For an archer build, what would be a good health to stamina ratio? Thank you very much.

like 4 to 1 I'd think, 1 being sprint away from enemies

I do about a 3:1 ratio. I don't zoom in that often, and enemies tend to close extremely fast and angry when stealth gets broken.

If you plan to get the zoom in perk and slow time perk, you'll need a good amount in stamina, as zooming drains it quickly. I'd say 2/3.

I think I am going to go with a 2:3 ratio because of the slow down perk. Thanks!

80/20 according to the guide.

I am also going to be playing on master so maybe I am going to need more health than stamina. Any more suggestions.

L23 atm, been going full health and 1 point in stamina.
I'm doing just fine now. But maybe that's because my 1h+shield skills are as good as my archery skills.
Sneak, good location, and tight aim make it possible to clear rooms without any detection.

You don't need zoom and the slowdown perk unless you have terrible aim. I go all out with health.

I am going to go with a 3:1 ratio. Thanks for all the suggestions!

Guide says 4:1 health to stamina ratio. I went with it for my archer character and it seems to work nicely.

I found 20/80 was very good early on.

Imo you can ignore health to an extent because enemys won't get to you anyway if you get a dog/companion, sneak and the stagger perk for archery.
The advantage is that you can carry much more stuff around, quickly earning a respectable sum of gold, which can be invested in training/houses. It also allows you to stay in slowmo much longer when facing a difficult situation.

My pure Archer is currently running around with Vigilance and Faendal on master difficulty and its doable, although challenging.