  The redshift factor $z$ is an invariant quantity of fundamental interest in
post-Newtonian and self-force descriptions of compact binaries. It connects
different approximation schemes, and plays a central role in the first law of
binary black hole mechanics, which links local quantities to asymptotic
measures of energy and angular momentum in these systems. Through this law, the
redshift factor is conjectured to have a close relation to the surface gravity
of the event horizons of black holes in circular orbits. We propose and
implement a novel method for extracting the redshift factor on apparent
horizons in numerical simulations of quasicircular binary inspirals. Our
results confirm the conjectured relationship between $z$ and the surface
gravity of the holes and that the first law holds to a remarkable degree for
binary inspirals. The redshift factor enables tests of analytic predictions for
$z$ in spacetimes where the binary is only approximately circular, giving a new
connection between analytic approximations and numerical simulations.
