Originally we removed offsets and Match changed the property mappings. Later we had to bring back offsets to keep all the functionality of the old transform constraint. Match now only sets the offsets.

The property mappings are up to you. They describe unit conversion from one property to another. If you aren't using clamp, then the exact ranges don't matter because the values are extrapolated. For example, you can map 0-100 to 0-100 and get a mapping with 100% scale (ie 1:1). Values outside the range being extrapolated (not clamped) means if the source value is out of range, say 500, the target value is 500. If you map 0-100 to 0-50 you get 50%: the target bone moves half as much as the source bone, 500 source gives 250 target. If you map 34-72 (a width of 38) to 143-162 (a width of 19) then you also get 50% scale (19/39=0.5) and it will behave identically. Those numbers are harder to read, so it's convenient to use easier to read ranges like 0-100.

If you are using clamp then the target values don't go out of the specified range, so you need to be much more careful what ranges you set. It depends on the range of motions you want to map, so we can't set them for you. We may add some visualization of the ranges though. Enable rulers (ctrl+shift+R) and take note of the values for the ranges you want. Make sure to look at the correct axes based on if you have Local checked. Make your ranges work with a simple constraint before making it more complex.

If you enable clamp and nothing moves, likely your target (right side) values are out of the clamp range. Look at your ranges more closely.

If your mapping causes the bone to move in setup, it's because the source value when put through your mapping does not equal the unconstrained target value. Set your ranges more carefully!

For example, say the source is 100 in setup and the target is 200. I want the target to move +/-30 when the source moves +/-15. I would set the ranges: 85-115 to 170-230. This mapping causes 100 to be mapped to 200, so the setup pose doesn't change, and the mapping also describes the amount of movement I want clamped.

Your ranges don't have to center the setup values. For example, same setup values 100 source, 200 target. This time I map 90-120 (which is -10 and +20 of the 100 setup) to 195-210 (-5 and +10 of the 200 target). With this mapping 100 source is still 200 target, but the range is asymmetrical relative to the setup values.

Source 77 is at the middle of 68-86.Target 306 is in the middle of 284-328. Those ranges will set your target bone to 306 when source is 77. Your screenshot shows 47.09 offset though, that will be added to the source. Try 0 offset. Also try a mix of 100, not -100, at least until you get it to work. You can flip the output by flipping the target range, eg 0-100 or 100-0.

The above will be wrong if you are looking at the wrong axes. When Local is checked, look at World axes. When Local is unchecked, look at Local axes for everything except translation. For that look at Parent axes.

Give that a try and let us know how it goes!

Thanks for the explanation, Nate. I had some problems of understanding as well, but now it is more clear to me.
@height13 I had the same issues and problems in my head as you. Thank you to come up with that topic to the right time . I hope the explanation from Nate could clear your problems too.

@borleech Great, I'm glad my ramblings were useful! Someday we'll have proper documentation.

Yes translation is X and Y.

The left Local checkbox is for the source, the right Local is for the target. They don't have to be the same, though they commonly are. The were always the same with old transform constraint, but there may be some clever setups that make use of having them differ. Local is often used when doing something with rotation, as world rotation is limited to 0-360 and repeats. That can actually be leveraged for interesting things, like this spider walk.

The usefulness of offset we debated a lot internally. Translate offset is definitely useful, as it allows you to simulate reparenting. Rotation offset is useful because it flips when the character flips, and some relatively rare scenarios need that. We had to have translation and rotation offsets to have exact parity with the old transform constraint, so people's projects don't break. Scale and shear offset aren't strictly needed, as they could be accomplished via property mappings. The only advantage they offer is it's easier to change the mappings without messing up the offsets -- less math for the user. If you are mapping properties straight across, the offsets and Match are very convenient so nothing moves in setup mode when mix is changed.

Your shoulder setup is neat, though I'm not sure the shoulder should really dislocate from the arm like that.

Be careful not to get too caught up in the fancy features! Many times you can solve things in a simpler way. You can do a lot with only weights, like this cake (check out the other tips there too):

For your shoulder, you could use Weld in the Weights view to make the top part of the arm move perfectly with the torso. Then the shoulder bone would just rotate without any constraints and the torso and shoulder would move appropriately.