From my small sample of experience ... i get like 2-3 sacred , 1-5 void , 10+ ancient (monthly)

Books are quite similar  to the above with respective rarity . But i also dont get a day without either a book or a shard unlike NM top chest ... 

But dont havent found any actual drop rate % list anywhere ,

Someone knows the drop rate.  

someone always knows something ;) 

Go to ayumi and search "loot"

I can't verify the numbers, but they are consistent with the daily data I recorded for 8 months.

Except for Seargent Shultz!  He knows nothing.

Neither does Jon Snow. :)

This is from Ayumilove web site

i

More specifically, it's from https://imgur.com/a/ebytw5F :)

This is the smartest and most helpful forum I have even been on.  Thanks again everyone.