A new calculation of the strain measure for entangled polymers is presented. in which the entanglement network is modeled as a set of entanglement points to which are attached four entanglement strands, randomly oriented in equilibrium. The network deforms nonaffinely to maintain a net zero force on each entanglement point. following a recent suggestion of Marrucci. The resulting strain measure in the case of uniaxial and biaxial extension as well as simple shear is well described by Q = C-alpha/tr(C-alpha) with alpha = 0.7, where C-1 is the Finger tensor. The resulting second normal stress ratio psi = -N-2/N-1 is (1 - alpha)/2 = 0.15. The original Doi-Edwards strain measure is well described except for the second normal stress by this same function with a = 0.8.