What advantage does it provide? Explaining with a figure would be helpful.
I tried to draw a free body diagram and equated the sum of force and moments to zero, but still was not able to find out.
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More compact configuration that fully utilizes the area of the leaf.
Avoid stresses concentrated on a single plane that is likely to cause the base material to progressively fail in shear or split.
The staggered arrangement is more stable. It provides better strength in resisting the incidental bending resulted from the weight of the door and missing/loose screw(s) on the door side leaf. (There is a couple in addition to the horizontal resistants of the bolts, albeit this advantage could be small and usually is unaccounted for.)
Staggering the screws will
give a better chance for some of them to penetrate into solid grain. and discourage toilet paper perforation pattern.
Provide for larger torque resistance.
keeping the hinge from develoing a loose play, flapping out of door jamb plane. prhibiting door settling slanted out of its frame.
Just adding to the rest of the answers, if the door hinge is thick enough to be assumed rigid, then the offset configuration offers better resistance to bending moments in at least two axis.
i.e: For the following reference system
It is noteworthy, that for a pure pullout force (which is somewhat similar to the first case of Y-bending) the offset configuration will not have any additional advantage to the straight line.
So (just summing up) the zig-zag configuration offers: