We have recently undergone an analysis of quadratic gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. This framework is a good candidate for a unitary and renormalizable theory of the gravitational fi eld; in particular, there are no propagators falling down faster than 1/p^2 . When treating the connection as an independent field, new degrees of freedom appear. A complete spin analysis of the torsionless connection field is performed, and its consequences are explored. The coupling to fermions is also discussed, as they turn out to be a source of torsion.