  We describe an updated calibration and diagnostic framework, Balrog, used to
directly sample the selection and photometric biases of the 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.
