Spin-helicity formalism for gluon-gluon amplitudes

[Silviu]

Hello! In Schwarz's QFT he introduces in chapter 27 the Spin-Helicity formalism as a way of calculating gluon-gluon interactions much easier than going through all the Feynman calculus from the beginning to the end. It seems so amazing, but I am not sure I understand what is the fundamental difference between the 2 approaches that makes one a lot easier than the other. The main difference (on which spin-helicity formalism is actually based) is the fact that momentum is treated like a bi-spinor and not a vector. Why is this approach so much simpler? Can someone give me some intuition to it? Thank you!