The first passage probability (FPP), of trafficked intracellular particles reaching a displacement L, in a given time t or inverse velocity S = t/L, can be calculated robustly from measured particle tracks. The FPP gives a measure of particle movement in which different types of motion, e.g. diffusion, ballistic motion, and transient run-rest motion, can readily be distinguished in a single graph, and compared with mathematical models. The FPP is attractive in that it offers a means of reducing the data in the measured tracks, without making assumptions about the mechanism of motion. For example, it does not employ smoothing, segmentation or arbitrary thresholds to discriminate between different types of motion in a particle track. In contrast to conventional mean square displacement analysis, FPP is sensitive to a small population of trafficked particles that move long distances (> or = 5 microm), which are thought to be crucial for efficient long range signaling in theories of network dynamics. Taking experimental data from tracked endocytic vesicles, and calculating the FPP, we see how molecular treatments affect the trafficking. We show the FPP can quantify complicated movement which is neither completely random nor completely deterministic, making it highly applicable to trafficked particles in cell biology.