Your analysis is close
It does add “something” to the existing track.
What it adds is a copy of the stereo track that has been manipulated in a rather (overly) complex way.
Let’s call the left channel “L”, the right channel “R”, the “Volume” setting “V” and the “Pan” setting “P”,
where “V” has been converted from dB to a linear scale 0 to 1,
and “P” has been converted from “negative %” to a range of -1 to 0.
I’m using “*” as the multiplication symbol, “+” for addition, and “-” for subtraction:
Original track = L | R
Processed left channel = (-1 * V * L * (P + 1) x 0.5) + (-1 x V x R * (P - 1) * -0.5)
Processed right channel = (-1 * V * R * (P + 1) x 0.5) + (-1 x V x L * (P - 1) * -0.5)
To see what’s happening, we can simplify these calculations as:
Processed left channel = V/2 * (((P - 1) * R) - ((P + 1) * L))
Processed right channel = V/2 * (((P - 1) * L) - ((P + 1) * R))
So, to the Left channel, it adds a bit of the inverted Left channel, and some Right channel.
Similarly, to the Right channel, it adds a bit of the inverted Right channel and some of the Left channel.
Assuming that the “Time offset - ms” is zero (default), adding a bit of “inverted” left channel to the original left channel, is equivalent to reducing the amount of original left channel.
One of the difficulties with many of David Sky’s plug-ins is that he often has controls that are “coupled”. That is, two (or more) controls interact with each other. In this case, the amount of “spread” is controlled by a combination of the “Inverted signal volume - db” and “Pan position” controls, according to the above formulae.
There’s a much easier way to do this.
Download and install the “Channel Mixer” plug-in from here: Missing features - Audacity Support
Normal “stereo” tracks don’t have a physical “center” channel, they just have “left” and “right”. “Center” is just audio that is common to both left and right. However, it is possible to represent stereo as “center” and “side” channels (called “mid-side encoding”), and the “Channel Mixer” plug-in can do that.
An important concept is that mid-side encoding and mid-side decoding, are essentially the same.
Mid = (Left + Right)/2
Side = (Left - Right)/2
Left = (Mid + Side)/2
Right = (Mid - Side)/2
The overall gain from round-trip encoding → decoding is -6.021 dB.
So, the process to reduce the “center” of a stereo track by 3 dB is:
- Apply “Channel Mixer” with “Mid-Side Decode” preset (this is actually “encoding” as mid-side stereo)
- Split stereo track (Splitting and Joining Stereo Tracks - Audacity Manual)
- Amplify the top track by -3 dB (this is the “center” / “mid” channel)
- Join the two tracks to create a stereo track
- Apply “Channel Mixer” with “Mid-Side Decode” preset (decode back to normal stereo)
- Amplify by 6.021 dB (make up for round-trip gain)