  This work introduces \emph{sharding} and \emph{Poissonization} as a unified
framework for analyzing prophet inequalities. Sharding involves splitting a
random variable into several independent random variables, shards, that
collectively mimic the original variable's behavior. We combine this with
Poissonization, where these shards are modeled using a Poisson distribution.
Despite the simplicity of our framework, we improve the competitive ratio
analysis of a dozen well studied prophet inequalities in the literature, some
of which have been studied for decades. This includes the
\textsc{Top-$1$-of-$k$} prophet inequality, prophet secretary inequality, and
semi-online prophet inequality, among others. This approach not only refines
the constants but also offers a more intuitive and streamlined analysis for
many prophet inequalities in the literature. Furthermore, it simplifies proofs
of several known results and may be of independent interest for other variants
of the prophet inequality, such as order-selection.
