  In communications, one frequently needs to detect a parameter vector $\hbx$
in a box from a linear model. The box-constrained rounding detector $\x^\sBR$
and Babai detector $\x^\sBB$ are often used to detect $\hbx$ due to their high
probability of correct detection, which is referred to as success probability,
and their high efficiency of implimentation. It is generally believed that the
success probability $P^\sBR$ of $\x^\sBR$ is not larger than the success
probability $P^\sBB$ of $\x^\sBB$. In this paper, we first present formulas for
$P^\sBR$ and $P^\sBB$ for two different situations: $\hbx$ is deterministic and
$\hbx$ is uniformly distributed over the constraint box. Then, we give a simple
example to show that $P^\sBR$ may be strictly larger than $P^\sBB$ if $\hbx$ is
deterministic, while we rigorously show that $P^\sBR\leq P^\sBB$ always holds
if $\hbx$ is uniformly distributed over the constraint box.
