  Accretion plays an important role in protoplanetary disk evolution, and it is
thought that the accretion mechanism changes between low- and high-mass stars.
Here, we characterize accretion in intermediate-mass, pre-main-sequence Herbig
Ae/Be (HAeBe) stars to search for correlations between accretion and system
properties. We present new high-resolution, near-infrared spectra from the
Immersion GRating INfrared Spectrograph for 102 HAeBes and analyze the
accretion-tracing Br$\gamma$ line at 2.166 $\mu$m. We also include the samples
of Fairlamb et al. and Donehew & Brittain, for a total of 155 targets. We find
a positive correlation between the Br$\gamma$ and stellar luminosity, with a
change in the slope between the Herbig Aes and Herbig Bes. We use
$L_{Br\gamma}$ to determine the accretion luminosity and accretion rate. We
find that the accretion luminosity and rate depend on stellar mass and age;
however, the trend disappears when normalizing the accretion luminosity by the
stellar luminosity. We classify the objects into flared (Group I) or flat
(Group II) disks and find that there is no trend with accretion luminosity or
rate, indicating that the disk dust structure is not impacting accretion. We
test for Br$\gamma$ variability in objects that are common to our sample and
previous studies. We find that the Br$\gamma$ line equivalent width is largely
consistent between the literature observations and those that we present here,
except in a few cases where we may be seeing changes in the accretion rate.
