The systematics of strong lens modeling quantified: the effects of
  constraint selection and redshift information on magnification, mass, and
  multiple image predictability
  Until now, systematic errors in strong gravitational lens modeling have been
acknowledged but never been fully quantified. Here, we launch an investigation
into the systematics induced by constraint selection. We model the simulated
cluster Ares 362 times using random selections of image systems with and
without spectroscopic redshifts and quantify the systematics using several
diagnostics: image predictability, accuracy of model-predicted redshifts,
enclosed mass, and magnification. We find that for models with $>15$ image
systems, the image plane rms does not decrease significantly when more systems
are added; however the rms values quoted in the literature may be misleading as
to the ability of a model to predict new multiple images. The mass is well
constrained near the Einstein radius in all cases, and systematic error drops
to $<2\%$ for models using $>10$ image systems. Magnification errors are
smallest along the straight portions of the critical curve, and the value of
the magnification is systematically lower near curved portions. For $>15$
systems, the systematic error on magnification is $\sim2\%$. We report no trend
in magnification error with fraction of spectroscopic image systems when
selecting constraints at random; however, when using the same selection of
constraints, increasing this fraction up to $\sim0.5$ will increase model
accuracy. The results suggest that the selection of constraints, rather than
quantity alone, determines the accuracy of the magnification. We note that
spectroscopic follow-up of at least a few image systems is crucial, as models
without any spectroscopic redshifts are inaccurate across all of our
diagnostics.
