentrated on the specific characteristics in the dispersion and material dependency of the laser-induced damage threshold respecting the polychromatic characteristics of the ultra-short pulse (USP) laser damage.