  Partial methods play an important role in formal methods and beyond. Recently
such methods were developed for parity games, where polynomial-time partial
solvers decide the winners of a subset of nodes. We investigate here how
effective polynomial-time partial solvers can be by studying interactions of
partial solvers based on generic composition patterns that preserve
polynomial-time computability. We show that use of such composition patterns
discovers new partial solvers - including those that merge node sets that have
the same but unknown winner - by studying games that composed partial solvers
can neither solve nor simplify. We experimentally validate that this
data-driven approach to refinement leads to polynomial-time partial solvers
that can solve all standard benchmarks of structured games. For one of these
polynomial-time partial solvers not even a sole random game from a few billion
random games of varying configuration was found that it won't solve completely.
