A recent estimate by the Kavli Institute for Particle Astrophysics and Cosmology (a joint institute of Stanford and SLAC) is that there are circa 100000 times as many 'nomad planets' as stars
I found "The Close Approach of Stars in the Solar Neighborhood, Matthews, R. A. J., Quarterly Journal of the Royal Astronomical Society, Vol. 35, NO. 1, P. 1, 1994" which estimated that the frequency of other stars passing within a given distance to be
$$ F_{r}(r) = \sqrt{2} \pi r^{2}\rho_{s}V_{s} $$
where
$$ V_{s} \approx 19.5 \text{ km}/\text{second} $$
and $$ \rho_{s} \approx 0.11 \text{ stars}/\text{parsec}^3 $$
resulting in
$$ F_{r}(r) \approx 10^{-5} r[\text{pc}]^{2} \text{year}^{-1} $$
Assuming that those estimates are accurate and substituting
$$ \rho_{s} \approx 11000 \text{ planets}/\text{parsec}^{3} $$
and
$$ r[\text{pc}] \approx 0.000145 \text{ parsecs} $$
we get a frequency of
$$ F_{r} \approx (10^{-5})(0.000145^{2})(10^{5})/\text{year} $$
or
$$ F_{r} \approx 2 \times 10^{-8}/\text{year} $$
This gives us a net 'close encounter' of the solar system with a nomad planet roughly every 50 million years.
Does this seem a reasonable estimate?