[adhesive_wombat]

I've thought about this quite a bit (while driving and using trains and buses) and it seems to me that if the schedule of the train (or bus or traffic light) is independent of your journey, such that you arrive at the station, stop or light at any point in the cycle with even probability, then arriving 10 seconds later will on average translate to a 10 second delay in the journey.

It's just that maybe 9 times out of 100, you didn't miss the train (or got through the light on the same cycle) and the other 1 time is the one where you miss the train or the light goes red just before you arrive.

Of course, being on time on average (i.e. 10 seconds ahead for 59 days, 10 minutes late once) doesn't cut it if your boss is "that kind". I'm fortunate in that my start times aren't strictly policed. If they were, you can bet if be there at 8:59:30 (sitting in the car reading if necessary) and out of the door at 5:00:30 (and probably again reading to let traffic dissipate).

Also doesn't take into account non-idenpendence: if you usually leave so that you arrive just in time, only a small delay can cause a disproportionate effect (a feature of systems with nonlinear feedback loops).