How Far Should A Roof Overhang A Gutter

In my opinion the shingles should never be exactly even with the edge of any drip edge flashing.
How far should a roof overhang a gutter. A typical gutter flashing l shaped usually has a 2 1 2 face however we often custom bend out own for situations where we need to cover more than 2 1 2. The reason for this is that whenever rain runs down any type of roof when it gets to the lower edge it clings to the tile or slate by capilliary action this means that the water actually runs around the bottom edge and slightlly back up the rear of the tile before gravity allows it to drop into the gutter. The bottom tile or slate of the roof covering should project at least half way into the gutter the ideal distance is between half way and two thirds of the way over. Anywhere from a 1 2 to a 1 overhang is acceptable as you can tell from the varying comments amongst the previous posters.
Each has their own reasoning for a slightly different amount of overhang. About 1 inch just enough to assure the water goes into the gutter and not behind it. The back edge of the gutter should tuck up behind the dripedge if you have it otherwise the edge of the shingles should extend well over the back half of the gutter so the drips cannot get behind it and rot the fascia board. Not good to start off with a new roof and gutters with this problem built in.
Here phil explains how much overhang a roof should have at the gutter. Metal is usually installed on rafters or strip sheathing rather than the solid decking used under other materials. For rainy climates where gutters will handle a larger amount of water for long periods they should have a maximum distance of 18 inches apart between them. If you live in a warm place with sporadic rain you can hang gutter hangers close to the middle of the gutter with a spacing of no more than 36 inches or three feet apart from the center.
Greater overhang becomes a point of leverage for gusts of wind to rip off your roofing. Most drip edges have 1 1 2 face and that 1 1 2 is not enough to cover the back of the gutter especially since by your own admission it is a 2 drop. A typical metal roof overhang may be 2 to 4 inches or even less.