  Several processes studied by the ATLAS experiment at the Large Hadron
Collider produce low-momentum $b$-flavored hadrons in the final state. This
paper describes the calibration of a dedicated tagging algorithm that
identifies $b$-flavored hadrons outside of hadronic jets by reconstructing the
soft secondary vertices originating from their decays. The calibration is based
on a proton-proton collision dataset at a center-of-mass energy of 13 TeV
corresponding to an integrated luminosity of 140 fb$^{-1}$. Scale factors used
to correct the algorithm's performance in simulated events are extracted for
the $b$-tagging efficiency and the mistag rate of the algorithm using a data
sample enriched in $t\bar{t}$ events. Several orthogonal measurement regions
are defined, binned as a function of the multiplicities of soft secondary
vertices and jets containing a $b$-flavored hadron in the event. The mistag
rate scale factors are estimated separately for events with low and high
average number of interactions per bunch crossing. The results, which are
derived from events with low missing transverse momentum, are successfully
validated in a phase space characterized by high missing transverse momentum
and therefore are applicable to new physics searches carried out in either
phase space regimes.
