  We investigate how the statistical distribution of extrasolar planets may be
combined with knowledge of the host stars' metallicity to yield constraints on
the migration histories of gas giant planets. At any radius, planets that
barely manage to form around the lowest metallicity stars accrete their
envelopes just as the gas disk is being dissipated, so the lower envelope of
planets in a plot of metallicity vs semi-major axis defines a sample of
non-migratory planets that will have suffered less than average migration
subsequent to gap opening. Under the assumption that metallicity largely
controls the initial surface density of planetesimals, we use simplified core
accretion models to calculate how the minimum metallicity needed for planet
formation varies as a function of semi-major axis. Models that do not include
core migration prior to gap opening (Type I migration) predict that the
critical metallicity is largely flat between the snow line and a semimajor axis
of about 6 AU, with a weak dependence on the initial surface density profile of
planetesimals. When slow Type I migration is included, the critical metallicity
is found to increase steadily from 1-10 AU. Large planet samples, that include
planets at modestly greater orbital radii than present surveys, therefore have
the potential to quantify the extent of migration in both Type I and Type II
regimes.
