Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch‐angle distributions on open field lines. We begin with a near‐Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field‐aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad‐hoc pitch‐angle scattering. Close to the Sun, pitch‐angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch‐angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large‐scale properties and topologies of field lines in the interplanetary medium. Although the pitch‐angle scattering term is independent of energy, time‐of‐flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.