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As more and more stereo cameras are installed on electronic devices, we are motivated to investigate how to leverage disparity information for autofocus. The main challenge is that stereo images captured for disparity estimation are subject to defocus blur unless the lenses of the stereo cameras are at the in-focus position. Therefore, it is important to investigate how the presence of defocus blur would affect stereo matching and, in turn, the performance of disparity estimation. In this paper, we give an analytical treatment of this fundamental issue of disparity-based autofocus by examining the relation between image sharpness and disparity error. A statistical approach that treats the disparity estimate as a random variable is developed. Our analysis provides a theoretical backbone for the empirical observation that, regardless of the initial lens position, disparity-based autofocus can bring the lens to the hill zone of the focus profile in one movement. The insight gained from the analysis is useful for the implementation of an autofocus system.