Understanding Tiling and Offset in the Material Inspector

I have a texture I am using as a compass bar. I am using a quad in the scene to hold the compass. I have determined the tiling of the texture based off of the distance from the camera, and the width of the quad.

Here is the texture on the quad using default tiling (1, 1) and offset (0, 0) values:

With tiling set to (0.5, 1) and offset to (0.25, 0) the texture makes sense; to re-center the texture when the tiling is less than one the offset needs to be half of the tiling value. However, when I set the tiling to a value that is not 0.5, this convention does not hold true.

Now with tiling (0.2, 1) and offset (0.1, 0) values closer to my needs:

It is obvious from this that the offset values are not being affected the way I thought. I want to know how offset is affected by changes to the tiling values, and how I would determine what value I need to have for offset to "re-center" the texture. Any help would be greatly appreciated.