My quick testing makes it seem that the center of a circle is closer to the circle "on average" than any point on the circle is.

A quick Python script suggests that a point on the circle is about 1.273 radii away from the other points on the circle on "average", while (by definition) the center is 1 radius away from all points on the circle.

So this fact about orbits seems related: the closest point to your orbit (on average) are things in the middle of it, which are near the center of your "circle".

Further testing supports this -- there's a gradient from the 1.273 at the "edge" to the 1.0 in the "center", as you shrink the radius of the circle you measure from.