  Exoplanet surveys of evolved stars have provided increasing evidence that the
formation of giant planets depends not only on stellar metallicity ([Fe/H]),
but also the mass ($M_\star$). However, measuring accurate masses for subgiants
and giants is far more challenging than it is for their main-sequence
counterparts, which has led to recent concerns regarding the veracity of the
correlation between stellar mass and planet occurrence. In order to address
these concerns we use HIRES spectra to perform a spectroscopic analysis on an
sample of 245 subgiants and derive new atmospheric and physical parameters. We
also calculate the space velocities of this sample in a homogeneous manner for
the first time. When reddening corrections are considered in the calculations
of stellar masses and a -0.12 M$_{\odot}$ offset is applied to the results, the
masses of the subgiants are consistent with their space velocity distributions,
contrary to claims in the literature. Similarly, our measurements of their
rotational velocities provide additional confirmation that the masses of
subgiants with $M_\star \geq 1.6$ M$_{\odot}$ (the "Retired A Stars") have not
been overestimated in previous analyses. Using these new results for our sample
of evolved stars, together with an updated sample of FGKM dwarfs, we confirm
that giant planet occurrence increases with both stellar mass and metallicity
up to 2.0 M$_{\odot}$. We show that the probability of formation of a giant
planet is approximately a one-to-one function of the total amount of metals in
the protoplanetary disk $M_\star 10^{[Fe/H]}$. This correlation provides
additional support for the core accretion mechanism of planet formation.
