Arrival time uncertainty is a major source of negative perception by riders, yet how this uncertainty manifests in the rider's experience is not well-studied. While operators constantly make efforts to improve reliability, and real-time arrival predictions reduce uncertainty for riders in transit, it is also possible to lessen frustration by better informing riders of system behavior beforehand. This work introduces a new method for understanding transit behavior through an analysis of historical arrival time data from San Francisco. The results identify impacts of timeliness on rider experience, such as that average wait time is minimized by showing up five minutes early, or that a five-minute transfer window will be successful 80 percent of the time. Categories of rider experience also are discovered, such as between daytime and evening users. More importantly, it is demonstrated how operators and trip planners can make use of this method to improve rider experience.