... just consider all those "wasted" strokes as offering to the sharpening gods anyway.-Cliff
This is something I've wondered about before, i.e. the effect of the inability to hone at a precise angle either with a guided system or freehand.
If the angle for each stroke varies normally about the intended target, then you get a bell shaped curve reflecting the actual stroke angle and the number of occurrences. The mean of the distribution would be the target angle and the standard deviation would be a measure of the inaccuracy in hitting the desired target.
The distribution would be symmetrical and half of the strokes would be less than the target angle and half would be greater. So by this theory half the strokes are always wasted.
Guided systems would have a tighter distribution around the target, but still half the strokes are wasted according to the above logic. So when the Sharpmaker Rods are perfectly aligned, only half the strokes count. If the stones are biased to an angle less than the knife bevel, then even fewer than half would reach the edge.