  Improvements in the number of confirmed planets and the precision of
observations imply a need to better understand subtle effects that may bias
interpretations of exoplanet observations. One such effect is the distortion of
a short period planet by its host star, affecting its derived density. We
extend the work of Burton et al., Correia, and others, using a gravitational
potential formulation to a sample of nearly 200 planets with periods less than
3 days. We find five planets exhibiting density variations of >10% and as many
as 20 planets with deviations >5%. We derive an analytic approximation for this
deviation as a function of the orbital period, transit depth, and mass ratio
between the planet and host star, allowing for rapid determination of such
tidal effects. We find that current density error bars are typically larger
than tidal deviations but that reducing the uncertainty on transit depth and
radial velocity (RV) amplitude by a factor of 3 causes tidal effects to
dominate density errors (>50%) in >40% of planets in our sample, implying that
in the near future upgraded observational precision will cause shape deviations
to become a bottleneck with regards to analysis of exoplanet compositions.
These two parameters are found to dominate uncertainties compared to errors on
stellar mass and radius. We identify a group of eight planets (including
WASP-19 b, HAT-P-7 b, and WASP-12 b) for which current density uncertainties
are as much as 4x smaller than the potential shift due to tides, implying a
possible 4{\sigma} bias on their density estimates.
