I am regularly surprised when I find people saying that you should focus one third of the way in the scene between the nearest and furthest things you want in focus. That rule presumes that the far DOF is normally about twice the near DOF. Some simple calculations show that this is true just exactly when the plane of exact focus is at distance
hyperfocal_distance/3 + focal length
Since the far DOF approaches infinity at the subject distance approaches the hyperfocal distance, it is clear that the one third rule can't be generally true. So why do so many people swear by it?
I think I've found a couple of reasons.
If your criterion to is to balance cocs in the film plane for points coming to focus on opposite sides of that plane, the usual analysis tells you that the correct place on the rail is the harmonic mean of the bellows extensions for the near and far points. (The harmonic mean is obtained by averaging the reciprocals of the two other distances and taking the reciprocal of that.) If the two distances are close together, which is always the case for bellows extensions outside the close-up range, the harmonic mean is very close to the actual mean, and that justifies the usual advice to set the position on the rail halfway between the near and far points.
What about subject distances? It turns out there is a basic symmetry, and the rule behind the lens translates into the same rule for subject distances: you should focus at the harmonic mean of the near and far subject distances (at least if the subject distance is less than the hyper-focal distance, in which case the far point is at infinity). But how about the ratio of far DOF to near DOF in that case. It turns out that this ratio is the same as the ratio of the far distance to the near distance. If that ratio is close to 1/3, then the 'one third into the subject' rule will be pretty close. A typical example might be a stone wall at about 5 meters and a wall of trees at 15 to 20 meters. On the other hand it is clear there are many circumstances where the rule won't work very well. It won't work if the far point is very far away compared to the near point, and it also won't work in the close-up range, where the DOF (usually) is roughly equal on both sides of the exact focus.
However, there is one thing that will save you if you use the one third rule outside the close-up range, at least if the far point isn't effectively at infinity, in which case, the rule doesn't make any sense. For distant points, large changes in subject distance translate into small changes in position on the rail. That means the difference on the rail between the proper position and the incorrect position won't be very large. Stopping down may easily compensate for any error.
It seems to me much simpler to use the mid-point along the rail instead of trying to estimate subject distances into the scene. But when will that be accurate? The same rule applies. The ratio of the bellows extensions for near and far points gives you the ratio of the distances of those points. So under what circumstances is that ratio close to one? Calculations show that this will be true outside the close-up range. Within the close-up range, further calculation shows that the ratio starts to depart significantly from one as you move to short focal length lenses with very small apertures. But, for close-up subjects, DOF at constant magnification is roughly independent of focal length, so there is no need to use short focal length lenses unless you want the resulting perspective. In such a circumstance, you should use the harmonic mean to find the position to focus at, whichever side of the lens you concentrate on. A further consequence of these calculations is that, for close-ups, the equality rule for DOF on both sides of the focus distance tends to break down when you use short focal length lenses with small apertures.