  We describe an updated calibration and diagnostic framework, Balrog, used to
directly sample the selection and photometric biases of Dark Energy Survey's
(DES) Year 3 (Y3) dataset. We systematically inject onto the single-epoch
images of a random 20% subset of the DES footprint an ensemble of nearly 30
million realistic galaxy models derived from DES Deep Field observations. These
augmented images are analyzed in parallel with the original data to
automatically inherit measurement systematics that are often too difficult to
capture with traditional generative models. The resulting object catalog is a
Monte Carlo sampling of the DES transfer function and is used as a powerful
diagnostic and calibration tool for a variety of DES Y3 science, particularly
for the calibration of the photometric redshifts of distant "source" galaxies
and magnification biases of nearer "lens" galaxies. The recovered Balrog
injections are shown to closely match the photometric property distributions of
the Y3 GOLD catalog, particularly in color, and capture the number density
fluctuations from observing conditions of the real data within 1% for a typical
galaxy sample. We find that Y3 colors are extremely well calibrated, typically
within ~1-8 millimagnitudes, but for a small subset of objects we detect
significant magnitude biases correlated with large overestimates of the
injected object size due to proximity effects and blending. We discuss
approaches to extend the current methodology to capture more aspects of the
transfer function and reach full coverage of the survey footprint for future
analyses.
