  Many surveys use maximum-likelihood (ML) methods to fit models when
extracting photometry from images. We show these ML estimators systematically
overestimate the flux as a function of the signal-to-noise ratio and the number
of model parameters involved in the fit. This bias is substantially worse for
resolved sources: while a 1% bias is expected for a 10$\sigma$ point source, a
10$\sigma$ resolved galaxy with a simplified Gaussian profile suffers a 2.5%
bias. This bias also behaves differently depending how multiple bands are used
in the fit: simultaneously fitting all bands leads the flux bias to become
roughly evenly distributed between them, while fixing the position in
"non-detection" bands (i.e. forced photometry) gives flux estimates in those
bands that are biased low, compounding a bias in derived colors. We show that
these effects are present in idealized simulations, outputs from the Hyper
Suprime-Cam fake object pipeline (SynPipe), and observations from Sloan Digital
Sky Survey Stripe 82. Prescriptions to correct for the ML bias in flux, and its
uncertainty, are provided.
