Enterprise Data Center System Admin/Engineer to Server Ratio [closed]

You provided a lot of data, but I think still more would be needed to give some kind of estimate on that number. First of all, what kind of duplication is present in your system? In other words, do you have 4 sets of 500 things, each running exactly the same server config? Or do you have 200 different servers/services, and only 10 boxes running each thing.

I think you need to go to the base level of each service, determine the activities necessary to support that service, then staff it appropriately. Since you will clearly have some duplication of expertises across multiple services, you may be able to consolidate your head count based on that, but I would start bottom up, rather than top down.