Strengthening, i.e. increased stress required to move a dislocation, in dilute or complex alloys arises from the totality of the interaction energies between the solutes and an individual dislocation. Prevailing theories for strengthening in bcc alloys consider only solute interactions in the core of the screw dislocation while computations suggest longer-range interactions. Here, a full statistical solute/screw interaction energy parameter relevant for predicting strengthening in random bcc alloys is presented. The parameter is valid for any number of constituent atoms and at any concentrations, thus including the range from dilute binary alloys to high-entropy alloys. The interaction energy parameter is then calculated for many bcc alloys in the Nb-Ta-V-Ti-Zr family using the Zhou-Johnson EAM potentials to demonstrate the spatial range of solutes contributing to this key quantity and to assess accuracy of previous simplified models. The interaction energy parameter is found to converge if solutes out to sixth neighbors are included while the simplified models are generally not very accurate. A recently-proposed correlation between solute/dislocation interaction energy and the solute/[111]/6 unstable stacking fault (USF) interaction energy is then assessed in detail. A very good correlation is found between the full interaction energy parameter introduced here and the solute/USF interaction energy. This points toward a simplified approach to estimating the interaction energy parameter using first-principles methods.