  The density profiles of dark matter haloes contain rich information about
their growth history and physical properties. One particularly interesting
region is the splashback radius, $R_{\rm sp}$, which marks the transition
between particles orbiting in the halo and particles undergoing first infall.
While the dependence of $R_{\rm sp}$ on the recent accretion rate is well
established and theoretically expected, it is not clear exactly what parts of
the accretion history $R_{\rm sp}$ responds to, and what other halo properties
might additionally influence its position. We comprehensively investigate these
questions by correlating the dynamically measured splashback radii of a large
set of simulated haloes with their individual growth histories as well as their
structural, dynamical, and environmental properties. We find that $R_{\rm sp}$
is sensitive to the accretion over one crossing time but largely insensitive to
the prior history (in contrast to concentration, which probes earlier epochs).
All secondary correlations are much weaker, but we discern a relatively higher
$R_{\rm sp}$ in less massive, older, more elliptical, and more tidally deformed
haloes. Despite these minor influences, we conclude that the splashback radius
is a clean indicator of a halo's growth over the past dynamical time. We
predict that the magnitude gap should be a promising observable indicator of a
halo's accretion rate and splashback radius.
