Before we begin, I know full-well that the answer changes based on the time-period, size of the estate, number of people being taken care of, amount of money available, and so forth. A correct answer would be able to give a [resident:staff] ratio or an accurate algorithm/formula to give an easily adjustable answer for needs beyond my own, both solutions offering a simplified break-down of what roles would be held by the staff.
What is the minimum number of staff members of each role (butler, maid, cook, groundskeeper, etc.) to keep a Medieval estate running smoothly?
The following should be assumed.
We are in the European late medieval period (where female staff were now more common than previously in case this makes a difference)
Use the modern-day United Kingdom area as a basis for any regional specifications if necessary
The estate is actively in-use
The estate is of sufficient size to house 100 people in separate rooms
Of those residents, assume 50 are men and 50 are women (for the sake of simplicity) and all are equal parts owners of the estate (despite that concept being an anachronism) [Meaning: There are 50 lords and 50 ladies of the estate.]
The staff live on-site in shared rooms equipped to house the minimum number of staff, the number of staff per shared room being within-reason for the time
The estate has the standard luxuries like a ballroom and so forth
The estate has formal gardens, but no farmland of its own
Neither money nor resources to finance/support this are an issue
No military force (such as knights) is necessary
There is no surrounding town, but that is not to say you cannot get to a town if you were to travel a short while by carriage
Staff Roles to consider
(Thanks to Alex P. for suggesting some staff I would never have thought of, and this list is mostly pulled from him/his source.)
Grooms, Maids, Butlers, Cooking Staff, Stable-Hands, Maintenance Staff, Sewers (Servers), Steward (Overseer), Gardeners/Groundskeepers, Cleaning Staff, Carriage Drivers, Secretaries, and Couriers.
I am listing what appear to be the most necessary roles for the core functionality of an estate. That said, an answer that excludes staff from these roles or includes unlisted staff is not inherently an incorrect answer as long as you show a reason for your assessment. I may be wrong in my assumption that all these staff roles are necessary or that only these roles are necessary and this list is subject to adjustment. Please, do not downvote others on the basis of included/excluded roles alone.
Requirements for a correct answer
Gives a ratio of [Residents:Staff], algorithm, or formula with a breakdown of necessary staff roles by numbers
Should not include any of the following: magic, modern/futuristic technology, demons/supernatural elements, MacGuffins, 7-headed chartreuse ostriches with naturally occurring lizard skin hats, and so on. I just want an as-close-as-possible to real-life view without consideration of these things.
I understand that some of the details I've given would be improbable/impossible from a real-world historical perspective, but I just want an as accurate as possible answer that can be easily worked with. If this question is presently unanswerable or unclear, please leave a comment saying how I can narrow this down and I will narrow it down in my next edit.
Alex P answered an earlier version of this question and his answer will be evaluated to reflect that.