The sharp upper edge of the nightside electron plasma sheet energy distribution observed at geosynchronous orbit is shown to provide a measure of the effective strength of the convection electric field that transports plasma sheet material into the inner magnetosphere. This association is statistically supported by the Kp and LT dependence of the observed median cutoff energies and yields inferred field strengths consistent with previous electric field measurements in this region. The temporal profile of convection typically consists of a sequence of bursts, where each convection enhancement lasts no more than a fraction of an hour. Simultaneous multipoint measurements show that these convection enhancements are observed first near midnight and then propagate sunward with speeds of ~5--30 km/s. They also reveal that the plasma sheet does not penetrate as deeply into the premidnight region as would be expected for a Volland-Stern electric field with a shielding parameter of γ = 2. Routine measurements of the plasma sheet electron cutoff energy by multiple geosynchronous satellites could provide a near-real-time monitor of the effective strength of the global convection electric field.