The figures change whenever we see them. I take a gamest view. I look at the size of the patrol area, the speed of the ships and calculate the number you need to do a decent job.
But that's just it - in Star Trek, Starfleet never does a decent job.
They're indecently absent when space monsters devour colonies, or when space diseases or madmen kill everybody there. They lose their own for months at an end. They defend borders that are 8,000 ly between the farthest points, yet enemies often sneak all the way to Earth. And after a century of exploration, they haven't gotten as far as Pollux...
So let's calculate the number needed. And then divide it by fifty.
Timo Saloniemi