Magnetic field effects on the yields of radical pair reactions are oftencharacterised by the "half-field" parameter, B1/2, which encodes useful information on spin relaxation radical recombination kinetics and electron-electron couplings as well as electron-nuclear hyperfine interactions. Here we use a variety of spin dynamics simulation methods to estimate the hyperfine-only values of B1/2 for the flavin-tryptophan radical pair, [FAD-TrpH+] thought to be the detector in the magnetic compass sense of migratory songbirds. The main findings are: (a) in the absence of fast recombination and spin relaxation [FAD-TrpH+] radical pairs in solution and in the putative magnetoreceptor protein cryptochrome have B1/2 = 1.89 mT and 2.46 mT respectively. (b) The widely used expression for B1/2 due to Weller et al. (Chem. Phys. Lett, 1983, 96, 24-27) is only applicable to small, short-lived ( 5 ns), rapidly tumbling radical pairs in solution, and is quantitatively unreliable in the context of magnetoreception. (c) In the absence of molecular tumbling, the low-field effect for [FAD-TrpH+] is predicted to be abolished by the anisotropic components of the hyperfine interactions. Armed with the 2.46 mT "base value" for cryptochrome, measurements of B1/2 can be used to understand the impact of spin relaxation on its performance as a magnetic compass sensor.