I've never worked out the math if you assume gaussian, to get specific numbers of minutes that function as specific odds of lateness, but I had the same rough insight in terms of accuracy versus calibration. In general, its easier to predict outcomes in advance if you shoot for less than you're capable of, but this can lead to lowered performance if it becomes habitual. With scheduling issues, one thing I've been experimenting with is finding treats to give myself during the "pad time" so that I don't just use up all the minutes on boring stuff. So, if I'm ready early, I get to read a trashy novel or poke around on LW until its really time to go.

The second order optimization is to switch out trashy novels and LW for something more "nutritious" that has similar ability to feel like a reward. Although LW is probably more nutritious than vampires or steampunk... :-)

Edit: Reading more, I see that Alicorn and DuncanS have similar tricks.