Random errors in LV AF are quite large in old cameras (such as the D3X, in my experience) but they seem to be very small in the latest professional models. In repeated LV AF and automatic focus fine tune operations I get a standard deviation of about 1-2 fine tune points with most lenses using the D5 body. I think repeating the operation a few times is advisable but that should be sufficient given adequate quality of focus test target, dark homogeneous background, and proper lighting on the main target. I think the same should apply for the dot method if you want to use it (one problem is the dot has in many cases a huge range where it is lit, making the information not so precise).
With the D3X, the dot method does not work well at all because the live view AF operation is so imprecise especially in an indoor setup with limited light available. Thankfully, live view and live view AF have improved a lot since. With the D750, the dot is active in a much larger range than with the D810, so with the D810 camera the dot method gives good starting points for real-world testing; with the D750 I have relied more on real world data than the dot method results because often the dot is active also at +20 or -20 so the midpoint of the range can not be estimated in such cases.
A more rigorous procedure involving taking of multiple shots at each fine tune setting, evaluating the contrast in the ruler area and determining the fine tune value that minimizes the autofocus offset can be used with any camera and it works well also with older cameras. However, the procedure is slow and tedious. Thankfully the newer cameras can be fine tuned in easier ways.