  Tree-level scattering amplitudes in Yang-Mills theory satisfy a recursion
relation due to Berends and Giele which yields e.g. the famous Parke-Taylor
formula for MHV amplitudes. We show that the origin of this recursion relation
becomes clear in the BV formalism, which encodes a field theory in an
$L_\infty$-algebra. The recursion relation is obtained in the transition to a
smallest representative in the quasi-isomorphism class of that
$L_\infty$-algebra, known as a minimal model. In fact, the quasi-isomorphism
contains all the information about the scattering theory. As we explain, the
computation of such a minimal model is readily performed in any BV quantisable
theory, which, in turn, produces recursion relations for its tree-level
scattering amplitudes.
