Abstract This paper introduces a novel anchor design principle to support anchor-based face detection for superior scaleinvariant performance, especially on tiny faces. To achieve this, we explicitly address the problem that anchor-based detectors drop performance drastically on faces with tiny sizes, e.g. less than 16 × 16 pixels. In this paper, we investigate why this is the case. We discover that current anchor design cannot guarantee high overlaps between tiny faces and anchor boxes, which increases the difficulty of training. The new Expected Max Overlapping (EMO) score is proposed which can theoretically explain the low overlapping issue and inspire several effective strategies of new anchor design leading to higher face overlaps, including anchor stride reduction with new network architectures, extra shifted anchors, and stochastic face shifting. Comprehensive experiments show that our proposed method significantly outperforms the baseline anchor-based detector, while consistently achieving state-of-the-art results on challenging face detection datasets with competitive runtime speed