  There remain significant uncertainties in the origin and evolution of black
holes in binary systems, in particular regarding their birth sites and the
influence of natal kicks. These are long-standing issues, but their debate has
been reinvigorated in the era of gravitational wave detections and the
improving precision of astrometric measurements. Using recent and archival
characterisation of Galactic black hole X-ray binaries (BHXBs), we report here
an apparent anticorrelation between P{orb} (system orbital periods) and scatter
in z (elevation above the Galactic plane). The absence of long period sources
at high z is not an obvious observational bias, and two possible explanatory
scenarios are qualitatively explored: (1) a disc origin for BHXBs followed by
natal kicks producing the scatter in z, with only the tightest binaries
preferentially surviving strong kicks; (2) a halo origin, with P{orb}
shortening through dynamical interactions in globular clusters (GCs). For the
latter case, we show a correspondence in z-scatter between BHXBs and the GCs
with most compact core radii of <0.1pc. However, the known absence of
outbursting BHXB transients within Galactic GCs remains puzzling in this case,
in contrast to the multitude of known GC neutron star XRBs. These results
provide an interesting observational constraint for any black hole binary
evolutionary model to satisfy.
