That doesn't explain the ones that are continually leave the station, with the prediction constantly resetting as the bus doesn't leave. Or the ones that don't show up, and then the next one does, right on time.

If you don't know where something is, you don't know where it is. To give a number anyway is disengenuous, and breaks trust. To do it all the time, and call your data 'real-time' without caveat - lying may be a strong word for it, but it's still appropriate.

NextBus always uses a straight-line estimate for the vehicle position within a few stops from the terminal. This is based on the departure times in the Muni published schedule. However, Muni operators and dispatchers do not adhere to this schedule in any way, so the estimates that NextBus gives near the beginning of Muni lines are pure fabrications. Lies, you might say.