Electron beams accelerated upward out of the ionosphere are commonly observed in the auroral acceleration region. We present a statistical study of their distribution in magnetic local time, invariant latitude, and altitude, and its dependence on whether the ionospheric foot point of the satellite is illuminated or dark. The occurrence probability maximizes at ~12% near 70¿ invariant latitude (ILAT) and midnight when the ionosphere is in darkness, and at ~1% near ~78¿ ILAT from ~0600 to 1300 magnetic local time (MLT) when the ionosphere is illuminated. When the ionosphere is in darkness, there is approximately an order of magnitude increase in the probability from ~1000 to ~4000 km in almost all local time sectors. When the ionosphere is sunlit, the rapid increase begins at a higher altitude, ~2500 km. The probability also increases with solar zenith angle, with the increase being slower and occurring at a higher solar zenith angle at lower altitudes. These observations are consistent with a scale-height and density-dependent mechanism for the parallel potential in the downward current region. More than 90% of the observed upflowing electron beams have characteristic energies between ~50 and ~300 eV. The statistical results suggest that there are many more beams with durations of <5 s (latitude widths of <0.2¿) and with lower energies.