I need to implement this in ACSIL because there does not seem to be any other way to get the Dominant Side Volume Percentage from Numbers Bars at each price level within a bar.

However, I have no idea how it is calculated. I feel that the explanation above is lacking. Could someone who understands it formalize it for me? -i.e put it in plain math.

One picture is worth a thousand words. In this picture, you see under the bar a number. This number represents in percentage the difference between Bid and Ask volume. If the Bid volume is greater than the Ask volume, this number is negative.The information comes from Numbers Bars Calculated Values study. And is shown by the Study Subgraph Absolute Value.
Bar at 14:00:
Ask + Bid = 35960
Ask Vol = 17031
Bid Vol = 18929
Number of Bid Vol is greater than Ask Vol, -1898. So this is a negative figure.
1898 is about 5% of total volume 35960.

The following user says Thank You to Jaap8242 for this post:

I was kind of more curious about the number shown at each price level (in numbers bars) and how that was derived. Could you expound on how what you said relates to that?

Let us use the case where the Ask volume is greater than the bid:

Meaning, if you have a Bid volume of 50 and an ask volume of 100, what is being asked is what percent is 100 of 150 -i.e 50+100. And the percentage value will be positive because the ask volume is greater than the bid.

It would be the opposite if the Bid volume was greater and the question would be what percent would the Bid volume be of the total volume -i.e sum of bid volume and ask volume for that price level.

The following user says Thank You to walidmujahid for this post: