I was wondering if silent running made muffled leggings add no benefit, I cannot tell.

I can't verify, but I think it would add to your detection score. Just because you can now run and sneak at the same time, you aren't 100% undetectable. I think the sneak four perk just gives you the same detection score when running as when not. So using muffled armor just adds to the players ability to remain hidden regardless of sneak 4.

you can't run in sneak it just does not decrease your detection by moving I just don't know if it includes noise or not

That's not what I meant. The sneak 4 perk gives you the same sneaking ability when running as when not. This still isn't 100% immunity to detection, so muffled armor will still add to the player's ability too remain undetected.

Anyway, that's my thoughts on the matter, I could be wrong.

thank you for your help I guess I will not have leaded armor after all.

I have Sneak 4 and agility at about 5. In my experience, even wearing power armor I am exceptionally cryptic.

Other day in the glowing sea (weaing a lead-painted suit of T-45), I crept RIGHT UP on a Deathclaw. He was all curled up next to a rock, taking a nap I guess. But when I saw him at a distance, I figured it was a carcass . . . pretty low visibility out there . . .

Got right up on top of him and was like "Ah that is weird, I'm point right at it and not getting an 'e' option . . . oh wait, is this a DeathClaw!? Holy crap its alive!"

Same thing with Ghouls, Behemoths, raiders, mirelurks, and many other critters.

Muffled might well help, but given I can effectively sneak in Power Armor with Sneak 4 and an intermediate agility, I would think it would be superfluous if not unnecessary in most situations.

I found this is true too. I've got the recon helmet on my T-60 PA, so when I sneak up on deathclaws in the glowing sea, they have a red glow indicating they aren't carcasses. I also have muffled combat armor on under the PA. I don't really know if it helps or not. But feral ghouls still target me if I'm not crouching sometimes.

wow Maby I should take muffled off, thank you (its what I wanted to hear)

I think one of the things I'll experiment with when I start modding is making Power Armor have a flat "very bad" modifer on stealth. It just makes no sense, unless of course it has a Stealth Boy kit installed, in which case it should still only reduce detection as it relates to the visual sensory field, and not the auditory or tactile field. Not sure how the engine differentiates those effects or if it actually does at all.

nope armor under power armor does not count effects, I tested with a chest price that gives me more AP
It gave me less AP when I entered power armor.

FO 4 is still a gamebryo engine game, so it probably works just like the older games when it comes to detection. Basically, there's a line of sight condition combined with a detection probability. That probability is modified by all the various effects, like perks, armor, stance, noise, etc... AFAIK there is only one calculation used to determine detection level. Modifying this value in a mod would work for all the effects you mentioned.

This.^

As someone who runs stealth in pretty much every game ever (not even because I enjoy stealth per se, but because I like to strategise and do recon), I can sneak around and be almost invisible in well-lit rooms. I can shoot people in the chest or face from 3 feet away whilst "Hidden", and I can hack Behemoths and Queens to death whilst they rotate to try to find me.

Yeah, the only bad places are certain areas where you're essentially not supposed to hide or wide open plains during the daytime. Everything else is pretty easy tbh.