Ductile frame structures are generally designed with column over-design factors (COF) to assure plastic hinges occurring in all beams and avoid unpreferable failure modes. In order to avoid story mechanisms of frame structure constructed with elastic-plastic materials, target COF has been investigated where the relative occurrence probability of most likely story mechanism is limited within a specific tolerance. In the present paper, the concept of basic and optimum column over-design factor for avoiding story mechanism are proposed and the value of them for multi-span multi-story ductile frames are presented based on a comprehensive investigation on the occurrence order of story mechanisms. The basic COF is defined as the critical value that the preferable failure mode and unpreferable failure mode are with the same failure probability, and it is the low limit assuring the entire beam-hinging pattern prior to story mechanisms. For a structure designed with a COF less than basic COF, the plastic hinges are easier to occur in partial stories to form story mechanism. The optimum COF is the most effective and economy COF to enhance the safety of structure, and it is resulted from the shift of priority of plastic hinges in different stories. The relationships between the basic and optimum COF with calculation parameters are also analyzed in this paper.