I wonder why impacts in the central region are essetially nonexistent.
Consider what the impact map would look like if the moons surface was rolled out flat. The distribution would look far more uniform. Although I agree the center band does look a bit sparse even considering the above.
Could the geosynchonous incidence of Moon toward Earth be a factor?
Picture yourself high above the north pole looking down on the earth from a vantage point at a right angle to the plane of the earths orbit. The earth is traveling an orbital path with a radius of 93 million miles which is nearly circular. The circumference of that path is a bit over 584 million miles and the travel time is 365.25 x 24 hour days. The tangential speed of the orbiting earth is therefore the circumference divided by the orbital period which is about 66,700 miles per hour. Looking down at the earth from "above" the plane of the ecliptic. (the remnant of the dust cloud that collapsed/condensed into the solar system) The hemisphere facing into the direction of travel is moving "forward" into the path of space junk moving through our orbital path and overtaking that moving junk at 66,700 mph. Conversely, the trailing hemisphere (looking back along our orbital path) is moving away from any space junk crossing our path which would have to catch up with us in order to score a hit.
The moon always keeps the same face toward the earth as it orbits us every 28 and some spare change days. It's orbit is very nearly circular and it is inclined slightly to the plane of the ecliptic.
When the moon is "full" it is fully illuminated by the sun because of it's orbital tilt which tells you it is either above or below the earth's shadow. From our observation point it is directly in line to the earth and then to the sun. Fourteen some days later it will be a "new" moon and completely dark. It is now halfway around it's orbit and is therefore between us and the sun.
When the moon is "full" only the hemisphere facing into the direction of travel(that is one half of the face of the moon visible to us and one half of the side we never see) around the sun is subject to collisions with "space junk" as it is moving through the debris at the same speed as earth (66,700 mph). It rather like bugs hitting a cars windshield, it's easy to visualize bugs hitting you (or you hitting bugs, macht nichts) while moving forward. It's also hard to picture a bug moving fast enough to hit the back window.
In seven days or so, the moon is waning and the hemisphere facing into the debris is the side we never see from earth. The Apollo missions brought back photographs giving humans their first view of the unknown face which appeared to be more ruggedly cratered.
Seven more days and the moon is "new" and the hemisphere facing into the direction of travel(that is the other half of the face of the moon visible to us and the other half of the side we never see)
Seven more days and the moon is "waxing" and the hemisphere facing into the direction of travel and the debris is the only face of the moon we can see from earth. However, the big difference and the answer to you original question is the earth is directly in front of the moon as we sweep through the debris field. In effect the earth is running interference for the moon and sweeps up the junk that would logically hit the central region of the visible face.
If this seems hard to visualize, think of what it must have been like for those shepherds watching their flocks by night?
Regards,
GtG
PS That's my story and I'm sticking to it...