The distribution of the accelerated points of fibers in roller drafting is the key to the evenness of the drafted slivers. The fiber length distribution is believed to affect the accelerated points. This approach is trying to give a quantitative expression of the influence. A parabolic density function is introduced for the expression of density functions and a generalized method is presented. The experiment shows that the parabolic-type density function is a better explanation for the distribution of the accelerated points in the drafting zone in terms of the consequent yarn unevenness. The statistical test verifies the distribution type. The analysis helps to understand the mechanism of the roller drafting and can be used in the optimization of the parameters in roller drafting.