  Building on the recent release of a new \emph{Gaia}-based blue straggler star
catalog in Galactic open star clusters (OCs), we explored the properties of
these stars in a cluster sample spanning a wide range in fundamental
parameters. We employed \emph{Gaia} EDR3 to assess the membership of any
individual blue or yellow straggler to their parent cluster. We then made use
of the \texttt{ASteCA} code to estimate the fundamental parameters of the
selected clusters, in particular, the binary fraction. With all this at hand,
we critically revisited the relation of the blue straggler population and the
latter. For the first time, we found a correlation between the number of blue
stragglers and the host cluster binary fraction and binaries. This supports the
hypothesis that binary evolution is the most viable scenario of straggler
formation in Galactic star clusters. The distribution of blue stragglers in the
Gaia color-magnitude diagram was then compared with a suite of composite
evolutionary sequences derived from binary evolutionary models that were run by
exploring a range of binary parameters: age, mass ratio, period, and so forth.
The excellent comparison between the bulk distribution of blue stragglers and
the composite evolutionary sequences loci further supports the binary origin of
most stragglers in OCs and paves the way for a detailed study of individual
blue stragglers
