Oystein once clarified that for every habitable star system on our map there are hundreds and up to a thousand uninhabitable systems between. Not sure if those numbers still hold, but that gives one an idea of how many stars jumpship captains have to work with.
If you
a) take a sample of all (known today) stars in a certain diameter of 3D sphere around Earth
b) constrain them to jumpable stars only - no solitary brown dwarfs etc
c) calculate their average distance from each other
d) based on that average distance cast them onto a
2D mapThen depending on diameter chosen for a) you get a pretty consistent result of around 10,000 to 11,000 stars within the area of the Inner Sphere on a 2D map base.
I've typically used 100 LY spheres around Earth as a sample base, as beyond that you get a bit unmanageable numbers initially (SIMBAD TAP lets you draw Gaia DR2 results out to about 300 LY before it hits its output limits).
You actually have to play with the local density a bit (it varies in real life too of course, although on a minor order of magnitude) in order to accomodate the numbers you need for the Alliance Grand Surveys, and depending on how you massage those numbers you´ll end up at 90-100% "once settled" systems within about 120 LY of Terra and the perception that humanity spread like cockroaches in the 22nd century.
In order to even accomodate those numbers though you also have to assume massive efforts of terraforming and domed colonies like Sirius V, and not just using statistically habitable planets as per the current set of rules. At one point i was looking into modeling that factor possibly based on Era, Tech Level and Economy, and came to the conclusion that most likely in the Periphery, what we're seeing on the map is pretty much what's out there in settled systems, with sufficiently sparse numbers to always allow some extra pirate base but nowhere on the scale of 1:1 added worlds as has been hinted at for the Houses.