Summary: Arkani-Hamed, Cachazo, Cheung and Kaplan [N. Arkani-Hamed et al., J. High Energy Phys. 2010, No. 3, Paper No. 110, 48 p. (2010; Zbl 1271.81169)] have proposed a Grassmannian formulation for the S-matrix of \( \mathcal{N} = 4 \) Yang-Mills as an integral over link variables. In parallel work, the connected prescription for computing tree amplitudes in Witten’s twistor string theory has also been written in terms of link variables. In this paper we extend the six-and seven-point results of M. Spradlin and A. Volovich [“From twistor string theory to recursion relations”, Phys. Rev. D 80, 085022 (2009) arxiv:0909.0229] and L. Dolan and P. Goddard [“Gluon tree amplitudes in open twistor string theory”, ibid. 12, 032 (2009) arxiv:0909.0499] by providing a simple analytic proof of the equivalence between the two formulas for all tree-level NMHV superamplitudes. Also we note that a simple deformation of the connected prescription integrand gives directly the ACCK Grassmannian integrand in the limit when the deformation parameters equal zero.