We give a numerical condition for right-handedness of a dynamically convex Reeb flow on S^3. Our condition is stated in terms of an asymptotic ratio between the amount of rotation of the linearised flow and the linking number of trajectories with a periodic orbit that spans a disk-like global surface of section. As an application, we find an explicit constant δ * < 0.7225 such that if a Riemannian metric on the 2-sphere is δ-pinched with δ > δ * , then its geodesic flow lifts to a right-handed flow on S^3. In particular, all finite collections of periodic orbits of such a geodesic flow bind open books whose pages are global surfaces of section.