While deep learning has been widely used for video analytics, such as video classification and action detection, dense action detection with fast-moving subjects from sports videos is still challenging. In this work, we release yet another sports video dataset $\textbf{P$^2$A}$ for $\underline{P}$ing $\underline{P}$ong-$\underline{A}$ction detection, which consists of 2,721 video clips collected from the broadcasting videos of professional table tennis matches in World Table Tennis Championships and Olympiads. We work with a crew of table tennis professionals and referees to obtain fine-grained action labels (in 14 classes) for every ping-pong action that appeared in the dataset and formulate two sets of action detection problems - action localization and action recognition. We evaluate a number of commonly-seen action recognition (e.g., TSM, TSN, Video SwinTransformer, and Slowfast) and action localization models (e.g., BSN, BSN++, BMN, TCANet), using $\textbf{P$^2$A}$ for both problems, under various settings. These models can only achieve 48% area under the AR-AN curve for localization and 82% top-one accuracy for recognition since the ping-pong actions are dense with fast-moving subjects but broadcasting videos are with only 25 FPS. The results confirm that $\textbf{P$^2$A}$ is still a challenging task and can be used as a benchmark for action detection from videos.