Belt balancers and the golden rule

[Danub]

I've been using this [docs.google.com] guide on belt balancing to build arbitrary balancers for my factories since it provides a simple to understand methodology and I don't really like just copying blueprints when I can't even understand how they work. Pretty much any optimized balancer beyond the 4x4 gives me dizzy spells if I try to understand them so being able to make balancers myself is great, even if they are far bulkier and uglier than optimized designs.

The problem is that the balancers you make with that method have the problem that there are input/output configurations that result in restricted throughput. To solve that problem, you can run the balanced belts through a second indentical balancer.
As per the golden rule, you shuffle N groups of M balancers through M groups of N balancers, then repeat that to achieve full throughput. My idea is that running N groups of M balancers through M groups of N balancers then shuffling that again through N groups of M balancers is enough to achieve full throughput, at least in the case of balancers of even size. It seems to me that this is what the 2 trailing splitters in a 4x4 do.

Can anyone confirm that idea or point out what my mistake is?

For a more practical presentation, consider the 8x8 at https://imgur.com/a/DsmWO
Though it's not and example of balancers built with the golden rule, it has the same problem. Doesn't shuffling the outputs of the two (shuffled) 4x4 balancers with 4 splitters end up in full throughput in any input/output configuration?

[DaBa]

Looks good to me, should work just fine based on the ratios that I can see. But I spent like 2 minutes looking at it and I only looked at the last image with any scrutiny, so it's still best to test in game, which you seem to have already done.

[DaBa]

I have a similar mindset to you btw, I wanted to figure out how to do things my way first. And I did, I figured out stuff how to balance belts myself and made some really bad looking balancers for my trains. But they worked.

Now that I am confident I understand the principles, I don't feel bad about grabbing some more compact designs from others.