I discuss results of a new combined fit to the B->D(∗)lν decay distributions to predict the B->D(∗)τν rates and determine the CKM matrix element |Vcb|. Past theoretical and experimental papers neglected uncertainties in the predictions for form factor ratios at order 1/m, which we include. We study in detail the theoretical uncertainties in the SM predictions for R(D) and R(D*). We calculate 1/m and alpha_s contributions to for all possible b->c currents, which has not been available for all form factors, and allow us to determine with improved precision how new physics may affect the B->D(∗)τν rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated. (This talk is based on https://arxiv.org/abs/1703.05330)