We attribute the recently discovered cosmic ray electron and cosmic ray positron excess components and their cutoffs to the acceleration in the supernova shock in the polar cap of exploding Wolf-Rayet and red supergiant stars. Considering a spherical surface at some radius around such a star, the magnetic field is radial in the polar cap as opposed to most of 4pi (the full solid angle), where the magnetic field is nearly tangential. This difference yields a flatter spectrum, and also an enhanced positron injection for the cosmic rays accelerated in the polar cap. This reasoning naturally explains the observations. Precise spectral measurements will be the test, as this predicts a simple E;{-2} spectrum for the new components in the source, steepened to E;{-3} in observations with an E;{-4} cutoff.