I think drops work in a variety of ways, so it's hard to provide exact numbers but this seems to be observational consensus (I think).

Recipes: my main source of purples come from daily writs, and this has been turned WAY up in homesteading. It's always seemed that a higher provision level increases odds of a purple drop. From containers, ZOS has said that higher legerdemain means better drops, so this would theoretically apply to purple recipes in containers like chests, wardrobes, urns, etc.

Motifs: for the most part, I think they keep players on an even playing field with motif RNGs. The exception might be motifs found in containers, where again ZOS has said some skills can increase quality of drops. There are others where I suspect RNG odds can be increased, such as Abahs Warch motif, which drops from Thieves Guild repeatable quests. It seems possible that higher Thieves Guild rank and/or legerdemain affects this, as my sneak khajiit gets them at a much higher rate than my non-sneak toons.

In general, knowing purple recipes and motifs does not give you a better chance of finding more. This misperception probably comes from the way that you get better stuff as you level higher, so it seems like it's coming from knowledge when it's not.

An exception is the recent homestead addition of mater crafting writs. Zos has confirmed that the odds of winning a master writ quest are affected by how much you know, including purple motifs for craft skills and purple recipes for provision. And trait research for everything.