  In this paper, we study compact binary millisecond pulsars with low- and very
low-mass companion stars (spiders) in the Galactic field, using data from the
latest Gaia data release (DR3). We infer the parallax distances of the optical
counterparts to spiders, which we use to estimate optical and X-ray
luminosities. We compare the parallax distances to those derived from radio
pulse dispersion measures and find that they have systematically larger values,
by 40% on average. We also test the correlation between X-ray and spin-down
luminosities, finding that most redbacks have a spin-down to X-ray luminosity
conversion efficiency of $\sim$0.1%, indicating a contribution from the
intrabinary shock. On the other hand, most black widows have an efficiency of
$\sim$0.01%, similar to the majority of the pulsar population. Finally, we find
that the bolometric optical luminosity significantly correlates with the
orbital period, with a large scatter due to different irradiated stellar
temperatures and binary properties. We interpret this correlation as the effect
of the increasing size of the Roche Lobe radius with the orbital period. With
this newly found correlation, an estimate of the optical magnitude can be
obtained from the orbital period and a distance estimate.
