Slave names were sometimes numbers. Naming conventions in Roman culture were apparently also fairly formal.[0] I would guess there's sufficient evidence here that a ratio of free to slave could be estimated.
In general, it seems like being a slave was not a great experience.[1]
[0]: https://en.wikipedia.org/wiki/Slavery_in_ancient_Rome#Treatm...
[1]: among other stories, the one concerning the murder of Lucius Pedanius Secundus sticks in my mind: https://en.wikipedia.org/wiki/Lucius_Pedanius_Secundus