The P300 is one of the most widely studied components of the human event-related potential. According to a longstanding view, the P300, and particularly its posterior subcomponent (i.e., the P3b), is driven by stimulus categorization. Whether the P3b relates to tactical processes involved in immediate responding or strategic processes that affect future behavior remains controversial, however. It is difficult to determine whether variability in P3b latencies relates to variability in response times because of limitations in the methods currently available to quantify the latency of the P3b during single trials. In this paper, we report results from the Psychomotor Vigilance Task (PVT), the Hitchcock Radar Task, and a 3-Stimulus Oddball Task. These represent variants of the one-, two-, and three-stimulus oddball paradigms commonly used to study the P3b. The PVT requires simple detection, whereas the Hitchcock Radar Task and the 3-Stimulus Task require detection and categorization. We apply a novel technique that combines hidden semi-Markov models and multi-voxel pattern analysis (HSMM-MVPA) to data from the three experiments. HSMM-MVPA revealed a processing stage in each task corresponding to the P3b. Trial-by-trial variability in the latency of the processing stage correlated with response times in the Hitchcock Radar Task and the 3-Stimulus Task, but not the PVT. These results indicate that the P3b reflects a stimulus categorization process, and that its latency is strongly associated with response times when the stimulus must be categorized before responding. In addition to those theoretical insights, the ability to detect the onset of the P3b and other components on a single-trial basis using HSMM-MVPA opens the door for new uses of mental chronometry in cognitive neuroscience.