Recent studies indicate that distributions of gaze are effective to evaluate the attractiveness of users' attention to media, such as web content or TV commercials. Because human eye movement measurements require some labor costs, computer simulations which predict human gaze shifts have shown promise. For these kinds of purposes, saliency-based mathematical models which calculate the most likely regions to gaze in these visual sceneries are frequently employed. These models are superior at predicting gaze positions at first sight, though, scan path simulations are not useful because they do not consider the history of gazed locations. Yamasaki & Kohama (2013) proposed a model to reproduce gaze shifts for searching for targets using conditional probability considering scanned logs of gaze positions. They calculated probability maps from the saliency distributions. However, objective evaluation methods of the scan paths in consideration of the history of gazed positions do not exist at the moment. In this study, we proposed new indexes by which the characteristics of gaze shifts are evaluated quantitatively. Proposed indexes are similarity of feature vectors, diffusion of gaze shifts, and angular changes on polar coordinates of gaze positions. We averaged these indexes in each passed five steps of gaze shifts to distinguish the characteristics of scan paths. Then, we compared actual human eye movements and simulated scan paths with these indexes. Simulated scan paths were obtained by an ordinary saliency based model, Yamasaki's model, and randomly selected locations. The results suggest that the characteristics of scanned positions on any visual scenery are able to be expressed quantitatively by these indexes, and these indexes are effective to evaluate the realisticness of computer simulations.